ECG-InterpBench: Benchmarking the Interpretability of ECG Foundation Models with Matched-Scale Sparse Autoencoders
Summary
ECG-InterpBench is a new benchmark that systematically evaluates the interpretability of ECG foundation model representations using matched-scale sparse autoencoders, covering reconstruction fidelity, clinical concept accessibility, and reproducibility across 450 cells.
arXiv:2607.27404v1 Announce Type: new
Abstract: Existing benchmarks for electrocardiogram foundation models primarily evaluate downstream predictive performance, providing limited insight into whether their internal representations can be faithfully decomposed, clinically interpreted, or reproduced across independent analyses. We introduce ECG-InterpBench, a benchmark designed to systematically evaluate the interpretability of ECG foundation-model representations. ECG-InterpBench uses sparse autoencoders as standardized measurement instruments and matches their capacity across models to enable controlled comparisons. We evaluate six frozen ECG foundation models across five standardized encoder depths, five matched dictionary widths, and three random seeds, producing a 450-cell interpretability atlas comprising 75 exactly matched six-model comparison blocks. The benchmark evaluates complementary dimensions of representation interpretability, including sparse reconstruction fidelity, single-feature accessibility and coverage of 49 clinically meaningful ECG measurements, and cross-seed feature reproducibility. The evaluation further quantifies patient-sampling uncertainty, depth- and seed-dependent variation, and sensitivity to the sparsity parameterization. The benchmark reveals that ECG foundation models exhibit distinct interpretability profiles. A matched replication on MIMIC-IV-ECG confirms that reconstruction fidelity and clinical accessibility identify different leading models. The benchmark is accompanied by executable evaluation code, standardized manifests, cell-level metrics, and reproducibility audits. ECG-InterpBench complements performance-centered ECG benchmarks by providing a capacity-controlled and reproducible framework for comparing ECG foundation models across distinct dimensions of representation interpretability.
View Cached Full Text
Cached at: 07/31/26, 10:02 AM
# ECG-InterpBench: Benchmarking the Interpretability of ECG Foundation Models with Matched-Scale Sparse Autoencoders Source: [https://arxiv.org/html/2607.27404](https://arxiv.org/html/2607.27404) Yixuan DuanandWei QiuDepartment of Electrical and Computer EngineeringRice UniversityHoustonTexasUSA[wq8@rice\.edu](https://arxiv.org/html/2607.27404v1/mailto:[email protected]) \(2027\) ###### Abstract\. Existing benchmarks for electrocardiogram foundation models primarily evaluate downstream predictive performance, providing limited insight into whether their internal representations can be faithfully decomposed, clinically interpreted, or reproduced across independent analyses\. We introduce ECG\-InterpBench, a benchmark designed to systematically evaluate the interpretability of ECG foundation\-model representations\. ECG\-InterpBench uses sparse autoencoders as standardized measurement instruments and matches their capacity across models to enable controlled comparisons\. We evaluate six frozen ECG foundation models across five standardized encoder depths, five matched dictionary widths, and three random seeds, producing a 450\-cell interpretability atlas comprising 75 exactly matched six\-model comparison blocks\. The benchmark evaluates complementary dimensions of representation interpretability, including sparse reconstruction fidelity, single\-feature accessibility and coverage of 49 clinically meaningful ECG measurements, and cross\-seed feature reproducibility\. The evaluation further quantifies patient\-sampling uncertainty, depth\- and seed\-dependent variation, and sensitivity to the sparsity parameterization\. The benchmark reveals that ECG foundation models exhibit distinct interpretability profiles\. A matched replication on MIMIC\-IV\-ECG confirms that reconstruction fidelity and clinical accessibility identify different leading models\. The benchmark is accompanied by executable evaluation code, standardized manifests, cell\-level metrics, and reproducibility audits\. ECG\-InterpBench complements performance\-centered ECG benchmarks by providing a capacity\-controlled and reproducible framework for comparing ECG foundation models across distinct dimensions of representation interpretability\. Benchmarking, Sparse Autoencoders, Mechanistic Interpretability, Electrocardiogram, Foundation Models, Representation Analysis ††copyright:none††journalyear:2027††conference:The 33rd ACM SIGKDD Conference on Knowledge Discovery and Data Mining; August 1–5, 2027; San Jose, CA, USA††ccs:Computing methodologies Representation of mathematical objects††ccs:Computing methodologies Unsupervised learning††ccs:Applied computing Health informatics††ccs:Information systems Data analytics## 1\.Introduction Figure 1\.Overview of ECG\-InterpBench\. \(a\) PTB\-XL and credentialed MIMIC\-IV ECGs are passed through six frozen ECG FMs, and layer representations are decomposed with BatchTopK SAEs\. \(b\) Each representation is evaluated separately for reconstruction fidelity, single\-feature clinical concept accessibility and coverage, and cross\-seed reproducibility\. \(c\) The matched\-scale design crosses six models, five relative depths, five expansion factors, and three seeds, producing 450 SAE cells for common\-scale model comparison\.The benchmark pipeline has three parts\. First, ECG datasets and clinical concepts are processed by six frozen ECG foundation models, and hidden representations from multiple layers are reconstructed by BatchTopK sparse autoencoders\. Second, the resulting representations are evaluated for reconstruction fidelity, concept accessibility and coverage, and cross\-seed reproducibility\. Third, six models, five relative depths, five expansion factors, and three random seeds form a matched 450\-cell comparison grid\.ECG foundation models \(ECG FMs\) learn general\-purpose representations that support diverse rhythm, morphology, and cardiovascular risk\-prediction tasks\(McKeen and others,[2025](https://arxiv.org/html/2607.27404#bib.bib2); Guet al\.,[2026](https://arxiv.org/html/2607.27404#bib.bib3); Naet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib7)\)\. Existing evaluations, however, focus primarily on downstream accuracy, transfer performance, or label efficiency\(Mehari and Strodthoff,[2022](https://arxiv.org/html/2607.27404#bib.bib36); Kiyassehet al\.,[2021](https://arxiv.org/html/2607.27404#bib.bib37); Vaid and others,[2023](https://arxiv.org/html/2607.27404#bib.bib38)\)\. These outcomes do not reveal how the hidden representation is organized: whether it can be faithfully decomposed, whether clinically relevant measurements are localized to identifiable features, or whether the same structure is recovered across independent decompositions\. This gap matters in clinical settings because a shared representation can propagate acquisition artifacts, demographic confounding, or cohort\-specific shortcuts to every downstream model built on it\(Rudin,[2019](https://arxiv.org/html/2607.27404#bib.bib39); Ghassemiet al\.,[2021](https://arxiv.org/html/2607.27404#bib.bib40); Tonekaboniet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib41)\)\. Existing interpretability tools address related but different questions\. Output attribution identifies waveform regions that influence a prediction, but it does not audit the organization of a task\-general hidden representation and may fail parameter\-randomization or other sanity checks\(Strodthoff and Strodthoff,[2019](https://arxiv.org/html/2607.27404#bib.bib43); Adebayoet al\.,[2018](https://arxiv.org/html/2607.27404#bib.bib18)\)\. Linear probes establish whether a clinical variable is decodable, but not whether it is localized to a small number of features, preserved by a faithful sparse decomposition, or recovered across independent SAE trainings\. Representation\-level interpretability is therefore not equivalent to predictive accuracy, linear decodability, or visually plausible saliency; it requires explicit, complementary measurements\(Murdochet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib42)\)\. Sparse autoencoders \(SAEs\) provide a scalable instrument for this audit by mapping dense activations into sparse codes and reconstructing the original representation from learned decoder directions\(Cunninghamet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib8); Gaoet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib9); Bussmannet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib10)\)\. Their behavior depends on dictionary width and sparsity, making capacity matching central to controlled cross\-model measurement\(Templeton and others,[2024](https://arxiv.org/html/2607.27404#bib.bib44); Lieberumet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib45); Makelovet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib30)\)\. ECG\-InterpBench therefore evaluates every FM with the same family of dictionary scales and sparsity settings and summarizes all models over common scale support\. This design separates differences among FM representations from differences in SAE measurement capacity\. ECG\-InterpBench uses a matched family of SAEs as the standardized measurement instrument and treats the frozen FM representation as the object being evaluated\. We operationalize representation interpretability along three separately reported axes: \(1\) sparse reconstruction fidelity and dictionary utilization; \(2\) train\-selected single\-feature accessibility and coverage of clinical ECG concepts; and \(3\) cross\-seed reproducibility of decoder features and selected feature subspaces\. Together, these axes provide a structured profile of how faithfully, locally, and reproducibly each representation can be interpreted\. We evaluate six frozen ECG FMs at five standardized relative depths, five matched SAE scales, and three random seeds\. The resulting 450\-cell atlas contains 75 comparison blocks in which all six models share the same target relative depth, dictionary capacity, sparsity protocol, and seed\. Comparisons are made only within these blocks and summarized over the same scale support for every model\. We additionally quantify patient\-sampling and design uncertainty and test sensitivity to an alternative sparsity parameterization\. Figure[1](https://arxiv.org/html/2607.27404#S1.F1)summarizes this capacity\-controlled design\. The benchmark reveals distinct, metric\-specific interpretability profiles\. Reconstruction fidelity, single\-feature clinical accessibility, and decoder reproducibility expose complementary strengths across ECG FMs\. A matched MIMIC\-IV\-ECG replication preserves the separation between reconstruction and accessibility leaders\. The resulting profile supports direct model comparison across all measured representation properties\. The benchmark implementation, experiment protocols, and manuscript artifacts are publicly available in our[GitHub repository](https://github.com/JayDuan123/2027-kdd-ECG-InterpBench)\. Our contributions are: - •We introduce a capacity\-controlled benchmark for comparing representation\-level interpretability across six ECG FMs under a matched SAE protocol\. - •We construct a 450\-cell matched\-scale interpretability atlas that maps how representation interpretability changes across encoder depth and SAE scale\. - •We define leakage\-controlled interpretability metrics spanning sparse fidelity, single\-feature clinical accessibility and coverage, and cross\-seed feature and subspace reproducibility\. - •We provide robust interpretability comparisons supported by patient and design uncertainty, sparsity sensitivity, and external\-cohort evaluation\. ## 2\.Related Work #### ECG foundation models\. Supervised deep ECG systems established high diagnostic performance for arrhythmia, multi\-label 12\-lead interpretation, and ventricular\-dysfunction screening\(Hannunet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib33); Ribeiroet al\.,[2020](https://arxiv.org/html/2607.27404#bib.bib34); Attiaet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib32)\)\. PTB\-XL subsequently enabled reproducible architecture benchmarking and transfer analysis\(Strodthoffet al\.,[2021](https://arxiv.org/html/2607.27404#bib.bib35)\), while contrastive, predictive, and masked\-reconstruction objectives showed that useful ECG representations can be learned without task labels\(Mehari and Strodthoff,[2022](https://arxiv.org/html/2607.27404#bib.bib36); Kiyassehet al\.,[2021](https://arxiv.org/html/2607.27404#bib.bib37); Vaid and others,[2023](https://arxiv.org/html/2607.27404#bib.bib38)\)\. The evaluated encoders use multimodal, contrastive, predictive, clustering, or spatio\-temporal objectives\. They are CSFM, CARDIAC\-FM, ECG\-FM, ECG\-JEPA, HuBERT\-ECG, and ST\-MEM\(Guet al\.,[2026](https://arxiv.org/html/2607.27404#bib.bib3); Liet al\.,[2026](https://arxiv.org/html/2607.27404#bib.bib4); McKeen and others,[2025](https://arxiv.org/html/2607.27404#bib.bib2); Kim,[2024](https://arxiv.org/html/2607.27404#bib.bib5); Coppolaet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib6); Naet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib7)\)\. Their released channel selection, sample rate, duration, tokenization, and pooling APIs differ\. We preserve those interfaces and standardize only the comparison coordinates—relative depth and SAE capacity\. #### Sparse representation analysis\. SAEs are motivated by sparse coding\(Olshausen and Field,[1997](https://arxiv.org/html/2607.27404#bib.bib16); Mairalet al\.,[2009](https://arxiv.org/html/2607.27404#bib.bib17)\)and have been used to recover interpretable directions from language, biological, and other foundation models\(Brickenet al\.,[2023](https://arxiv.org/html/2607.27404#bib.bib11); Simon and Zou,[2025](https://arxiv.org/html/2607.27404#bib.bib12)\)\. Large\-scale dictionary releases and scaling studies show that dictionary width, sparsity, reconstruction, and feature quality interact\(Cunninghamet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib8); Gaoet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib9); Templeton and others,[2024](https://arxiv.org/html/2607.27404#bib.bib44); Lieberumet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib45)\); BatchTopK makes the batch\-level activation budget explicit\(Bussmannet al\.,[2024](https://arxiv.org/html/2607.27404#bib.bib10)\)\. Evaluations of SAE fidelity, sparse probing, and intervention further caution that no single metric establishes interpretability\(Makelovet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib30); Karvonenet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib31)\)\. These results motivate a capacity sweep, but they also imply that a cross\-model study must match the sweep rather than select a separate favorable capacity for each encoder\. Prior work applies TopK SAEs to EEG transformers across layers and scales, evaluating dictionary health, clinical semantics, steering, and spectral decoding\(Lehn\-Schiøleret al\.,[2026](https://arxiv.org/html/2607.27404#bib.bib1)\)\. ECG\-InterpBench focuses instead on controlled interpretability comparisons across ECG foundation models\. It restricts primary comparisons to common scales, integrates identical scale support for every model, pairs patient resamples across models, freezes concept selection before test evaluation, and evaluates seed\-level feature identity against random matching\. #### Concept and benchmark evaluation\. Interpretability depends on the intended audience and use, and medical explanations require evaluation against clinical needs rather than visual plausibility alone\(Murdochet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib42); Rudin,[2019](https://arxiv.org/html/2607.27404#bib.bib39); Tonekaboniet al\.,[2019](https://arxiv.org/html/2607.27404#bib.bib41); Ghassemiet al\.,[2021](https://arxiv.org/html/2607.27404#bib.bib40)\)\. ECG attribution studies can recover diagnostically relevant waveform regions\(Strodthoff and Strodthoff,[2019](https://arxiv.org/html/2607.27404#bib.bib43)\), but output attribution answers a different question from auditing the organization of a task\-general hidden representation\. Concept activation vectors define supervised directions\(Kimet al\.,[2018](https://arxiv.org/html/2607.27404#bib.bib13)\), concept bottlenecks expose human\-specified intermediate variables\(Kohet al\.,[2020](https://arxiv.org/html/2607.27404#bib.bib14)\), and LEACE removes linearly decodable subspaces in closed form\(Belroseet al\.,[2023](https://arxiv.org/html/2607.27404#bib.bib15)\)\. These methods likewise answer different questions from an unsupervised sparse dictionary\. Explanation methods can pass qualitative inspection while failing sanity, leakage, or control tests\(Adebayoet al\.,[2018](https://arxiv.org/html/2607.27404#bib.bib18); Jethaniet al\.,[2023](https://arxiv.org/html/2607.27404#bib.bib19)\)\. SAE studies accordingly report heterogeneous criteria, including one\-dimensional binary probe loss, automated explanation, TCAV, intervention selectivity, and reconstruction fidelity\(Gaoet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib9); Lehn\-Schiøleret al\.,[2026](https://arxiv.org/html/2607.27404#bib.bib1); Karvonenet al\.,[2025](https://arxiv.org/html/2607.27404#bib.bib31)\)\. Those values are not numerically commensurate with held\-out Pearson correlation for continuous ECG measurements, so we do not assign our correlation scale a literature\-wide “strong alignment” threshold\. Our benchmark instead uses it as a leakage\-controlled relative comparison under matched ECG\-FM depth–scale blocks, while retaining every failed cell in a fixed denominator\. ## 3\.Benchmark Design ### 3\.1\.Source cohorts, frozen models, and representations PTB\-XL supplies 21,799 twelve\-lead ECGs and 49 waveform\-derived measurement and morphology concepts\(Wagneret al\.,[2020](https://arxiv.org/html/2607.27404#bib.bib20)\)\. We use the existing patient\-disjoint split: 15,149 records for training, 3,325 for validation, and 3,325 for test\. The test set contains 2,862 unique patients\. Every model receives the same ordered record manifest, and preprocessing statistics are estimated on training records only\. PTB\-XL is the source cohort for the primary benchmark\. For external validation, we repeat the complete 450\-cell multiscale SAE audit on a credentialed, patient\-partitioned MIMIC\-IV\-ECG manifest of 100,000 ECGs from 48,491 patients \(Appendix[E](https://arxiv.org/html/2607.27404#A5)\)\. All six pretrained encoders remain frozen throughout the benchmark\. We update no FM parameters and perform no task\-specific fine\-tuning; only the SAEs are trained on activations extracted from the fixed checkpoints\. Each encoder is called through its released preprocessing path \(Appendix[C](https://arxiv.org/html/2607.27404#A3), Table[S3](https://arxiv.org/html/2607.27404#A3.T3)\)\. We audit pre\-projection transformer\-layer states for CARDIAC\-FM; its released 768\-to\-512 pooled projection is used only in the downstream stage and is not the dimension of the source layer atlas\. Consequently, all six source layer atlases haved=768d=768\. Figure 2\.Single\-coordinate clinical accessibility across the matched SAE atlas\. \(a\) Test mean absolute concept correlation over five relative depths and five exactly matched expansion factors; circles mark each model’s peak cell\. \(b\) Common\-scale semantic AUC with paired patient\-cluster 95% intervals\. \(c\) Mean concept\-level common\-scale AUC by ECG concept family\. Features are selected on the training subset and frozen before held\-out evaluation\.A three\-panel figure shows six depth\-scale heatmaps for ECG foundation models, a forest plot of common\-scale semantic AUC with confidence intervals, and a dot plot of mean concept accessibility by ECG concept family\.Figure 3\.Patient\-bootstrap FM profiles at each common SAE scale: \(a\) reconstructionR2R^\{2\}, \(b\) train\-selected single\-coordinate clinical accessibility, and \(c\) concept coverage at\|r\|≥0\.20\|r\|\\geq 0\.20\. Lines compare models at identicalEEand therefore identical absoluteNN; bands are paired 95% patient\-cluster intervals\.Three line panels show reconstruction, train\-selected single\-coordinate clinical accessibility, and concept coverage for six models over five matched expansion factors, with confidence bands\. ### 3\.2\.Standardized depth and exact scale matching For an encoder exposingLLaudited states, target relative depthq∈\{0,\.25,\.5,\.75,1\}q\\in\\\{0,\.25,\.5,\.75,1\\\}maps to \(1\)ℓ\(q\)=⌊q\(L−1\)\+12⌋\.\\ell\(q\)=\\left\\lfloor q\(L\-1\)\+\\tfrac\{1\}\{2\}\\right\\rfloor\.We record bothqqand the realized depthℓ/\(L−1\)\\ell/\(L\-1\)\. CSFM maps to layers\(0,1,3,4,5\)\(0,1,3,4,5\); each 12\-state encoder maps to\(0,3,6,8,11\)\(0,3,6,8,11\)\. Relative depth provides a shared coordinate for aligning early, intermediate, and final representation stages across encoders with different layer counts\. This alignment enables systematic depth\-wise comparison of where reconstruction fidelity, clinical accessibility, and reproducible sparse structure emerge across models\. For a batch of standardized activationsX∈ℝB×dX\\in\\mathbb\{R\}^\{B\\times d\}, BatchTopK computes positive pre\-activations and retains the largestBkBkvalues over the complete batch: \(2\)P\\displaystyle P=ReLU\(\(X−bd\)We⊤\+be\),\\displaystyle=\\operatorname\{ReLU\}\\\!\\left\(\(X\-b\_\{d\}\)W\_\{e\}^\{\\top\}\+b\_\{e\}\\right\),\(3\)Z\\displaystyle Z=BatchTopKBk\(P\),X^=ZWd⊤\+bd\.\\displaystyle=\\operatorname\{BatchTopK\}\_\{Bk\}\(P\),\\qquad\\widehat\{X\}=ZW\_\{d\}^\{\\top\}\+b\_\{d\}\.Decoder columns are constrained to unit norm\. Thuskkspecifies the batch\-average active\-feature budget, while the reported realized meanL0L\_\{0\}summarizes per\-record activation sparsity\. The primary grid fixes expansionE=N/d∈\{1,4,8,16,32\}E=N/d\\in\\\{1,4,8,16,32\\\}andk/d=1/8k/d=1/8\. Becaused=768d=768for every source layer, all models use exactly the same widths \(4\)N∈\{768,3072,6144,12288,24576\}N\\in\\\{768,3072,6144,12288,24576\\\}and the samek=96k=96at every scale\. Each SAE is trained for 8,000 steps with batch size 256, Adam learning rate3×10−43\\times 10^\{\-4\}, and seed 4311, 4312, or 4313\. The complete grid contains \(5\)6models×5depths×5scales×3seeds=4506\\ \\text\{models\}\\times 5\\ \\text\{depths\}\\times 5\\ \\text\{scales\}\\times 3\\ \\text\{seeds\}=450cells, arranged as 75 blocks in which all six FMs share the same target depth,NN,kk, and seed\. Primary contrasts pair all models at the same prespecifiedEEand summarize performance over the shared scale grid, with scale choices fixed before test evaluation\. ### 3\.3\.Leakage\-controlled single\-coordinate clinical accessibility Concept values are aligned by ECG identifier and standardized with training\-split means and standard deviations\. A missing or non\-finite value is replaced by the training mean, which is zero in standardized coordinates\. Coordinate selection uses the same deterministic 4,096\-record subset of the training split in every cell\. For conceptccand SAE code coordinatejj, letrjctrainr^\{\\mathrm\{train\}\}\_\{jc\}denote their correlation on that subset\. We select \(6\)jc∗=argmaxj\|rjctrain\|j\_\{c\}^\{\*\}=\\arg\\max\_\{j\}\|r^\{\\mathrm\{train\}\}\_\{jc\}\|once and evaluate the same coordinate on validation and test records\. The test single\-coordinate accessibility score is the mean\|rjc∗ctest\|\|r^\{\\mathrm\{test\}\}\_\{j\_\{c\}^\{\*\}c\}\|over 49 concepts; coverage is the fraction with\|rjc∗ctest\|≥\.20\|r^\{\\mathrm\{test\}\}\_\{j\_\{c\}^\{\*\}c\}\|\\geq\.20\. Training\-only selection fixes every SAE coordinate, layer, and scale before held\-out evaluation\. This estimand quantifies how strongly one sparse coordinate locally exposes each concept, and the\.20\.20cutoff provides a consistent descriptive operating point across models\. ### 3\.4\.Fixed\-scale accessibility calibration At the commonE=8E=8cells \(N=6144,k=96N=6144,k=96\), we compare seven readouts: fixed\-α=10\\alpha=10ridge from the dense state, full SAE code, or 16/four train\-ranked SAE coordinates; and fit\-free train\-selected native, SAE, or random coordinates\. Dense coordinates are evaluated once per model–depth, whereas SAE metrics average three seeds\. The random control averages 20 shared seeds, each projecting the normalized state ontoNNGaussian unit directions before the same ReLU, BatchTopK, batch order, and training\-only selection\. We report held\-out mean\|r\|\|r\|, coverage at\|r\|≥\.20\|r\|\\geq\.20, paired differences, and random\-seed percentile intervals\. Coordinates and readout settings are fixed from the training data before validation and test outcomes are used for held\-out evaluation\. ### 3\.5\.Metric\-specific FM profiles #### Measurement fidelity\. We report normalized reconstructionR2=1−SSE/SSTR^\{2\}=1\-\\mathrm\{SSE\}/\\mathrm\{SST\}, dead\-feature fraction, realized meanL0L\_\{0\}, and the fraction of layer–scale cells satisfying the preregistered validation fidelity gate \(R2≥\.90R^\{2\}\\geq\.90and dead fraction<\.20<\.20\)\. Reconstruction quantifies how faithfully the sparse instrument preserves a representation and is interpreted alongside clinical accessibility\. #### Single\-coordinate clinical accessibility\. Train\-selected test correlation and concept coverage quantify how locally the fixed concept panel is exposed by individual sparse\-code coordinates\. Their primary role is relative model comparison under an identical selection and capacity protocol\. Joint interpretation with reconstruction fidelity connects local concept exposure to the quality of the underlying sparse decomposition\. #### Reproducibility\. Within each model, depth, and scale, we retain up to the 256 most active non\-dead decoder directions per seed according to validation firing rate\. Hungarian matching maximizes signed decoder cosine for each seed pair\. We report matched cosine above a 100\-permutation random\-pairing floor and normalized overlap between the selected decoder subspaces\. #### Common\-scale summary\. For metric curvem\(E\)m\(E\), the model profile is the normalized log\-scale area \(7\)AUCE\(m\)=1log32−log1∫log1log32m\(eu\)𝑑u,\\operatorname\{AUC\}\_\{E\}\(m\)=\\frac\{1\}\{\\log 32\-\\log 1\}\\int\_\{\\log 1\}^\{\\log 32\}m\(e^\{u\}\)\\,du,Here,EEis the SAE expansion factor, evaluated at\{1,4,8,16,32\}\\\{1,4,8,16,32\\\}, andm\(E\)m\(E\)may denote reconstructionR2R^\{2\}, single\-coordinate mean\|r\|\|r\|, concept coverage, matched decoder cosine, or selected\-subspace overlap\. We approximate the integral by trapezoidal integration over these five points inlogE\\log E\. Division bylog32−log1\\log 32\-\\log 1makesAUCE\\operatorname\{AUC\}\_\{E\}a normalized average across SAE scales\. The resulting scale summary is then averaged over the five depths and three seeds as specified by each inferential analysis\. Fidelity, single\-coordinate accessibility, coverage, and stability jointly define the model’s multiscale interpretability profile\. ### 3\.6\.Paired uncertainty and multiplicity The primary test inference resamples PTB\-XL patients with replacement 2,000 times and retains all records belonging to a sampled patient\. The sorted patient set and bootstrap seed are identical across all 450 cells, enabling paired FM differences\. BatchTopK codes are computed once in the frozen original test order with batch size 256; bootstrap weights are then applied to patient\-aggregated sufficient statistics, preserving a common encoding across all resamples\. Reconstruction uses the frozen full\-test reference mean in the SST term for every bootstrap draw\. These intervals quantify held\-out patient sampling uncertainty conditional on the frozen reference, FM and SAE weights, and train\-selected coordinates\. The three SAE seeds are averaged within each draw\. A second 10,000\-sample crossed bootstrap resamples the five depth units and three SAE seeds to quantify design variation after integrating the frozen scale curve\. Pairwise model contrasts are adjusted by Benjamini–Hochberg within each metric family\(Benjamini and Hochberg,[1995](https://arxiv.org/html/2607.27404#bib.bib25)\)\. Scale sensitivity is summarized by Kendall rank correlation between every pair of commonEEvalues\. Together, patient and design intervals characterize complementary sources of uncertainty: held\-out patient sampling and depth–seed design variation\. ### 3\.7\.Sparsity sensitivity The primary fixed\-k/dk/darm holds the absolute active budget constant while dictionary width grows\. A preregistered mid\-depth sensitivity arm instead fixesk/N=1/64k/N=1/64, givingk∈\{12,48,96,192,384\}k\\in\\\{12,48,96,192,384\\\}over the same five exact widths, six models, and three seeds\. At relative depthq=0\.5q=0\.5, this arm retains the primary training protocol and usesN=\{768,3072,6144,12288,24576\}N=\\\{768,3072,6144,12288,24576\\\}withk=N/64=\{12,48,96,192,384\}k=N/64=\\\{12,48,96,192,384\\\}\. It evaluates the stability of metric\-specific FM ordering under an alternative sparsity parameterization, with both arms and their comparison preregistered before test evaluation\. Table 1\.Final\-layer input\-harmonization audit\.Δ\\Deltavalues are changes in test mean\|r\|\|r\|from the native protocol\. Coverage is the joint\-protocol fraction of 49 concepts reaching\|r\|≥0\.20\|r\|\\geq 0\.20; CKA compares joint and native test representations\.Table 2\.MIMIC\-IV\-ECG held\-out multiscale SAE profiles\. Reconstruction, semantic alignment, and coverage are normalized expansion\-curve AUCs averaged over five relative depths\. Stability is matched decoder\-feature cosine across SAE seeds; subspace stability is normalized overlap of the selected decoder subspaces\. Higher is better except for dead\-feature fraction\. ## 4\.Results ### 4\.1\.ECG FMs have distinct depth–scale decomposition surfaces Figure[2](https://arxiv.org/html/2607.27404#S3.F2)summarizes single\-coordinate clinical accessibility at three resolutions: test depth–scale surfaces for every FM, paired patient\-bootstrap common\-scale semantic AUCs, and concept\-family profiles\. The corresponding reconstruction and dead\-feature atlases are included in Appendix[D](https://arxiv.org/html/2607.27404#A4)\. These surfaces are the primary result object: a model can localize clinical measurements more strongly at one depth while requiring a wider dictionary or exhibiting less stable atom identity elsewhere\. We therefore retain all 25 depth–scale cells per model as the prespecified multiscale evaluation surface\. Interpretability is consequently represented as a structured profile of sparse reconstructability, single\-coordinate clinical accessibility, coverage, and feature reproducibility\. Common\-scale AUC provides a capacity\-robust comparison within each axis, while the underlying depth–scale surfaces support operating\-point selection for specific analysis goals\. ### 4\.2\.Matched\-scale curves produce metric\-specific FM orderings Figure[3](https://arxiv.org/html/2607.27404#S3.F3)compares all FMs only at the sameEE\. Shaded regions are paired patient\-cluster intervals after averaging the three fixed SAE seeds and five target depths\. For reconstruction, the highest common\-scale point estimate is HuBERT\-ECG \(AUC 0\.985, 95% CI \[0\.985, 0\.985\], bootstrap rank\-1 probability 1\.000\)\. The complete reconstruction order is HuBERT\-ECG\>\>ECG\-JEPA\>\>CSFM\>\>ECG\-FM\>\>CARDIAC\-FM\>\>ST\-MEM, with 15 of 15 pairwise contrasts surviving BH correction\. Single\-coordinate clinical accessibility has a separate ordering: ECG\-JEPA\>\>ECG\-FM\>\>CARDIAC\-FM\>\>ST\-MEM\>\>HuBERT\-ECG\>\>CSFM, with 13 of 15 FM contrasts surviving BH correction\. The matched model\-level profile is complemented by substantial concept\-level resolution: for ECG\-JEPA, the 49 concept\-specific common\-scale AUCs have median 0\.406 and interquartile range 0\.250–0\.442; 26 concepts reach at least 0\.40, eight reach at least 0\.50, and four reach at least 0\.60\. Ventricular rate, QRS duration, P\-wave detection, and mean RR are among the most locally accessible concepts\. Concept coverage similarly orders the models as CARDIAC\-FM\>\>ECG\-FM\>\>ECG\-JEPA\>\>ST\-MEM\>\>HuBERT\-ECG\>\>CSFM, with 13 BH\-significant pairwise contrasts\. Exact common\-scale AUC estimates and paired confidence intervals are provided in Appendix Table[S1](https://arxiv.org/html/2607.27404#A1.T1)\. Appendix[E](https://arxiv.org/html/2607.27404#A5)reports the MIMIC\-IV\-ECG replication, preserving metric\-specific leaders\. Table[1](https://arxiv.org/html/2607.27404#S3.T1)summarizes the final\-layer input\-harmonization audit detailed in Appendix[F](https://arxiv.org/html/2607.27404#A6); the six\-model accessibility order is preserved under the harmonized protocols\. Figure 4\.Metric\-specific common\-scale AUC estimates and paired patient\-cluster intervals for \(a\) reconstruction, \(b\) single\-coordinate clinical accessibility, and \(c\) concept coverage\. A higher value is favorable within each panel, and the panels jointly characterize complementary dimensions of representation interpretability\.Three forest plots compare six ECG foundation models on reconstruction, single\-coordinate clinical accessibility, and concept coverage after integrating the same five SAE scales\. ### 4\.3\.External validation preserves metric\-specific leaders We repeated the complete 450\-cell multiscale SAE audit on a credentialed, patient\-partitioned MIMIC\-IV\-ECG cohort; cohort construction and sensitivity analyses are detailed in Appendix[E](https://arxiv.org/html/2607.27404#A5)\. Table[2](https://arxiv.org/html/2607.27404#S3.T2)reports the held\-out model profiles after integrating the same five\-point expansion curve and averaging over the same five relative depths\. The replication reveals complementary leaders across interpretability dimensions\. HuBERT\-ECG has the highest reconstruction profile \(0\.990\), whereas ECG\-JEPA has the highest single\-feature semantic alignment \(0\.324\) and concept coverage \(0\.781\)\. ECG\-FM has the lowest dead\-feature fraction \(0\.099\) and the highest feature stability \(0\.378\), while CSFM has the highest subspace stability \(0\.778\)\. Together, reconstruction fidelity, local clinical accessibility, dictionary utilization, and cross\-seed reproducibility provide a multidimensional comparison of the six models\. ### 4\.4\.A calibration ladder separates availability from localization Detailed calibration results are provided in Appendix Table[S2](https://arxiv.org/html/2607.27404#A2.T2)\. The full SAE retains 79\.9–87\.4% of dense\-ridge mean\|r\|\|r\|\. Single SAE coordinates outperform the mean of 20 matched random dictionaries by 0\.034–0\.088 across every model’s five depths, with 78\.8–87\.8% concept–depth wins\. These held\-out results demonstrate consistent recovery of clinically aligned sparse structure by the learned SAE dictionaries across all six ECG FMs\. This calibration connects distributed concept availability with sparse localization\. Full\-code readouts quantify preserved clinical information, and single\-coordinate readouts identify aligned sparse features across all six FMs\. Together, these readouts establish the SAE profile as a common sparse instrument for comparing FMs\. The single\-coordinate profile quantifies how strongly each clinical measurement is localized to one train\-selected SAE coordinate and retained under held\-out evaluation\. Its 49\-concept macro\-average supports standardized model\-level comparison, while the concept\-level distribution reveals a substantial high\-accessibility subset and resolves differences across waveform measurements\. Together, these views provide both a common summary and concept\-specific resolution of sparse clinical accessibility\. ### 4\.5\.Rank stability is itself a benchmark result Rank stability across SAE capacities is quantified over all ten pairs of commonEEvalues\. Reconstruction rank agreement has median Kendallτ=1\.00\\tau=1\.00and minimumτ=1\.00\\tau=1\.00; single\-coordinate accessibility has medianτ=0\.73\\tau=0\.73and minimumτ=0\.73\\tau=0\.73; coverage has medianτ=0\.73\\tau=0\.73and minimumτ=0\.60\\tau=0\.60\. Figure[4](https://arxiv.org/html/2607.27404#S4.F4)presents common\-scale AUC as a capacity\-robust summary, complemented by full curves for decisions tied to a particular SAE budget\. Rank agreement acrossEEdirectly tests whether an FM conclusion survives measurement capacity\. The shared expansion grid provides a capacity\-aware assessment of FM ordering under a common evaluation protocol\. The current atlas also matches absolute width because every audited layer hasd=768d=768\.   Figure 5\.Robustness axes\. \(a\) Cross\-seed decoder matching above random and \(b\) selected\-subspace overlap over common scale\. Panels \(c\)–\(e\) show mid\-depth common\-scale AUC for reconstruction, clinical accessibility, and concept coverage under fixedk/dk/dand fixedk/Nk/N; the diagonal denotes unchanged profiles\.Five equal\-size panels show feature stability curves and sparsity\-sensitivity scatter plots for six models, with a separate legend below the panels\. ### 4\.6\.Feature identity and sparse fidelity are different axes Cross\-seed matching asks whether a favorable fidelity or accessibility profile is implemented by reproducible decoder directions\. The highest above\-random matched\-cosine AUC belongs to ECG\-FM \(0\.371\), whereas the highest selected\-subspace overlap AUC belongs to CSFM \(0\.757\)\. Figure[5](https://arxiv.org/html/2607.27404#S4.F5)\(a\)–\(b\) shows how both quantities change over common scale\. Joint reporting of stability, reconstruction, and single\-coordinate clinical accessibility captures complementary representation properties\. Feature\-level matching and selected\-subspace overlap resolve two complementary forms of reproducibility across SAE seeds\. ### 4\.7\.Model ordering is tested under a second sparsity parameterization To isolate the effect of the active\-code budget, we compare the primary fixed\-k/dk/darm with a preregistered fixed\-k/Nk/Narm at relative depthq=0\.5q=0\.5\. Becaused=768d=768, the primary arm usesk=96k=96at everyEE, whereas the sensitivity arm usesk=\{12,48,96,192,384\}k=\\\{12,48,96,192,384\\\}forE=\{1,4,8,16,32\}E=\\\{1,4,8,16,32\\\}; dictionary widths, models, seeds, and training settings remain matched\. Reconstruction ordering is highly stable across the two arms \(median/minimum Kendallτ=1\.00/0\.87\\tau=1\.00/0\.87\), while accessibility \(0\.73/0\.600\.73/0\.60\) and coverage \(0\.87/0\.470\.87/0\.47\) respond more to the active budget, with the largest coverage reordering atE=16E=16\. Relative to fixed\-k/dk/d, fixed\-k/Nk/Nchanges common\-scale AUC by−0\.012\-0\.012to−0\.042\-0\.042for reconstruction,−0\.004\-0\.004to−0\.014\-0\.014for accessibility, and−0\.027\-0\.027to\+0\.016\+0\.016for coverage\. At the sharedE=8E=8anchor, both arms useN=6144,k=96N=6144,k=96, and independently trained cells differ by at most0\.02720\.0272\. Figure[5](https://arxiv.org/html/2607.27404#S4.F5)\(c\)–\(e\) displays the corresponding model\-level profiles\. ## 5\.Limitations and Claim Boundary First,the current benchmark covers six representative ECG foundation models spanning a diverse set of encoder architectures and pretraining objectives\. Although this collection enables controlled comparisons across these models, future versions could incorporate newly released ECG foundation models and additional model scales to further broaden the benchmark\. Second,the clinical concept inventory emphasizes waveform measurements and diagnostic concepts that can be evaluated consistently across models and cohorts\. Extending the inventory to finer\-grained morphological patterns, continuous physiological attributes, longitudinal changes, and expert\-annotated concepts could provide a more comprehensive view of representation interpretability\. Third,ECG\-InterpBench uses a standardized SAE capacity and sparsity grid to ensure matched comparisons across encoders\. Future work could evaluate finer\-grained capacity ranges, alternative sparsity objectives, and additional dictionary\-learning methods while preserving the same capacity\-controlled evaluation protocol\. These extensions would also facilitate adaptation of the benchmark to foundation models for EEG, medical imaging, electronic health records, and other clinical modalities\. Throughout, ECG\-InterpBench characterizes the structure of frozen model representations under a matched SAE protocol; it does not establish physiological mechanisms, clinical utility, or prospective patient outcomes\. The reported model orderings are therefore specific to the evaluated representation properties and should not be interpreted as rankings of diagnostic performance or overall clinical value\. ## 6\.Conclusion ECG\-InterpBench uses a calibrated multi\-scale SAE family to audit and compare ECG foundation\-model representations\. Its core unit is an exact six\-model matched block\. The resulting depth–scale profiles, paired patient inference, seed stability, sparsity sensitivity, and dense\-to\-single calibration distinguish faithful sparse reconstruction, distributed concept availability, single\-coordinate accessibility, and reproducible feature identity\. This design turns ECG\-FM interpretability into a systematic and reproducible model\-comparison problem\. More broadly, ECG\-InterpBench provides a general framework for identifying where, at what capacity, and how consistently clinically meaningful structure emerges within foundation\-model representations\. By connecting representation geometry with clinical concepts across models and scales, it establishes a foundation for the principled development and selection of interpretable ECG foundation models\. The same capacity\-controlled auditing framework can be extended to other clinical foundation models, including those for medical imaging, electroencephalography, electronic health records, physiological time series, and multimodal patient data\. With modality\-specific clinical concepts and matched representation interfaces, this framework can support systematic interpretability comparisons across a broader range of medical AI systems\. ## 7\.Ethics and Responsible Use All analyses use de\-identified secondary ECG datasets under their respective licenses and data\-access agreements\. No new participants were recruited, and no clinical intervention was performed\. PTB\-XL provides the directly accessible public reproduction path for the benchmark, while MIMIC\-IV\-ECG is a publicly available dataset that requires credentialed access through an application and approval process\. Released artifacts exclude restricted waveforms, protected metadata, and record\-level MIMIC identifiers\. ECG\-InterpBench is a research benchmark for evaluating the representation\-level interpretability of ECG foundation models\. Its outputs are not intended for direct use in diagnosis, treatment, patient management, or other clinical decision\-making settings\. The accompanying artifact includes executable evaluation code, standardized manifests, aggregate and configuration\-level metrics, fixed random and bootstrap seeds, audit outputs, and figure\-generation scripts\. The public PTB\-XL workflow supports end\-to\-end reproducible evaluation, while the MIMIC\-IV\-ECG analysis provides an additional reproduction path for approved credentialed users\. Model weights and source datasets remain governed by their original repositories, licenses, and access requirements\. ## References - J\. Adebayo, J\. Gilmer, M\. Muelly, I\. Goodfellow, M\. Hardt, and B\. Kim \(2018\)Sanity checks for saliency maps\.InAdvances in Neural Information Processing Systems,Vol\.31\.External Links:[Link](https://arxiv.org/abs/1810.03292)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p2.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p2.1)\. - Z\. I\. Attia, S\. Kapa, F\. Lopez\-Jimenez, P\. M\. McKie, D\. J\. Ladewig, G\. Satam, P\. A\. Pellikka, M\. Enriquez\-Sarano, P\. A\. Noseworthy, T\. M\. Munger, S\. J\. Asirvatham, C\. G\. Scott, R\. E\. Carter, and P\. A\. Friedman \(2019\)Screening for cardiac contractile dysfunction using an artificial intelligence\-enabled electrocardiogram\.Nature Medicine25,pp\. 70–74\.External Links:[Document](https://dx.doi.org/10.1038/s41591-018-0240-2)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - N\. Belrose, D\. Schneider\-Joseph, S\. Ravfogel, R\. Cotterell, E\. Raff, and S\. Biderman \(2023\)LEACE: perfect linear concept erasure in closed form\.InAdvances in Neural Information Processing Systems,Vol\.36\.External Links:[Link](https://arxiv.org/abs/2306.03819)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - Y\. Benjamini and Y\. Hochberg \(1995\)Controlling the false discovery rate: a practical and powerful approach to multiple testing\.Journal of the Royal Statistical Society: Series B \(Methodological\)57\(1\),pp\. 289–300\.External Links:[Document](https://dx.doi.org/10.1111/j.2517-6161.1995.tb02031.x)Cited by:[§3\.6](https://arxiv.org/html/2607.27404#S3.SS6.p2.1)\. - T\. Bricken, A\. Templeton, J\. Batson, B\. Chen, A\. Jermyn, T\. Conerly, N\. Turner, C\. Anil, C\. Denison, A\. Askell,et al\.\(2023\)Towards monosemanticity: decomposing language models with dictionary learning\.Transformer Circuits Thread\.External Links:[Link](https://transformer-circuits.pub/2023/monosemantic-features/index.html)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - B\. Bussmann, P\. Leask, and N\. Nanda \(2024\)BatchTopK sparse autoencoders\.arXiv preprint arXiv:2412\.06410\.External Links:[Link](https://arxiv.org/abs/2412.06410)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - E\. Coppola, M\. Savardi, M\. Massussi, M\. Adamo, M\. Metra, and A\. Signoroni \(2024\)HuBERT\-ECG as a self\-supervised foundation model for broad and scalable cardiac applications\.medRxiv\.External Links:[Document](https://dx.doi.org/10.1101/2024.11.14.24317328)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - H\. Cunningham, A\. Ewart, L\. Riggs, R\. Huben, and L\. Sharkey \(2024\)Sparse autoencoders find highly interpretable features in language models\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=F76bwRSLeK)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - L\. Gao, T\. Dupré la Tour, H\. Tillman, G\. Goh, R\. Troll, A\. Radford, I\. Sutskever, J\. Leike, and J\. Wu \(2025\)Scaling and evaluating sparse autoencoders\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=tcsZt9ZNKD)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p2.1)\. - M\. Ghassemi, L\. Oakden\-Rayner, and A\. L\. Beam \(2021\)The false hope of current approaches to explainable artificial intelligence in health care\.The Lancet Digital Health3\(11\),pp\. e745–e750\.External Links:[Document](https://dx.doi.org/10.1016/S2589-7500%2821%2900208-9)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - B\. Gow, T\. Pollard, L\. A\. Nathanson, A\. Johnson, B\. Moody, C\. Fernandes, N\. Greenbaum, J\. W\. Waks, P\. Eslami, T\. Carbonati,et al\.\(2023\)Cited by:[Appendix E](https://arxiv.org/html/2607.27404#A5.p1.3)\. - X\. Gu, W\. Tang, J\. Han, V\. Sangha, F\. Liu, S\. N\. Gowda, A\. H\. Ribeiro, P\. Schwab, K\. Branson, L\. Clifton,et al\.\(2026\)Cardiac health assessment across scenarios and devices using a multimodal foundation model pretrained on data from 1\.7 million individuals\.Nature Machine Intelligence8\(2\),pp\. 220–233\.External Links:[Document](https://dx.doi.org/10.1038/s42256-026-01180-5)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - A\. Y\. Hannun, P\. Rajpurkar, M\. Haghpanahi, G\. H\. Tison, C\. Bourn, M\. P\. Turakhia, and A\. Y\. Ng \(2019\)Cardiologist\-level arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network\.Nature Medicine25,pp\. 65–69\.External Links:[Document](https://dx.doi.org/10.1038/s41591-018-0268-3)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - N\. Jethani, M\. Sudarshan, Y\. Aphinyanaphongs, and R\. Ranganath \(2023\)Have we learned to explain?: how interpretability methods can learn to encode predictions in their interpretations\.InProceedings of the 26th International Conference on Artificial Intelligence and Statistics,Proceedings of Machine Learning Research, Vol\.206,pp\. 1459–1491\.External Links:[Link](https://proceedings.mlr.press/v206/jethani23a.html)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p2.1)\. - A\. Karvonen, C\. Rager, J\. Lin, C\. Tigges, J\. Bloom, D\. Chanin, Y\. Lau, E\. Farrell, C\. McDougall, K\. Ayonrinde, M\. Wearden, A\. Conmy, S\. Marks, and N\. Nanda \(2025\)SAEBench: a comprehensive benchmark for sparse autoencoders in language model interpretability\.arXiv preprint arXiv:2503\.09532\.External Links:[Link](https://arxiv.org/abs/2503.09532)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p2.1)\. - B\. Kim, M\. Wattenberg, J\. Gilmer, C\. Cai, J\. Wexler, F\. Viégas, and R\. Sayres \(2018\)Interpretability beyond feature attribution: quantitative testing with concept activation vectors \(TCAV\)\.InProceedings of the 35th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.80,pp\. 2668–2677\.External Links:[Link](https://proceedings.mlr.press/v80/kim18d.html)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - S\. Kim \(2024\)Learning general representation of 12\-lead electrocardiogram with a joint\-embedding predictive architecture\.arXiv preprint arXiv:2410\.08559\.External Links:[Link](https://arxiv.org/abs/2410.08559)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - D\. Kiyasseh, T\. Zhu, and D\. A\. Clifton \(2021\)CLOCS: contrastive learning of cardiac signals across space, time, and patients\.InProceedings of the 38th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.139,pp\. 5606–5615\.External Links:[Link](https://proceedings.mlr.press/v139/kiyasseh21a.html)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - P\. W\. Koh, T\. Nguyen, Y\. S\. Tang, S\. Mussmann, E\. Pierson, B\. Kim, and P\. Liang \(2020\)Concept bottleneck models\.InProceedings of the 37th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.119,pp\. 5338–5348\.External Links:[Link](https://proceedings.mlr.press/v119/koh20a.html)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - W\. Lehn\-Schiøler, M\. R\. Kjær, R\. Thapa, M\. G\. Pedersen, A\. Storgaard Mosquera, N\. Williams, R\. Gatej, T\. Lehn\-Schiøler, A\. Brink\-Kjær, S\. Puthusserypady, S\. Beniczky, J\. Zou, and L\. K\. Hansen \(2026\)Mechanistic interpretability of EEG foundation models via sparse autoencoders\.arXiv preprint arXiv:2605\.13930\.External Links:[Link](https://arxiv.org/abs/2605.13930)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p2.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p2.1)\. - F\. Li, S\. Li, Y\. Qian, B\. Chen, J\. A\. Brody, V\. Yogeswaran, K\. L\. Wiggins, C\. M\. Sitlani, J\. C\. Bis, A\. Shojaie,et al\.\(2026\)CARDIAC\-FM: a multimodal foundation model for cardiovascular risk prediction using ECG and cardiac MRI\.medRxiv\.External Links:[Document](https://dx.doi.org/10.64898/2026.03.16.26348526)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - T\. Lieberum, S\. Rajamanoharan, A\. Conmy, L\. Smith, N\. Sonnerat, V\. Varma, J\. Kramár, A\. Dragan, R\. Shah, and N\. Nanda \(2024\)Gemma Scope: open sparse autoencoders everywhere all at once on Gemma 2\.arXiv preprint arXiv:2408\.05147\.External Links:[Link](https://arxiv.org/abs/2408.05147)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - J\. Mairal, F\. Bach, J\. Ponce, and G\. Sapiro \(2009\)Online dictionary learning for sparse coding\.InProceedings of the 26th International Conference on Machine Learning,pp\. 689–696\.External Links:[Document](https://dx.doi.org/10.1145/1553374.1553463)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - A\. Makelov, G\. Lange, and N\. Nanda \(2025\)Towards principled evaluations of sparse autoencoders for interpretability and control\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=1Njl73JKjB)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - K\. McKeenet al\.\(2025\)ECG\-FM: an open electrocardiogram foundation model\.JAMIA Open8\(5\),pp\. ooaf122\.External Links:[Document](https://dx.doi.org/10.1093/jamiaopen/ooaf122)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - T\. Mehari and N\. Strodthoff \(2022\)Self\-supervised representation learning from 12\-lead ECG data\.Computers in Biology and Medicine141,pp\. 105114\.External Links:[Document](https://dx.doi.org/10.1016/j.compbiomed.2021.105114)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - W\. J\. Murdoch, C\. Singh, K\. Kumbier, R\. Abbasi\-Asl, and B\. Yu \(2019\)Definitions, methods, and applications in interpretable machine learning\.Proceedings of the National Academy of Sciences116\(44\),pp\. 22071–22080\.External Links:[Document](https://dx.doi.org/10.1073/pnas.1900654116)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p2.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - Y\. Na, M\. Park, Y\. Tae, and S\. Joo \(2024\)Guiding masked representation learning to capture spatio\-temporal relationship of electrocardiogram\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=WcOohbsF4H)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p2.1)\. - B\. A\. Olshausen and D\. J\. Field \(1997\)Sparse coding with an overcomplete basis set: a strategy employed by V1?\.Vision Research37\(23\),pp\. 3311–3325\.External Links:[Document](https://dx.doi.org/10.1016/S0042-6989%2897%2900169-7)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - A\. H\. Ribeiro, M\. H\. Ribeiro, G\. M\. M\. Paixão, D\. M\. Oliveira, P\. R\. Gomes, J\. A\. Canazart, M\. P\. S\. Ferreira, C\. R\. Andersson, P\. W\. Macfarlane, W\. Meira, T\. B\. Schön, and A\. L\. P\. Ribeiro \(2020\)Automatic diagnosis of the 12\-lead ECG using a deep neural network\.Nature Communications11,pp\. 1760\.External Links:[Document](https://dx.doi.org/10.1038/s41467-020-15432-4)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - C\. Rudin \(2019\)Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead\.Nature Machine Intelligence1,pp\. 206–215\.External Links:[Document](https://dx.doi.org/10.1038/s42256-019-0048-x)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - E\. Simon and J\. Zou \(2025\)InterPLM: discovering interpretable features in protein language models via sparse autoencoders\.Nature Methods\.External Links:[Document](https://dx.doi.org/10.1038/s41592-025-02836-7)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - N\. Strodthoff and C\. Strodthoff \(2019\)Detecting and interpreting myocardial infarction using fully convolutional neural networks\.Physiological Measurement40\(1\),pp\. 015001\.External Links:[Document](https://dx.doi.org/10.1088/1361-6579/aaf34d)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p2.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - N\. Strodthoff, P\. Wagner, T\. Schaeffter, and W\. Samek \(2021\)Deep learning for ECG analysis: benchmarks and insights from PTB\-XL\.IEEE Journal of Biomedical and Health Informatics25\(5\),pp\. 1519–1528\.External Links:[Document](https://dx.doi.org/10.1109/JBHI.2020.3022989)Cited by:[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - A\. Templetonet al\.\(2024\)Scaling monosemanticity: extracting interpretable features from Claude 3 Sonnet\.Transformer Circuits Thread\.External Links:[Link](https://transformer-circuits.pub/2024/scaling-monosemanticity/index.html)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p3.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px2.p1.1)\. - S\. Tonekaboni, S\. Joshi, M\. D\. McCradden, and A\. Goldenberg \(2019\)What clinicians want: contextualizing explainable machine learning for clinical end use\.InProceedings of the 4th Machine Learning for Healthcare Conference,Proceedings of Machine Learning Research, Vol\.106,pp\. 359–380\.External Links:[Link](https://proceedings.mlr.press/v106/tonekaboni19a.html)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px3.p1.1)\. - A\. Vaidet al\.\(2023\)A foundational vision transformer improves diagnostic performance for electrocardiograms\.npj Digital Medicine6,pp\. 108\.External Links:[Document](https://dx.doi.org/10.1038/s41746-023-00840-9)Cited by:[§1](https://arxiv.org/html/2607.27404#S1.p1.1),[§2](https://arxiv.org/html/2607.27404#S2.SS0.SSS0.Px1.p1.1)\. - P\. Wagner, N\. Strodthoff, R\. Bousseljot, D\. Kreiseler, F\. I\. Lunze, W\. Samek, and T\. Schaeffter \(2020\)PTB\-XL, a large publicly available electrocardiography dataset\.Scientific Data7,pp\. 154\.External Links:[Document](https://dx.doi.org/10.1038/s41597-020-0495-6)Cited by:[§3\.1](https://arxiv.org/html/2607.27404#S3.SS1.p1.1)\. ## Appendix ACommon\-Scale Model Profiles Table[S1](https://arxiv.org/html/2607.27404#A1.T1)reports the exact model\-level common\-scale AUC estimates and paired patient\-cluster confidence intervals underlying the visual comparison in Figure[4](https://arxiv.org/html/2607.27404#S4.F4)\. Table S1\.Common\-five\-scale model profiles with paired patient\-cluster 95% intervals\. The semantic column reports the train\-selected single\-coordinate\|r\|\|r\|AUC defined in Section[3](https://arxiv.org/html/2607.27404#S3)\. Each AUC integrates the sameE∈\{1,4,8,16,32\}E\\in\\\{1,4,8,16,32\\\}support and averages the same five depth targets and three SAE seeds\. ## Appendix BFixed\-Scale Accessibility Calibration Table[S2](https://arxiv.org/html/2607.27404#A2.T2)reports the complete held\-out calibration that compares distributed ridge readouts with increasingly localized SAE, native\-coordinate, and random\-coordinate readouts at the commonE=8E=8scale\. Table S2\.Held\-outE=8E=8accessibility calibration over five depths and 49 concepts\. Ridge columns report mean\|r\|\|r\|\. One\-dimensional entries report mean\|r\|\|r\|/coverage at\|r\|≥\.20\|r\|\\geq\.20; SAE values average three seeds and random values average 20 dictionaries\. All coordinates are selected on training data only\. ## Appendix CFrozen Source\-Layer Interfaces Table[S3](https://arxiv.org/html/2607.27404#A3.T3)defines the representation\-extraction contract used throughout the benchmark\. Each released checkpoint is frozen and evaluated through its native lead selection, temporal resolution, and tokenization path\. The models consequently receive inputs ranging from eight to twelve leads and from 2,250 to 5,000 samples, while the audited states are taken before any model\-specific downstream projection that would change the source width\. Preserving these interfaces measures the representations available under realistic model use rather than introducing an untrained common tokenizer\. Table S3\.Frozen source\-layer interfaces\. The benchmark preserves each released ECG input path while matching the analyzed layer width\. “Layers” counts available audited states, including the indexed boundary states used by the released extraction code\.The shared audited widthd=768d=768permits exact capacity matching: the five expansion factors correspond to absolute dictionary widthsN∈\{768,3072,6144,12288,24576\}N\\in\\\{768,3072,6144,12288,24576\\\}, with the primary active budget fixed atk=96k=96\. Relative depth maps the six available CSFM states and the twelve states exposed by each other encoder onto the same five index positions, providing a common coordinate over each encoder trajectory\. Table[S3](https://arxiv.org/html/2607.27404#A3.T3)specifies the resulting representation interfaces, and Appendix[F](https://arxiv.org/html/2607.27404#A6)tests how heterogeneous waveform interfaces affect the final\-layer model ordering\. ## Appendix DAdditional Depth–Scale Atlases Figures[A1](https://arxiv.org/html/2607.27404#A4.F1)and[A2](https://arxiv.org/html/2607.27404#A4.F2)expose the two validation fidelity diagnostics for all 150 model–depth–scale configurations underlying the 450 trained SAE cells\. Each heatmap cell averages the three fixed SAE seeds, and each metric uses one shared color scale across all six models\. These complete surfaces complement the clinical\-accessibility atlas in Figure[2](https://arxiv.org/html/2607.27404#S3.F2)and prevent a favorable depth or dictionary width from being selected in isolation\. Figure A1\.Validation reconstructionR2R^\{2\}over the complete matched depth–scale atlas\.Six heatmaps show sparse\-autoencoder reconstruction over five relative depths and five exactly matched expansion factors\.Reconstruction remains high overall but does not improve monotonically with dictionary width under the fixedk=96k=96budget\. Averaged descriptively over all models, depths, and seeds, validationR2R^\{2\}is 0\.968, 0\.953, 0\.949, 0\.947, and 0\.948 forE=1,4,8,16,E=1,4,8,16,and 32, respectively\. The model\-averaged profiles range from 0\.918 for ST\-MEM to 0\.986 for HuBERT\-ECG, while the depth average falls from 0\.978 at the initial state to approximately 0\.937 at relative depths 0\.5–0\.75 before reaching 0\.962 at the final state\. Thus additional dictionary coordinates do not substitute for model\- and depth\-specific reconstruction structure when the active\-code budget is held constant\. Figure A2\.Validation dead\-feature fraction over the complete matched depth–scale atlas\.Six heatmaps show dead\-feature fractions over five relative depths and five exactly matched expansion factors\.Dictionary utilization changes much more strongly with scale\. The corresponding mean dead\-feature fractions are 0\.019, 0\.042, 0\.127, 0\.338, and 0\.604 fromE=1E=1throughE=32E=32\. Model\-level averages range from 0\.137 for ECG\-FM to 0\.337 for HuBERT\-ECG, and the initial\-state average \(0\.388\) is substantially higher than the averages near relative depths 0\.5 and 0\.75 \(0\.156 and 0\.158\)\. HuBERT\-ECG therefore combines the highest descriptive reconstruction average with the highest dead\-feature average, directly illustrating that sparse fidelity and dictionary utilization are distinct properties\. Reconstruction, dead\-feature fraction, and the preregistered validation fidelity gate jointly characterize operating points across the complete dictionary\-width curve\. ## Appendix ECredentialed MIMIC\-IV\-ECG Replication We repeated the multiscale SAE audit on the credentialed MIMIC\-IV\-ECG cohort\(Gowet al\.,[2023](https://arxiv.org/html/2607.27404#bib.bib23)\)\. The fixed manifest contains 100,000 ECGs from 48,491 patients, partitioned by patient into 70,260 training, 9,768 validation, and 19,972 test records; 54,591 records have complete waveform\-derived measurements\. Source waveforms and identifiers remain in the credentialed environment\. The replication uses the same six frozen encoders, relative depths\{0,\.25,\.5,\.75,1\}\\\{0,\.25,\.5,\.75,1\\\}, expansion factorsE∈\{1,4,8,16,32\}E\\in\\\{1,4,8,16,32\\\},k=96k=96, three SAE seeds, and 8,000 training steps as the primary benchmark, for 450 completed SAE cells\. For this SAE\-only analysis, semantic alignment and coverage use seven continuous waveform concepts: heart rate, QRS duration, PR interval, a QT\-like interval, and global R\-, ST\-, and T\-amplitude measurements\. The model\-level held\-out profiles are reported in Table[2](https://arxiv.org/html/2607.27404#S3.T2); this appendix provides the cohort, uncertainty, and scale–depth sensitivity details\. Patient\-cluster uncertainty uses 2,000 test\-set bootstrap draws over 6,609 patients, retaining all ECGs from each sampled patient\. The leading profiles are precise: HuBERT\-ECG reconstruction is 0\.9905 \(95% CI 0\.9904–0\.9906\), while ECG\-JEPA semantic alignment is 0\.3244 \(0\.3190–0\.3299\) and coverage is 0\.7810 \(0\.7400–0\.8057\)\. The intervals quantify patient\-sampling uncertainty conditional on the frozen encoders, trained SAEs, and training\-selected coordinates\. The aggregate sensitivity analysis in Table[S4](https://arxiv.org/html/2607.27404#A5.T4)demonstrates the resolution gained from a multiscale, multidepth audit\. Across expansion factors, reconstruction remains near 0\.97, semantic alignment is highest atE=1E=1, and the dead\-feature fraction traces dictionary utilization from 0\.032 atE=1E=1to 0\.636 atE=32E=32\. Across depth, semantic alignment is highest near relative depth 0\.5 and coverage peaks near 0\.75\. These profiles show how MIMIC representation properties vary jointly with SAE capacity and encoder depth\. Table S4\.MIMIC\-IV\-ECG scale and depth sensitivity, aggregated across the six models\. Expansion rows average over five depths; depth rows average over five expansions\. All rows average the three SAE seeds\.Matched decoder features vary across seeds \(model\-level stability AUC 0\.293–0\.378\), whereas their selected subspaces are more reproducible \(overlap AUC 0\.702–0\.778\)\. This distinction identifies the selected subspace as the more stable unit for cross\-seed interpretation and supports model\-level conclusions about reproducible representation structure\. The release audit passes all requirements with 450/450 SAE cells and no missing matched depth–scale block\. Together, these results provide a complete credentialed\-cohort replication of the benchmark profile\. ## Appendix FInput\-Interface Harmonization Audit The primary benchmark preserves each released model’s input interface to reflect realistic use, but this choice could confound encoder differences with lead selection, sampling, or windowing\. We therefore repeated final\-layer dense\-coordinate accessibility under four protocols on the same 21,799 PTB\-XL records and patient split\.*Native*retains each released interface\.*Lead*supplies the common independent leads I, II, and V1–V6 and reconstructs the dependent limb leads for 12\-lead models usingIII=II−I\\mathrm\{III\}=\\mathrm\{II\}\-\\mathrm\{I\},aVR=−\(I\+II\)/2\\mathrm\{aVR\}=\-\(\\mathrm\{I\}\+\\mathrm\{II\}\)/2,aVL=I−II/2\\mathrm\{aVL\}=\\mathrm\{I\}\-\\mathrm\{II\}/2, andaVF=II−I/2\\mathrm\{aVF\}=\\mathrm\{II\}\-\\mathrm\{I\}/2\.*Temporal*maps the complete 10\-second waveform to a common 250\-Hz, 2,500\-point grid before adapting its length to each checkpoint\.*Joint*applies both transformations\. All harmonized waveforms are constructed in physical units and standardized per lead\. Tokenizers, patch embeddings, and pretrained weights remain model\-native; this is therefore a waveform\-harmonized, tokenizer\-native audit rather than a shared\-tokenizer experiment\. For each of 49 waveform concepts, the best dense coordinate and its sign are selected only on a fixed 4,096\-record subset of the training split\. Mean absolute correlation and coverage at\|r\|≥0\.20\|r\|\\geq 0\.20are then evaluated without reselection on 3,325 patient\-disjoint test records\. We additionally compare each harmonized representation with its native counterpart using linear CKA\. Uncertainty uses 2,000 patient\-cluster bootstrap draws, with Benjamini–Hochberg correction applied across the 18 model\-level comparisons and, separately, across all concept\-level comparisons\. The model\-level results are reported in Table[1](https://arxiv.org/html/2607.27404#S3.T1)\. Figure A3\.Final\-layer accessibility under native, lead\-harmonized, temporal\-harmonized, and jointly harmonized inputs\. Left: test mean absolute correlation after training\-only coordinate selection\. Center: concept coverage at\|r\|≥0\.20\|r\|\\geq 0\.20\. Right: linear CKA between each harmonized representation and its native counterpart\.Three grouped bar charts compare six ECG foundation models under four input protocols\. Lead harmonization leaves accessibility and representations nearly unchanged\. Temporal and joint harmonization modestly lower accessibility for CARDIAC\-FM and ECG\-FM and produce the largest representation change for ST\-MEM\.Lead harmonization preserves mean\|r\|\|r\|within 0\.0006 and achieves lead\-to\-native CKA of at least 0\.9999\. Temporal harmonization yields changes ofΔ=−0\.0058\\Delta=\-0\.0058for CARDIAC\-FM \(95% CI\[−0\.0095,−0\.0022\]\[\-0\.0095,\-0\.0022\],q=0\.016q=0\.016\),Δ=−0\.0048\\Delta=\-0\.0048for ECG\-FM \(95% CI\[−0\.0083,−0\.0013\]\[\-0\.0083,\-0\.0013\],q=0\.016q=0\.016\), andΔ=−0\.0131\\Delta=\-0\.0131for ST\-MEM \(95% CI\[−0\.0196,−0\.0067\]\[\-0\.0196,\-0\.0067\],q=0\.009q=0\.009\)\. The nearly identical joint and temporal effects identify time\-grid and window handling as the source of the measurable changes\. ST\-MEM’s joint CKA of 0\.770 reflects the contrast between its native centered 9\-second crop and the harmonized complete 10\-second record mapped to 2,250 input points\. Model\-level coverage is stable after FDR correction \(allq=1\.0q=1\.0\), and the six\-model ordering by mean accessibility is identical under every protocol \(Spearmanρ=1\.0\\rho=1\.0; Kendallτ=1\.0\\tau=1\.0\)\. Coverage ordering is also stable \(Spearmanρ=0\.971\\rho=0\.971for temporal and joint\)\. ECG\-JEPA and HuBERT\-ECG mean differences range from3\.5×10−53\.5\\times 10^\{\-5\}to5\.7×10−45\.7\\times 10^\{\-4\}, further demonstrating the close agreement between native and harmonized accessibility profiles\. Overall, the stable ordering across all four input protocols indicates that the observed cross\-model differences primarily reflect encoder\-representation structure\. Lead harmonization has negligible effect, and temporal harmonization preserves the ordering across models\. This audit strengthens the attribution of the benchmark profiles to the learned representations\. ## Appendix GValidation\-Matched SAE–Dense Intervention Selectivity The accessibility analyses ask whether a concept can be read from one coordinate\. We additionally test whether a sparse coordinate can change a frozen concept readout with less spillover than a native dense coordinate\. This is a final\-layer, matched\-effect comparison over the same 49 waveform concepts\. Both methods receive 768 candidate coordinates: the native FM dimensions for Dense and a fixed, target\-independent 768\-coordinate subset of theE=8E=8dictionary for SAE\. For each concept, the top five coordinates and the high\-concept centroid are selected using training data only\. Intervention doses are then calibrated on validation data to a common achievable target\-readout change, capped at\+0\.25\+0\.25standard deviations, with a minimum feasible change of0\.050\.05and interpolation coefficient at most one\. Features, centroids, and doses are frozen before patient\-disjoint test evaluation\. The SAE arm uses three training seeds and 20 fixed candidate subsets per seed\. Primary inference requires a concept to pass the validation effect gate for all three seeds; failed concepts remain in the fixed denominator and are not replaced\. The two primary endpoints are cross\-family off\-target root mean square change and the corresponding wrong\-behavior index \(WBI\), defined as off\-target RMS divided by the absolute target effect\. Lower values indicate a more selective intervention\. Confidence intervals and two\-sided tests use 2,000 paired patient\-cluster bootstrap draws, followed by Benjamini–Hochberg correction over the preregistered metric families\. Table S5\.Final\-layer matched\-effect comparison atk=5k=5across the five models satisfying the all\-seed validation gate\. The eligibility countnnrequires all three SAE seeds to pass the gate\. WBI and deltas are measured on the patient\-disjoint test split; negative SAE–Dense deltas favor SAE\.Figure A4\.SAE–Dense differences in cross\-family off\-target RMS and WBI with paired patient\-cluster 95% confidence intervals\. Negative values favor SAE; model labels give the number of concepts satisfying the strict all\-seed gate\.Two forest plots show negative SAE\-minus\-Dense differences and paired 95 percent confidence intervals for off\-target RMS and wrong\-behavior index across five models with validation\-qualified concepts\.Figure[A4](https://arxiv.org/html/2607.27404#A7.F4)visualizes the paired bootstrap contrasts\. All ten 95% confidence intervals lie entirely below zero, showing consistent SAE reductions in both off\-target RMS and WBI across the five models\. Off\-target RMS differences range from−0\.014\-0\.014for HuBERT\-ECG to−0\.087\-0\.087for CSFM, while WBI differences range from−0\.176\-0\.176to−1\.189\-1\.189for the same models\. CSFM shows the largest reduction on both endpoints, and the favorable direction remains consistent across eligibility sets ranging from 5 to 15 concepts\. Across the resulting model–concept evaluations, SAE has a favorable and FDR\-significant difference in all 10 model–metric tests \(q≤\.0011q\\leq\.0011\)\. At a validation\-matched frozen readout effect, the selected SAE coordinates consistently produce less cross\-family readout spillover than native dense coordinates\.
Similar Articles
Mechanistic Interpretability of EEG Foundation Models via Sparse Autoencoders
This paper applies TopK Sparse Autoencoders to three EEG foundation models (SleepFM, REVE, LaBraM) to extract interpretable feature dictionaries and introduces a framework for concept steering, revealing representational failures and clinical entanglements.
CADENCE: A Cardiac Atom Dictionary for Interpretable Neural Concept Extraction from ECG Foundation Models
CADENCE uses sparse autoencoders to decompose ECG foundation model representations into interpretable physiological concepts, significantly improving alignment with clinical phenotypes and waveform morphology.
Quantifying Explainable AI-introduced signal noise on ECG data with Spectral Entropy
The paper proposes using spectral entropy as a metric to quantify noise introduced by explainability techniques in ECG arrhythmia classification, helping to distinguish true model signal from XAI-generated artifacts.
Do ECG Foundation Models Transfer to Rare Cardiac Diseases? Evidence from Brugada Syndrome Detection
This study evaluates nine ECG foundation models for Brugada syndrome detection, finding that pre-training provides optimization stability but not transferable clinical knowledge, challenging assumptions about the benefits of large-scale pre-training for rare diseases.
The Identity Trap in EEG Foundation Models: A Diagnostic Audit
This paper identifies and diagnoses the 'Identity Trap' in EEG foundation models, where high accuracy may stem from subject-identity features rather than genuine clinical biomarkers. It proposes FMScope, a frozen-representation protocol to disentangle these signals, and demonstrates that subject-identity confounding is universal across three models and removable with linear methods.