预测拟合度相似但潜在动力学不同：表征脑疾病个性化模型中学习到的动力学结构

# Similar Predictive Fit but Different Latent Dynamics: Characterizing Learned Dynamical Structure in Personalized Models of Brain Disorders
Source: [https://arxiv.org/html/2610.10850](https://arxiv.org/html/2610.10850)
Rita Huan\-Ting PengAffiliation:University of Illinois Urbana\-Champaign, Urbana, IL, USAAffiliation:Carle Foundation Hospital, Urbana, IL, USAEmail:[htpeng2@illinois\.edu](mailto:[email protected])Nhat Bui

###### Abstract

As AI models move toward clinical decision\-making and personalized treatment, understanding*what*a model learns becomes important beyond predictive accuracy alone\. This is particularly relevant in clinical populations, where patients are heterogeneous and latent representations learned by large\-scale models remain difficult to interpret\. We investigate whether personalized latent dynamics can reveal clinically associated differences even when predictive fit is similar\. We employ a lightweight CNN–Transformer EEG foundation model, pretrained on the large\-scale Temple University EEG Corpus \(TUEG\), to extract segment\-level EEG representations\. Using the Temple University Epilepsy Corpus \(TUEP\) as a clinical testbed, these representations are mapped to a shared latent\-state space, and sparse multinomial logistic transition distributions \(mLTD\) are fit independently to each subject to obtain personalized latent transition\-dependency graphsWnW\_\{n\}\. Group analyses usen=198n\{=\}198labeled subjects \(99 epilepsy / 99 non\-epilepsy\)\. Atk=4k\{=\}4, epilepsy subjects exhibit substantially denser learned dependency structure than non\-epilepsy subjects \(mean nonzero dependencies: 10\.01 vs\. 5\.67; Mann–Whitneyp=1\.1×10−7p\{=\}1\.1\\times 10^\{\-7\}\), with the same group\-level pattern observed atk=6k\{=\}6\(19\.90 vs\. 13\.46;p=5\.2×10−5p\{=\}5\.2\\times 10^\{\-5\}\)\. Graph\-derived features retain moderate subject\-level group discrimination under stratified 5\-fold subject\-wise cross\-validation \(AUROC 0\.68 atk=4k\{=\}4and 0\.65 atk=6k\{=\}6\)\. In contrast, within\-subject held\-out log\-likelihood is nearly identical between groups atk=4k\{=\}4\(−0\.992\-0\.992vs\.−0\.991\-0\.991;p=0\.95p\{=\}0\.95\), and next\-state prediction is similarly matched \(AUROC 0\.855 vs\. 0\.861;p=0\.54p\{=\}0\.54\)\. Therefore, similar predictive fit does not imply similar learned dynamics: the two groups are comparably predictable under their personalized models while differing substantially in the internal dynamical structure learned by those models\. This distinction is important even before individual latent states acquire clinical interpretation, because predictive equivalence alone is insufficient to establish that personalized models have learned equivalent internal dynamics\. These findings motivate complementary evaluation of predictive validity and learned dynamical structure before extending such models toward intervention\-aware patient world modeling\.

Keywords:patient world models; personalized dynamical models; EEG foundation models; latent dynamics; epilepsy; transition\-dependency graphs\.

## 1Introduction

Artificial intelligence \(AI\) is increasingly being developed for clinical applications, including personalized treatment and intervention\-related decision\-making\([Rajpurkar et al\., 2022](https://arxiv.org/html/2610.10850#bib.bib8);[Vasey et al\., 2022](https://arxiv.org/html/2610.10850#bib.bib10)\)\. In neurological disorders, machine\-learning approaches are also being explored for personalized and adaptive interventions, including closed\-loop brain stimulation\([Chandrabhatla et al\., 2023](https://arxiv.org/html/2610.10850#bib.bib3)\)\. Patient world models extend this direction by seeking to represent how an individual’s state evolves over time and, ultimately, how that trajectory may change under intervention\. Nevertheless, the development and evaluation of AI models still focuses heavily on predictive performance, while providing more limited understanding of what information these models learn internally\. This issue becomes increasingly important as models are pretrained on large\-scale heterogeneous data and transferred across tasks, populations, or disorders, as in foundation models\([Rajpurkar et al\., 2022](https://arxiv.org/html/2610.10850#bib.bib8)\)\. In clinical applications, limited understanding of learned representations may introduce uncertainty into their interpretation and use for decision\-making\. This issue is particularly relevant because patient populations are heterogeneous, disease\-related alterations may differ substantially across individuals, and learned latent states often lack definitive state\-level clinical ground truth\. A model may therefore achieve good predictive performance without clearly revealing what patient\-specific information it has learned\.

This challenge is particularly relevant for neurological disorders, where brain activity is inherently dynamic and disease\-related alterations may be expressed not only in static neural patterns, but also in how neural states evolve over time\. Epilepsy provides a particularly clear example: it has long been conceptualized as a dynamical disorder involving transitions among different brain states, and contemporary work increasingly emphasizes the time\-evolving organization of epileptic brain networks\([Da Silva et al\., 2003](https://arxiv.org/html/2610.10850#bib.bib4);[Bröhl et al\., 2024](https://arxiv.org/html/2610.10850#bib.bib2)\)\. EEG directly measures electrical brain activity with high temporal resolution, making it well suited for investigating such temporal organization\. For personalized patient models, it is therefore important not only to identify latent brain states, but also to characterize how these states evolve over time and how previous states are related to future states\. However, comparable predictive performance does not necessarily indicate that personalized models have learned similar temporal organization\. Even when subject\-specific models achieve comparable predictive fit, their learned patterns of temporal dependencies may differ substantially across individuals or clinical groups\. Predictive performance alone may therefore overlook clinically associated differences in the dynamical structure learned by these personalized models\. This leads to a simple but important question:

> *If personalized models achieve similar predictive performance, does this necessarily mean that they have learned similar temporal dynamics?*

We therefore test the hypothesis that similar predictive fit does not necessarily imply similar learned latent dynamical structure\.

#### Motivating progression\.

Preliminary analyses from the same research program provide two earlier levels of evidence motivating the present study \(Appendix[A](https://arxiv.org/html/2610.10850#A1)\)\. First, our lightweight EEG foundation model was pretrained on approximately 18,800 hours of the large\-scale Temple University EEG Corpus \(TUEG\) and demonstrated competitive frozen cross\-disorder transfer on Temple University Hospital Abnormal EEG Corpus \(TUAB\) and Temple University Epilepsy Corpus \(TUEP\), with an elbow neark=4k\{=\}4for latent\-state discovery\. Second, comparison with an independently pretrained encoder \(LUNA\-Base\) showed that absolute state\-occupancy patterns were strongly encoder\-dependent, whereas occupancy\-informed alignment yielded descriptive concordance of epilepsy\-associated occupancy changes \(rΔ=0\.96r\_\{\\Delta\}\{=\}0\.96; exploratory\)\. Building on these findings, we move beyond representation and state occupancy to subject\-specific temporal dynamics\. State occupancy describes*where and how often*a subject visits latent states, but not*how the subject moves between them*\.

#### Present study\.

We investigate this question using scalp EEG, with epilepsy as a clinical testbed\. Using the TUEP\([Obeid and Picone, 2016](https://arxiv.org/html/2610.10850#bib.bib7)\), frozen representations from our EEG foundation model are mapped to a shared latent\-state space, and the temporal dependencies among these states are modeled independently for each subject using multinomial logistic transition distributions \(mLTD\)\([Tank et al\., 2021](https://arxiv.org/html/2610.10850#bib.bib9)\)\. For each subject, mLTD estimates a sparse latent transition\-dependency graphWnW\_\{n\}that summarizes predictive temporal dependencies among latent states\. We then evaluate the resulting personalized models from two complementary perspectives\. First,predictive validityasks whether an individual’s model can predict that same subject’s held\-out trajectory\. Second,characterization of learned dynamical structureasks how the model organizes temporal dependencies within that individual and whether this organization contains clinically associated information\.

Our goal is not to classify epilepsy, but to use epilepsy versus non\-epilepsy as a clinical contrast to examine whether similar predictive fit can be associated with different learned dynamical structures\.

#### Contributions\.

We \(i\) separate within\-subject predictive validity from characterization of learned dynamical structure; \(ii\) demonstrate a fit–structure dissociation that is robust acrossk=4k\{=\}4andk=6k\{=\}6latent\-state resolutions; and \(iii\) show that personalized dependency structure contains moderate epilepsy\-associated information\. These results motivate structural characterization before extending personalized dynamical models toward intervention\-conditioned patient world modeling\.

The present study is observational and presents this pipeline as an intermediate step for evaluating personalized dynamical models before their extension toward intervention\-aware clinical applications\.

## 2Methods

### 2\.1Experimental pipeline

Two EEG datasets, TUEG and TUEP, were used for model pretraining and personalized latent\-dynamics analysis, respectively, following previous EEG foundation\-model studies\([Zhou et al\., 2026](https://arxiv.org/html/2610.10850#bib.bib12);[Jiang et al\., 2024](https://arxiv.org/html/2610.10850#bib.bib6);[Wang et al\., 2025](https://arxiv.org/html/2610.10850#bib.bib11)\)\. EEG recordings were band\-pass filtered between 0\.3 and 75 Hz, notch filtered at 60 Hz, mapped to the standard 19\-channel international 10–20 montage, resampled to 200 Hz, and divided into non\-overlapping 30\-s segments\. Signal amplitudes were normalized to approximately±100​μ\\pm 100~\\muV and subsequently scaled to\[−1,1\]\[\-1,1\]\. Our lightweight EEG encoder was pretrained on 2,259,998 TUEG segments, corresponding to approximately 18,800 hours of EEG, using self\-supervised reconstruction\. The encoder was frozen throughout all TUEP analyses; no task\-specific fine\-tuning was performed\.

We obtained mLTD fits for 200 TUEP subjects\. Group analyses usen=198n\{=\}198labeled subjects \(99 epilepsy / 99 non\-epilepsy\); two recordings with missing group labels were excluded from all between\-group comparisons\. As illustrated in Figure[1](https://arxiv.org/html/2610.10850#S2.F1), each 30\-s EEG segment was mapped by the frozen encoder to a 128\-dimensional representation\. A single globalkk\-means model was then applied across subjects to obtain a shared latent\-state space\. We usek=4k\{=\}4as the primary latent\-state resolution, motivated by the elbow observed in our preliminary analysis of the TUEP representation space \(Appendix[A](https://arxiv.org/html/2610.10850#A1)\)\. We additionally evaluatek=6k\{=\}6as a finer state\-space resolution to assess whether the main findings are robust to the choice ofkk\. Because changingkkchanges the discretization of the latent space, individual states and dependencies are not assumed to correspond directly between the two resolutions\.

For each subjectnn, this procedure produces a discrete latent\-state trajectory

𝐬\(n\)=\(s1\(n\),…,sTn\(n\)\),st\(n\)∈\{1,…,k\},\\mathbf\{s\}^\{\(n\)\}=\\left\(s^\{\(n\)\}\_\{1\},\\ldots,s^\{\(n\)\}\_\{T\_\{n\}\}\\right\),\\qquad s^\{\(n\)\}\_\{t\}\\in\\\{1,\\ldots,k\\\},where each state label corresponds to one non\-overlapping 30\-s EEG segment\.

The latent\-state definitions are shared across subjects, whereas the temporal model is estimated independently for each subject\. Clinical labels \(epilepsy/non\-epilepsy\) are not used during representation extraction, clustering, or personalized model fitting\. They are introduced only during post\-estimation group\-level evaluation\.

![Refer to caption](https://arxiv.org/html/2610.10850v1/figures/fig_1.png)Figure 1:Pipeline for personalized latent\-dynamics modeling from scalp EEG\.Non\-overlapping 30\-s EEG segments are encoded using our frozen EEG foundation model and mapped to shared latent\-state spaces using globalkk\-means atk=4k\{=\}4andk=6k\{=\}6\. Each segment is assigned a discrete state label, producing a subject\-specific state sequence\. The sequence is modeled independently for each subject using mLTD with group\-lasso regularization across temporal lags, yielding a sparse, directed, weighted transition\-dependency graphWn∈ℝk×kW\_\{n\}\\in\\mathbb\{R\}^\{k\\times k\}\.
### 2\.2Personalized latent dynamics with mLTD

State occupancy describes how often a subject visits each latent state but not how the state sequence evolves\. We therefore model each subject’s latent\-state trajectory as a categorical time series using mLTD\([Tank et al\., 2021](https://arxiv.org/html/2610.10850#bib.bib9)\)\.

For each subjectnn, given the precedingLLlatent states, the subject\-specific model estimates

Pn​\(st\(n\)=j∣st−1\(n\),…,st−L\(n\)\),j∈\{1,…,k\}\.P\_\{n\}\\left\(s\_\{t\}^\{\(n\)\}=j\\mid s\_\{t\-1\}^\{\(n\)\},\\ldots,s\_\{t\-L\}^\{\(n\)\}\\right\),\\qquad j\\in\\\{1,\\ldots,k\\\}\.\(1\)
#### Sparse temporal dependencies\.

mLTD uses group\-sparse regularization across temporal lags to identify which directed state\-to\-state dependencies contribute to next\-state prediction\. For each subject, the fitted dependencies are summarized by

Wn=\[Wn,11⋯Wn,1​k⋱Wn,k​1⋯Wn,k​k\]∈ℝk×k,W\_\{n\}=\\begin\{bmatrix\}W\_\{n,11\}&\\cdots&W\_\{n,1k\}\\\\ \\vdots&\\ddots&\\vdots\\\\ W\_\{n,k1\}&\\cdots&W\_\{n,kk\}\\end\{bmatrix\}\\in\\mathbb\{R\}^\{k\\times k\},\(2\)whereWn,i​jW\_\{n,ij\}summarizes the retained predictive dependency from preceding latent stateiito future latent statejjacross the modeled temporal lags\. Thus,Wn,i​j=0W\_\{n,ij\}=0indicates that the dependencyi→ji\\rightarrow jis not retained by the sparse model, whereasWn,i​j≠0W\_\{n,ij\}\\neq 0indicates a retained predictive temporal relationship\. For example,Wn,12≠0W\_\{n,12\}\\neq 0indicates that previous occurrences of state 1 contribute to predicting future occurrences of state 2, conditional on the modeled state history\.

We refer toWnW\_\{n\}as alatent transition\-dependency matrix, or equivalently as a sparse, directed, weightedlatent transition\-dependency graph\. Importantly,WnW\_\{n\}is not a conventional Markov transition\-probability matrix: its entries summarize learned predictive dependency strengths and are not required to sum to one\. Diagonal entries represent within\-state self\-dependencies, whereas off\-diagonal entries represent predictive dependencies between different latent states\. Although the group\-sparse formulation has a Granger\-style predictive interpretation\([Granger, 1969](https://arxiv.org/html/2610.10850#bib.bib5);[Bressler and Seth, 2011](https://arxiv.org/html/2610.10850#bib.bib1)\), the present analysis is observational\. We therefore interpret the dependencies inWnW\_\{n\}as learned predictive temporal relationships rather than causal interactions between physiological brain states\.

### 2\.3Personalized model selection

The maximum lag orderLLand sparsity parameterλ\\lambdawere selected independently for each subject using 5\-fold time\-series cross\-validation\. We searched

L∈\{1,…,10\},λ∈\{10−6,10−4,10−2,1\}\.L\\in\\\{1,\\ldots,10\\\},\\qquad\\lambda\\in\\\{10^\{\-6\},10^\{\-4\},10^\{\-2\},1\\\}\.Because each latent\-state observation corresponds to a 30\-s EEG segment,L=1,…,10L\{=\}1,\\ldots,10represents preceding state histories ranging from 30 s to 300 s \(5 min\)\. For each subjectnn, the optimal hyperparameters were selected by maximizing mean held\-out log\-likelihood,

\(Ln∗,λn∗\)=arg​maxL,λ⁡ℒ¯CV,n​\(L,λ\),\(L\_\{n\}^\{\\ast\},\\lambda\_\{n\}^\{\\ast\}\)=\\operatorname\*\{arg\\,max\}\_\{L,\\lambda\}\\overline\{\\mathcal\{L\}\}\_\{\\mathrm\{CV\},n\}\(L,\\lambda\),\(3\)whereℒ¯CV,n\\overline\{\\mathcal\{L\}\}\_\{\\mathrm\{CV\},n\}denotes the mean held\-out cross\-validation log\-likelihood for subjectnn\.

The selected model defines the subject\-specific dependency graphWnW\_\{n\}\. Models for which regularization removed all state\-pair dependencies, yielding an all\-zeroWnW\_\{n\}, were designatednull models\. Null models were retained in the primary analysis and separately examined in sensitivity analyses\.

### 2\.4Evaluation of personalized latent dynamics

We evaluate each personalized model along two complementary axes:predictive validityandlearned dynamical structure\.

#### Predictive validity\.

Predictive validity asks how well the model predicts unseen latent\-state transitions from the same subject and is quantified using mean held\-out cross\-validation log\-likelihood,

ℱn=ℒ¯CV,n,\\mathcal\{F\}\_\{n\}=\\overline\{\\mathcal\{L\}\}\_\{\\mathrm\{CV\},n\},\(4\)together with within\-subject next\-state AUROC\. Held\-out log\-likelihood quantifies the probability assigned by the personalized model to state transitions that actually occur in unseen data, whereas next\-state AUROC evaluates discrimination of future latent states\.

#### Learned dynamical structure\.

Learned dynamical structure is characterized fromWnW\_\{n\}\. Our primary structural measure is the number of retained nonzero dependencies,

En=∑i=1k∑j=1k𝕀⁡\(Wn,i​j≠0\),E\_\{n\}=\\sum\_\{i=1\}^\{k\}\\sum\_\{j=1\}^\{k\}\\mathbb\{I\}\\\!\\left\(W\_\{n,ij\}\\neq 0\\right\),\(5\)with normalized dependency density

Dn=Enk2,D\_\{n\}=\\frac\{E\_\{n\}\}\{k^\{2\}\},\(6\)where diagonal self\-dependencies are included among thek2k^\{2\}possible entries\. Thus,Dn∈\[0,1\]D\_\{n\}\\in\[0,1\]represents the proportion of all possible state\-to\-state predictive dependencies retained by the subject\-specific model\. We additionally examine mean diagonal self\-dependency strength and null\-model prevalence\. Becausek=4k\{=\}4andk=6k\{=\}6define different discretizations of the latent space, individual states and dependencies are not assumed to correspond directly across resolutions\. Epilepsy versus non\-epilepsy differences in these dynamical measures are assessed using Mann–Whitney tests\.

#### Clinical information inWnW\_\{n\}\.

As a secondary analysis, we ask whether the subject\-specific organization ofWnW\_\{n\}contains information associated with epilepsy status\. We represent eachWnW\_\{n\}at three levels of structural detail:scalar summaries\(global dependency count/density and self\-dependency strength\),graph\-derived features\(summary properties of the directed weighted dependency graph\), andfull\-matrix features,𝐰n=vec⁡\(Wn\)∈ℝk2\\mathbf\{w\}\_\{n\}=\\operatorname\{vec\}\(W\_\{n\}\)\\in\\mathbb\{R\}^\{k^\{2\}\}, which preserve individual state\-to\-state dependency weights\.

Each feature representation is evaluated using L2\-regularized, class\-balanced logistic regression with stratified 5\-fold subject\-wise cross\-validation\. The resulting group\-classification AUROC quantifies how well structural information derived fromWnW\_\{n\}distinguishes epilepsy from non\-epilepsy subjects\. This is distinct from the within\-subject next\-state AUROC, which evaluates how well each personalized mLTD model predicts future latent states\.

## 3Results

### 3\.1Similar predictive fit but different learned dynamical structure

Our central question is whether comparable within\-subject predictive performance implies similar learned latent dynamics \(Fig\.[2](https://arxiv.org/html/2610.10850#S3.F2)A–B; Table[1](https://arxiv.org/html/2610.10850#S3.T1)\)\.

#### Predictive fit is comparable\.

Atk=4k\{=\}4, held\-out CV log\-likelihood was nearly identical in epilepsy and non\-epilepsy \(−0\.992\-0\.992vs\.−0\.991\-0\.991;p=0\.95p\{=\}0\.95\), as was within\-subject next\-state AUROC \(0\.8550\.855vs\.0\.8610\.861;p=0\.54p\{=\}0\.54\)\. Held\-out CV log\-likelihood likewise did not differ atk=6k\{=\}6\(−1\.399\-1\.399vs\.−1\.370\-1\.370;p=0\.18p\{=\}0\.18\)\. Thus, the personalized models achieved comparable out\-of\-sample predictive fit across groups, while the learned dependency structures nevertheless differed substantially\.

#### Learned structure differs\.

Despite comparable predictive fit, epilepsy subjects retained substantially more nonzero dependencies than non\-epilepsy subjects atk=4k\{=\}4\(10\.01 vs\. 5\.67;p=1\.1×10−7p\{=\}1\.1\\times 10^\{\-7\}\), corresponding to normalized dependency densities of0\.6260\.626and0\.3540\.354, respectively\. Thus, the epilepsy models retained approximately 62\.6% of all possible state\-to\-state predictive dependencies, compared with 35\.4% in the non\-epilepsy models, indicating a denser predictive dependency structure in the learned latent dynamics\.

The same group\-level densification was observed atk=6k\{=\}6\(19\.90 vs\. 13\.46;p=5\.2×10−5p\{=\}5\.2\\times 10^\{\-5\}; normalized densities:0\.5530\.553vs\.0\.3740\.374\), showing that the structural difference persisted after accounting for the larger number of possible dependencies atk=6k\{=\}6\. Mean diagonal self\-dependency was higher in epilepsy atk=4k\{=\}4\(0\.2190\.219vs\.0\.1520\.152;p=1\.7×10−4p\{=\}1\.7\\times 10^\{\-4\}\) but not atk=6k\{=\}6\(p=0\.18p\{=\}0\.18\)\. Figure[2](https://arxiv.org/html/2610.10850#S3.F2)A shows that epilepsy\-associated densification is broadly positive acrosskkand lag strata, whereas Fig\.[2](https://arxiv.org/html/2610.10850#S3.F2)B shows overlapping held\-out CV log\-likelihood distributions\.

k=4k\{=\}4k=6k\{=\}6MetricNonEpippNonEpippPredictive fitHeld\-out CV LL−0\.991\-0\.991−0\.992\-0\.9920\.95−1\.370\-1\.370−1\.399\-1\.3990\.18Learned dynamical structureNonzero dependenciesEnE\_\{n\}5\.6710\.011\.1×10−71\.1\{\\times\}10^\{\-7\}13\.4619\.905\.2×10−55\.2\{\\times\}10^\{\-5\}Normalized densityDnD\_\{n\}0\.3540\.626–0\.3740\.553–Mean diag\.WnW\_\{n\}0\.1520\.2191\.7×10−41\.7\{\\times\}10^\{\-4\}0\.2010\.2120\.18Table 1:Similar predictive fit, different learned structure\(n=198n\{=\}198; 99 epilepsy / 99 non\-epilepsy; Mann–Whitney\)\. Held\-out CV LL measures within\-subject predictive validity\.EnE\_\{n\}denotes the number of retained nonzero dependencies, andDn=En/k2D\_\{n\}=E\_\{n\}/k^\{2\}denotes the corresponding normalized dependency density\. BecauseDnD\_\{n\}is a constant rescaling ofEnE\_\{n\}within eachkk, separate significance tests are not reported\. Mean diagonal strength summarizes self\-dependency inWnW\_\{n\}\.![Refer to caption](https://arxiv.org/html/2610.10850v1/figures/fig_2.png)Figure 2:Main result overview\.\(A\) Epilepsy minus non\-epilepsy nonzero\-dependency counts acrosskkand lag\. \(B\) Within\-subject held\-out CV log\-likelihood atk=4k\{=\}4andk=6k\{=\}6\(comparable predictive fit\)\. \(C\) Group discrimination fromWnW\_\{n\}features \(discussed in Section[3\.2](https://arxiv.org/html/2610.10850#S3.SS2)\)\. Dashed line in \(C\): chance AUROC \(0\.50\.5\)\.

### 3\.2Clinical information in learned dynamical structure

We next ask whether different representations of the subject\-specific dependency matrixWnW\_\{n\}contain information associated with epilepsy status \(Fig\.[2](https://arxiv.org/html/2610.10850#S3.F2)C; Table[2](https://arxiv.org/html/2610.10850#S3.T2); Appendix Fig\.[4](https://arxiv.org/html/2610.10850#A2.F4)\)\.

Atk=4k\{=\}4, scalar summaries, graph\-derived features, and vectorized full\-matrix features achieved group\-classification AUROCs of0\.6970\.697,0\.6790\.679, and0\.6150\.615, respectively\. Atk=6k\{=\}6, the corresponding AUROCs were0\.6770\.677,0\.6450\.645, and0\.6540\.654\. These moderate AUROCs indicate that the learned dynamical structure contains information associated with epilepsy status, despite comparable within\-subject predictive fit across groups\.

Table 2:Between\-group discrimination from three representations ofWnW\_\{n\}: global scalar summaries, graph\-derived features, and the vectorized full dependency matrix \(stratified 5\-fold subject\-wise CV;n=198n\{=\}198\)\.
### 3\.3Sensitivity and robustness

Atk=4k\{=\}4, null \(all\-zero\)WnW\_\{n\}occurred in29/9929/99non\-epilepsy vs\.8/998/99epilepsy subjects; atk=6k\{=\}6,10/9910/99vs\.8/998/99\. Excluding null models, scalar group AUROC remained above chance \(0\.6650\.665atk=4k\{=\}4;0\.7220\.722atk=6k\{=\}6\), so densification / discrimination is not solely an artifact of all\-zero graphs\.

Group\-meanWnW\_\{n\}heatmaps \(Appendix Fig\.[3](https://arxiv.org/html/2610.10850#A2.F3)\), ROC curves \(Appendix Fig\.[4](https://arxiv.org/html/2610.10850#A2.F4)\), and lag\-wise robustness checks \(Appendix[C](https://arxiv.org/html/2610.10850#A3)\) are reported in the appendix\. The lag analysis separates exploratory best\-lag subsets from full\-cohort CV likelihood and should not be interpreted as a full\-cohort fixed\-lagWnW\_\{n\}comparison\.

## 4Discussion

### 4\.1Similar predictive fit can conceal different learned dynamics

The central finding is that epilepsy and non\-epilepsy subjects are similarly predictable under their personalized mLTD models but exhibit substantially different learned dependency structures\. Atk=4k\{=\}4, epilepsy subjects retained approximately 62\.6% of the possible directed dependencies, compared with 35\.4% in non\-epilepsy subjects\. Atk=6k\{=\}6, the corresponding normalized dependency densities were 55\.3% and 37\.4%, respectively\. Thus, although increasingkkincreases the absolute number of possible dependencies, the epilepsy group remained relatively denser after normalization by the size of the latent\-state space\. This group\-level structural difference was observed despite comparable held\-out predictive fit at both resolutions\.

This fit–structure dissociation highlights two distinct aspects of personalized model evaluation\. Held\-out likelihood and next\-state AUROC ask whether a model predicts an individual’s unseen latent\-state transitions\. Properties ofWnW\_\{n\}, in contrast, characterize how the model organizes temporal dependencies among those states\. Comparable predictive performance therefore does not imply that personalized models have learned equivalent dynamical organization\. Features derived fromWnW\_\{n\}additionally provided moderate epilepsy versus non\-epilepsy discrimination, suggesting that clinically associated information is present in the organization of learned latent dynamics even when overall predictive fit is similar\. These associations should not, however, be interpreted as diagnostic performance or as evidence that the learned dependencies represent physiological causal interactions\.

#### Why this matters\.

This analysis addresses a fundamental model\-evaluation question: whether comparable predictive performance is sufficient to conclude that personalized models have learned comparable internal dynamics\. Our results show that it is not\. Two clinical groups can be similarly predictable while their personalized models organize temporal dependencies differently\. Establishing this distinction is important before assigning physiological meaning to latent structure or extending such models toward intervention\-aware reasoning\. Clinical interpretation of individual states and dependencies therefore represents a subsequent validation step rather than a prerequisite for characterizing learned dynamical structure\.

### 4\.2Implications for patient world models

The present results do not establishWnW\_\{n\}as a complete patient world model\. Rather, they identify an intermediate evaluation problem before personalized dynamical models are extended toward intervention\-aware reasoning\. A patient world model should ultimately characterize both how an individual’s state evolves and how that trajectory changes under clinically relevant interventions\. Our results show why predictive fit alone is insufficient: similar predictability can coexist with substantially different learned latent dynamics\.

A natural extension is to condition dynamics on a measured intervention or perturbationutu\_\{t\},

P\(xt\+1∣xt:t−L\+1,ut\),P\\\!\\left\(x\_\{t\+1\}\\mid x\_\{t:t\-L\+1\},u\_\{t\}\\right\),\(7\)and characterize intervention\-associated structural change, for exampleΔ​Wn=Wnpost−Wnpre\\Delta W\_\{n\}=W\_\{n\}^\{\\mathrm\{post\}\}\-W\_\{n\}^\{\\mathrm\{pre\}\}\. Such analyses require longitudinal or intervention\-conditioned data and appropriate causal assumptions; the present observational study provides a preceding structural characterization step\.

## 5Limitations and Responsible Use

#### Limitations\.

The learnedkk\-means states are unsupervised and do not have established clinical or physiological semantics\. The present analysis is observational and case–control; differences inWnW\_\{n\}therefore represent predictive temporal dependencies rather than causal disease mechanisms or treatment effects\. The higher null\-model prevalence among non\-epilepsy subjects atk=4k\{=\}4may partly contribute to the observed density difference, although non\-null sensitivity analyses indicate that clinically associated structural information is not solely attributable to all\-zero graphs\. The personalized analysis also uses representations from a single frozen EEG foundation model, and cross\-encoder concordance of subject\-specificWnW\_\{n\}remains to be established\. Finally, prospective, test–retest, and longitudinal analyses will be required to establish the stability and clinical generalizability of the learned dynamical structure\.

#### Responsible use\.

The learned dependency graphs should be interpreted as research descriptors of model\-learned latent dynamics rather than direct representations of underlying neurophysiology\. Our framework provides a potential approach for evaluating whether clinically associated dynamical structure is present in a learned latent space before such representations are incorporated into downstream clinical AI or intervention\-aware models\. The resulting dependencies should not be interpreted as diagnostic biomarkers, causal brain graphs, or direct physiological connectivity maps\. Accordingly, they should not be used for autonomous diagnosis, treatment selection, or intervention planning without prospective clinical validation\.

## 6Conclusion

We investigated whether personalized latent dynamical models can reveal clinically associated information beyond predictive fit alone\. On TUEP, epilepsy and non\-epilepsy subjects showed comparable within\-subject predictive performance but substantially different learned dependency structures, with denser latent transition\-dependency graphs in epilepsy\. Features derived from these graphs additionally retained moderate information for clinical group discrimination\. The central result is therefore not that mLTD provides a strong epilepsy classifier, but that similar predictive fit does not imply similar learned latent dynamics\. These findings motivate evaluating predictive validity and learned dynamical structure separately\. Characterizing whether personalized latent dynamics are predictively supported, stable, and clinically informative may provide an important intermediate step before such models are extended toward intervention\-aware patient world modeling\.

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## Appendix APreliminary Analyses Motivating the Present Study

These preliminary analyses motivate the progression frozen encoder→\\rightarrowshared latent states→\\rightarrowsubject\-specific mLTD→Wn\\rightarrow W\_\{n\}\. They are*not*independent validation of the dependency\-graph results in the main text\.

#### Frozen EEG representations\.

Our CNN–Transformer encoder \(≈\\approx1\.46M parameters\) was pretrained by self\-supervised reconstruction on 2,259,998 non\-overlapping 30\-s TUEG segments \(≈\\approx18,800 hours\)\. Under a frozen\-encoder protocol, it achieved TUAB AUC85\.24±5\.6185\.24\\pm 5\.61\(accuracy80\.25±5\.9180\.25\\pm 5\.91\) and TUEP AUC67\.35±5\.9167\.35\\pm 5\.91\(accuracy69\.00±3\.2469\.00\\pm 3\.24; sensitivity75\.00±14\.1475\.00\\pm 14\.14; F170\.37±4\.0170\.37\\pm 4\.01\)\. Clustering of TUEP embeddings showed an elbow neark=4k\{=\}4, motivating the primary state\-space resolution used in the main analysis\.

#### Cross\-encoder occupancy \(exploratory\)\.

We comparedk=4k\{=\}4occupancy profiles from our encoder with those from an independently pretrained LUNA\-Base encoder\. Absolute group\-level occupancy was essentially uncorrelated across encoders \(r=−0\.06r\{=\}\-0\.06non\-epilepsy;r=0\.03r\{=\}0\.03epilepsy\)\. After Hungarian alignment on group occupancy signatures, epilepsy\-associated occupancy changesΔ​oi=o¯i,Epi−o¯i,Non\\Delta o\_\{i\}=\\bar\{o\}\_\{i,\\mathrm\{Epi\}\}\-\\bar\{o\}\_\{i,\\mathrm\{Non\}\}showed descriptive concordancerΔ=0\.96r\_\{\\Delta\}\{=\}0\.96\. This comparison is exploratory: alignment andΔ​o\\Delta oboth use group\-level occupancy, only four states are matched, and the result does not establish state\-level physiological equivalence or validate subject\-specificWnW\_\{n\}\.

## Appendix BSupplementary Figures

![Refer to caption](https://arxiv.org/html/2610.10850v1/figures/fig_3.png)Figure 3:Group\-mean transition\-dependency matrices\.MeanWnW\_\{n\}atk=4k\{=\}4\(top\) andk=6k\{=\}6\(bottom\) for non\-epilepsy \(left\) and epilepsy \(right\)\. Epilepsy maps are generally denser / stronger, consistent with Table[1](https://arxiv.org/html/2610.10850#S3.T1)\. Latent states are unsupervised and unlabeled\.![Refer to caption](https://arxiv.org/html/2610.10850v1/figures/fig_4.png)Figure 4:Between\-group ROC curvesfrom graph\-derivedWnW\_\{n\}features \(Section[3\.2](https://arxiv.org/html/2610.10850#S3.SS2)\)\. These AUROCs measure epilepsy vs\. non\-epilepsy discrimination and are distinct from within\-subject next\-state prediction \(≈0\.86\\approx 0\.86\)\.
## Appendix CLag Robustness Checks

We report two complementary lag analyses atk=4k\{=\}4\(Fig\.[5](https://arxiv.org/html/2610.10850#A3.F5); Tables[3](https://arxiv.org/html/2610.10850#A3.T3)–[4](https://arxiv.org/html/2610.10850#A3.T4)\)\. They address different questions and should be interpreted separately\.

#### Best\-lag densification \(exploratory\)\.

For each lagLL, we restrict to subjects whose personalized selected lag equalsLLand compare nonzero\-dependency countsEnE\_\{n\}between groups \(Fig\.[5](https://arxiv.org/html/2610.10850#A3.F5)A; Table[3](https://arxiv.org/html/2610.10850#A3.T3)\)\. Subset sizes are small; this is*not*a full\-cohort fixed\-lag comparison ofWnW\_\{n\}\.

#### Full\-cohort predictive fit vs\. lag\.

For alln=198n\{=\}198labeled subjects, we take the best regularization at each lag from the model\-selection grid and compare held\-out CV log\-likelihood between groups \(Fig\.[5](https://arxiv.org/html/2610.10850#A3.F5)B; Table[4](https://arxiv.org/html/2610.10850#A3.T4)\)\. Predictive fit remains matched at every lag \(p≥0\.37p\\geq 0\.37\), with nearly identical mean held\-out CV log\-likelihood in epilepsy and non\-epilepsy\. Thus, group differences in learned dependency structure are not explained by one group systematically selecting a more \(or less\) predictive lag: the two groups remain similarly well calibrated for next\-state prediction across the lag grid, reinforcing that comparable predictive fit can coexist with different dynamical organization\.

![Refer to caption](https://arxiv.org/html/2610.10850v1/figures/fig_5.png)Figure 5:Lag checks atk=4k\{=\}4\.\(A\) MeanEnE\_\{n\}among subjects with best\_lag=L=L\(small subsets; exploratory\)\. \(B\) Held\-out CV log\-likelihood vs\. lag for all labeled subjects \(n=198n\{=\}198; mean±\\pmSD\)\. Fit remains matched across groups\.Table 3:Best\-lag subset densification atk=4k\{=\}4\(exploratory\)\.EEdenotes mean nonzero dependencies;Δ​E=\\Delta E=epilepsy−\-non\-epilepsy \(Mann–Whitneypp\)\.Table 4:Full\-cohort held\-out CV log\-likelihood vs\. lag atk=4k\{=\}4\(best regularization at each lag;n=99n\{=\}99per group; Mann–Whitneypp\)\.