SPERA：基于球形先验的 EEG 基础模型——几何与频率感知的潜空间预测

# SPERA: Spherical Prior EEG Foundation Model with Geometry- and Frequency-Aware Latent Prediction
Source: [https://arxiv.org/html/2610.10571](https://arxiv.org/html/2610.10571)
Minsu KimYe\-Sung KimAffiliation:Department of Artificial Intelligence, Hanyang University, Seoul, Republic of KoreaHyeseong JeonAffiliation:Department of Artificial Intelligence, Hanyang University, Seoul, Republic of KoreaWooseok HyungAffiliation:Department of Artificial Intelligence, Hanyang University, Seoul, Republic of KoreaJoshua LeeAffiliation:Department of Artificial Intelligence, Hanyang University, Seoul, Republic of KoreaChang\-Hwan Im††thanks:Corresponding author\.ich@hanyang\.ac\.krAffiliation:Department of Biomedical Engineering, Hanyang University, Seoul, Republic of Korea

###### Abstract

Electroencephalography \(EEG\) provides a non\-invasive measure of ongoing neural activity, but building general\-purpose EEG models remains challenging due to the heterogeneity of subjects, devices, and electrode montages\. Existing EEG foundation models predominantly rely on reconstruction\-based objectives defined on the observed signal, which contains both neural and non\-neural components\. We introduce SPERA222Code:[https://github\.com/sees4321/SPERA\_EEG](https://github.com/sees4321/SPERA_EEG)\(Spherical Prior EEG Representation Architecture\), an EEG foundation model that adopts the joint\-embedding predictive architecture \(JEPA\) to predict in latent space\. SPERA introduces a Legendre\-polynomial spatial prior, incorporated into attention to encode varying scalp electrode geometries\. Two further components adapt the model to EEG: factorized temporal and spatial attention interleaved with periodic full\-attention blocks, and a relational spectral regularizer aligning latent similarity structure with spectral views\. Pretrained on approximately 80,000 hours of EEG from 29,048 subjects across 106 datasets, SPERA achieves the highest average balanced accuracy across nine downstream tasks spanning clinical, cognitive, and BCI applications\. SPERA further exhibits strong parameter efficiency under linear probing and robustness across varying recording conditions, suggesting its potential as a general\-purpose backbone for diverse EEG analyses\.

## 1Introduction

Electroencephalography \(EEG\) reflects dynamic neural activity and underlying brain states\. With high temporal resolution and ease of acquisition, EEG is widely used across clinical diagnosis, cognitive neuroscience, and brain\-computer interface \(BCI\) applications\[[133](https://arxiv.org/html/2610.10571#bib.bib133),[88](https://arxiv.org/html/2610.10571#bib.bib88),[17](https://arxiv.org/html/2610.10571#bib.bib17),[146](https://arxiv.org/html/2610.10571#bib.bib146)\]\. Deep learning models have achieved strong performance in interpreting these signals\[[2](https://arxiv.org/html/2610.10571#bib.bib2),[120](https://arxiv.org/html/2610.10571#bib.bib120)\]\.

Despite this progress, building a general\-purpose EEG model remains challenging due to the heterogeneity of EEG data\. EEG signals vary significantly across individuals\[[121](https://arxiv.org/html/2610.10571#bib.bib121)\]and are recorded under diverse experimental conditions with different devices and electrode configurations\[[19](https://arxiv.org/html/2610.10571#bib.bib19)\]\. This makes it difficult to learn representations that transfer across datasets and subjects\.

Inspired by foundation models in vision and language\[[112](https://arxiv.org/html/2610.10571#bib.bib112),[40](https://arxiv.org/html/2610.10571#bib.bib40)\], recent EEG foundation models such as LaBraM\[[57](https://arxiv.org/html/2610.10571#bib.bib57)\], CBraMod\[[150](https://arxiv.org/html/2610.10571#bib.bib150)\], and REVE\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]have explored scalable self\-supervised pretraining, using masked reconstruction or token\-prediction objectives whose targets are derived from the input signal\. EEG recordings contain both neural activity and non\-neural components such as muscle and ocular artifacts\. Reconstruction\-based objectives define their prediction targets on all components present in the observed signal, which motivates considering prediction targets defined at the representation level\. We therefore adopt the joint\-embedding predictive architecture \(JEPA\)\[[8](https://arxiv.org/html/2610.10571#bib.bib8)\]\.

We propose the Spherical Prior EEG Representation Architecture \(SPERA\), a representation learning framework for EEG built on latent\-space prediction\. Beyond this objective, our central contribution is a Legendre polynomial spherical prior incorporated into attention, providing a learnable pairwise geometric bias that reflects the spherical structure of scalp EEG and applies to arbitrary montages\. Two further components adapt the backbone to EEG: factorized temporal and spatial attention interleaved with periodic full\-attention blocks for cross\-axis interactions, and a relational spectral regularizer that induces frequency\-aware latents by aligning pairwise similarity structure with spectral views\.

Building on these components, we pretrain SPERA on a multi\-domain EEG corpus comprising approximately 80,000 hours of recordings from 29,048 subjects across 106 datasets\. We evaluate SPERA on nine diverse downstream tasks spanning clinical, cognitive, and BCI applications and compare it with prior EEG foundation models\. We further investigate the scaling behavior of latent\-space prediction under EEG\-aware design, with a focus on parameter efficiency under linear probing \(LP\)\.

## 2Related Work

#### Self\-Supervised Objectives for EEG

Most existing EEG foundation models\[[57](https://arxiv.org/html/2610.10571#bib.bib57),[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94),[79](https://arxiv.org/html/2610.10571#bib.bib79),[75](https://arxiv.org/html/2610.10571#bib.bib75)\]rely on masked modeling objectives with targets derived from the input signal, including reconstructed signal patches and discrete neural tokens\. Such targets therefore include both neural and non\-neural components of the observed signal\. JEPA models\[[8](https://arxiv.org/html/2610.10571#bib.bib8),[9](https://arxiv.org/html/2610.10571#bib.bib9)\]instead predict in latent space, and several EEG models have moved in this direction: latent prediction against a momentum\-updated target encoder\[[87](https://arxiv.org/html/2610.10571#bib.bib87)\], representation alignment paired with auxiliary patch reconstruction\[[149](https://arxiv.org/html/2610.10571#bib.bib149)\], generative diffusion whose denoising activations serve as representations\[[110](https://arxiv.org/html/2610.10571#bib.bib110)\], and direct applications of JEPA to EEG\[[45](https://arxiv.org/html/2610.10571#bib.bib45),[53](https://arxiv.org/html/2610.10571#bib.bib53),[95](https://arxiv.org/html/2610.10571#bib.bib95)\]\. However, none of these explicitly encode the pairwise geometric relationships between electrodes, which vary across montage configurations\. We use a latent prediction objective over a montage\-variable token grid, with masking of temporal regions and spatial neighborhoods defined by 3D electrode coordinates, and scale it to a multi\-domain corpus spanning over a hundred datasets\.

#### Electrode Geometry in EEG Modeling

A central challenge for EEG foundation models is the heterogeneity of electrode montages across datasets\. BIOT adds channel embeddings and relative position embeddings\[[155](https://arxiv.org/html/2610.10571#bib.bib155)\], CBraMod uses asymmetric conditional positional encoding to adapt to diverse EEG formats\[[150](https://arxiv.org/html/2610.10571#bib.bib150)\], and REVE introduces a 4D positional encoding scheme for arbitrary electrode arrangements\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\. Recent JEPA\-style EEG models also introduce spatial inductive biases, including 3D coordinate\-based positional embeddings\[[45](https://arxiv.org/html/2610.10571#bib.bib45)\], video\-like spatio\-temporal tokenization\[[53](https://arxiv.org/html/2610.10571#bib.bib53)\], and coordinate\-aware channel mixing with Fourier features\[[95](https://arxiv.org/html/2610.10571#bib.bib95)\]\. We instead encode electrode geometry directly into attention using a Legendre\-based spherical prior, providing a learnable pairwise bias derived from the biophysical geometry of the scalp\[[102](https://arxiv.org/html/2610.10571#bib.bib102),[21](https://arxiv.org/html/2610.10571#bib.bib21)\]\.

#### Spatio\-Temporal Modeling in EEG

EEG signals exhibit distinct spatial and temporal dependencies, motivating attention factorization along each axis\. A related factorized design has been used in video understanding, where TimeSformer and ViViT apply temporal and spatial attention sequentially within each block\[[18](https://arxiv.org/html/2610.10571#bib.bib18),[7](https://arxiv.org/html/2610.10571#bib.bib7)\]\. In EEG, CBraMod models spatial and temporal dependencies in parallel using criss\-cross attention\[[150](https://arxiv.org/html/2610.10571#bib.bib150)\], while CSBrain\[[162](https://arxiv.org/html/2610.10571#bib.bib162)\]combines cross\-scale spatio\-temporal tokenization with structured sparse attention over local temporal windows and anatomical regions\. State\-space models use Mamba\-based backbones for EEG sequence modeling\[[151](https://arxiv.org/html/2610.10571#bib.bib151)\]\. LuMamba uses learned\-query cross\-attention to unify variable electrode configurations before temporal modeling\[[20](https://arxiv.org/html/2610.10571#bib.bib20)\]\. These approaches capture spatial and temporal structure in different ways\. However, our setting introduces two additional design considerations: EEG channel montages vary across datasets, unlike the fixed spatial grids used in these video models, and purely factorized attention restricts direct cross\-axis interaction\. We address these considerations by combining explicit electrode\-geometry encoding with a hybrid backbone that interleaves factorized and full\-attention blocks\.

#### Spectral Objectives in EEG Pretraining

Frequency components are key features of EEG signals, motivating spectral objectives in several pretraining methods\. LaBraM trains its tokenizer with vector\-quantized neural spectrum prediction\[[57](https://arxiv.org/html/2610.10571#bib.bib57)\], and Pradeepkumar et al\.\[[109](https://arxiv.org/html/2610.10571#bib.bib109)\]introduce time\-frequency motif learning for frequency\-aware EEG tokenization\. We complement this line of work with a relational spectral regularizer that aligns pairwise similarity structure between latents and spectral views, without predicting absolute spectral values\.

## 3Methods

![Refer to caption](https://arxiv.org/html/2610.10571v1/fig_01.png)Figure 1:Overview of the SPERA pretraining framework\.We denote an EEG recording as𝐗∈ℝC×T\\mathbf\{X\}\\in\\mathbb\{R\}^\{C\\times T\}, whereCCis the number of electrodes andTTis the number of time samples\. Each electrode is associated with a 3D anatomical coordinate, collectively represented as𝐄∈ℝC×3\\mathbf\{E\}\\in\\mathbb\{R\}^\{C\\times 3\}\. To tokenize𝐗\\mathbf\{X\}, each of theCCchannels is divided intoPtP\_\{t\}non\-overlapping 1\-second temporal patches at a sampling rate offs=f\_\{s\}=200 Hz, resulting in a total ofN=C⋅PtN=C\\cdot P\_\{t\}tokens\. Each token is uniquely indexed by a \(channel, time\-patch\) tuple\(c,p\)\(c,p\)on the spatio\-temporal grid\. Unlike token sequences in language or vision, EEG signals have dataset\-specific spatio\-temporal grids, as channel montages vary across datasets\. This cross\-dataset variability and the two\-axis structure of the token space motivate the architectural choices described in this section\.

### 3\.1Self\-Supervised Objective: Spatio\-Temporal JEPA

#### JEPA Objective

Figure[1](https://arxiv.org/html/2610.10571#S3.F1)illustrates the overall pretraining framework\. Raw EEG contains muscle and ocular artifacts that persist after preprocessing, so an input\-space reconstruction objective requires reproducing them alongside neural activity\. We adopt JEPA\[[8](https://arxiv.org/html/2610.10571#bib.bib8)\], which predicts latent representations of masked target regions from visible context\. SPERA consists of a student encoderfθf\_\{\\theta\}and a teacher encoderfξf\_\{\\xi\}; the teacher receives no gradients and is updated as an exponential moving average \(EMA\) offθf\_\{\\theta\}\. On the spatio\-temporal grid, we partition the token indices into disjoint context and target sets,𝒞\\mathcal\{C\}and𝒯\\mathcal\{T\}\. The student encodes only the context tokens to produce𝐙ctx\\mathbf\{Z\}\_\{\\text\{ctx\}\}\. The teacher encodes the full token sequence, and𝐙tgt\\mathbf\{Z\}\_\{\\text\{tgt\}\}is obtained by selecting the teacher outputs at the target positions\. A two\-layer cross\-attention predictorgϕg\_\{\\phi\}predicts𝐙^tgt\\hat\{\\mathbf\{Z\}\}\_\{\\text\{tgt\}\}from𝐙ctx\\mathbf\{Z\}\_\{\\text\{ctx\}\}\. For each target position, a query is formed by adding the target coordinate embedding to a single learnable vector shared across all target positions, and is refined by cross\-attending to𝐙ctx\\mathbf\{Z\}\_\{\\text\{ctx\}\}\. Following prior work\[[9](https://arxiv.org/html/2610.10571#bib.bib9)\], the model is trained to minimize theℓ1\\ell\_\{1\}distance in latent space:

ℒJEPA=1\|𝒯\|​D​∑\(c,p\)∈𝒯‖𝐳^c,p−𝐳c,p‖1,\\mathcal\{L\}\_\{\\text\{JEPA\}\}=\\frac\{1\}\{\|\\mathcal\{T\}\|D\}\\sum\_\{\(c,p\)\\in\\mathcal\{T\}\}\\left\\\|\\hat\{\\mathbf\{z\}\}\_\{c,p\}\-\\mathbf\{z\}\_\{c,p\}\\right\\\|\_\{1\},\(1\)where𝐳^c,p\\hat\{\\mathbf\{z\}\}\_\{c,p\}and𝐳c,p\\mathbf\{z\}\_\{c,p\}denote the predicted and teacher latents at position\(c,p\)\(c,p\), andDDis the embedding dimension\.

#### Masking Strategy

For each sample, temporal masking is activated with probability 0\.8, and spatial masking is activated independently with probability 0\.8\. If neither is activated, we default to temporal masking\. Temporal masks follow a semantic subsequence preserving \(SSP\) strategy\[[87](https://arxiv.org/html/2610.10571#bib.bib87)\]: rather than masking random individual time patches, we preserve contiguous blocks of patches to ensure the context carries coherent temporal structure\. Spatial masks select a random electrode as a center and mask itskk\-nearest neighbors based on 3D Euclidean distance, withk=max⁡\(1,⌊ρs⋅C⌉\)k=\\max\(1,\\lfloor\\rho\_\{s\}\\cdot C\\rceil\)for a sampled spatial ratioρs\\rho\_\{s\}\. Masking ratios are drawn uniformly from \[0\.15, 0\.35\] for time and \[0\.10, 0\.30\] for space \(ρs\\rho\_\{s\}\)\.

#### Student Augmentation

We apply EEG\-specific perturbations to the student’s context input: temporal amplitude scaling and additive Gaussian noise, together with Gaussian jitter to electrode coordinates\. Augmentation hyperparameters are reported in Appendix[C\.1](https://arxiv.org/html/2610.10571#A3.SS1)\.

### 3\.2Encoder Architecture

Dense full attention allows interactions among all spatio\-temporal token pairs but does not explicitly distinguish temporal and spatial dependencies\. We adopt a hybrid backbone of factorized attention blocks interleaved with periodic full\-attention blocks for cross\-axis interactions\.

#### Hybrid Attention Blocks

The base block factorizes attention along each axis separately\. Atemporal attentionpass operates independently over thePtP\_\{t\}time patches within each channel, followed by aspatial attentionpass over theCCchannels at each time patch\. Every fourth block is a full self\-attention block that attends jointly over allN=C⋅PtN=C\\cdot P\_\{t\}tokens, enabling cross\-axis interactions\. Both attention block types share standard transformer design choices: a pre\-norm architecture with layer normalization \(LN\), a SwiGLU MLP\[[128](https://arxiv.org/html/2610.10571#bib.bib128)\], and rotary position embeddings \(RoPE\)\[[139](https://arxiv.org/html/2610.10571#bib.bib139)\]applied along the temporal axis \(in both the encoder and the predictor\)\.

### 3\.3Electrode Geometry Encoding with Spherical Prior

To handle varying electrode montages across datasets, we incorporate simple coordinate embeddings and Legendre\-based spherical priors\. The Legendre prior is implemented in two forms: a pairwise Legendre bias for factorized attention blocks and Legendre anchor encoding for full\-attention blocks\. The two are assigned to attention types based on computational considerations analyzed in Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)\.

#### Coordinate Embedding

A direct approach to spatial conditioning is a per\-token additive embedding derived from electrode coordinates\. We normalize each coordinate onto the unit sphere and pass it through a linear projection\. The resulting channel\-wise embedding is scaled by a learnable scalarα\\alpha, initialized to zero, and shared across all temporal patches of the same electrode\.

#### Legendre Spatial Bias

Scalp EEG electrodes lie approximately on a spherical head surface, and we exploit this structure to build a biophysically motivated spatial prior on the sphere itself\. Legendre polynomials provide a natural basis for parameterizing pairwise functions of angular separation on the sphere and have been used in conventional EEG analysis\[[102](https://arxiv.org/html/2610.10571#bib.bib102),[21](https://arxiv.org/html/2610.10571#bib.bib21)\]\. We therefore use a truncated Legendre expansion to encode pairwise electrode geometry as an additive attention bias\.

Within each factorized attention block, the spatial attention pass computes attention overCCchannels at a fixed time patch\. To encode pairwise geometric relationships between electrodes, we introduce a learnable additive attention biasbi​jb\_\{ij\}between channeliiand channeljj, defined as a truncated Legendre polynomial expansion of their cosine similarity on the unit sphere:

bi​j=∑ℓ=0Lwℓ​Pℓ​\(𝐞i⊤​𝐞j\),b\_\{ij\}=\\sum\_\{\\ell=0\}^\{L\}w\_\{\\ell\}\\,P\_\{\\ell\}\\\!\\left\(\\mathbf\{e\}\_\{i\}^\{\\top\}\\mathbf\{e\}\_\{j\}\\right\),\(2\)where𝐞\\mathbf\{e\}denotes unit\-normalized coordinates,LLis the maximum polynomial degree,PℓP\_\{\\ell\}is theℓ\\ell\-th Legendre polynomial, andwℓw\_\{\\ell\}are learnable scalar coefficients\. Unlike classical formulations that fixwℓw\_\{\\ell\}to a closed\-form decay \(e\.g\.,\(2​ℓ\+1\)/\[ℓm​\(ℓ\+1\)m\]\(2\\ell\+1\)/\[\\ell^\{m\}\(\\ell\+1\)^\{m\}\]in spherical splines\), we let the coefficients be learned end\-to\-end\. This bias is pairwise, geometry\-aware, and dataset\-agnostic, requiring no assumption about the number or identity of electrodes\.

#### Legendre Anchor Encoding

The pairwise Legendre bias in Eq\. \(2\) directly encodes the angular relationship between each pair of electrodes\. In the dense implementation, applying this pairwise bias in full\-attention blocks requires materializing anN×NN\\times Nscore\-bias matrix, which incurs substantial memory and computational overhead\. We therefore construct an anchor\-based alternative from the same Legendre geometry\. Instead of expanding the relationship between every pair of electrodes, we represent each electrode by its Legendre\-expanded similarities to a finite set of learnable anchor directions on the unit sphere\. These anchor\-based geometry encodings are then injected into the queries and keys of the full\-attention blocks\.

We compute a per\-channel spatial featureϕc\\boldsymbol\{\\phi\}\_\{c\}using a set ofMMlearnable anchor points𝐚^m\\hat\{\\mathbf\{a\}\}\_\{m\}on the unit sphere, expanding the cosine similarity between each electrode and each anchor via Legendre polynomials:

gc,m=∑ℓ=0Lωm,ℓ​Pℓ​\(𝐞c⊤​𝐚^m\),ϕc=LN⁡\(Wproj​\[gc,1,…,gc,M\]\),g\_\{c,m\}=\\sum\_\{\\ell=0\}^\{L\}\\omega\_\{m,\\ell\}\\,P\_\{\\ell\}\\\!\\left\(\\mathbf\{e\}\_\{c\}^\{\\top\}\\hat\{\\mathbf\{a\}\}\_\{m\}\\right\),\\qquad\\boldsymbol\{\\phi\}\_\{c\}=\\mathrm\{LN\}\\\!\\left\(W\_\{\\mathrm\{proj\}\}\\,\[g\_\{c,1\},\\ldots,g\_\{c,M\}\]\\right\),\(3\)𝐪~i=𝐪i\+ΓQ​ϕci,𝐤~j=𝐤j\+ΓK​ϕcj,si​j=𝐪~i⊤​𝐤~jd,\\tilde\{\\mathbf\{q\}\}\_\{i\}=\\mathbf\{q\}\_\{i\}\+\\Gamma\_\{Q\}\\boldsymbol\{\\phi\}\_\{c\_\{i\}\},\\qquad\\tilde\{\\mathbf\{k\}\}\_\{j\}=\\mathbf\{k\}\_\{j\}\+\\Gamma\_\{K\}\\boldsymbol\{\\phi\}\_\{c\_\{j\}\},\\qquad s\_\{ij\}=\\frac\{\\tilde\{\\mathbf\{q\}\}\_\{i\}^\{\\top\}\\tilde\{\\mathbf\{k\}\}\_\{j\}\}\{\\sqrt\{d\}\},\(4\)whereωm,ℓ\\omega\_\{m,\\ell\}are learnable anchor\-specific coefficients andWprojW\_\{\\mathrm\{proj\}\}is a linear projection\. Here,cic\_\{i\}denotes the channel index of tokenii, andddis the attention head dimension\. The geometry featureϕc\\boldsymbol\{\\phi\}\_\{c\}is added to queries and keys via projectionsΓQ\\Gamma\_\{Q\}andΓK\\Gamma\_\{K\}, applied after temporal RoPE\. Expanding Eq\. \(4\) gives four terms: content–content, an anchor\-induced geometry–geometry term, and two content–geometry cross terms \(see Appendix[F\.3](https://arxiv.org/html/2610.10571#A6.SS3)for details\)\. The coefficients in Eqs\. \(2\)–\(3\), as well as the anchor directions𝐚^m\\hat\{\\mathbf\{a\}\}\_\{m\}, are shared globally across layers and heads\. In the anchor\-based formulation, layer\-specific adaptation is introduced through the block\-specific projectionsΓQ,ΓK\\Gamma\_\{Q\},\\Gamma\_\{K\}\.

### 3\.4Relational Spectral Regularizer

Frequency components are key features of EEG signals, but incorporating spectral objectives into a JEPA framework is not straightforward\. Direct spectrum reconstruction would introduce an absolute signal\-derived target, whereas our goal is to regularize spectral relationships without reconstructing spectral values\. Therefore, we introduce a relational spectral regularizer \(RSReg\) that aligns the pairwise similarity structure of the predicted representations with that of the corresponding spectral targets\. This design is inspired by relation\-preserving distillation\[[98](https://arxiv.org/html/2610.10571#bib.bib98),[97](https://arxiv.org/html/2610.10571#bib.bib97)\], which supervises pairwise relational structure\. Here, the target relations are computed deterministically from spectral views of EEG patches, not from another network\.

For each target token\(c,p\)\(c,p\),𝐬c,p\\mathbf\{s\}\_\{c,p\}is the log\-power spectrum of its 1\-second raw patch, computed via a Hann\-windowed FFT using frequency bins within the 1–45 Hz band, and z\-score normalized across frequency bins\. The predictor output𝐳^c,p\\hat\{\\mathbf\{z\}\}\_\{c,p\}is passed through a small projectorhψh\_\{\\psi\}to obtain𝐫c,p=hψ​\(𝐳^c,p\)\\mathbf\{r\}\_\{c,p\}=h\_\{\\psi\}\(\\hat\{\\mathbf\{z\}\}\_\{c,p\}\)\. We align the pairwise similarity matrices of𝐫\\mathbf\{r\}and𝐬\\mathbf\{s\}through a KL divergence loss:

ℒspec=KL\(σ\(𝐒𝐒⊤/τs\)∥σ\(𝐑𝐑⊤/τz\)\),\\mathcal\{L\}\_\{\\text\{spec\}\}=\\mathrm\{KL\}\\\!\\left\(\\sigma\\\!\\left\(\\mathbf\{S\}\\mathbf\{S\}^\{\\top\}/\\tau\_\{s\}\\right\)\\,\\Big\\\|\\,\\sigma\\\!\\left\(\\mathbf\{R\}\\mathbf\{R\}^\{\\top\}/\\tau\_\{z\}\\right\)\\right\),\(5\)where𝐒\\mathbf\{S\}and𝐑\\mathbf\{R\}are row\-wiseℓ2\\ell\_\{2\}\-normalized matrices of𝐬\\mathbf\{s\}and𝐫\\mathbf\{r\}, respectively,σ⁡\(⋅\)\\sigma\(\\cdot\)denotes row\-wise softmax, andτs,τz\\tau\_\{s\},\\tau\_\{z\}are temperature hyperparameters\. Similarity matrices are computed per recording, with diagonal entries masked before softmax\. The KL loss is averaged over target\-token rows within each recording, then equally across recordings in the effective batch\. This preserves relative spectral relationships among tokens without constraining their absolute spectral values, inducing frequency\-aware latent representations through relational spectral supervision\. The total training loss is:

ℒ=ℒJEPA\+λ​ℒspec\.\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{JEPA\}\}\+\\lambda\\,\\mathcal\{L\}\_\{\\text\{spec\}\}\.\(6\)

## 4Experiments

### 4\.1Pretraining

#### Dataset Collection

We collected a large\-scale pretraining corpus spanning approximately 80,000 hours of EEG recordings from 29,048 subjects, yielding 2\.67 million channel\-hours and 9\.60 billion tokens in total\. To the best of our knowledge, this is the largest multi\-domain EEG pretraining corpus reported for a general\-purpose EEG foundation model\. The corpus is organized into three categories \(clinical, cognitive, and BCI\), comprising 82\.08%, 16\.21%, and 1\.71% of the total recording time, respectively\. The pretraining dataset exhibits substantial heterogeneity in electrode montages, covering a wide range of channel counts and layouts across sources\. A summary of the dataset composition and a complete list of included sources are provided in Appendix[B](https://arxiv.org/html/2610.10571#A2)\.

#### Preprocessing Pipeline

We apply a standardized preprocessing pipeline to all recordings\. Power line noise is removed via a notch filter at 50 or 60 Hz depending on the recording country\. EEG recordings are then bandpass filtered between 0\.5 and 75 Hz and resampled tofs=f\_\{s\}=200 Hz\. Each channel iszz\-score normalized to account for cross\-dataset variability in electrode impedance and amplifier gain\. For datasets that provide digitized 3D electrode locations, we use the recorded coordinates directly; for those that specify only channel labels \(e\.g\., the 10–20 system\), we assign coordinates from the corresponding standard montage in MNE\-Python\[[39](https://arxiv.org/html/2610.10571#bib.bib39)\]\. In addition, amplitude values exceeding±\\pm15 standard deviations are clipped to suppress residual artifacts, as in\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\. Each recording is segmented into non\-overlapping windows of either 10 or 60 seconds depending on the source task\. Among the 60\-second segments, those whose token count exceeds 4,096 are further split into 30\-second chunks for training efficiency, preserving contiguous temporal structure\.

#### Implementation Details

We train all models with AdamW\[[77](https://arxiv.org/html/2610.10571#bib.bib77)\]\. The learning rate follows a cosine schedule with linear warmup, and the teacher encoder is updated via an EMA with a cosine momentum schedule\. We pretrain four model sizes: SPERA\-Tiny \(18M\), SPERA\-Small \(48M\), SPERA\-Base \(194M\), and SPERA\-Large \(396M\)\. Full hyperparameter details are provided in Appendix[C\.1](https://arxiv.org/html/2610.10571#A3.SS1)\.

### 4\.2Experimental Setup

#### Downstream Task Datasets

We evaluate SPERA on nine datasets spanning diverse clinical, cognitive, and BCI tasks: BCIC2020\-3\[[56](https://arxiv.org/html/2610.10571#bib.bib56)\], BCIC\-IV\-2a\[[143](https://arxiv.org/html/2610.10571#bib.bib143)\], PhysioNet\-MI\[[38](https://arxiv.org/html/2610.10571#bib.bib38),[122](https://arxiv.org/html/2610.10571#bib.bib122)\], FACED\[[23](https://arxiv.org/html/2610.10571#bib.bib23)\], mental arithmetic \(MAT\)\[[164](https://arxiv.org/html/2610.10571#bib.bib164)\], ISRUC\[[63](https://arxiv.org/html/2610.10571#bib.bib63)\], Mumtaz\[[89](https://arxiv.org/html/2610.10571#bib.bib89)\], TUAB\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\], and TUEV\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\]\. These nine tasks are the intersection of the CBraMod and REVE evaluation suites\. We adopt the same train/validation/test splits and preprocessing pipeline as baseline EEG foundation models\[[155](https://arxiv.org/html/2610.10571#bib.bib155),[57](https://arxiv.org/html/2610.10571#bib.bib57),[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\. Table[1](https://arxiv.org/html/2610.10571#S4.T1)summarizes these datasets\.

Table 1:Summary of downstream task datasets\.TaskDataset\# Samples\# ChannelsDuration \(s\)\# ClassesImagined Speech ClassificationBCIC2020\-36,0006435Motor Imagery ClassificationBCIC\-IV\-2a5,1842244PhysioNet\-MI9,8376444Emotion RecognitionFACED10,33232109Mental Stress DetectionMAT1,7072052Sleep StagingISRUC88,1406305Mental Disorder DiagnosisMumtaz7,1431952EEG Abnormality DetectionTUAB409,45516102Event Type ClassificationTUEV112,4911656

#### Baseline Models and Evaluation Protocol

We compare SPERA against both non\-foundation and foundation model baselines\. Non\-foundation baselines include EEGNet\[[70](https://arxiv.org/html/2610.10571#bib.bib70)\], EEGConformer\[[135](https://arxiv.org/html/2610.10571#bib.bib135)\], SPaRCNet\[[58](https://arxiv.org/html/2610.10571#bib.bib58)\], ContraWR\[[156](https://arxiv.org/html/2610.10571#bib.bib156)\], CNN\-Transformer\[[100](https://arxiv.org/html/2610.10571#bib.bib100)\], FFCL\[[73](https://arxiv.org/html/2610.10571#bib.bib73)\], ST\-Transformer\[[134](https://arxiv.org/html/2610.10571#bib.bib134)\], EEG2Rep\[[87](https://arxiv.org/html/2610.10571#bib.bib87)\], and EEGDM\[[110](https://arxiv.org/html/2610.10571#bib.bib110)\], while foundation model baselines include BIOT\[[155](https://arxiv.org/html/2610.10571#bib.bib155)\], LaBraM\[[57](https://arxiv.org/html/2610.10571#bib.bib57)\], CBraMod\[[150](https://arxiv.org/html/2610.10571#bib.bib150)\], REVE\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\], CSBrain\[[162](https://arxiv.org/html/2610.10571#bib.bib162)\], CodeBrain\[[79](https://arxiv.org/html/2610.10571#bib.bib79)\], EEGMamba\[[151](https://arxiv.org/html/2610.10571#bib.bib151)\], GRAM\[[75](https://arxiv.org/html/2610.10571#bib.bib75)\], LuMamba\[[20](https://arxiv.org/html/2610.10571#bib.bib20)\], EEGPT\[[149](https://arxiv.org/html/2610.10571#bib.bib149)\], and Laya\[[95](https://arxiv.org/html/2610.10571#bib.bib95)\]\.

We evaluate SPERA under two protocols, LP and linear probing followed by fine\-tuning \(LPFT\)\. LP freezes the pretrained encoder and trains a linear classification head on mean\-pooled token features, while LPFT additionally fine\-tunes the encoder after the LP stage\. For each task, hyperparameters and checkpoints are selected on the validation set, and the held\-out test set is used exclusively for final evaluation\. Baseline results are extracted from the original publications\[[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94),[162](https://arxiv.org/html/2610.10571#bib.bib162)\]; their downstream adaptation protocols vary across studies \(e\.g\., CBraMod uses an MLP classification head\)\. Balanced accuracy is used as the primary metric; each experiment is repeated over five random seeds, and results are reported as mean±\\pmstandard deviation\. For SPERA, the overall average is computed per seed as the unweighted mean across the nine datasets, and the reported standard deviation is taken across the resulting five seed\-wise averages\. Baseline results, including reported averages and standard deviations, are taken from the original publications\.

### 4\.3Downstream Task Results

Table[2](https://arxiv.org/html/2610.10571#S4.T2)summarizes LPFT performance across the nine downstream tasks and four SPERA model scales\. Per\-task Welch tests over five seeds, Holm\-corrected across the nine comparisons, find significant gains for SPERA\-Base on five tasks: BCIC2020\-3, TUEV, BCIC\-IV\-2a, ISRUC, and TUAB\. PhysioNet\-MI is borderline \(pHolm=p\_\{\\mathrm\{Holm\}\}=0\.052\) and no task shows a significant loss\. Among the significant differences, the largest gains are observed on TUEV \(\+\+0\.078; 6\-class clinical event\) and BCIC2020\-3 \(\+\+0\.050; 5\-class imagined speech\)\. The differences on FACED, MAT, and Mumtaz did not reach statistical significance after Holm correction\. Mumtaz in particular shows limited headroom, with balanced accuracy remaining generally high across foundation models and model scales\. SPERA performs consistently on both BCIC\-IV\-2a \(22 channels\) and PhysioNet\-MI \(64 channels\), two motor\-imagery tasks with different electrode layouts\. Per\-task differences with confidence intervals, for both SPERA\-Base and SPERA\-Large, are reported in Appendix[D\.10](https://arxiv.org/html/2610.10571#A4.SS10)\.

Table 2:Experimental results on nine downstream tasks\. SPERA models are evaluated under the LPFT protocol, while baseline results are taken from the original publications using their reported downstream adaptation protocols\. The results are reported as mean balanced accuracy±\\pmstandard deviation over five random seeds\. The best performance for each task is highlighted in bold\.MethodsBCIC2020\-3BCIC\-IV\-2aPhysioNet\-MIFACEDMATEEGNet0\.4413±0\.00960\.4413\\pm 0\.00960\.4482±0\.00940\.4482\\pm 0\.00940\.5814±0\.01250\.5814\\pm 0\.01250\.4090±0\.01220\.4090\\pm 0\.01220\.6770±0\.01160\.6770\\pm 0\.0116EEGConformer0\.4506±0\.01330\.4506\\pm 0\.01330\.4696±0\.01060\.4696\\pm 0\.01060\.6049±0\.01040\.6049\\pm 0\.01040\.4559±0\.01250\.4559\\pm 0\.01250\.6805±0\.01230\.6805\\pm 0\.0123SPaRCNet0\.4426±0\.01560\.4426\\pm 0\.01560\.4635±0\.01170\.4635\\pm 0\.01170\.5932±0\.01520\.5932\\pm 0\.01520\.4673±0\.01550\.4673\\pm 0\.01550\.6879±0\.01070\.6879\\pm 0\.0107ContraWR0\.4257±0\.01620\.4257\\pm 0\.01620\.4678±0\.01250\.4678\\pm 0\.01250\.5892±0\.01330\.5892\\pm 0\.01330\.4887±0\.00780\.4887\\pm 0\.00780\.6631±0\.00970\.6631\\pm 0\.0097CNN\-Transformer0\.4533±0\.00920\.4533\\pm 0\.00920\.4600±0\.01080\.4600\\pm 0\.01080\.6053±0\.01180\.6053\\pm 0\.01180\.4697±0\.01320\.4697\\pm 0\.01320\.6779±0\.02680\.6779\\pm 0\.0268FFCL0\.4678±0\.01970\.4678\\pm 0\.01970\.4470±0\.01430\.4470\\pm 0\.01430\.5726±0\.00920\.5726\\pm 0\.00920\.4673±0\.01580\.4673\\pm 0\.01580\.6798±0\.01420\.6798\\pm 0\.0142ST\-Transformer0\.4126±0\.01220\.4126\\pm 0\.01220\.4575±0\.01450\.4575\\pm 0\.01450\.6035±0\.00810\.6035\\pm 0\.00810\.4810±0\.00790\.4810\\pm 0\.00790\.6631±0\.01730\.6631\\pm 0\.0173BIOT0\.4920±0\.00860\.4920\\pm 0\.00860\.4748±0\.00930\.4748\\pm 0\.00930\.6153±0\.01540\.6153\\pm 0\.01540\.5118±0\.01180\.5118\\pm 0\.01180\.6875±0\.01860\.6875\\pm 0\.0186LaBraM\-Base0\.5060±0\.01550\.5060\\pm 0\.01550\.4869±0\.00850\.4869\\pm 0\.00850\.6173±0\.01220\.6173\\pm 0\.01220\.5273±0\.01070\.5273\\pm 0\.01070\.6909±0\.01250\.6909\\pm 0\.0125CBraMod0\.5373±0\.01080\.5373\\pm 0\.01080\.5138±0\.00660\.5138\\pm 0\.00660\.6417±0\.00910\.6417\\pm 0\.00910\.5509±0\.00890\.5509\\pm 0\.00890\.7256±0\.01320\.7256\\pm 0\.0132CSBrain0\.6004±0\.01870\.6004\\pm 0\.01870\.5657±0\.00710\.5657\\pm 0\.00710\.6304±0\.00900\.6304\\pm 0\.00900\.5752±0\.00420\.5752\\pm 0\.00420\.7558±0\.01060\.7558\\pm 0\.0106REVE\-Base0\.5635±0\.01230\.5635\\pm 0\.01230\.6396±0\.00950\.6396\\pm 0\.00950\.6480±0\.01400\.6480\\pm 0\.01400\.5646±0\.01640\.5646\\pm 0\.01640\.7660±0\.03550\.7660\\pm 0\.0355SPERA\-Tiny0\.4827±\\pm0\.01730\.5326±\\pm0\.01380\.6117±\\pm0\.00930\.4849±\\pm0\.01550\.6971±\\pm0\.0229SPERA\-Small0\.5733±\\pm0\.01350\.6085±\\pm0\.01560\.6400±\\pm0\.01120\.5132±\\pm0\.01670\.7238±\\pm0\.0198SPERA\-Base0\.6504±\\pm0\.01220\.6816±\\pm0\.01470\.6726±\\pm0\.00720\.5754±\\pm0\.01750\.7778±\\pm0\.0216SPERA\-Large0\.6883±\\pm0\.01420\.7023±\\pm0\.01440\.6817±\\pm0\.00870\.5919±\\pm0\.01860\.8021±\\pm0\.0203MethodsISRUCMumtazTUABTUEVAverageEEGNet0\.7154±0\.01210\.7154\\pm 0\.01210\.9232±0\.01040\.9232\\pm 0\.01040\.7642±0\.00360\.7642\\pm 0\.00360\.3876±0\.01430\.3876\\pm 0\.01430\.5941±0\.00370\.5941\\pm 0\.0037EEGConformer0\.7400±0\.01330\.7400\\pm 0\.01330\.9308±0\.01170\.9308\\pm 0\.01170\.7758±0\.00490\.7758\\pm 0\.00490\.4074±0\.01640\.4074\\pm 0\.01640\.6128±0\.00440\.6128\\pm 0\.0044SPaRCNet0\.7487±0\.00750\.7487\\pm 0\.00750\.9316±0\.00950\.9316\\pm 0\.00950\.7896±0\.00180\.7896\\pm 0\.00180\.4161±0\.02620\.4161\\pm 0\.02620\.6156±0\.00470\.6156\\pm 0\.0047ContraWR0\.7402±0\.01260\.7402\\pm 0\.01260\.9195±0\.01150\.9195\\pm 0\.01150\.7746±0\.00410\.7746\\pm 0\.00410\.4384±0\.03490\.4384\\pm 0\.03490\.6119±0\.00530\.6119\\pm 0\.0053CNN\-Transformer0\.7363±0\.00870\.7363\\pm 0\.00870\.9305±0\.00680\.9305\\pm 0\.00680\.7777±0\.00220\.7777\\pm 0\.00220\.4087±0\.01610\.4087\\pm 0\.01610\.6133±0\.00450\.6133\\pm 0\.0045FFCL0\.7277±0\.01820\.7277\\pm 0\.01820\.9314±0\.00380\.9314\\pm 0\.00380\.7848±0\.00380\.7848\\pm 0\.00380\.3979±0\.01040\.3979\\pm 0\.01040\.6085±0\.00440\.6085\\pm 0\.0044ST\-Transformer0\.7381±0\.02050\.7381\\pm 0\.02050\.9135±0\.01030\.9135\\pm 0\.01030\.7966±0\.00230\.7966\\pm 0\.00230\.3984±0\.02280\.3984\\pm 0\.02280\.6071±0\.00480\.6071\\pm 0\.0048BIOT0\.7527±0\.01210\.7527\\pm 0\.01210\.9358±0\.00520\.9358\\pm 0\.00520\.7959±0\.00570\.7959\\pm 0\.00570\.5281±0\.02250\.5281\\pm 0\.02250\.6438±0\.00440\.6438\\pm 0\.0044LaBraM\-Base0\.7633±0\.01020\.7633\\pm 0\.01020\.9409±0\.00790\.9409\\pm 0\.00790\.8140±0\.00190\.8140\\pm 0\.00190\.6409±0\.00650\.6409\\pm 0\.00650\.6653±0\.00310\.6653\\pm 0\.0031CBraMod0\.7865±0\.01100\.7865\\pm 0\.01100\.9560±0\.00560\.9560\\pm 0\.00560\.8289±0\.00220\.8289\\pm 0\.00220\.6671±0\.01070\.6671\\pm 0\.01070\.6898±0\.00510\.6898\\pm 0\.0051CSBrain0\.7925±0\.00300\.7925\\pm 0\.00300\.9643±0\.01550\.9643\\pm 0\.01550\.8172±0\.00430\.8172\\pm 0\.00430\.6903±0\.00590\.6903\\pm 0\.00590\.71020\.7102REVE\-Base0\.7819±0\.00780\.7819\\pm 0\.00780\.9644±\\pm0\.00970\.8315±0\.00140\.8315\\pm 0\.00140\.6759±0\.02290\.6759\\pm 0\.02290\.7150±0\.00570\.7150\\pm 0\.0057SPERA\-Tiny0\.7719±\\pm0\.01240\.9236±\\pm0\.00340\.8104±\\pm0\.00440\.7035±\\pm0\.02730\.6687±\\pm0\.0064SPERA\-Small0\.7852±\\pm0\.00960\.9450±\\pm0\.00480\.8318±\\pm0\.00320\.7384±\\pm0\.02580\.7066±\\pm0\.0057SPERA\-Base0\.8137±\\pm0\.00750\.9637±\\pm0\.00180\.8488±\\pm0\.00350\.7684±\\pm0\.02830\.7502±\\pm0\.0050SPERA\-Large0\.8142±\\pm0\.01060\.9702±\\pm0\.00160\.8608±\\pm0\.00290\.7869±\\pm0\.02860\.7665±\\pm0\.0053

### 4\.4Model Scaling Analysis

Figure 2:Model scaling under LP\. Mean balanced accuracy across nine downstream tasks is shown for SPERA models ranging from 18M to 396M parameters\. The shaded region denotes one standard deviation across five random seeds\. Horizontal lines indicate the corresponding LP results of REVE\-Base \(69M\) and REVE\-Large \(408M\)\.Table[2](https://arxiv.org/html/2610.10571#S4.T2)shows that average downstream performance improves with model scale under LPFT\. To further examine how the pretrained representations themselves scale, independently of full encoder fine\-tuning, we evaluate the four model sizes \(18M, 48M, 194M, and 396M\) using LP across all nine downstream tasks\. Per\-task LP results are reported in Appendix[D\.9](https://arxiv.org/html/2610.10571#A4.SS9)\. Figure[2](https://arxiv.org/html/2610.10571#S4.F2)shows that average balanced accuracy under LP improves with model size from 0\.584 at 18M to 0\.684 at 396M\. The largest gain occurs between 48M and 194M \(\+0\.060\), which coincides with the largest jump in hidden dimension \(512→\\rightarrow896\)\. The smaller improvement from 194M to 396M \(\+0\.023\) suggests diminishing returns at the current corpus size\. A similar pattern is observed under LPFT in Table[2](https://arxiv.org/html/2610.10571#S4.T2), where the average increases from 0\.669 to 0\.767 across the four scales, with a smaller gain from Base to Large\. In addition, SPERA\-Small \(48M\) achieves performance comparable to that of REVE\-Base \(69M\), and SPERA\-Base \(194M\) exceeds REVE\-Large \(408M\) by \+0\.013 under LP despite using less than half the parameters\.

### 4\.5Ablation Study and Efficiency Analysis

Table 3:Ablation studies on the encoder architecture, RSReg, and electrode geometry encoding\. All models are based on SPERA\-Small \(48M\) and evaluated using LP on motor imagery, sleep staging, and EEG abnormality detection tasks\. Results are reported as mean balanced accuracy±\\pmstandard deviation over five random seeds\. The best result per column is inbold; the second\-best result isunderlined\.VariantPhysioNet\-MIISRUCTUABAverageEncoder ArchitectureFull Attention Only0\.4450±0\.01240\.4450\\pm 0\.01240\.7097±0\.02180\.7097\\pm 0\.02180\.7749±0\.00240\.7749\\pm 0\.00240\.6432±0\.00840\.6432\\pm 0\.0084Factorized Attention Only0\.4833±0\.00910\.4833\\pm 0\.00910\.7153±0\.01870\.7153\\pm 0\.01870\.7865±0\.00660\.7865\\pm 0\.00660\.6617±0\.00730\.6617\\pm 0\.0073Hybrid \+ Late Full0\.4871±0\.01810\.4871\\pm 0\.01810\.6973±0\.01550\.6973\\pm 0\.01550\.7860±0\.00450\.7860\\pm 0\.00450\.6568±0\.00810\.6568\\pm 0\.0081RSRegNo RSReg0\.5182±\\pm0\.01840\.6994±0\.02050\.6994\\pm 0\.02050\.7759±0\.00460\.7759\\pm 0\.00460\.6645±0\.00930\.6645\\pm 0\.0093Electrode Geometry EncodingCoordinate Embedding Only0\.4821±0\.01500\.4821\\pm 0\.01500\.7009±0\.02680\.7009\\pm 0\.02680\.7744±0\.00560\.7744\\pm 0\.00560\.6525±0\.01040\.6525\\pm 0\.0104Legendre Bias Only0\.5193±\\pm0\.01060\.7320±\\pm0\.01820\.7929±\\pm0\.00340\.6814±\\pm0\.0071Legendre Anchor Encoding Only0\.5071±0\.01970\.5071\\pm 0\.01970\.7137±0\.02010\.7137\\pm 0\.02010\.7855±0\.00280\.7855\\pm 0\.00280\.6688±0\.00940\.6688\\pm 0\.0094Learnable Pairwise MLP0\.4463±0\.02030\.4463\\pm 0\.02030\.6679±0\.02640\.6679\\pm 0\.02640\.7671±0\.00670\.7671\\pm 0\.00670\.6271±0\.01130\.6271\\pm 0\.0113REVE Spatial Encoding0\.4921±0\.01740\.4921\\pm 0\.01740\.6910±0\.02120\.6910\\pm 0\.02120\.7607±0\.00910\.7607\\pm 0\.00910\.6479±0\.00910\.6479\\pm 0\.0091Gaussian \(Geodesic\)0\.4512±0\.01610\.4512\\pm 0\.01610\.6977±0\.02250\.6977\\pm 0\.02250\.7705±0\.00890\.7705\\pm 0\.00890\.6398±0\.01010\.6398\\pm 0\.0101SPERA\-Small0\.5227±\\pm0\.01120\.7206±\\pm0\.02400\.7869±\\pm0\.00620\.6767±\\pm0\.0110

Table 4:Computational efficiency and memory profiling using the SPERA\-Small model\. All measurements are conducted on a single NVIDIA RTX 5000 Ada GPU with a batch size of 1 and a sequence lengthN=N=3,840 \(64 channels×\\times60 patches\)\. ‘Mem’ denotes peak GPU memory\.ArchitectureLegendre PriorParams \(M\)Matmul FLOPs \(G\)Mem \(GB\)Throughput \(tok/s\)FullBias37\.9653\.02\.5120,260Anchor Encoding38\.7653\.11\.6175,769FactorizedBias50\.6399\.01\.7097,043Anchor Encoding51\.3399\.11\.7890,714HybridBias47\.4462\.52\.2652,263Anchor Encoding48\.2462\.61\.6696,165Off47\.4462\.51\.59100,259SPERA\-SmallFull \(Anchor Encoding\)\+ Factorized \(Bias\)47\.6462\.51\.9592,866

To understand the contribution of each component, we conduct ablation studies on the encoder architecture, RSReg, and electrode geometry encoding\. Given the substantial computational cost of repeatedly pretraining the SPERA\-Base model \(194M\), we adopt the SPERA\-Small model \(48M\) as a proxy, evaluated on motor imagery, sleep staging, and EEG abnormality detection tasks using LP\. We jointly analyze accuracy \(Table[3](https://arxiv.org/html/2610.10571#S4.T3)\) and computational efficiency \(Table[4](https://arxiv.org/html/2610.10571#S4.T4)\) to assess both representational quality and viability under realistic compute budgets\.

#### Component Ablations

We ablate three components: the hybrid attention backbone, RSReg, and the Legendre\-based spatial priors\. Neither full nor factorized attention alone matches our periodic hybrid design, and a variant that concentrates full\-attention blocks at the end of the network \(“Hybrid \+ Late Full” in Table[3](https://arxiv.org/html/2610.10571#S4.T3)\) improves over full\-only but still underperforms periodic interleaving\. This suggests that periodic cross\-axis interaction benefits EEG modeling\. Removing RSReg lowers average accuracy by 0\.012, with the largest drop on ISRUC \(−\-0\.021\), suggesting a benefit of frequency\-aware supervision\. The Legendre prior improves average accuracy by 0\.024 over coordinate embeddings alone \(0\.6767 vs\. 0\.6525\), and outperforms both REVE’s spatial encoding substituted for our Legendre prior \(0\.6479\) and a Gaussian bias on geodesic electrode distance \(0\.6398\)\. The lower performance of the pairwise MLP suggests that the structured Legendre parameterization is beneficial under the present training setup\. Further geometry variants are reported in Appendix[F\.1](https://arxiv.org/html/2610.10571#A6.SS1)\. We next examine the computational trade\-offs that determine which Legendre implementation is used in each attention type\.

#### Accuracy\-Efficiency Trade\-off

Factorized attention reduces the matrix\-multiplication cost substantially at our sequence length \(NN= 3,840\), from 653 GFLOPs for full attention to 399 GFLOPs, despite having more parameters due to the additional axis\-specific projections \(50\.6M vs\. 37\.9M\)\. The hybrid architecture lies between the two at 462\.5 GFLOPs, reflecting its combination of factorized blocks with periodic full\-attention blocks\. Here, matrix\-multiplication FLOPs include linear projections and the attention matrix multiplications, with one multiply\-accumulate counted as two FLOPs\.

The Legendre implementation has little effect on the matrix\-multiplication cost but strongly affects realized throughput\. Under full attention, the pairwise Legendre bias requires anN×NN\\times Nscore\-bias matrix and prevents the fused attention path used in our implementation \(i\.e\., FlashAttention via PyTorch SDPA\), reducing throughput to 20,260 tok/s despite nearly identical matrix\-multiplication FLOP counts for the bias\- and anchor\-based implementations \(653\.0 vs\. 653\.1 GFLOPs\)\. The anchor encoding instead injects geometry features into the queries and keys while preserving the fused attention path, reaching 75,769 tok/s\. In factorized attention, the smaller attention matrices make the explicit pairwise bias practical, achieving 97,043 tok/s compared with 90,714 tok/s for the anchor encoding\.

These observations motivate our final design: we use the anchor encoding in full\-attention blocks to preserve throughput and the pairwise Legendre bias in factorized layers, where its computational cost is small\. The resulting model achieves accuracy comparable to that of the bias\-only hybrid configuration while providing 1\.78×\\timeshigher throughput \(92,866 vs\. 52,263 tok/s\) and 14% lower peak memory \(1\.95 vs\. 2\.26 GB\), at the cost of a 0\.005 decrease in average balanced accuracy\.

### 4\.6Additional Analyses

We provide further analyses in the appendix, including controlled comparisons of the pretraining objective and corpus \(Appendix[E\.1](https://arxiv.org/html/2610.10571#A5.SS1)\), temporal positional encoding and masking strategy \(Appendices[E\.2](https://arxiv.org/html/2610.10571#A5.SS2)and[E\.3](https://arxiv.org/html/2610.10571#A5.SS3)\), analyses of the Legendre spherical prior \(Appendix[F](https://arxiv.org/html/2610.10571#A6)\), few\-shot performance \(Appendix[G](https://arxiv.org/html/2610.10571#A7)\), noise and ocular\-artifact robustness \(Appendix[H](https://arxiv.org/html/2610.10571#A8)\), and learned representation analysis \(Appendix[I](https://arxiv.org/html/2610.10571#A9)\)\.

## 5Limitations and Future Work

While our scaling analysis covers four model sizes from 18M to 396M parameters, we did not investigate scaling at the billion\-parameter scale due to limited computational resources\. Furthermore, the diminishing returns observed beyond 194M suggest that further gains may require expanded data rather than parameters alone, but we did not systematically disentangle the contributions of corpus size, model capacity, and architectural priors to the observed scaling behavior\. A systematic characterization of these factors remains an important direction for future investigation\. Beyond scale, the spherical prior assumes surface electrodes; extending it to intracranial recordings would require incorporating radial information, as discussed in Appendix[F\.5](https://arxiv.org/html/2610.10571#A6.SS5)\.

We evaluate SPERA on nine diverse downstream tasks spanning clinical, cognitive, and BCI domains; however, the tasks are focused on classification problems over fixed\-duration EEG segments ranging from 3 to 30 seconds\. Further validation is therefore needed to assess generalization to continuous decoding, regression targets, and long\-horizon clinical prediction\. In addition, demographic metadata such as age, sex, ethnicity, and clinical status are not consistently available across our pretraining datasets, limiting a comprehensive fairness analysis of the learned representations across subpopulations\. Addressing these gaps will be important before clinical or consumer deployment\.

## 6Conclusion

We present SPERA, a foundation model for EEG that learns representations through latent\-space prediction\. SPERA encodes scalp electrode geometry into attention through a Legendre\-polynomial spatial prior, supported by a hybrid attention backbone and a relational spectral regularizer\.

Across nine downstream tasks, SPERA\-Base exceeds the strongest baseline \(REVE\-Base; Table[2](https://arxiv.org/html/2610.10571#S4.T2)\) by 0\.035 in average balanced accuracy\. The largest significant gains are observed on fine\-grained multi\-class tasks, including imagined speech and clinical event classification\. The scaling analysis further shows that SPERA\-Base exceeds REVE\-Large under LP despite using less than half the parameters\. Controlled ablations show that latent prediction outperforms a matched reconstruction objective and that the Legendre prior outperforms the alternative geometry encodings we evaluated\.

Overall, the results support latent\-space prediction, geometry\-aware spatial modeling, and frequency\-aware supervision as complementary components for EEG representation learning across heterogeneous datasets and electrode montages\. These findings provide a basis for future work on scalable and transferable EEG representation learning\.

## Acknowledgments and Disclosure of Funding

This work was supported by the Samsung Science & Technology Foundation Program \(SRFC\-IT2401\-05\)\.

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## Appendix AComputing Resources

To ensure reproducibility, we report the detailed computing environment, as follows:

- •Hardware:HP Z8 Fury G5 Workstation equipped with an Intel Xeon w5\-3425 CPU, 128 GB of RAM, and dual NVIDIA RTX 5000 Ada Generation GPUs\.
- •Software & Environment:The environment is set up on Ubuntu 24\.04\.4 LTS and Python 3\.10\.20, supported by CUDA Toolkit 13\.0 and cuDNN 9\.15 for hardware acceleration\. Model implementation and training are built upon PyTorch 2\.10\.0 and the Hugging Face ecosystem, utilizingtransformers5\.3\.0 andaccelerate1\.13\.0\. Data preprocessing is performed using MNE\-Python 1\.11\.0\.
- •Training Efficiency & Cost:To maximize training efficiency, we employed distributed data parallel \(DDP\) across both GPUs and utilized Bfloat16 \(BF16\) mixed\-precision training\. The total computational cost for pretraining our largest model is approximately 287 GPU hours\.
- •Code & Model Availability:Our codebase is provided through the repository linked in the paper, including training, evaluation, and preprocessing scripts\.

## Appendix BPretraining Corpus

Datasets are collected from multiple public repositories, including OpenNeuro\[[83](https://arxiv.org/html/2610.10571#bib.bib83)\], MOABB\[[6](https://arxiv.org/html/2610.10571#bib.bib6)\], PhysioNet\[[38](https://arxiv.org/html/2610.10571#bib.bib38)\], NSRR\[[159](https://arxiv.org/html/2610.10571#bib.bib159)\], TUH\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\], Brainclinics \([https://brainclinics\.com/resources](https://brainclinics.com/resources); see also\[[145](https://arxiv.org/html/2610.10571#bib.bib145)\]\), and the Max Planck Institute\[[10](https://arxiv.org/html/2610.10571#bib.bib10)\]\. Table[5](https://arxiv.org/html/2610.10571#A2.T5)reports subject counts adjusted for known cross\-dataset overlaps, and Table[6](https://arxiv.org/html/2610.10571#A2.T6)lists per\-dataset counts\. To avoid double\-counting, known subject\-level overlaps are removed \(e\.g\., overlaps among the Shin2017 series\[[129](https://arxiv.org/html/2610.10571#bib.bib129)\], Lee2019 series\[[71](https://arxiv.org/html/2610.10571#bib.bib71)\], and OpenNeuro datasets ds007169\[[15](https://arxiv.org/html/2610.10571#bib.bib15)\]/ds007262\[[14](https://arxiv.org/html/2610.10571#bib.bib14)\]\)\. In addition, to prevent any evaluation leakage, subjects reserved for downstream tasks \(TUAB and TUEV\) are excluded from the TUH corpus\. For HSP\[[140](https://arxiv.org/html/2610.10571#bib.bib140)\], we use the small training subset released for the PhysioNet Challenge 2026\[[114](https://arxiv.org/html/2610.10571#bib.bib114)\]\. Unless otherwise noted, reported hours reflect the pretraining corpus after these exclusions\.

Table 5:Summary statistics of the pretraining corpus \(aggregated from dataset\-level metadata\)\.Grouping\# SubjectsHours \(h\)\# DatasetsBy CategoryClinical21,91665,38711Cognitive6,24812,91555BCI8841,36240By Channel Count3–3222,72866,0514033–641,9632,11442\>64\>644,35711,49924By Segment Length10 s3,4141,9674630 s4,23611,3781960 s21,39866,31941Total29,04879,664106Table 6:Datasets used in the pretraining corpus\.DatasetRepository\# SubjectsHours \(h\)ChannelsLicenseClinicalTUH\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\]TUH12,29925,785Mostly 30–41NEDC Data UseAgreementTDBRAIN\[[145](https://arxiv.org/html/2610.10571#bib.bib145)\]Brainclinics1,27481\.6726Brainclinics DataUse AgreementMESA\[[24](https://arxiv.org/html/2610.10571#bib.bib24)\]NSRR2,05610,5683NSRR Data UseAgreementSiena\[[29](https://arxiv.org/html/2610.10571#bib.bib29),[30](https://arxiv.org/html/2610.10571#bib.bib30)\]PhysioNet1414129CC BY 4\.0I\-CARE\[[4](https://arxiv.org/html/2610.10571#bib.bib4),[3](https://arxiv.org/html/2610.10571#bib.bib3)\]PhysioNet60722,27819CC BY\-NC\-SA 4\.0HSP \(subset\)\[[140](https://arxiv.org/html/2610.10571#bib.bib140),[114](https://arxiv.org/html/2610.10571#bib.bib114)\]Kaggle1,1035,7996BDSP License 1\.5\.0HMS\[[59](https://arxiv.org/html/2610.10571#bib.bib59)\]Kaggle1,9502378CC BY\-NC 4\.0NMT\[[64](https://arxiv.org/html/2610.10571#bib.bib64)\]Zenodo2,41747419CC BY 4\.0ds002778\[[117](https://arxiv.org/html/2610.10571#bib.bib117)\]OpenNeuro312\.3332CC0ds004902\[[154](https://arxiv.org/html/2610.10571#bib.bib154)\]OpenNeuro7117\.6261CC0ds007020\[[55](https://arxiv.org/html/2610.10571#bib.bib55)\]OpenNeuro943\.6063CC0CognitiveMPI\-Lemon\[[10](https://arxiv.org/html/2610.10571#bib.bib10)\]Max PlanckInstitute21548\.3559PDDLTHINGS2\[[37](https://arxiv.org/html/2610.10571#bib.bib37)\]FigShare1079\.2564CC BY 4\.0ds002680\[[27](https://arxiv.org/html/2610.10571#bib.bib27)\]OpenNeuro1417\.8519CC0ds002721\[[26](https://arxiv.org/html/2610.10571#bib.bib26)\]OpenNeuro3125\.1719CC0ds003004\[[93](https://arxiv.org/html/2610.10571#bib.bib93)\]OpenNeuro3447\.25134CC0ds003690\[[115](https://arxiv.org/html/2610.10571#bib.bib115)\]OpenNeuro7545\.1359CC0ds003825\[[44](https://arxiv.org/html/2610.10571#bib.bib44)\]OpenNeuro5045\.7563CC0ds003885\[[127](https://arxiv.org/html/2610.10571#bib.bib127)\]OpenNeuro2426\.80128CC0ds003969\[[28](https://arxiv.org/html/2610.10571#bib.bib28)\]OpenNeuro9865\.6564CC0ds004043\[[86](https://arxiv.org/html/2610.10571#bib.bib86)\]OpenNeuro2018\.0363CC0ds004147\[[46](https://arxiv.org/html/2610.10571#bib.bib46)\]OpenNeuro129\.5031CC0ds004148\[[152](https://arxiv.org/html/2610.10571#bib.bib152)\]OpenNeuro6060\.0064CC0ds004264\[[48](https://arxiv.org/html/2610.10571#bib.bib48)\]OpenNeuro217\.2731CC0ds004315\[[22](https://arxiv.org/html/2610.10571#bib.bib22)\]OpenNeuro5021\.0460CC0ds004356\[[126](https://arxiv.org/html/2610.10571#bib.bib126)\]OpenNeuro2246\.0334CC0ds004395\[[60](https://arxiv.org/html/2610.10571#bib.bib60)\]OpenNeuro3648,687128CC0ds004408\[[31](https://arxiv.org/html/2610.10571#bib.bib31)\]OpenNeuro1918\.68128CC0ds004477\[[96](https://arxiv.org/html/2610.10571#bib.bib96)\]OpenNeuro913\.4879CC0ds004561\[[148](https://arxiv.org/html/2610.10571#bib.bib148)\]OpenNeuro2311\.3561CC0ds004572\[[62](https://arxiv.org/html/2610.10571#bib.bib62)\]OpenNeuro5247\.3758CC0ds004582\[[82](https://arxiv.org/html/2610.10571#bib.bib82)\]OpenNeuro7333\.6559CC0ds004603\[[78](https://arxiv.org/html/2610.10571#bib.bib78)\]OpenNeuro3730\.6164CC0ds004706\[[119](https://arxiv.org/html/2610.10571#bib.bib119)\]OpenNeuro34468128CC0ds004816\[[42](https://arxiv.org/html/2610.10571#bib.bib42)\]OpenNeuro2010\.5063CC0ds004951\[[49](https://arxiv.org/html/2610.10571#bib.bib49)\]OpenNeuro1125\.7563CC0ds005095\[[163](https://arxiv.org/html/2610.10571#bib.bib163)\]OpenNeuro4816\.4863CC0ds005121\[[131](https://arxiv.org/html/2610.10571#bib.bib131)\]OpenNeuro3440\.1764CC0ds005189\[[50](https://arxiv.org/html/2610.10571#bib.bib50)\]OpenNeuro3019\.2861CC0ds005273\[[118](https://arxiv.org/html/2610.10571#bib.bib118)\]OpenNeuro3351\.1763CC0ds005410\[[99](https://arxiv.org/html/2610.10571#bib.bib99)\]OpenNeuro8122\.9463CC0ds005505\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro136105128CC BY\-SA 4\.0ds005506\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro150115128CC BY\-SA 4\.0ds005507\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro184142128CC BY\-SA 4\.0ds005508\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro324137128CC BY\-SA 4\.0ds005509\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro330251128CC BY\-SA 4\.0ds005510\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro13492\.20128CC BY\-SA 4\.0ds005511\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro381250128CC BY\-SA 4\.0ds005512\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro257164128CC BY\-SA 4\.0ds005514\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro295183128CC BY\-SA 4\.0ds005515\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro533148128CC BY\-SA 4\.0ds005516\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]OpenNeuro430245128CC BY\-SA 4\.0ds005594\[[144](https://arxiv.org/html/2610.10571#bib.bib144)\]OpenNeuro1612\.1764CC0ds005620\[[11](https://arxiv.org/html/2610.10571#bib.bib11)\]OpenNeuro2116\.2562CC0ds005662\[[132](https://arxiv.org/html/2610.10571#bib.bib132)\]OpenNeuro8079\.8564CC0ds006018\[[54](https://arxiv.org/html/2610.10571#bib.bib54)\]OpenNeuro12750\.3926CC0ds006434\[[138](https://arxiv.org/html/2610.10571#bib.bib138)\]OpenNeuro6612032CC0ds006480\[[65](https://arxiv.org/html/2610.10571#bib.bib65)\]OpenNeuro6869\.9865CC0ds006850\[[158](https://arxiv.org/html/2610.10571#bib.bib158)\]OpenNeuro6378\.3064CC0ds006861\[[81](https://arxiv.org/html/2610.10571#bib.bib81)\]OpenNeuro12010032CC0ds006866\[[80](https://arxiv.org/html/2610.10571#bib.bib80)\]OpenNeuro14812262CC0ds006921\[[111](https://arxiv.org/html/2610.10571#bib.bib111)\]OpenNeuro3816\.0163CC0ds006923\[[108](https://arxiv.org/html/2610.10571#bib.bib108)\]OpenNeuro14033\.85128CC0ds007172\[[113](https://arxiv.org/html/2610.10571#bib.bib113)\]OpenNeuro10047\.8932CC0ds007176\[[51](https://arxiv.org/html/2610.10571#bib.bib51)\]OpenNeuro4525\.0858CC0HBN\_NC\[[130](https://arxiv.org/html/2610.10571#bib.bib130)\]Child MindInstitute458251128CC BY\-NC\-SA 4\.0BCIds003846\[[35](https://arxiv.org/html/2610.10571#bib.bib35)\]OpenNeuro1922\.3863CC0ds004152\[[47](https://arxiv.org/html/2610.10571#bib.bib47)\]OpenNeuro2111\.2731CC0ds004284\[[147](https://arxiv.org/html/2610.10571#bib.bib147)\]OpenNeuro189\.43128CC0ds004324\[[13](https://arxiv.org/html/2610.10571#bib.bib13)\]OpenNeuro2619\.1828CC0ds004357\[[41](https://arxiv.org/html/2610.10571#bib.bib41)\]OpenNeuro1611\.28128CC0ds004817\[[43](https://arxiv.org/html/2610.10571#bib.bib43)\]OpenNeuro2011\.8863CC0ds005089\[[1](https://arxiv.org/html/2610.10571#bib.bib1)\]OpenNeuro3662\.7663CC0ds005262\[[85](https://arxiv.org/html/2610.10571#bib.bib85)\]OpenNeuro1224\.628CC0ds005586\[[16](https://arxiv.org/html/2610.10571#bib.bib16)\]OpenNeuro2333\.4960CC0ds005697\[[74](https://arxiv.org/html/2610.10571#bib.bib74)\]OpenNeuro5170\.6764CC0ds007169\[[15](https://arxiv.org/html/2610.10571#bib.bib15)\]OpenNeuro184\.9019CC0ds007262\[[14](https://arxiv.org/html/2610.10571#bib.bib14)\]OpenNeuro184\.4319CC0AlexMI\[[12](https://arxiv.org/html/2610.10571#bib.bib12)\]MOABB81\.0916CC BY\-SA 4\.0Beetl2021\_A\[[153](https://arxiv.org/html/2610.10571#bib.bib153)\]MOABB31\.0063CC BY 4\.0BI2014a\[[68](https://arxiv.org/html/2610.10571#bib.bib68)\]MOABB6412\.3216CC BY 4\.0BI2014b\[[69](https://arxiv.org/html/2610.10571#bib.bib69)\]MOABB382\.3132CC BY 4\.0BI2015a\[[66](https://arxiv.org/html/2610.10571#bib.bib66)\]MOABB4311\.4832CC BY 4\.0BI2015b\[[67](https://arxiv.org/html/2610.10571#bib.bib67)\]MOABB4425\.8732CC BY 4\.0BNCI2003\_004\[[32](https://arxiv.org/html/2610.10571#bib.bib32)\]MOABB53\.97118CC BY 4\.0BNCI2014\_004\[[72](https://arxiv.org/html/2610.10571#bib.bib72)\]MOABB926\.193CC BY\-ND 4\.0BNCI2014\_008\[[116](https://arxiv.org/html/2610.10571#bib.bib116)\]MOABB83\.118CC BY\-NC\-ND 4\.0BNCI2014\_009\[[5](https://arxiv.org/html/2610.10571#bib.bib5)\]MOABB101\.5816CC BY\-NC\-ND 4\.0BNCI2015\_001\[[34](https://arxiv.org/html/2610.10571#bib.bib34)\]MOABB1216\.6613CC BY\-NC\-ND 4\.0BNCI2015\_003\[[125](https://arxiv.org/html/2610.10571#bib.bib125)\]MOABB100\.918CC BY\-NC\-ND 4\.0BNCI2015\_004\[[123](https://arxiv.org/html/2610.10571#bib.bib123)\]MOABB913\.7230CC BY\-NC\-ND 4\.0Cho2017\[[25](https://arxiv.org/html/2610.10571#bib.bib25)\]MOABB5220\.4664CC BY 4\.0Dreyer2023\[[33](https://arxiv.org/html/2610.10571#bib.bib33)\]MOABB8768\.1227CC BY 4\.0EPFLP300\[[52](https://arxiv.org/html/2610.10571#bib.bib52)\]MOABB82\.7932Not SpecifiedKalunga2016\[[61](https://arxiv.org/html/2610.10571#bib.bib61)\]MOABB122\.568CC BY 4\.0Lee2019ERP\[[71](https://arxiv.org/html/2610.10571#bib.bib71)\]MOABB5457\.8562GPL\-3\.0Lee2019MI\[[71](https://arxiv.org/html/2610.10571#bib.bib71)\]MOABB5442\.8162GPL\-3\.0Lee2019SSVEP\[[71](https://arxiv.org/html/2610.10571#bib.bib71)\]MOABB5440\.4562GPL\-3\.0Ofner2017\[[92](https://arxiv.org/html/2610.10571#bib.bib92)\]MOABB1513\.3361CC BY 4\.0Schirrmeister2017\[[124](https://arxiv.org/html/2610.10571#bib.bib124)\]MOABB1426\.44128CC BY 4\.0Shin2017A\[[129](https://arxiv.org/html/2610.10571#bib.bib129)\]MOABB2914\.4130GPL\-3\.0Shin2017B\[[129](https://arxiv.org/html/2610.10571#bib.bib129)\]MOABB2914\.4330GPL\-3\.0Sosulski2019\[[136](https://arxiv.org/html/2610.10571#bib.bib136)\]MOABB1318\.3031CC BY\-SA 4\.0Stieger2021\[[137](https://arxiv.org/html/2610.10571#bib.bib137)\]MOABB6261560CC BY\-NC 4\.0Weibo2014\[[157](https://arxiv.org/html/2610.10571#bib.bib157)\]MOABB1012\.4460CC0Zhou2016\[[161](https://arxiv.org/html/2610.10571#bib.bib161)\]MOABB46\.2414CC BY 4\.0
## Appendix CPretraining Details

### C\.1Detailed Hyperparameters

In this section, we present the detailed hyperparameters for pretraining our models\. Table[7](https://arxiv.org/html/2610.10571#A3.T7)summarizes the universal settings shared across all model sizes, including the core architecture, optimization schedule, and augmentation parameters\. Table[8](https://arxiv.org/html/2610.10571#A3.T8)details the specific architectural dimensions and learning rates scaled for the 18M, 48M, 194M, and 396M models\.

Table 7:Hyperparameters for the SPERA model pretraining\.HyperparameterValueEEG Input & TokenizationSampling Rate200 HzPatch Size1\.0 secMasking & Student AugmentationTime/Spatial Mask Probability0\.80 / 0\.80Time Mask Ratio \(Min/Max\)0\.15 / 0\.35Spatial Mask Ratio \(Min/Max\)0\.10 / 0\.30Amplitude Gain \(Min/Max\)0\.80 / 1\.20Gaussian Noise Std \(Min/Max\)0\.00 / 0\.03Coordinate Jitter \(Prob/Std\)0\.50 / 0\.05ArchitectureMLP Type / RatioSwiGLU / 4\.0Predictor Layers2Encoder ArchitectureHybrid \(Full Attn Every 4th Layer\)NormalizationLayer NormalizationDropout \(Residual/Attention\)0\.0Temporal EmbeddingRoPE \(θ=\\theta=10000\)Legendre Degree \(LL\)8Legendre Anchor Points \(MM\)32OptimizationOptimizerAdamW \(β1=\\beta\_\{1\}=0\.9,β2=\\beta\_\{2\}=0\.95\)Weight Decay0\.05Total Steps47,000Input Tokens per Update \(Nominal\)393,216\- Context / Target Tokens262,144 / 131,072LR SchedulerWarmup\-Cosine AnnealingWarmup Ratio0\.05EMA ScheduleCosine Annealing \(0\.996→\\to0\.9999\)Relational Spectral RegularizerWeight ScheduleDelayed Linear Ramp\-DecayWeight Bounds0→\\to0\.02→\\to0\.002Schedule Steps5% \(Ramp Start\), 10% \(Peak\), 50% \(Decay Start\)Projection Dimension128Temperature \(τz,τs\\tau\_\{z\},\\tau\_\{s\}\)0\.1, 0\.1Table 8:Scale\-specific architecture and optimization hyperparameters\. Attention and predictor head counts and hidden dimensions are identical within each model size\. Learning rates are scaled according to the model size\.Model SizeParamsLayersHidden DimAttention HeadsPeak LRTiny18M838444\.0×10−44\.0\\times 10^\{\-4\}Small48M1251283\.5×10−43\.5\\times 10^\{\-4\}Base194M16896143\.0×10−43\.0\\times 10^\{\-4\}Large396M251024162\.5×10−42\.5\\times 10^\{\-4\}
### C\.2Pretraining Token Accounting and Loss Curve

We train SPERA for 47,000 optimization steps, corresponding to approximately two epochs over the pretraining corpus\. Optimization steps are triggered adaptively: microbatches accumulate until the cumulative target\-token count reaches the per\-update budget of 131,072 tokens \(Table[7](https://arxiv.org/html/2610.10571#A3.T7)\), so the number of microbatches per update varies\.

Figure 3:Pretraining loss curve of the SPERA\-Base \(194M\) model\. The model is trained for approximately 47,000 steps \(∼\\sim2 epochs of the pretraining corpus\)\. The raw per\-step loss \(light\) is shown together with an exponential moving average for readability \(solid\); this plot\-level smoothing is distinct from the EMA used to update the teacher encoder\.Figure[3](https://arxiv.org/html/2610.10571#A3.F3)shows the pretraining loss curve of the SPERA\-Base \(194M\) model\. Each epoch realizes∼\\sim9\.45B input tokens \(∼\\sim6\.25B context,∼\\sim3\.20B target\), or∼\\sim98\.4% of the∼\\sim9\.60B nominal token count derived from corpus statistics \(Table[5](https://arxiv.org/html/2610.10571#A2.T5)\)\. The remaining∼\\sim1\.6% corresponds to rare\(C,Pt\)\(C,P\_\{t\}\)shape buckets that do not accumulate a full microbatch within the dataloader’s pending window and are dropped by the shape\-aware batcher\. The residual is small because the unit that is dropped is a rare shape bucket rather than a dataset: even our smallest dataset \(∼\\sim0\.91 h, 8 channels\) produces∼\\sim26K tokens, exceeding the per\-microbatch budget\. The resulting loss curve \(Figure[3](https://arxiv.org/html/2610.10571#A3.F3)\) converges smoothly and stabilizes around 0\.05 by the end of training\.

## Appendix DDetailed Downstream Task Results

In this section, we describe each downstream dataset, its preprocessing procedure, and the full experimental results\. For all datasets, we follow the preprocessing pipelines of prior works\[[155](https://arxiv.org/html/2610.10571#bib.bib155),[57](https://arxiv.org/html/2610.10571#bib.bib57),[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94)\]to ensure direct comparison with baseline models\. While we report balanced accuracy as the primary metric in the main text, we additionally report task\-specific metrics commonly used in prior EEG foundation model evaluations\[[155](https://arxiv.org/html/2610.10571#bib.bib155),[57](https://arxiv.org/html/2610.10571#bib.bib57),[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\. For multi\-class classification tasks, we report Cohen’sκ\\kappaand weighted F1\-score in addition to balanced accuracy\. For binary classification tasks, we report AUC\-PR and AUROC in addition to balanced accuracy\. SPERA results are reported as mean±\\pmstandard deviation over five random seeds; baseline statistics follow the evaluation protocols of the source publications\. Each downstream task table includes only baseline models whose original studies report results on that task\. A dash indicates that the corresponding model does not report that dataset or metric\. Unless otherwise specified, all results are obtained using the SPERA\-Base \(194M\) model\.

### D\.1Imagined Speech Classification

Table 9:The results of different methods on imagined speech classification \(BCIC2020\-3, 5\-class\)\.MethodsBalanced AccuracyCohen’sκ\\kappaWeighted F1EEGNet0\.4413±0\.00960\.4413\\pm 0\.00960\.3016±0\.01230\.3016\\pm 0\.01230\.4413±0\.01020\.4413\\pm 0\.0102EEGConformer0\.4506±0\.01330\.4506\\pm 0\.01330\.3133±0\.01830\.3133\\pm 0\.01830\.4488±0\.01540\.4488\\pm 0\.0154SPaRCNet0\.4426±0\.01560\.4426\\pm 0\.01560\.3033±0\.02330\.3033\\pm 0\.02330\.4420±0\.01080\.4420\\pm 0\.0108ContraWR0\.4257±0\.01620\.4257\\pm 0\.01620\.3078±0\.02180\.3078\\pm 0\.02180\.4407±0\.01820\.4407\\pm 0\.0182CNN\-Transformer0\.4533±0\.00920\.4533\\pm 0\.00920\.3166±0\.01180\.3166\\pm 0\.01180\.4506±0\.01270\.4506\\pm 0\.0127FFCL0\.4678±0\.01970\.4678\\pm 0\.01970\.3301±0\.03590\.3301\\pm 0\.03590\.4689±0\.02050\.4689\\pm 0\.0205ST\-Transformer0\.4126±0\.01220\.4126\\pm 0\.01220\.2941±0\.01590\.2941\\pm 0\.01590\.4247±0\.01380\.4247\\pm 0\.0138BIOT0\.4920±0\.00860\.4920\\pm 0\.00860\.3650±0\.01760\.3650\\pm 0\.01760\.4917±0\.00790\.4917\\pm 0\.0079LaBraM\-Base0\.5060±0\.01550\.5060\\pm 0\.01550\.3800±0\.02420\.3800\\pm 0\.02420\.5054±0\.02050\.5054\\pm 0\.0205CBraMod0\.5373±0\.01080\.5373\\pm 0\.01080\.4216±0\.01630\.4216\\pm 0\.01630\.5383±0\.00960\.5383\\pm 0\.0096REVE\-Base0\.5635±0\.01230\.5635\\pm 0\.01230\.4543±0\.01540\.4543\\pm 0\.01540\.5633±0\.01240\.5633\\pm 0\.0124CSBrain0\.6004±0\.01870\.6004\\pm 0\.01870\.5006±0\.02330\.5006\\pm 0\.02330\.6003±0\.01920\.6003\\pm 0\.0192CodeBrain0\.6101±0\.00520\.6101\\pm 0\.00520\.5127±0\.00650\.5127\\pm 0\.00650\.6101±0\.00530\.6101\\pm 0\.0053EEGMamba0\.5305±0\.01090\.5305\\pm 0\.01090\.4183±0\.01570\.4183\\pm 0\.01570\.5347±0\.00820\.5347\\pm 0\.0082SPERA0\.6504±\\pm0\.01220\.5630±\\pm0\.01520\.6498±\\pm0\.0129BCIC2020\-3\[[56](https://arxiv.org/html/2610.10571#bib.bib56)\]is a 5\-class imagined speech dataset\. Fifteen subjects are instructed to silently imagine pronouncing one of five phrases \(“hello”, “help me”, “stop”, “thank you”, and “yes”\) without articulation\. EEG signals are recorded from 64 channels at 256 Hz, and resampled to 200 Hz\. Each trial consists of a 3\-second segment, yielding 6,000 samples in total with predefined train/validation/test splits of 60/10/10 trials per class\.

As shown in Table[9](https://arxiv.org/html/2610.10571#A4.T9), SPERA achieves 0\.6504 balanced accuracy, with Cohen’sκ\\kappaof 0\.5630 and weighted F1 of 0\.6498\.

### D\.2Motor Imagery Classification

BCIC\-IV\-2a\[[143](https://arxiv.org/html/2610.10571#bib.bib143)\]is a 4\-class motor imagery dataset comprising nine subjects performing left hand, right hand, both feet, and tongue imagery\. EEG signals are recorded across two sessions using 22 electrodes at 250 Hz\. Each trial is cropped to the 2–6 s segment, bandpass filtered to 0\.5–99\.5 Hz, and resampled to 200 Hz, yielding 5,184 4\-second samples\. Following prior work\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\], Euclidean alignment is additionally applied\. We adopt a subject\-independent split, with subjects 1–5, 6–7, and 8–9 used for training, validation, and test, respectively\.

PhysioNet\-MI\[[38](https://arxiv.org/html/2610.10571#bib.bib38),[122](https://arxiv.org/html/2610.10571#bib.bib122)\]is a 4\-class motor imagery dataset recorded from 64 channels at 160 Hz, covering left fist, right fist, both fists, and both feet imagery\. We extract 4\-second segments yielding 9,837 samples, and apply a subject\-independent split with subjects 1–70, 71–89, and 90–109 for training, validation, and test, respectively\. All recordings are loaded at 128 Hz with a 64 Hz low\-pass filter and subsequently resampled to 200 Hz\.

The detailed experimental results for both motor imagery tasks are summarized in Table[10](https://arxiv.org/html/2610.10571#A4.T10)\. SPERA improves over REVE\-Base on both BCIC\-IV\-2a \(\+\+0\.0420\) and PhysioNet\-MI \(\+\+0\.0246\) in balanced accuracy, with similar trends in the other two metrics\. The improvement is consistent across the two datasets despite their differing channel counts \(22 vs\. 64\) and acquisition protocols\.

Table 10:The results of different methods on motor imagery classification\.MethodsBCIC\-IV\-2a, 4\-classPhysioNet\-MI, 4\-classBalanced AccuracyCohen’sκ\\kappaWeighted F1Balanced AccuracyCohen’sκ\\kappaWeighted F1EEGNet0\.4482±0\.00940\.4482\\pm 0\.00940\.2693±0\.01200\.2693\\pm 0\.01200\.4226±0\.01080\.4226\\pm 0\.01080\.5814±0\.01250\.5814\\pm 0\.01250\.4468±0\.01990\.4468\\pm 0\.01990\.5796±0\.01150\.5796\\pm 0\.0115EEGConformer0\.4696±0\.01060\.4696\\pm 0\.01060\.2924±0\.01410\.2924\\pm 0\.01410\.4533±0\.01280\.4533\\pm 0\.01280\.6049±0\.01040\.6049\\pm 0\.01040\.4736±0\.01710\.4736\\pm 0\.01710\.6062±0\.00950\.6062\\pm 0\.0095SPaRCNet0\.4635±0\.01170\.4635\\pm 0\.01170\.2847±0\.01470\.2847\\pm 0\.01470\.4432±0\.01200\.4432\\pm 0\.01200\.5932±0\.01520\.5932\\pm 0\.01520\.4564±0\.02340\.4564\\pm 0\.02340\.5937±0\.01470\.5937\\pm 0\.0147ContraWR0\.4678±0\.01250\.4678\\pm 0\.01250\.2905±0\.01600\.2905\\pm 0\.01600\.4413±0\.01420\.4413\\pm 0\.01420\.5892±0\.01330\.5892\\pm 0\.01330\.4527±0\.02480\.4527\\pm 0\.02480\.5918±0\.01160\.5918\\pm 0\.0116CNN\-Transformer0\.4600±0\.01080\.4600\\pm 0\.01080\.2800±0\.01480\.2800\\pm 0\.01480\.4460±0\.01140\.4460\\pm 0\.01140\.6053±0\.01180\.6053\\pm 0\.01180\.4725±0\.02230\.4725\\pm 0\.02230\.6041±0\.01050\.6041\\pm 0\.0105FFCL0\.4470±0\.01430\.4470\\pm 0\.01430\.2627±0\.01760\.2627\\pm 0\.01760\.4238±0\.01390\.4238\\pm 0\.01390\.5726±0\.00920\.5726\\pm 0\.00920\.4323±0\.01820\.4323\\pm 0\.01820\.5701±0\.00790\.5701\\pm 0\.0079ST\-Transformer0\.4575±0\.01450\.4575\\pm 0\.01450\.2733±0\.01900\.2733\\pm 0\.01900\.4471±0\.01420\.4471\\pm 0\.01420\.6035±0\.00810\.6035\\pm 0\.00810\.4712±0\.01990\.4712\\pm 0\.01990\.6053±0\.00750\.6053\\pm 0\.0075BIOT0\.4748±0\.00930\.4748\\pm 0\.00930\.2997±0\.01340\.2997\\pm 0\.01340\.4607±0\.01250\.4607\\pm 0\.01250\.6153±0\.01540\.6153\\pm 0\.01540\.4875±0\.02720\.4875\\pm 0\.02720\.6158±0\.01970\.6158\\pm 0\.0197LaBraM\-Base0\.4869±0\.00850\.4869\\pm 0\.00850\.3159±0\.01540\.3159\\pm 0\.01540\.4728±0\.01050\.4728\\pm 0\.01050\.6173±0\.01220\.6173\\pm 0\.01220\.4912±0\.01920\.4912\\pm 0\.01920\.6177±0\.01410\.6177\\pm 0\.0141CBraMod0\.5138±0\.00660\.5138\\pm 0\.00660\.3518±0\.00940\.3518\\pm 0\.00940\.4984±0\.00850\.4984\\pm 0\.00850\.6417±0\.00910\.6417\\pm 0\.00910\.5222±0\.01690\.5222\\pm 0\.01690\.6427±0\.01000\.6427\\pm 0\.0100REVE\-Base0\.6396±0\.00950\.6396\\pm 0\.00950\.5194±0\.01260\.5194\\pm 0\.01260\.6339±0\.01100\.6339\\pm 0\.01100\.6480±0\.01400\.6480\\pm 0\.01400\.5306±0\.01870\.5306\\pm 0\.01870\.6484±0\.01700\.6484\\pm 0\.0170CSBrain0\.5657±0\.00710\.5657\\pm 0\.00710\.4209±0\.00930\.4209\\pm 0\.00930\.5637±0\.00870\.5637\\pm 0\.00870\.6304±0\.00900\.6304\\pm 0\.00900\.5071±0\.01200\.5071\\pm 0\.01200\.6308±0\.00950\.6308\\pm 0\.0095EEGMamba–––0\.6323±0\.00840\.6323\\pm 0\.00840\.5131±0\.01240\.5131\\pm 0\.01240\.6342±0\.00980\.6342\\pm 0\.0098SPERA0\.6816±\\pm0\.01470\.5755±\\pm0\.01970\.6817±\\pm0\.01550\.6726±\\pm0\.00720\.5633±\\pm0\.00960\.6731±\\pm0\.0080

### D\.3Emotion Recognition

FACED\[[23](https://arxiv.org/html/2610.10571#bib.bib23)\]is a 9\-class emotion recognition dataset comprising 123 subjects recorded using 32 channels at 250 Hz, covering amusement, inspiration, joy, tenderness, anger, fear, disgust, sadness, and neutral\. EEG signals are resampled to 200 Hz and segmented into 10\-second samples, yielding 10,332 samples in total\. Subjects 1–80, 81–100, and 101–123 are used for training, validation, and test, respectively\.

Detailed results for emotion recognition are shown in Table[11](https://arxiv.org/html/2610.10571#A4.T11)\. SPERA and CSBrain achieve nearly identical balanced accuracy \(0\.5754 vs\. 0\.5752\)\. CodeBrain reports higher values on all three metrics; FACED is the only task among the nine where a recent model leads SPERA on every metric\.

Table 11:The results of different methods on emotion recognition \(FACED, 9\-class\)\.MethodsBalanced AccuracyCohen’sκ\\kappaWeighted F1EEGNet0\.4090±0\.01220\.4090\\pm 0\.01220\.3342±0\.02510\.3342\\pm 0\.02510\.4124±0\.01410\.4124\\pm 0\.0141EEGConformer0\.4559±0\.01250\.4559\\pm 0\.01250\.3858±0\.01860\.3858\\pm 0\.01860\.4514±0\.01070\.4514\\pm 0\.0107SPaRCNet0\.4673±0\.01550\.4673\\pm 0\.01550\.3978±0\.02890\.3978\\pm 0\.02890\.4729±0\.01330\.4729\\pm 0\.0133ContraWR0\.4887±0\.00780\.4887\\pm 0\.00780\.4231±0\.01510\.4231\\pm 0\.01510\.4884±0\.00740\.4884\\pm 0\.0074CNN\-Transformer0\.4697±0\.01320\.4697\\pm 0\.01320\.4017±0\.01680\.4017\\pm 0\.01680\.4720±0\.01250\.4720\\pm 0\.0125FFCL0\.4673±0\.01580\.4673\\pm 0\.01580\.3987±0\.03830\.3987\\pm 0\.03830\.4699±0\.01450\.4699\\pm 0\.0145ST\-Transformer0\.4810±0\.00790\.4810\\pm 0\.00790\.4137±0\.01330\.4137\\pm 0\.01330\.4795±0\.00960\.4795\\pm 0\.0096BIOT0\.5118±0\.01180\.5118\\pm 0\.01180\.4476±0\.02540\.4476\\pm 0\.02540\.5136±0\.01120\.5136\\pm 0\.0112LaBraM\-Base0\.5273±0\.01070\.5273\\pm 0\.01070\.4698±0\.01880\.4698\\pm 0\.01880\.5288±0\.01020\.5288\\pm 0\.0102CBraMod0\.5509±0\.00890\.5509\\pm 0\.00890\.5041±0\.01220\.5041\\pm 0\.01220\.5618±0\.00930\.5618\\pm 0\.0093REVE\-Base0\.5646±0\.01640\.5646\\pm 0\.01640\.5080±0\.01910\.5080\\pm 0\.01910\.5659±0\.01720\.5659\\pm 0\.0172CSBrain0\.5752±0\.00420\.5752\\pm 0\.00420\.5204±0\.00360\.5204\\pm 0\.00360\.5796±0\.00310\.5796\\pm 0\.0031CodeBrain0\.5941±\\pm0\.00980\.5406±\\pm0\.00840\.5953±\\pm0\.0113EEGMamba0\.5646±0\.00960\.5646\\pm 0\.00960\.5134±0\.01270\.5134\\pm 0\.01270\.5673±0\.00760\.5673\\pm 0\.0076SPERA0\.5754±0\.01750\.5754\\pm 0\.01750\.5122±0\.02860\.5122\\pm 0\.02860\.5711±0\.01380\.5711\\pm 0\.0138
### D\.4Mental Stress Detection

Mental arithmetic \(MAT\)\[[164](https://arxiv.org/html/2610.10571#bib.bib164)\]is a 2\-class mental stress dataset comprising 36 subjects recorded using 20 channels at 500 Hz, distinguishing resting state from active mental arithmetic\. EEG signals are bandpass filtered \(0\.5–45 Hz\), resampled to 200 Hz, and segmented into 1,707 5\-second samples\. Subjects 1–28, 29–32, and 33–36 are used for training, validation, and test, respectively\.

The experimental results are shown in Table[12](https://arxiv.org/html/2610.10571#A4.T12)\. SPERA exceeds REVE\-Base by\+\+0\.0118 in balanced accuracy and\+\+0\.0454 in AUROC, while its AUC\-PR is lower\.

Table 12:The results of different methods on mental stress detection \(MAT, 2\-class\)\.MethodsBalanced AccuracyAUC\-PRAUROCEEGNet0\.6770±0\.01160\.6770\\pm 0\.01160\.5763±0\.01020\.5763\\pm 0\.01020\.7321±0\.01080\.7321\\pm 0\.0108EEGConformer0\.6805±0\.01230\.6805\\pm 0\.01230\.5829±0\.01340\.5829\\pm 0\.01340\.7424±0\.01280\.7424\\pm 0\.0128SPaRCNet0\.6879±0\.01070\.6879\\pm 0\.01070\.5825±0\.01930\.5825\\pm 0\.01930\.7418±0\.01320\.7418\\pm 0\.0132ContraWR0\.6631±0\.00970\.6631\\pm 0\.00970\.5787±0\.01640\.5787\\pm 0\.01640\.7332±0\.00820\.7332\\pm 0\.0082CNN\-Transformer0\.6779±0\.02680\.6779\\pm 0\.02680\.5777±0\.02850\.5777\\pm 0\.02850\.7258±0\.03360\.7258\\pm 0\.0336FFCL0\.6798±0\.01420\.6798\\pm 0\.01420\.5786±0\.02660\.5786\\pm 0\.02660\.7330±0\.01980\.7330\\pm 0\.0198ST\-Transformer0\.6631±0\.01730\.6631\\pm 0\.01730\.5672±0\.02590\.5672\\pm 0\.02590\.7132±0\.01740\.7132\\pm 0\.0174BIOT0\.6875±0\.01860\.6875\\pm 0\.01860\.6004±0\.01950\.6004\\pm 0\.01950\.7536±0\.01440\.7536\\pm 0\.0144LaBraM\-Base0\.6909±0\.01250\.6909\\pm 0\.01250\.5999±0\.01550\.5999\\pm 0\.01550\.7721±0\.00930\.7721\\pm 0\.0093CBraMod0\.7256±0\.01320\.7256\\pm 0\.01320\.6267±0\.00990\.6267\\pm 0\.00990\.7905±0\.00730\.7905\\pm 0\.0073REVE\-Base0\.7660±0\.03550\.7660\\pm 0\.03550\.7470±\\pm0\.08070\.8450±0\.05140\.8450\\pm 0\.0514CSBrain0\.7558±0\.01060\.7558\\pm 0\.01060\.6696±0\.02210\.6696\\pm 0\.02210\.8478±0\.02970\.8478\\pm 0\.0297CodeBrain0\.7514±0\.02030\.7514\\pm 0\.02030\.7177±0\.04210\.7177\\pm 0\.04210\.8707±0\.02090\.8707\\pm 0\.0209SPERA0\.7778±\\pm0\.02160\.7291±\\pm0\.02260\.8904±\\pm0\.0196
### D\.5Sleep Staging

Table 13:The results of different methods on sleep staging \(ISRUC, 5\-class\)\.MethodsBalanced AccuracyCohen’sκ\\kappaWeighted F1EEGNet0\.7154±0\.01210\.7154\\pm 0\.01210\.7040±0\.01730\.7040\\pm 0\.01730\.7513±0\.01240\.7513\\pm 0\.0124EEGConformer0\.7400±0\.01330\.7400\\pm 0\.01330\.7143±0\.01620\.7143\\pm 0\.01620\.7634±0\.01500\.7634\\pm 0\.0150SPaRCNet0\.7487±0\.00750\.7487\\pm 0\.00750\.7097±0\.01320\.7097\\pm 0\.01320\.7624±0\.00920\.7624\\pm 0\.0092ContraWR0\.7402±0\.01260\.7402\\pm 0\.01260\.7178±0\.01560\.7178\\pm 0\.01560\.7610±0\.01370\.7610\\pm 0\.0137CNN\-Transformer0\.7363±0\.00870\.7363\\pm 0\.00870\.7129±0\.01210\.7129\\pm 0\.01210\.7719±0\.01050\.7719\\pm 0\.0105FFCL0\.7277±0\.01820\.7277\\pm 0\.01820\.7016±0\.02910\.7016\\pm 0\.02910\.7614±0\.01970\.7614\\pm 0\.0197ST\-Transformer0\.7381±0\.02050\.7381\\pm 0\.02050\.7013±0\.03520\.7013\\pm 0\.03520\.7681±0\.01750\.7681\\pm 0\.0175DeepSleepNet0\.7419±0\.01440\.7419\\pm 0\.01440\.7036±0\.02410\.7036\\pm 0\.02410\.7643±0\.01220\.7643\\pm 0\.0122U\-Sleep0\.7586±0\.01160\.7586\\pm 0\.01160\.7209±0\.01430\.7209\\pm 0\.01430\.7805±0\.01050\.7805\\pm 0\.0105BIOT0\.7527±0\.01210\.7527\\pm 0\.01210\.7192±0\.02310\.7192\\pm 0\.02310\.7790±0\.01460\.7790\\pm 0\.0146LaBraM\-Base0\.7633±0\.01020\.7633\\pm 0\.01020\.7231±0\.01820\.7231\\pm 0\.01820\.7810±0\.01330\.7810\\pm 0\.0133CBraMod0\.7865±0\.01100\.7865\\pm 0\.01100\.7442±0\.01520\.7442\\pm 0\.01520\.8011±0\.00990\.8011\\pm 0\.0099REVE\-Base0\.7819±0\.00780\.7819\\pm 0\.00780\.7500±0\.01560\.7500\\pm 0\.01560\.8005±0\.01350\.8005\\pm 0\.0135CSBrain0\.7925±0\.00300\.7925\\pm 0\.00300\.7406±0\.01020\.7406\\pm 0\.01020\.7990±0\.00910\.7990\\pm 0\.0091CodeBrain0\.7835±0\.00330\.7835\\pm 0\.00330\.7476±0\.00400\.7476\\pm 0\.00400\.8020±0\.00180\.8020\\pm 0\.0018EEGMamba0\.7899±0\.00930\.7899\\pm 0\.00930\.7486±0\.01220\.7486\\pm 0\.01220\.8054±0\.00760\.8054\\pm 0\.0076SPERA \(single\-segment\)0\.8093±\\pm0\.01080\.7542±\\pm0\.01870\.8115±\\pm0\.0150SPERA \(sequence\-to\-sequence\)0\.8137±\\pm0\.00750\.7662±\\pm0\.01210\.8217±\\pm0\.0097ISRUC\[[63](https://arxiv.org/html/2610.10571#bib.bib63)\]is a 5\-class sleep staging dataset comprising 100 subjects recorded using 6 channels at 200 Hz\. EEG signals are segmented into 30\-second epochs and annotated according to the AASM standard \(Wake, N1, N2, N3, REM\)\. Subjects 1–80, 81–90, and 91–100 are used for training, validation, and test, respectively\. Subject 8 was excluded from the final dataset due to missing requisite EEG channels \(e\.g\., F3, F4\), resulting in a total of 88,140 samples\. Sleep staging is commonly framed as a sequence\-to\-sequence classification problem with a sequence length of 20 consecutive 30\-second epochs to model sleep stage transitions\[[107](https://arxiv.org/html/2610.10571#bib.bib107)\]\. Following the protocol of CBraMod\[[150](https://arxiv.org/html/2610.10571#bib.bib150)\], we adopt this standard setting and additionally report single\-segment classification results to assess the quality of our pretrained representations without sequential context\. We further include two widely recognized sleep\-staging\-specific baselines, DeepSleepNet\[[142](https://arxiv.org/html/2610.10571#bib.bib142)\]and U\-Sleep\[[103](https://arxiv.org/html/2610.10571#bib.bib103)\], in order to compare against classical methods established in the sleep staging literature\.

Full classification results are summarized in Table[13](https://arxiv.org/html/2610.10571#A4.T13)\. The single\-segment variant alone \(0\.8093\) exceeds the strongest baseline \(CSBrain, 0\.7925\) in balanced accuracy, indicating that the gain does not require the sequence\-to\-sequence formulation\. The sequence\-to\-sequence variant further improves performance to 0\.8137\. These results indicate that SPERA remains effective on ISRUC, which has the fewest channels \(6\) and the longest segment duration \(30 s\) among the nine downstream datasets\.

### D\.6Mental Disorder Diagnosis

Mumtaz\[[89](https://arxiv.org/html/2610.10571#bib.bib89)\]is a 2\-class depression detection dataset comprising 34 patients with major depressive disorder \(MDD\) and 30 normal controls, recorded using 19 channels at 256 Hz\. Only eyes\-open and eyes\-closed resting\-state sessions are used; MDD subject 8 is excluded because only a P300 recording is available\. EEG signals are bandpass filtered \(0\.3–75 Hz\), notch filtered \(50 Hz\), resampled to 200 Hz, and segmented into 5\-second samples\. Following the publicly released preprocessing implementation of prior EEG foundation model studies\[[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94)\]111The textual descriptions in\[[150](https://arxiv.org/html/2610.10571#bib.bib150),[94](https://arxiv.org/html/2610.10571#bib.bib94)\]report subject counts of 24/5/5 MDD and 19/4/5 controls, whereas applying the released preprocessing code to the resting\-state recordings yields 22/5/6 and 21/4/5, respectively\. We follow the released implementation, which determines the data partition used in the experiments\., we apply the released train/validation/test partition\. The resulting split contains 22/5/6 MDD and 21/4/5 control subjects \(33 MDD and 30 controls in total\), yielding a total of 7,143 5\-second samples consistent with prior work\.

The experimental results are summarized in Table[14](https://arxiv.org/html/2610.10571#A4.T14)\. SPERA and REVE\-Base are comparable in balanced accuracy \(0\.9637 vs\. 0\.9644\), with SPERA achieving the highest AUC\-PR and AUROC\. SPERA also exhibits the smallest across\-seed standard deviation in balanced accuracy \(±\\pm0\.0018\) among all compared methods\.

Table 14:The results of different methods on mental disorder diagnosis \(Mumtaz, 2\-class\)\.MethodsBalanced AccuracyAUC\-PRAUROCEEGNet0\.9232±0\.01040\.9232\\pm 0\.01040\.9626±0\.00950\.9626\\pm 0\.00950\.9639±0\.00930\.9639\\pm 0\.0093EEGConformer0\.9308±0\.01170\.9308\\pm 0\.01170\.9684±0\.01050\.9684\\pm 0\.01050\.9702±0\.01010\.9702\\pm 0\.0101SPaRCNet0\.9316±0\.00950\.9316\\pm 0\.00950\.9754±0\.00650\.9754\\pm 0\.00650\.9781±0\.00830\.9781\\pm 0\.0083ContraWR0\.9195±0\.01150\.9195\\pm 0\.01150\.9589±0\.01020\.9589\\pm 0\.01020\.9621±0\.00920\.9621\\pm 0\.0092CNN\-Transformer0\.9305±0\.00680\.9305\\pm 0\.00680\.9757±0\.00740\.9757\\pm 0\.00740\.9742±0\.00550\.9742\\pm 0\.0055FFCL0\.9314±0\.00380\.9314\\pm 0\.00380\.9717±0\.00210\.9717\\pm 0\.00210\.9753±0\.00330\.9753\\pm 0\.0033ST\-Transformer0\.9135±0\.01030\.9135\\pm 0\.01030\.9578±0\.00860\.9578\\pm 0\.00860\.9594±0\.00590\.9594\\pm 0\.0059BIOT0\.9358±0\.00520\.9358\\pm 0\.00520\.9736±0\.00340\.9736\\pm 0\.00340\.9758±0\.00420\.9758\\pm 0\.0042LaBraM\-Base0\.9409±0\.00790\.9409\\pm 0\.00790\.9798±0\.00930\.9798\\pm 0\.00930\.9782±0\.00570\.9782\\pm 0\.0057CBraMod0\.9560±0\.00560\.9560\\pm 0\.00560\.9923±0\.00320\.9923\\pm 0\.00320\.9921±0\.00250\.9921\\pm 0\.0025REVE\-Base0\.9644±\\pm0\.00970\.9961±0\.00130\.9961\\pm 0\.00130\.9957±0\.00150\.9957\\pm 0\.0015CSBrain0\.9643±0\.01550\.9643\\pm 0\.01550\.9936±0\.00340\.9936\\pm 0\.00340\.9956±0\.00200\.9956\\pm 0\.0020SPERA0\.9637±\\pm0\.00180\.9973±\\pm0\.00070\.9975±\\pm0\.0010
### D\.7EEG Abnormality Detection

TUAB\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\]is a 2\-class EEG abnormality detection dataset recorded using 23 channels at 250 Hz, with 16 common bipolar montage channels used for analysis\. EEG signals are resampled to 200 Hz and segmented into 409,455 10\-second samples\. The original train/test split is adopted, with the training set further divided into training and validation subsets \(80%:20%\)\. TUAB is excluded from our pretraining corpus, preventing any evaluation leakage\.

Table 15:The results of different methods on EEG abnormality detection \(TUAB, 2\-class\)\.MethodsBalanced AccuracyAUC\-PRAUROCEEGNet0\.7642±0\.00360\.7642\\pm 0\.00360\.8299±0\.00430\.8299\\pm 0\.00430\.8412±0\.00300\.8412\\pm 0\.0030EEGConformer0\.7758±0\.00490\.7758\\pm 0\.00490\.8427±0\.00540\.8427\\pm 0\.00540\.8445±0\.00380\.8445\\pm 0\.0038SPaRCNet0\.7896±0\.00180\.7896\\pm 0\.00180\.8414±0\.00180\.8414\\pm 0\.00180\.8676±0\.00110\.8676\\pm 0\.0011ContraWR0\.7746±0\.00410\.7746\\pm 0\.00410\.8421±0\.01040\.8421\\pm 0\.01040\.8456±0\.00740\.8456\\pm 0\.0074CNN\-Transformer0\.7777±0\.00220\.7777\\pm 0\.00220\.8433±0\.00390\.8433\\pm 0\.00390\.8461±0\.00130\.8461\\pm 0\.0013FFCL0\.7848±0\.00380\.7848\\pm 0\.00380\.8448±0\.00650\.8448\\pm 0\.00650\.8569±0\.00510\.8569\\pm 0\.0051ST\-Transformer0\.7966±0\.00230\.7966\\pm 0\.00230\.8521±0\.00260\.8521\\pm 0\.00260\.8707±0\.00190\.8707\\pm 0\.0019EEG2Rep––0\.8843±0\.03090\.8843\\pm 0\.0309BIOT0\.7959±0\.00570\.7959\\pm 0\.00570\.8792±0\.00230\.8792\\pm 0\.00230\.8815±0\.00430\.8815\\pm 0\.0043LaBraM\-Base0\.8140±0\.00190\.8140\\pm 0\.00190\.8965±0\.00160\.8965\\pm 0\.00160\.9022±0\.00080\.9022\\pm 0\.0008LaBraM\-Large0\.8226±0\.00150\.8226\\pm 0\.00150\.9130±0\.00050\.9130\\pm 0\.00050\.9127±0\.00050\.9127\\pm 0\.0005LaBraM\-Huge0\.8258±0\.00110\.8258\\pm 0\.00110\.9204±0\.00110\.9204\\pm 0\.00110\.9162±0\.00160\.9162\\pm 0\.0016CBraMod0\.8289±0\.00220\.8289\\pm 0\.00220\.9258±0\.00080\.9258\\pm 0\.00080\.9227±0\.00110\.9227\\pm 0\.0011REVE\-Base0\.8315±0\.00140\.8315\\pm 0\.00140\.9281±0\.00090\.9281\\pm 0\.00090\.9245±0\.00130\.9245\\pm 0\.0013CSBrain0\.8172±0\.00430\.8172\\pm 0\.00430\.9005±0\.00660\.9005\\pm 0\.00660\.8957±0\.00460\.8957\\pm 0\.0046CodeBrain0\.8294±0\.00130\.8294\\pm 0\.00130\.9100±0\.00060\.9100\\pm 0\.00060\.9030±0\.00090\.9030\\pm 0\.0009LuMamba0\.8099±0\.00220\.8099\\pm 0\.00220\.8918±0\.00320\.8918\\pm 0\.00320\.8825±0\.00380\.8825\\pm 0\.0038SPERA0\.8488±\\pm0\.00350\.9287±\\pm0\.00450\.9253±\\pm0\.0046As shown in Table[15](https://arxiv.org/html/2610.10571#A4.T15), SPERA improves balanced accuracy by\+\+0\.0173 over REVE\-Base, with smaller gains in AUC\-PR and AUROC\.

### D\.8Event Type Classification

TUEV\[[91](https://arxiv.org/html/2610.10571#bib.bib91)\]is a 6\-class EEG event classification dataset recorded using 23 channels at 250 Hz, covering spike and sharp wave, generalized periodic epileptiform discharges, periodic lateralized epileptiform discharges, eye movement, artifact, and background\. EEG signals from 16 common bipolar montage channels are resampled to 200 Hz and segmented into 112,491 5\-second samples\. The original train/test split is adopted, with the training set further divided into training and validation subsets \(80%:20%\)\. As with TUAB, TUEV is excluded from our pretraining corpus\.

The experimental results are summarized in Table[16](https://arxiv.org/html/2610.10571#A4.T16)\. SPERA achieves the highest balanced accuracy among the evaluated methods \(0\.7684\)\. EEGDM reports higher Cohen’sκ\\kappaand weighted F1 than SPERA, while GRAM reports the highest weighted F1\.

Table 16:The results of different methods on event type classification \(TUEV, 6\-class\)\.MethodsBalanced AccuracyCohen’sκ\\kappaWeighted F1EEGNet0\.3876±0\.01430\.3876\\pm 0\.01430\.3577±0\.01550\.3577\\pm 0\.01550\.6539±0\.01200\.6539\\pm 0\.0120EEGConformer0\.4074±0\.01640\.4074\\pm 0\.01640\.3967±0\.01950\.3967\\pm 0\.01950\.6983±0\.01520\.6983\\pm 0\.0152SPaRCNet0\.4161±0\.02620\.4161\\pm 0\.02620\.4233±0\.01810\.4233\\pm 0\.01810\.7024±0\.01040\.7024\\pm 0\.0104ContraWR0\.4384±0\.03490\.4384\\pm 0\.03490\.3912±0\.02370\.3912\\pm 0\.02370\.6893±0\.01360\.6893\\pm 0\.0136CNN\-Transformer0\.4087±0\.01610\.4087\\pm 0\.01610\.3815±0\.01340\.3815\\pm 0\.01340\.6854±0\.02900\.6854\\pm 0\.0290FFCL0\.3979±0\.01040\.3979\\pm 0\.01040\.3732±0\.01880\.3732\\pm 0\.01880\.6783±0\.01200\.6783\\pm 0\.0120ST\-Transformer0\.3984±0\.02280\.3984\\pm 0\.02280\.3765±0\.03060\.3765\\pm 0\.03060\.6823±0\.01900\.6823\\pm 0\.0190EEG2Rep0\.5295±0\.01580\.5295\\pm 0\.0158–0\.7508±0\.01210\.7508\\pm 0\.0121EEGDM0\.7557±0\.01470\.7557\\pm 0\.01470\.7423±\\pm0\.01360\.8688±0\.00660\.8688\\pm 0\.0066BIOT0\.5281±0\.02250\.5281\\pm 0\.02250\.5273±0\.02490\.5273\\pm 0\.02490\.7492±0\.00800\.7492\\pm 0\.0080LaBraM\-Base0\.6409±0\.00650\.6409\\pm 0\.00650\.6637±0\.00930\.6637\\pm 0\.00930\.8312±0\.00520\.8312\\pm 0\.0052LaBraM\-Large0\.6581±0\.01560\.6581\\pm 0\.01560\.6622±0\.01360\.6622\\pm 0\.01360\.8315±0\.00400\.8315\\pm 0\.0040LaBraM\-Huge0\.6616±0\.01700\.6616\\pm 0\.01700\.6745±0\.01950\.6745\\pm 0\.01950\.8329±0\.00860\.8329\\pm 0\.0086CBraMod0\.6671±0\.01070\.6671\\pm 0\.01070\.6772±0\.00960\.6772\\pm 0\.00960\.8342±0\.00640\.8342\\pm 0\.0064REVE\-Base0\.6759±0\.02290\.6759\\pm 0\.02290\.6783±0\.01990\.6783\\pm 0\.01990\.8451±0\.01290\.8451\\pm 0\.0129CSBrain0\.6903±0\.00590\.6903\\pm 0\.00590\.6833±0\.00470\.6833\\pm 0\.00470\.8333±0\.00570\.8333\\pm 0\.0057CodeBrain0\.6428±0\.00620\.6428\\pm 0\.00620\.6912±0\.01010\.6912\\pm 0\.01010\.8362±0\.00480\.8362\\pm 0\.0048GRAM0\.7487±0\.01510\.7487\\pm 0\.01510\.7130±0\.03330\.7130\\pm 0\.03330\.8824±\\pm0\.0158SPERA0\.7684±\\pm0\.02830\.7320±0\.03660\.7320\\pm 0\.03660\.8619±0\.01780\.8619\\pm 0\.0178
### D\.9Linear Probing Results

Table[17](https://arxiv.org/html/2610.10571#A4.T17)reports the full per\-task LP results across all nine downstream datasets\. The largest gains over baselines are observed on BCIC2020\-3 and TUEV, where SPERA\-Large surpasses REVE\-Large by over 0\.1 in balanced accuracy\. On BCIC\-IV\-2a, PhysioNet\-MI, MAT, and Mumtaz, SPERA models reach competitive but not superior performance\. Mumtaz in particular shows limited headroom, with most foundation models exceeding 0\.9 balanced accuracy\. While most tasks improve with model size, PhysioNet\-MI, FACED, and MAT show non\-monotonic scaling under LP\.

Table 17:LP results on nine downstream tasks\. The results are reported as mean balanced accuracy±\\pmstandard deviation over five random seeds\. The best performance for each task is highlighted in bold\. Baseline model results are extracted from\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\. The standard deviations for the average performance of the baseline models are omitted as they are not reported in the original paper\.MethodsParamsBCIC2020\-3BCIC\-IV\-2aPhysioNet\-MIFACEDMATCBraMod4M0\.374±0\.0070\.374\\pm 0\.0070\.376±0\.0060\.376\\pm 0\.0060\.531±0\.0150\.531\\pm 0\.0150\.261±0\.0130\.261\\pm 0\.0130\.605±0\.0200\.605\\pm 0\.020REVE\-Base69M0\.390±0\.0170\.390\\pm 0\.0170\.517±0\.0150\.517\\pm 0\.0150\.510±0\.0120\.510\\pm 0\.0120\.422±0\.0280\.422\\pm 0\.0280\.740±\\pm0\.073REVE\-Large408M0\.378±0\.0210\.378\\pm 0\.0210\.603±\\pm0\.0110\.617±\\pm0\.0000\.469±0\.0070\.469\\pm 0\.0070\.665±0\.1030\.665\\pm 0\.103SPERA\-Tiny18M0\.324±0\.0240\.324\\pm 0\.0240\.497±0\.0090\.497\\pm 0\.0090\.532±0\.0070\.532\\pm 0\.0070\.343±0\.0090\.343\\pm 0\.0090\.689±0\.0140\.689\\pm 0\.014SPERA\-Small48M0\.407±0\.0150\.407\\pm 0\.0150\.497±0\.0130\.497\\pm 0\.0130\.523±0\.0110\.523\\pm 0\.0110\.363±0\.0170\.363\\pm 0\.0170\.630±0\.0220\.630\\pm 0\.022SPERA\-Base194M0\.502±\\pm0\.0110\.560±\\pm0\.0100\.551±\\pm0\.0090\.478±\\pm0\.0110\.672±\\pm0\.014SPERA\-Large396M0\.593±\\pm0\.0190\.590±\\pm0\.0140\.583±\\pm0\.0080\.469±\\pm0\.0100\.693±\\pm0\.016MethodsParamsISRUCMumtazTUABTUEVAverageCBraMod4M0\.430±0\.0430\.430\\pm 0\.0430\.907±0\.0270\.907\\pm 0\.0270\.500±0\.0000\.500\\pm 0\.0000\.482±0\.0370\.482\\pm 0\.0370\.496REVE\-Base69M0\.662±0\.0300\.662\\pm 0\.0300\.931±0\.0210\.931\\pm 0\.0210\.809±0\.0040\.809\\pm 0\.0040\.508±0\.0730\.508\\pm 0\.0730\.610REVE\-Large408M0\.758±0\.0010\.758\\pm 0\.0010\.980±\\pm0\.0090\.809±0\.0040\.809\\pm 0\.0040\.550±0\.0140\.550\\pm 0\.0140\.648SPERA\-Tiny18M0\.687±0\.0270\.687\\pm 0\.0270\.885±0\.0290\.885\\pm 0\.0290\.784±0\.0030\.784\\pm 0\.0030\.517±0\.0070\.517\\pm 0\.0070\.584±0\.0060\.584\\pm 0\.006SPERA\-Small48M0\.721±0\.0240\.721\\pm 0\.0240\.929±0\.0110\.929\\pm 0\.0110\.787±0\.0060\.787\\pm 0\.0060\.558±0\.0100\.558\\pm 0\.0100\.601±0\.0050\.601\\pm 0\.005SPERA\-Base194M0\.772±\\pm0\.0140\.944±\\pm0\.0150\.821±\\pm0\.0020\.651±\\pm0\.0080\.661±\\pm0\.003SPERA\-Large396M0\.775±\\pm0\.0190\.957±\\pm0\.0320\.842±\\pm0\.0030\.653±\\pm0\.0080\.684±\\pm0\.005

Table[18](https://arxiv.org/html/2610.10571#A4.T18)additionally compares SPERA\-Base under LP with recent models on TUAB and TUEV, the tasks from our evaluation suite that overlap with their reported evaluations\. SPERA\-Base attains the highest balanced accuracy on both tasks\. On TUEV, however, EEGPT reports a higher Cohen’sκ\\kappaand weighted F1\.

Table 18:LP comparison with recent models on TUAB and TUEV\. For the binary TUAB task, we report AUC\-PR and AUROC; for the 6\-class TUEV task, we report Cohen’sκ\\kappaand weighted F1\. Baseline numbers are taken from the original publications\. Laya evaluates TUAB under its own LP protocol, in which reproduced baseline scores differ substantially from those in Table[17](https://arxiv.org/html/2610.10571#A4.T17)\.MethodsTUAB, 2\-classTUEV, 6\-classBalanced AccuracyAUC\-PRAUROCBalanced AccuracyCohen’sκ\\kappaWeighted F1EEGPT0\.798±0\.0030\.798\\pm 0\.003–0\.872±0\.0050\.872\\pm 0\.0050\.623±0\.0110\.623\\pm 0\.0110\.635±\\pm0\.0130\.819±\\pm0\.006EEG2Rep––0\.832±0\.0330\.832\\pm 0\.0330\.433±0\.0310\.433\\pm 0\.031–0\.700±0\.0320\.700\\pm 0\.032Laya0\.798±0\.0070\.798\\pm 0\.007–––––SPERA\-Base0\.821±\\pm0\.0020\.898±\\pm0\.0010\.901±\\pm0\.0020\.651±\\pm0\.0080\.580±0\.0150\.580\\pm 0\.0150\.784±0\.0080\.784\\pm 0\.008

Table 19:Per\-task significance under LPFT\. The comparator is the highest\-balanced\-accuracy baseline among methods reporting results on all nine downstream tasks; methods with partial task coverage are excluded\.Δ\\Deltadenotes the balanced\-accuracy difference relative to the comparator, brackets show 95% confidence intervals, and bold indicatespHolm<0\.05p\_\{\\mathrm\{Holm\}\}<0\.05\.SPERA\-Base \(194M\)SPERA\-Large \(396M\)TaskComparator𝚫\\boldsymbol\{\\Delta\}\[95% CI\]𝒑\\boldsymbol\{p\}𝒑Holm\\boldsymbol\{p\_\{\\text\{Holm\}\}\}𝚫\\boldsymbol\{\\Delta\}\[95% CI\]𝒑\\boldsymbol\{p\}𝒑Holm\\boldsymbol\{p\_\{\\text\{Holm\}\}\}BCIC2020\-3CSBrain\+0\.0500\+0\.0500\[\+0\.026\+0\.026,\+0\.074\+0\.074\]0\.0020\.011\+0\.0879\+0\.0879\[\+0\.063\+0\.063,\+0\.112\+0\.112\]<0\.001<0\.001< 0\.001TUEVCSBrain\+0\.0781\+0\.0781\[\+0\.043\+0\.043,\+0\.113\+0\.113\]0\.0030\.014\+0\.0966\+0\.0966\[\+0\.061\+0\.061,\+0\.132\+0\.132\]0\.0010\.008BCIC\-IV\-2aREVE\-Base\+0\.0420\+0\.0420\[\+0\.023\+0\.023,\+0\.061\+0\.061\]0\.0010\.009\+0\.0627\+0\.0627\[\+0\.044\+0\.044,\+0\.081\+0\.081\]<0\.001<0\.001< 0\.001ISRUCCSBrain\+0\.0212\+0\.0212\[\+0\.012\+0\.012,\+0\.030\+0\.030\]0\.0020\.011\+0\.0217\+0\.0217\[\+0\.009\+0\.009,\+0\.035\+0\.035\]0\.0080\.033TUABREVE\-Base\+0\.0173\+0\.0173\[\+0\.013\+0\.013,\+0\.022\+0\.022\]<0\.001<0\.0010\.001\+0\.0293\+0\.0293\[\+0\.026\+0\.026,\+0\.033\+0\.033\]<0\.001<0\.001< 0\.001PhysioNet\-MIREVE\-Base\+0\.0246\+0\.0246\[\+0\.007\+0\.007,\+0\.042\+0\.042\]0\.0130\.052\+0\.0337\+0\.0337\[\+0\.016\+0\.016,\+0\.051\+0\.051\]0\.0030\.014MATREVE\-Base\+0\.0118\+0\.0118\[−0\.033\-0\.033,\+0\.056\+0\.056\]0\.5471\.000\+0\.0361\+0\.0361\[−0\.008\-0\.008,\+0\.080\+0\.080\]0\.0930\.279FACEDCSBrain\+0\.0002\+0\.0002\[−0\.021\-0\.021,\+0\.022\+0\.022\]0\.9811\.000\+0\.0167\+0\.0167\[−0\.006\-0\.006,\+0\.040\+0\.040\]0\.1150\.279MumtazREVE\-Base−0\.0007\-0\.0007\[−0\.013\-0\.013,\+0\.011\+0\.011\]0\.8811\.000\+0\.0058\+0\.0058\[−0\.006\-0\.006,\+0\.018\+0\.018\]0\.2540\.279

### D\.10Per\-Task Significance

We evaluate the statistical significance of SPERA’s task\-level performance differences across the nine downstream tasks\. For consistency across tasks, the comparator pool is restricted to baselines with balanced\-accuracy results reported on all nine tasks \(Table[2](https://arxiv.org/html/2610.10571#S4.T2)\); methods with partial task coverage are excluded\. For each task, SPERA is compared with the highest\-performing baseline in this pool using Welch’stt\-test over five random seeds, with Holm correction applied across the nine tasks separately for each SPERA model\. The tests are two\-sided, and the 95% confidence intervals are pointwise and are not adjusted for multiple comparisons\. The tests are unpaired because baseline results are taken from the original publications and per\-seed values are unavailable\.

Table[19](https://arxiv.org/html/2610.10571#A4.T19)reports the difference in balanced accuracyΔ\\Deltawith its 95% confidence interval, alongside raw and Holm\-correctedpp\-values\. For SPERA\-Base, five tasks remain significant after correction: BCIC2020\-3, TUEV, BCIC\-IV\-2a, ISRUC, and TUAB\. PhysioNet\-MI is borderline \(pHolm=p\_\{\\mathrm\{Holm\}\}=0\.052\)\. The differences on FACED, MAT, and Mumtaz did not reach statistical significance after correction\. Mumtaz shows limited headroom, with generally high balanced accuracy across foundation models and model scales\. For MAT, the estimated performance difference is small relative to the across\-seed variability, and the confidence interval includes zero, whereas on FACED, SPERA\-Base and CSBrain achieve nearly identical balanced accuracy \(0\.5754 vs\. 0\.5752\)\.

SPERA\-Large shows a largerΔ\\Deltathan SPERA\-Base on every task: the same five tasks remain significant, and PhysioNet\-MI also reaches significance after correction\. FACED, MAT, and Mumtaz remain non\-significant\. We report the main\-text claim for SPERA\-Base, the default model used throughout the paper, and include SPERA\-Large here for completeness\.

## Appendix EAdditional Ablation Experiments

### E\.1Pretraining Objective and Corpus

The ablations in Table[3](https://arxiv.org/html/2610.10571#S4.T3)vary architectural components while holding the primary prediction objective and corpus fixed\. Here we vary those two factors instead, to separate the contribution of latent\-space prediction from that of the pretraining data\. Both variants use the SPERA\-Small backbone and follow the ablation protocol of Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5): LP on PhysioNet\-MI, ISRUC, and TUAB\. Each configuration is evaluated over five random seeds\.

For the reconstruction variant, we replace the latent prediction objective with input\-space reconstruction\. The predictor outputs are decoded back to raw patches by a linear head and the model is trained against the masked input patches, so that the target is computed from the raw signal\. All other components, including the Legendre prior, the hybrid backbone, and the relational spectral regularizer, are unchanged\.

For the REVE corpus variant, we restrict pretraining to dataset sources shared with REVE\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]to assess the effect of this corpus restriction on SPERA’s downstream performance\. The proxy comprises 81 datasets from our corpus that are also listed in REVE’s pretraining corpus, totaling 61,191 h from 22,994 subjects, comparable in duration to the approximately 60,000 h reported for REVE\. The 25 excluded datasets account for 18,473 h and contribute 6,054 additional subjects; 16,367 h are sleep recordings from MESA and the HSP subset, and the remaining 2,106 h come from 23 datasets\.

Replacing latent prediction with input\-space reconstruction lowers average balanced accuracy by 0\.022 with the backbone, corpus, and token budget held fixed, and the drop is consistent across all three tasks\. Pretraining on the REVE corpus proxy lowers the average by 0\.005\. Specifically, PhysioNet\-MI and TUAB are nearly identical, while ISRUC is lower by 0\.016\. This is consistent with the composition of the excluded data, 89% of which is sleep recordings, and ISRUC is the only sleep\-staging task among the three\.

Table 20:Ablation of the pretraining objective and corpus\. All variants use the SPERA\-Small backbone under the ablation protocol of Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)\. Results are mean balanced accuracy±\\pmstandard deviation over five random seeds\.Reconstruction Headreplaces latent prediction with input\-space reconstruction;REVE Corpuspretrains on the 81\-dataset proxy for the corpus used by REVE\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]\.VariantsPhysioNet\-MIISRUCTUABAverageSPERA\-Small \(latent prediction\)0\.523±\\pm0\.0110\.721±\\pm0\.0240\.787±0\.0060\.787\\pm 0\.0060\.677±\\pm0\.011w/ Reconstruction Head0\.499±0\.0150\.499\\pm 0\.0150\.706±0\.0190\.706\\pm 0\.0190\.761±0\.0110\.761\\pm 0\.0110\.655±0\.0130\.655\\pm 0\.013w/ REVE Corpus0\.522±0\.0130\.522\\pm 0\.0130\.705±0\.0210\.705\\pm 0\.0210\.788±\\pm0\.0080\.672±0\.0100\.672\\pm 0\.010

### E\.2Temporal Positional Encoding

SPERA applies rotary position embeddings \(RoPE\) along the temporal patch axis, while electrode position is supplied by the Legendre prior along the spatial axis\. We ablate the temporal encoding by replacing RoPE with a standard sinusoidal absolute position embedding added to the patch embeddings, keeping the spatial encoding, the backbone, and the pretraining objective fixed\. The variant follows the ablation protocol of Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)\. Note that the substitution affects the temporal axis only: in the factorized spatial pass RoPE is already disabled, and the geometry encodings continue to provide positional information there\.

The result is summarized in Table[21](https://arxiv.org/html/2610.10571#A5.T21)\. RoPE is stronger on all three tasks, by 0\.022 on average, supporting its use as the temporal positional encoding in the present architecture\. This result is also consistent with prior reports that relative positional schemes can generalize across varying sequence lengths\[[139](https://arxiv.org/html/2610.10571#bib.bib139)\]\. The three tasks in this ablation use 4\-s, 30\-s, and 10\-s segments for PhysioNet\-MI, ISRUC, and TUAB, respectively, corresponding to 4, 30, and 10 temporal tokens per channel with 1\-s patches\.

Table 21:Ablation of the temporal positional encoding\. Both variants use the SPERA\-Small backbone under the ablation protocol of Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)\. Results are mean balanced accuracy±\\pmstandard deviation over five random seeds; the best result in each column is in bold\. The spatial encoding is unchanged in both variants\.VariantsPhysioNet\-MIISRUCTUABAverageRoPE \(SPERA\-Small\)0\.523±\\pm0\.0110\.721±\\pm0\.0240\.787±\\pm0\.0060\.677±\\pm0\.011Sinusoidal absolute0\.502±0\.0130\.502\\pm 0\.0130\.699±0\.0200\.699\\pm 0\.0200\.764±0\.0100\.764\\pm 0\.0100\.655±0\.0110\.655\\pm 0\.011

### E\.3Masking Strategy

To assess the impact of our masking strategy, we conduct an ablation comparing two strategies: block masking and semantic subsequence preserving \(SSP\) masking\. We evaluate both strategies across three downstream tasks at five levels of expected masking ratio under LP using SPERA\-Small\. The total masking ratio is determined by independent temporal and spatial masking processes, each applied with probabilityp=p=0\.8\. To prevent the trivial case where no tokens are masked, temporal masking is applied as a fallback\. The expected total masking ratioρ\\rhois computed as the expected union of the masked regions, assuming independence between temporal and spatial masking\. We define five difficulty levels \(ρ≈\\rho\\approx0\.27, 0\.34, 0\.45, 0\.65, 0\.75\); detailed hyperparameter ranges for each level are summarized in Table[22](https://arxiv.org/html/2610.10571#A5.T22)\.

Table 22:Masking ratio hyperparameters per difficulty level\. The expected masking ratioρ\\rhoaccounts for the combined application of spatial and temporal masking, including the fallback condition\.LevelSpatial RangeSpatial MeanTemporal RangeTemporal MeanExpected Ratio \(ρ\\rho\)00\.05 – 0\.250\.150\.10 – 0\.300\.200\.2710\.10 – 0\.300\.200\.15 – 0\.350\.250\.3420\.18 – 0\.320\.250\.30 – 0\.440\.370\.4530\.27 – 0\.430\.350\.52 – 0\.680\.600\.6540\.36 – 0\.540\.450\.62 – 0\.790\.710\.75

Figure 4:Masking strategy analysis across five difficulty levels on PhysioNet\-MI, ISRUC, and TUAB\. The blue line represents the performance of block masking, while the red line represents the performance of SSP masking\. The shaded areas indicate one standard deviation across five random seeds\.As shown in Figure[4](https://arxiv.org/html/2610.10571#A5.F4), SSP masking generally outperforms block masking, with the best performance on each task achieved under SSP atρ≈\\rho\\approx0\.34\. This suggests that preserving semantic subsequences is beneficial for learning transferable EEG representations\.

### E\.4Additional Metrics for Component Ablations

Table[3](https://arxiv.org/html/2610.10571#S4.T3)reports balanced accuracy only\. Table[23](https://arxiv.org/html/2610.10571#A5.T23)adds Cohen’sκ\\kappaand weighted F1 for the multi\-class tasks and AUC\-PR and AUROC for binary TUAB, on the same runs\. Balanced accuracy is repeated so that the comparison can be read within a single table\. On each task the two leading variants are the same under every metric\.

Table 23:Additional metrics for the component ablations of Table[3](https://arxiv.org/html/2610.10571#S4.T3)\. Each cell reports balanced accuracy followed by two task\-appropriate metrics: Cohen’sκ\\kappaand weighted F1 for the multi\-class tasks, AUC\-PR and AUROC for binary TUAB\. The best result per column is inbold; the second\-best isunderlined\.VariantPhysioNet\-MIISRUCTUAB\(BAcc /κ\\kappa/ wF1\)\(BAcc /κ\\kappa/ wF1\)\(BAcc / AUC\-PR / AUROC\)Encoder ArchitectureFull Attention Only0\.4450 / 0\.2600 / 0\.44920\.7097 / 0\.6314 / 0\.71310\.7749 / 0\.8538 / 0\.8541Factorized Attention Only0\.4833 / 0\.3111 / 0\.47810\.7153 / 0\.6378 / 0\.71870\.7865 / 0\.8656 / 0\.8650Hybrid \+ Late Full0\.4871 / 0\.3161 / 0\.48200\.6973 / 0\.6194 / 0\.70090\.7860 / 0\.8651 / 0\.8645RSRegNo RSReg0\.5182 / 0\.3576 / 0\.51380\.6994 / 0\.6198 / 0\.70290\.7759 / 0\.8548 / 0\.8550Electrode Geometry EncodingCoordinate Emb Only0\.4821 / 0\.3095 / 0\.47690\.7009 / 0\.6215 / 0\.70440\.7744 / 0\.8533 / 0\.8536Legendre Bias Only0\.5193 / 0\.3591 / 0\.51490\.7320 / 0\.6566 / 0\.73520\.7929 / 0\.8722 / 0\.8710Legendre Anchor Encoding Only0\.5071 / 0\.3428 / 0\.50250\.7137 / 0\.6360 / 0\.71710\.7855 / 0\.8646 / 0\.8640Learnable Pairwise MLP0\.4463 / 0\.2617 / 0\.44030\.6679 / 0\.5842 / 0\.68260\.7671 / 0\.8458 / 0\.8468REVE Spatial Encoding0\.4921 / 0\.3228 / 0\.48620\.6910 / 0\.6159 / 0\.69430\.7607 / 0\.8412 / 0\.8420Gaussian \(Geodesic\)0\.4512 / 0\.2683 / 0\.44890\.6977 / 0\.6189 / 0\.70100\.7705 / 0\.8501 / 0\.8511SPERA\-Small0\.5227 / 0\.3636 / 0\.51840\.7206 / 0\.6438 / 0\.72390\.7869 / 0\.8660 / 0\.8653

## Appendix FAnalysis of the Legendre Spherical Prior

### F\.1Geometry Encoding Ablations

Building on the electrode geometry ablation in Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5), we evaluate a broader set of alternative geometry encodings\. Everything outside the geometry encoding is held fixed\.*Coordinate Embedding Only*removes the pairwise prior and retains the linear embedding of 3D electrode coordinates\.*Anisotropic SH*replaces the rotation\-invariant Legendre expansion with a general spherical\-harmonic \(SH\) prior that permits direction\-dependent interactions and contains the isotropic Legendre family as a special case\.*Gaussian \(Geodesic\)*replaces the expansion with a radial basis function \(RBF\) kernel of geodesic electrode distance, with learnable width and amplitude\.*REVE 4D Encoding*ports the coupled spatio\-temporal encoding of REVE\[[94](https://arxiv.org/html/2610.10571#bib.bib94)\]as published, which also replaces our temporal RoPE\. Since that conflates spatial and temporal handling, we derive*REVE Spatial Encoding*, which imports only the 3D coordinate component and leaves RoPE in place, isolating the geometry comparison\.

The results are summarized in Table[24](https://arxiv.org/html/2610.10571#A6.T24)\. The Legendre prior is the strongest configuration on all three tasks, and REVE’s encoding provides no transfer advantage in our backbone\. Replacing REVE’s joint 4D encoding with its spatial component while retaining RoPE improves performance on all three tasks, with the largest increase on ISRUC \(0\.593 to 0\.691\)\. At matched temporal handling, REVE’s Fourier encoding is comparable to our linear coordinate embedding, and the improvement comes from adding the prior on top\. The geodesic Gaussian fixes the kernel to a monotone decay in distance, whereas our expansion learns its profile end\-to\-end; the learned kernel is not monotone \(Appendix[F\.2](https://arxiv.org/html/2610.10571#A6.SS2)\)\. The anisotropic SH prior also underperforms the isotropic Legendre prior \(0\.658 vs\. 0\.677 average\), providing no empirical benefit from the added directional flexibility under the present setting\.

Table 24:Geometry encoding ablations\. All variants use the SPERA\-Small backbone under the ablation protocol of Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)\. Results are mean balanced accuracy±\\pmstandard deviation over five random seeds; the best result in each column is in bold\.Geometry EncodingPhysioNet\-MIISRUCTUABAverageAnisotropic SH0\.501±0\.0130\.501\\pm 0\.0130\.706±0\.0170\.706\\pm 0\.0170\.767±0\.0080\.767\\pm 0\.0080\.658±0\.0130\.658\\pm 0\.013Coordinate Embedding Only0\.482±0\.0150\.482\\pm 0\.0150\.701±0\.0270\.701\\pm 0\.0270\.774±0\.0060\.774\\pm 0\.0060\.653±0\.0100\.653\\pm 0\.010REVE Spatial Encoding0\.492±0\.0170\.492\\pm 0\.0170\.691±0\.0210\.691\\pm 0\.0210\.761±0\.0090\.761\\pm 0\.0090\.648±0\.0090\.648\\pm 0\.009Gaussian \(Geodesic\)0\.451±0\.0160\.451\\pm 0\.0160\.698±0\.0230\.698\\pm 0\.0230\.771±0\.0090\.771\\pm 0\.0090\.640±0\.0100\.640\\pm 0\.010REVE 4D Encoding0\.445±0\.0150\.445\\pm 0\.0150\.593±0\.0280\.593\\pm 0\.0280\.712±0\.0100\.712\\pm 0\.0100\.583±0\.0170\.583\\pm 0\.017Legendre prior \(SPERA\-Small\)0\.523±\\pm0\.0110\.721±\\pm0\.0240\.787±\\pm0\.0060\.677±\\pm0\.011

### F\.2Learned Coefficients and Angular Bias Profile

To examine what spatial structure is learned by the pairwise Legendre bias, we analyze the coefficients of the pretrained SPERA\-Base model before downstream fine\-tuning\. The pairwise bias of Eq\. \(2\) can be written as a rotation\-invariant angular bias function

K⁡\(θ\)=∑ℓ=0Lwℓ​Pℓ​\(cos⁡θ\),K\(\\theta\)=\\sum\_\{\\ell=0\}^\{L\}w\_\{\\ell\}P\_\{\\ell\}\(\\cos\\theta\),\(7\)whereθ\\thetadenotes the angular separation between two electrodes\. BecauseP0​\(cos⁡θ\)=1P\_\{0\}\(\\cos\\theta\)=1, the degree\-0 term contributes only an angle\-independent offset\. We therefore exclude it when analyzing the relative shape of the learned spatial kernel\.

As shown in Table[25](https://arxiv.org/html/2610.10571#A6.T25), the learned coefficients are concentrated at low Legendre degrees\. Degrees 1–3 account for 93\.1% of the summed squared coefficients over degrees 1–8, indicating that the learned bias is dominated by broad, smoothly varying angular structure\. EvaluatingK⁡\(θ\)K\(\\theta\)over angular separations from0∘0^\{\\circ\}to180∘180^\{\\circ\}using the learned coefficients shows that the bias reaches its maximum at approximately20\.0∘20\.0^\{\\circ\}and its minimum at180∘180^\{\\circ\}, assigning relatively higher bias to nearby electrode pairs than to widely separated or antipodal pairs\. The nonzero location of the maximum also shows that this locality\-oriented profile is not a simple monotonic decay with angular distance\.

Table 25:Learned pairwise Legendre coefficients of the pretrained SPERA\-Base model\. Degree 0 is omitted because it contributes only an angle\-independent offset\.Legendre degree12345678Coefficient0\.13320\.08310\.04150\.0074−\-0\.0003−\-0\.0205−\-0\.0089−\-0\.0376

### F\.3Decomposition of the Anchor\-Based Attention

Unlike the pairwise Legendre bias of Eq\. \(2\), the anchor\-based formulation injects the geometry featureϕc\\boldsymbol\{\\phi\}\_\{c\}into the queries and keys\. Expanding Eq\. \(4\) therefore yields four score components:

si​j=1d​\(𝐪i\+ΓQ​ϕci\)⊤​\(𝐤j\+ΓK​ϕcj\)=1d​\(𝐪i⊤​𝐤j⏟content–content\+𝐪i⊤​ΓK​ϕcj\+\(ΓQ​ϕci\)⊤​𝐤j⏟content–geometry\+\(ΓQ​ϕci\)⊤​ΓK​ϕcj⏟geometry–geometry\)\.\\begin\{split\}s\_\{ij\}&=\\frac\{1\}\{\\sqrt\{d\}\}\\big\(\\mathbf\{q\}\_\{i\}\+\\Gamma\_\{Q\}\\boldsymbol\{\\phi\}\_\{c\_\{i\}\}\\big\)^\{\\\!\\top\}\\big\(\\mathbf\{k\}\_\{j\}\+\\Gamma\_\{K\}\\boldsymbol\{\\phi\}\_\{c\_\{j\}\}\\big\)\\\\ &=\\frac\{1\}\{\\sqrt\{d\}\}\\Big\(\\underbrace\{\\mathbf\{q\}\_\{i\}^\{\\top\}\\mathbf\{k\}\_\{j\}\}\_\{\\text\{content\-\-content\}\}\+\\underbrace\{\\mathbf\{q\}\_\{i\}^\{\\top\}\\Gamma\_\{K\}\\boldsymbol\{\\phi\}\_\{c\_\{j\}\}\+\(\\Gamma\_\{Q\}\\boldsymbol\{\\phi\}\_\{c\_\{i\}\}\)^\{\\top\}\\mathbf\{k\}\_\{j\}\}\_\{\\text\{content\-\-geometry\}\}\+\\underbrace\{\(\\Gamma\_\{Q\}\\boldsymbol\{\\phi\}\_\{c\_\{i\}\}\)^\{\\top\}\\Gamma\_\{K\}\\boldsymbol\{\\phi\}\_\{c\_\{j\}\}\}\_\{\\text\{geometry\-\-geometry\}\}\\Big\)\.\\end\{split\}\(8\)
The geometry–geometry term captures pairwise interaction between the Legendre anchor encodings, while the two cross terms couple token content with electrode geometry\. These cross terms have no counterpart in Eq\. \(2\), where geometry enters only as an additive pairwise score bias\.

We measure the contribution of each term to the pre\-softmax logit using its root\-mean\-square magnitude over randomly sampled token pairs and attention heads in each full\-attention block\. The two content–geometry cross terms together exceed the geometry–geometry term in every full\-attention block of both SPERA\-Base and SPERA\-Large, by factors of 1\.3 to 13\. Content–content remains the largest single term except in the earliest full\-attention block, where the two cross terms combined exceed it in both models\.

### F\.4Pairwise\-Bias and Anchor\-Based Implementations

The two implementations differ in how geometry enters attention and therefore in computational cost\. In the pairwise Legendre bias form, the Legendre valuesPℓ​\(𝐞i⊤​𝐞j\)P\_\{\\ell\}\(\\mathbf\{e\}\_\{i\}^\{\\top\}\\mathbf\{e\}\_\{j\}\)are computed once per forward pass and reused, so the overhead does not arise from evaluating the polynomials\. Instead, adding the pairwise Legendre bias to the attention scores requires anN×NN\\times Nbias matrix and prevents the fused attention path used in our implementation\. We test whether this overhead can be reduced using PyTorch’s FlexAttention, whosescore\_modapplies the pairwise Legendre bias inside the fused kernel without materializing the full score matrix\.

Table[26](https://arxiv.org/html/2610.10571#A6.T26)compares three whole\-model configurations of SPERA\-Small\. Throughput increases from 52,263 to 66,326 tok/s with FlexAttention, but remains about 29% below that of the anchor\-based design\. Since the anchor form costs only 0\.005 average balanced accuracy relative to the pairwise bias \(Table[3](https://arxiv.org/html/2610.10571#S4.T3)\), we retain it in the full\-attention blocks\.

Table 26:Training throughput for three whole\-model configurations of SPERA\-Small, measured under the setting of Table[4](https://arxiv.org/html/2610.10571#S4.T4)\. Only the treatment of the prior in full\-attention blocks differs; factorized layers use the pairwise Legendre bias throughout\.Prior in full\-attention blocksThroughput \(tok/s\)Pairwise Legendre Bias52,263Pairwise Legendre Bias with FlexAttention66,326Legendre Anchor Encoding \(SPERA\)92,866
### F\.5Extension to Intracranial Recordings

For scalp EEG, electrodes are distributed over the scalp surface, and we therefore represent their locations using unit\-normalized directions\. For iEEG and sEEG, where electrodes occupy the brain volume, radial position also becomes informative\. The construction can be extended to the solid ball𝔹3\\mathbb\{B\}^\{3\}while retaining the same rotation\-invariant angular structure\. On the solid ball, separable solutions of the Laplacian eigenproblem consist of a radial part given by spherical Bessel functionsjℓj\_\{\\ell\}and an angular spherical\-harmonic part\. Using the corresponding rotation\-invariant angular form yields

k⁡\(𝐱i,𝐱j\)=∑ℓ,nwℓ​n​jℓ​\(κn​ri\)​jℓ​\(κn​rj\)​Pℓ​\(𝐞i⊤​𝐞j\),k\(\\mathbf\{x\}\_\{i\},\\mathbf\{x\}\_\{j\}\)=\\sum\_\{\\ell,n\}w\_\{\\ell n\}\\,j\_\{\\ell\}\(\\kappa\_\{n\}r\_\{i\}\)\\,j\_\{\\ell\}\(\\kappa\_\{n\}r\_\{j\}\)\\,P\_\{\\ell\}\(\\mathbf\{e\}\_\{i\}^\{\\top\}\\mathbf\{e\}\_\{j\}\),\(9\)whererir\_\{i\}and𝐞i\\mathbf\{e\}\_\{i\}are the radius and unit direction of electrodeii,nnindexes radial modes,κn\\kappa\_\{n\}denotes the radial wavenumber, andwℓ​nw\_\{\\ell n\}are learnable coefficients\. The angular Legendre structure is retained and radius enters through a learnable radial basis; the surface prior used in this paper is the special case of a shared radius\.

Two practical obstacles remain: intracranial electrode positions require coregistration to a common anatomical space, such as the Montreal Neurological Institute \(MNI\) template, before a shared radial basis is meaningful, and the high\-gamma content that carries much of the information in intracranial recordings lies outside our 0\.5–75 Hz preprocessing pipeline, so the tokenizer would need revision\. We leave this extension to future work\.

### F\.6Spatial Attribution Analysis

We examine whether the model’s electrode\-level attributions align with known EEG neurophysiological patterns\. We use Integrated Gradients \(IG\)\[[141](https://arxiv.org/html/2610.10571#bib.bib141)\]on the fine\-tuned SPERA\-Base model, quantifying each electrode’s contribution to the classification\. We focus on motor imagery \(MI\), for which the relevant cortical regions and class\-dependent spatial organization are well established\[[106](https://arxiv.org/html/2610.10571#bib.bib106)\]\.

IG is computed against a zero baseline on the test split\. Per\-class IG maps are strongly correlated \(mean pairwiserr= 0\.68 on PhysioNet\-MI, and 0\.66 on BCIC\-IV\-2a\), being dominated by a shared channel\-saliency profile that concentrates on the sensorimotor electrodes: mean absolute IG is 3\.5–4\.5 at C3, C4, CP3, and CP4 on PhysioNet\-MI against 1\.7–2\.4 elsewhere, and 25–41 at CP3, CP4, FC3, and FC4 on BCIC\-IV\-2a against 15\.7–17\.5 in frontal and parietal regions\. This shared profile is consistent with reliance on signals recorded over sensorimotor scalp regions\. To highlight class\-relative spatial differences, we apply a two\-step normalization: each class map is divided by its mean over channels, and each channel is then divided by its mean over classes\. In these normalized maps, 1\.0 corresponds to the across\-class mean for each channel\. We summarize the class\-relative maps over the sensorimotor strip \(all FC\*, C\*, and CP\* electrodes\), split into left, right, and midline groups, using a lateralization index LI = \(right−\-left\) / \(right \+ left\) and a mediality index MedIdx = midline / mean \(left, right\)\.

Table 27:Class\-relative attribution over the sensorimotor strip for BCIC\-IV\-2a and PhysioNet\-MI\. Each value is the class\-relative IG after the two\-step normalization\. LI==\(SM\-right−\-SM\-left\) / \(SM\-right\+\+SM\-left\); MedIdx==SM\-mid//mean \(SM\-left, SM\-right\)\.DatasetClassSM\-leftSM\-rightSM\-midLIMedIdxBCIC\-IV\-2aLeft hand0\.9531\.0950\.959\+\+0\.0690\.937Right hand1\.0810\.9910\.872−\-0\.0440\.841Feet0\.9710\.9361\.133−\-0\.0181\.187Tongue0\.9940\.9781\.036−\-0\.0081\.051PhysioNet\-MILeft fist0\.9421\.1230\.980\+\+0\.0880\.949Right fist1\.0150\.9920\.803−\-0\.0120\.800Both fists0\.9880\.9151\.088−\-0\.0381\.144Both feet1\.0560\.9701\.129−\-0\.0421\.115![Refer to caption](https://arxiv.org/html/2610.10571v1/fig_05.png)Figure 5:Class\-relative attribution topographic maps on BCIC\-IV\-2a and PhysioNet\-MI\. Maps are computed separately for each class after two\-step class\-relative normalization\.On BCIC\-IV\-2a, the two unimanual classes follow the expected pattern \(Table[27](https://arxiv.org/html/2610.10571#A6.T27)\): LI is positive for left\-hand and negative for right\-hand imagery, and Figure[5](https://arxiv.org/html/2610.10571#A6.F5)shows the corresponding increase over the sensorimotor region contralateral to the imagined hand, consistent with the established lateralization of hand motor imagery\[[104](https://arxiv.org/html/2610.10571#bib.bib104),[90](https://arxiv.org/html/2610.10571#bib.bib90)\]\. The feet class has the highest mediality and a correspondingly central pattern around the midline, reflecting the medial cortical representation of the lower limbs\[[104](https://arxiv.org/html/2610.10571#bib.bib104),[101](https://arxiv.org/html/2610.10571#bib.bib101)\]\. The tongue class has the smallest absolute LI of the four and is broadly distributed across the sensorimotor strip without the unilateral concentration seen for the hand classes, in line with reports of distributed parietofrontal involvement during tongue motor imagery\[[36](https://arxiv.org/html/2610.10571#bib.bib36)\]\.

PhysioNet\-MI shows the same organization, though more weakly for the right\-fist class: attribution shifts toward the right hemisphere for the left fist and only marginally toward the left hemisphere for the right fist\. Both bilateral classes have MedIdx above 1 while both unimanual classes fall below it, and the topographic maps place their attribution around central and midline sensorimotor sites\.

## Appendix GFew\-Shot Experiments

To evaluate the data efficiency of SPERA, we conduct few\-shot LP experiments on BCIC\-IV\-2a, PhysioNet\-MI, and ISRUC \(motor imagery and sleep staging\)\. For each dataset, the encoder is frozen and only a linear classifier is trained using a limited subset of the original training split\. We evaluate six training data ratios: 1%, 2%, 5%, 10%, 25%, and 50%\. The subsets are sampled in a class\-balanced manner based on the smallest class size in the training set\. All experiments are repeated over five random seeds, and we report the mean balanced accuracy with standard deviation\.

Across all three datasets, performance improves steadily as the training ratio increases \(Figure[6](https://arxiv.org/html/2610.10571#A7.F6)\)\. On BCIC\-IV\-2a, SPERA\-Base surpasses the REVE\-Base reference using 10% of the training data\. PhysioNet\-MI shows a more gradual trend, with the 50% setting closing the gap to the full\-data SPERA\-Base reference\. On ISRUC, SPERA\-Base exceeds the REVE\-Base reference with only 2% of the training data and approaches the full\-data SPERA\-Base reference at higher ratios\. These results indicate that SPERA provides data\-efficient EEG representations\.

Figure 6:Few\-shot LP results of SPERA\-Base on BCIC\-IV\-2a, PhysioNet\-MI, and ISRUC\. The blue curve shows the mean balanced accuracy of SPERA\-Base under limited labeled training data, with the shaded area indicating one standard deviation across five random seeds\. Dashed horizontal lines indicate the full\-data LP results of SPERA\-Base and REVE\-Base\.
## Appendix HNoise Robustness Analysis

We evaluate noise robustness under LP using SPERA\-Small, CBraMod, and REVE\-Base\. To isolate the effect of the pretraining objective, we additionally include the matched reconstruction variant from Appendix[E\.1](https://arxiv.org/html/2610.10571#A5.SS1), which differs only in the prediction target\. Since CBraMod and REVE do not report noise robustness results, we re\-evaluate their publicly released checkpoints together with the noise\-free condition under the same protocol\. For each checkpoint, the encoder is frozen and the linear classifier and feature\-normalization statistics are fitted only on unperturbed training features and then kept fixed across test conditions\. We consider additive Gaussian noise and injected ocular artifacts separately\.

### H\.1Gaussian Noise

Gaussian noise robustness is evaluated on TUAB, ISRUC, and PhysioNet\-MI\. Additive Gaussian white noise is applied only to the test inputs under five conditions: noise\-free, 10 dB, 5 dB, 0 dB, and−\-5 dB\. Noise variance is determined independently for each channel from its mean squared signal amplitude to match the target signal\-to\-noise ratio \(SNR\)\.

As shown in Figure[7](https://arxiv.org/html/2610.10571#A8.F7), SPERA\-Small generally maintains higher mean balanced accuracy than the comparison models across the evaluated noise conditions\. The matched JEPA and reconstruction variants show broadly similar degradation patterns, while JEPA maintains higher mean accuracy in nearly all evaluated conditions\. Thus, the accuracy advantage of latent prediction generally persists under additive Gaussian corruption\.

Figure 7:Gaussian noise robustness on PhysioNet\-MI, ISRUC, and TUAB under LP\. Frozen encoders with linear classifiers trained on unperturbed data are evaluated on test inputs with additive Gaussian noise at 10, 5, 0, and−5\-5dB\. Shaded regions denote one standard deviation across five random seeds\.
### H\.2Physiological Ocular Artifacts

We further evaluate robustness to ocular artifacts on PhysioNet\-MI and TUAB using electrooculographic \(EOG\) waveforms from EEGdenoiseNet\[[160](https://arxiv.org/html/2610.10571#bib.bib160)\]; ISRUC is excluded because the ocular artifact injection protocol is not appropriate for sleep EEG\. Ocular artifacts are projected onto each montage using the empirical propagation factors reported by Lins et al\.\[[76](https://arxiv.org/html/2610.10571#bib.bib76)\]\. For TUAB, bipolar\-channel factors are obtained by subtracting those of the constituent electrodes; for PhysioNet\-MI, factors are estimated by three\-dimensional thin\-plate spline interpolation with a linear term, enforcing symmetry for the vertical field and antisymmetry for the horizontal field\. For each trial, independently sampled vertical and horizontal EOG waveforms are normalized, projected using these spatial fields, and combined using the reported horizontal\-to\-vertical saccade amplitude ratio\. A shared intermittent envelope leaves at least 30% of each trial without added artifacts, after which the combined artifact is scaled to the target SNR based on trial\-level mean EEG and artifact power across channels and time\.

Figure 8:Ocular\-artifact robustness on PhysioNet\-MI and TUAB under LP\. Frozen encoders with linear classifiers trained on unperturbed data are evaluated on test inputs with injected EEGdenoiseNet EOG artifacts at 10, 5, 0, and−5\-5dB\. Shaded regions denote one standard deviation across five random seeds\.Figure[8](https://arxiv.org/html/2610.10571#A8.F8)shows task\-dependent robustness patterns under injected ocular artifacts\. On TUAB, SPERA\-Small achieves the highest mean balanced accuracy across all conditions, whereas CBraMod performs best under the injected\-artifact conditions on PhysioNet\-MI\. In the matched objective comparison, JEPA remains above reconstruction under every condition on both datasets\. From noise\-free to−\-5 dB, the decrease is smaller for JEPA on PhysioNet\-MI \(0\.201 vs\. 0\.208\) and TUAB \(0\.080 vs\. 0\.107\), with the larger difference observed on TUAB\.

## Appendix IRepresentation Analysis

### I\.1UMAP Visualization of Learned Representations

To qualitatively examine the structure of learned representations, we apply uniform manifold approximation and projection \(UMAP\)\[[84](https://arxiv.org/html/2610.10571#bib.bib84)\]to PhysioNet\-MI, ISRUC, and TUAB\. For each dataset, we visualize three representation levels: \(i\) raw EEG samples, \(ii\) features from the frozen pretrained encoder, and \(iii\) features after task\-specific fine\-tuning\. The results are shown in Figure[9](https://arxiv.org/html/2610.10571#A9.F9)\.

The first column shows that raw EEG samples exhibit no clear class\-wise structure across all three datasets\. The second column reveals that the frozen pretrained features already capture task\-related structure to varying degrees\. On ISRUC, sleep stages exhibit clearly distinguishable clusters even without task\-specific supervision, with Wake, N3, and REM occupying separate areas of the embedding space\. TUAB shows a weaker but visible separation between normal and abnormal recordings, while PhysioNet\-MI exhibits more limited class\-level structure at this stage\. The third column shows that, after fine\-tuning, all three datasets form clearer and more separable clusters\.

![Refer to caption](https://arxiv.org/html/2610.10571v1/fig_09.png)Figure 9:UMAP visualization of representations from the SPERA\-Base model on three downstream tasks\. Columns correspond to raw EEG, frozen pretrained features, and fine\-tuned features\. Rows correspond to PhysioNet\-MI, ISRUC, and TUAB\.
### I\.2Linear Accessibility and Encoder Adaptation

In terms of average balanced accuracy across the nine tasks, SPERA\-Base leads REVE\-Base by 0\.051 under LP and by 0\.035 under LPFT \(Tables[2](https://arxiv.org/html/2610.10571#S4.T2)and[17](https://arxiv.org/html/2610.10571#A4.T17)\)\. At the aggregate level, SPERA\-Base remains ahead under both protocols, although several task\-level differences vary with model scale and adaptation\. Under LP, REVE\-Base leads SPERA\-Base on MAT, while REVE\-Large leads SPERA\-Large on BCIC\-IV\-2a, PhysioNet\-MI, and Mumtaz\. BCIC\-IV\-2a and PhysioNet\-MI are motor\-imagery tasks that involve frequency\-specific sensorimotor activity\[[105](https://arxiv.org/html/2610.10571#bib.bib105)\], while MAT has been used to study spectral changes during mental arithmetic\[[164](https://arxiv.org/html/2610.10571#bib.bib164)\], motivating us to examine the linear accessibility of band\-power information\.

We regress channel\-wise relative power in five frequency bands \(delta to gamma\) from frozen encoder representations using a linear readout on per\-channel token features\. Table[28](https://arxiv.org/html/2610.10571#A9.T28)reports held\-out macro Pearson’srr, averaged over channel–band targets\. Because SPERA and REVE differ in architecture, tokenization, corpus, and pretraining objective, we additionally evaluate the matched reconstruction variant of SPERA\-Small from Appendix[E\.1](https://arxiv.org/html/2610.10571#A5.SS1)\.

Table 28:Band\-power decodability from frozen representations\. Values are held\-out macro Pearson’srr, averaged over channel–band targets\.MethodBCIC\-IV\-2aPhysioNet\-MIMATAverageSPERA\-Small0\.3950\.4820\.3050\.394Reconstruction Head0\.5920\.6400\.4830\.572REVE\-Base0\.7350\.6800\.5890\.668Across all three tasks, band power is more linearly decodable from the matched reconstruction variant than from SPERA\-Small, with REVE\-Base showing the highest values\. On PhysioNet\-MI, however, the same objective swap increases band\-power decodability from 0\.482 to 0\.640 while lowering LP accuracy from 0\.523 to 0\.499 \(Appendix[E\.1](https://arxiv.org/html/2610.10571#A5.SS1)\), indicating that greater band\-power accessibility alone does not explain the downstream accuracy difference\.

To further investigate the LP–LPFT divergence, we test how much of the performance gap can be recovered by limited encoder adaptation\. Unfreezing only the last of SPERA\-Base’s 16 encoder blocks after LP recovers 49%, 71%, and 61% of the LP–LPFT gain on BCIC\-IV\-2a \(0\.560 to 0\.619\), PhysioNet\-MI \(0\.551 to 0\.637\), and MAT \(0\.672 to 0\.736\), respectively\. These results suggest that a substantial portion of the LP–LPFT gap can be recovered through limited encoder adaptation\.

## NeurIPS Paper Checklist

1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]
4. Justification: The abstract and Section[1](https://arxiv.org/html/2610.10571#S1)describe SPERA as an EEG representation\-learning framework based on latent\-space prediction, with a Legendre\-polynomial spherical prior for electrode geometry, a hybrid attention backbone, and a relational spectral regularizer\. The empirical claims regarding downstream performance, scaling and parameter efficiency, and robustness are supported by Sections[4\.3](https://arxiv.org/html/2610.10571#S4.SS3)–[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)and Appendices[D](https://arxiv.org/html/2610.10571#A4)–[I](https://arxiv.org/html/2610.10571#A9)\.
5. Guidelines: - •The answer\[N/A\]means that the abstract and introduction do not include the claims made in the paper\. - •The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations\. A\[No\]or\[N/A\]answer to this question will not be perceived well by the reviewers\. - •The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings\. - •It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper\.
6. 2\.Limitations
7. Question: Does the paper discuss the limitations of the work performed by the authors?
8. Answer:\[Yes\]
9. Justification: Section[5](https://arxiv.org/html/2610.10571#S5)discusses limitations regarding \(i\) scaling beyond 396M parameters, \(ii\) the lack of systematic disentanglement of corpus size, model capacity, and architectural priors in the observed scaling behavior, \(iii\) the surface\-electrode assumption of the spherical prior, \(iv\) evaluation restricted to classification over fixed\-duration EEG segments of 3–30 seconds, and \(v\) incomplete demographic metadata for comprehensive fairness analysis\.
10. Guidelines: - •The answer\[N/A\]means that the paper has no limitation while the answer\[No\]means that the paper has limitations, but those are not discussed in the paper\. - •The authors are encouraged to create a separate “Limitations” section in their paper\. - •The paper should point out any strong assumptions and how robust the results are to violations of these assumptions \(e\.g\., independence assumptions, noiseless settings, model well\-specification, asymptotic approximations only holding locally\)\. The authors should reflect on how these assumptions might be violated in practice and what the implications would be\. - •The authors should reflect on the scope of the claims made, e\.g\., if the approach was only tested on a few datasets or with a few runs\. In general, empirical results often depend on implicit assumptions, which should be articulated\. - •The authors should reflect on the factors that influence the performance of the approach\. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting\. Or a speech\-to\-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon\. - •The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size\. - •If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness\. - •While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren’t acknowledged in the paper\. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community\. Reviewers will be specifically instructed to not penalize honesty concerning limitations\.
11. 3\.Theory assumptions and proofs
12. Question: For each theoretical result, does the paper provide the full set of assumptions and a complete \(and correct\) proof?
13. Answer:\[N/A\]
14. Justification: The paper presents an empirical contribution and does not include theoretical results such as theorems, propositions, or lemmas requiring formal proof\.
15. Guidelines: - •The answer\[N/A\]means that the paper does not include theoretical results\. - •All the theorems, formulas, and proofs in the paper should be numbered and cross\-referenced\. - •All assumptions should be clearly stated or referenced in the statement of any theorems\. - •The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition\. - •Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material\. - •Theorems and Lemmas that the proof relies upon should be properly referenced\.
16. 4\.Experimental result reproducibility
17. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper \(regardless of whether the code and data are provided or not\)?
18. Answer:\[Yes\]
19. Justification: Section[3](https://arxiv.org/html/2610.10571#S3)specifies the model architecture, training objectives, masking strategy, and augmentation, while Sections[4\.1](https://arxiv.org/html/2610.10571#S4.SS1)–[4\.2](https://arxiv.org/html/2610.10571#S4.SS2)describe the pretraining corpus, preprocessing, and downstream evaluation\. Appendices[A](https://arxiv.org/html/2610.10571#A1)–[D](https://arxiv.org/html/2610.10571#A4)provide computing resources, corpus information, hyperparameters, and dataset\-specific evaluation details, and Appendices[E](https://arxiv.org/html/2610.10571#A5)–[I](https://arxiv.org/html/2610.10571#A9)document the protocols for the additional ablations and analyses\.
20. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •If the paper includes experiments, a\[No\]answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not\. - •If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable\. - •Depending on the contribution, reproducibility can be accomplished in various ways\. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model\. In general\. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model \(e\.g\., in the case of a large language model\), releasing of a model checkpoint, or other means that are appropriate to the research performed\. - •While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution\. For example 1. \(a\)If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm\. 2. \(b\)If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully\. 3. \(c\)If the contribution is a new model \(e\.g\., a large language model\), then there should either be a way to access this model for reproducing the results or a way to reproduce the model \(e\.g\., with an open\-source dataset or instructions for how to construct the dataset\)\. 4. \(d\)We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility\. In the case of closed\-source models, it may be that access to the model is limited in some way \(e\.g\., to registered users\), but it should be possible for other researchers to have some path to reproducing or verifying the results\.
21. 5\.Open access to data and code
22. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
23. Answer:\[Yes\]
24. Justification: Our codebase is provided as a link in the paper \([https://github\.com/sees4321/SPERA\_EEG](https://github.com/sees4321/SPERA_EEG)\), including training, evaluation, and preprocessing scripts together with a README detailing the environment setup and exact commands to reproduce the main results\. All pretraining and downstream datasets are publicly available, with sources and licenses listed in Appendix[B](https://arxiv.org/html/2610.10571#A2)\.
25. Guidelines: - •The answer\[N/A\]means that paper does not include experiments requiring code\. - • - •While we encourage the release of code and data, we understand that this might not be possible, so\[No\]is an acceptable answer\. Papers cannot be rejected simply for not including code, unless this is central to the contribution \(e\.g\., for a new open\-source benchmark\)\. - •The instructions should contain the exact command and environment needed to run to reproduce the results\. See the NeurIPS code and data submission guidelines \([https://neurips\.cc/public/guides/CodeSubmissionPolicy](https://neurips.cc/public/guides/CodeSubmissionPolicy)\) for more details\. - •The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc\. - •The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines\. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why\. - •At submission time, to preserve anonymity, the authors should release anonymized versions \(if applicable\)\. - •Providing as much information as possible in supplemental material \(appended to the paper\) is recommended, but including URLs to data and code is permitted\.
26. 6\.Experimental setting/details
27. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, how they were chosen, type of optimizer\) necessary to understand the results?
28. Answer:\[Yes\]
29. Justification: Section[4\.1](https://arxiv.org/html/2610.10571#S4.SS1)specifies the optimizer and pretraining setup, and Section[4\.2](https://arxiv.org/html/2610.10571#S4.SS2)describes SPERA’s LP and LPFT protocols, validation\-based hyperparameter selection, and baseline evaluation settings\. Appendix[C\.1](https://arxiv.org/html/2610.10571#A3.SS1)provides the full hyperparameters across all model sizes, while Appendix[D](https://arxiv.org/html/2610.10571#A4)documents the dataset\-specific preprocessing and train/validation/test splits, including implementation\-specific details\.
30. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them\. - •The full details can be provided either with the code, in appendix, or as supplemental material\.
31. 7\.Experiment statistical significance
32. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
33. Answer:\[Yes\]
34. Justification: SPERA experiments are repeated over five random seeds and reported as mean±\\pmone standard deviation; for the aggregate results, variability is computed across the corresponding seed\-wise averages\. Appendix[D\.10](https://arxiv.org/html/2610.10571#A4.SS10)additionally reports unpaired Welch’stt\-tests with 95% confidence intervals and Holm correction across the nine tasks separately for each SPERA model, while figure captions specify shaded one\-standard\-deviation bands where applicable\.
35. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The authors should answer\[Yes\]if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper\. - •The factors of variability that the error bars are capturing should be clearly stated \(for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions\)\. - •The method for calculating the error bars should be explained \(closed form formula, call to a library function, bootstrap, etc\.\) - •The assumptions made should be given \(e\.g\., Normally distributed errors\)\. - •It should be clear whether the error bar is the standard deviation or the standard error of the mean\. - •It is OK to report 1\-sigma error bars, but one should state it\. The authors should preferably report a 2\-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified\. - •For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range \(e\.g\., negative error rates\)\. - •If error bars are reported in tables or plots, the authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text\.
36. 8\.Experiments compute resources
37. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
38. Answer:\[Yes\]
39. Justification: Appendix[A](https://arxiv.org/html/2610.10571#A1)details the computing environment, including the hardware \(HP Z8 workstation with two NVIDIA RTX 5000 Ada GPUs\), software stack \(PyTorch 2\.10\.0, CUDA 13\.0\), and training efficiency strategies \(DDP and BF16 mixed precision\)\. Pretraining the largest model \(SPERA\-Large, 396M\) takes approximately 287 GPU hours\. Section[4\.5](https://arxiv.org/html/2610.10571#S4.SS5)and Table[4](https://arxiv.org/html/2610.10571#S4.T4)additionally report throughput and peak GPU memory for the attention and Legendre prior variants\. Additional experiments and ablations were conducted primarily with SPERA\-Small \(48M\), including the matched objective and corpus controls, and therefore required substantially less compute per run than the largest\-model pretraining\.
40. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage\. - •The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute\. - •The paper should disclose whether the full research project required more compute than the experiments reported in the paper \(e\.g\., preliminary or failed experiments that didn’t make it into the paper\)\.
41. 9\.Code of ethics
43. Answer:\[Yes\]
44. Justification: We have reviewed the NeurIPS Code of Ethics and confirm that this research conforms to it in all respects\.
45. Guidelines: - •The answer\[N/A\]means that the authors have not reviewed the NeurIPS Code of Ethics\. - •If the authors answer\[No\], they should explain the special circumstances that require a deviation from the Code of Ethics\. - •The authors should make sure to preserve anonymity \(e\.g\., if there is a special consideration due to laws or regulations in their jurisdiction\)\.
46. 10\.Broader impacts
47. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
48. Answer:\[Yes\]
49. Justification: SPERA can support clinical applications such as sleep staging, abnormal\-event detection, and mental disorder screening, as well as assistive BCI applications including motor imagery and imagined speech decoding, particularly in settings with limited labeled data\. On the negative side, EEG\-based models could be misused for unconsented brain\-state inference or surveillance, and premature clinical deployment without additional validation could lead to incorrect diagnostic decisions\. Fairness considerations also arise from potential demographic imbalance in the pretraining corpus, as noted in Section[5](https://arxiv.org/html/2610.10571#S5)\. We therefore caution against direct clinical or consumer deployment without further validation, fairness audits, and appropriate human oversight\.
50. Guidelines: - •The answer\[N/A\]means that there is no societal impact of the work performed\. - •If the authors answer\[N/A\]or\[No\], they should explain why their work has no societal impact or why the paper does not address societal impact\. - •Examples of negative societal impacts include potential malicious or unintended uses \(e\.g\., disinformation, generating fake profiles, surveillance\), fairness considerations \(e\.g\., deployment of technologies that could make decisions that unfairly impact specific groups\), privacy considerations, and security considerations\. - •The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments\. However, if there is a direct path to any negative applications, the authors should point it out\. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate Deepfakes for disinformation\. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster\. - •The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from \(intentional or unintentional\) misuse of the technology\. - •If there are negative societal impacts, the authors could also discuss possible mitigation strategies \(e\.g\., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML\)\.
51. 11\.Safeguards
52. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse \(e\.g\., pre\-trained language models, image generators, or scraped datasets\)?
53. Answer:\[N/A\]
54. Justification: The released model is a representation encoder for EEG signals and does not generate content; it does not pose the high\-risk misuse concerns associated with generative language or image models\. The pretraining corpus consists of EEG recordings from established public repositories \(e\.g\., OpenNeuro, MOABB, PhysioNet, NSRR, TUH\) under their respective data use agreements, with no scraped or unverified content \(Appendix[B](https://arxiv.org/html/2610.10571#A2)\)\.
55. Guidelines: - •The answer\[N/A\]means that the paper poses no such risks\. - •Released models that have a high risk for misuse or dual\-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters\. - •Datasets that have been scraped from the Internet could pose safety risks\. The authors should describe how they avoided releasing unsafe images\. - •We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort\.
56. 12\.Licenses for existing assets
57. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
58. Answer:\[Yes\]
59. Justification: All baseline models, prior EEG foundation models, pretraining datasets, and downstream datasets are properly cited at first mention \(Sections[4\.1](https://arxiv.org/html/2610.10571#S4.SS1)and[4\.2](https://arxiv.org/html/2610.10571#S4.SS2); Appendix[B](https://arxiv.org/html/2610.10571#A2)\)\. Appendix[B](https://arxiv.org/html/2610.10571#A2)\(Table[6](https://arxiv.org/html/2610.10571#A2.T6)\) lists each of the 106 pretraining datasets together with its source platform and license \(e\.g\., CC0, CC BY 4\.0, CC BY\-NC\-SA 4\.0, GPL\-3\.0, and the NEDC, NSRR, Brainclinics, and BDSP data use agreements\)\. The software stack is reported with version numbers in Appendix[A](https://arxiv.org/html/2610.10571#A1)\(PyTorch 2\.10\.0, transformers 5\.3\.0, accelerate 1\.13\.0, MNE\-Python 1\.11\.0\)\. All assets are used in compliance with their respective licenses and terms of use\.
60. Guidelines: - •The answer\[N/A\]means that the paper does not use existing assets\. - •The authors should cite the original paper that produced the code package or dataset\. - •The authors should state which version of the asset is used and, if possible, include a URL\. - •The name of the license \(e\.g\., CC\-BY 4\.0\) should be included for each asset\. - •For scraped data from a particular source \(e\.g\., website\), the copyright and terms of service of that source should be provided\. - •If assets are released, the license, copyright information, and terms of use in the package should be provided\. For popular datasets,[paperswithcode\.com/datasets](https://paperswithcode.com/datasets)has curated licenses for some datasets\. Their licensing guide can help determine the license of a dataset\. - •For existing datasets that are re\-packaged, both the original license and the license of the derived asset \(if it has changed\) should be provided\. - •If this information is not available online, the authors are encouraged to reach out to the asset’s creators\.
61. 13\.New assets
62. Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
63. Answer:\[Yes\]
64. Justification: We release SPERA, a new pretrained EEG foundation model, together with training, evaluation, and preprocessing code\. The architecture, training procedure, hyperparameters, and computing environment are documented in Section[3](https://arxiv.org/html/2610.10571#S3), Section[4\.1](https://arxiv.org/html/2610.10571#S4.SS1), and Appendices[A](https://arxiv.org/html/2610.10571#A1)–[C\.1](https://arxiv.org/html/2610.10571#A3.SS1)\.
65. Guidelines: - •The answer\[N/A\]means that the paper does not release new assets\. - •Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates\. This includes details about training, license, limitations, etc\. - •The paper should discuss whether and how consent was obtained from people whose asset is used\. - •At submission time, remember to anonymize your assets \(if applicable\)\. You can either create an anonymized URL or include an anonymized zip file\.
66. 14\.Crowdsourcing and research with human subjects
67. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
68. Answer:\[N/A\]
69. Justification: This work does not involve any crowdsourcing or new data collection from human subjects\. All EEG data are obtained from existing public repositories under their respective data use agreements \(Appendix[B](https://arxiv.org/html/2610.10571#A2)\)\.
70. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper\. - •According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector\.
71. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
72. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
73. Answer:\[N/A\]
74. Justification: This work does not involve new research with human subjects\. All EEG recordings come from existing public datasets whose original collection was approved by the relevant institutional review boards or equivalent oversight bodies, as documented in their respective source publications \(Appendix[B](https://arxiv.org/html/2610.10571#A2)\)\.
75. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Depending on the country in which research is conducted, IRB approval \(or equivalent\) may be required for any human subjects research\. If you obtained IRB approval, you should clearly state this in the paper\. - •We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution\. - •For initial submissions, do not include any information that would break anonymity \(if applicable\), such as the institution conducting the review\.
76. 16\.Declaration of LLM usage
77. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does*not*impact the core methodology, scientific rigor, or originality of the research, declaration is not required\.
78. Answer:\[N/A\]
79. Justification: LLMs were not used as a component of the core methodology of this research\.
80. Guidelines: - •The answer\[N/A\]means that the core method development in this research does not involve LLMs as any important, original, or non\-standard components\. - •Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described\.