Title: EvoBrain: Dynamic Multi-Channel EEG Graph Modeling for Time-Evolving Brain Networks
Venue: NeurIPS 2025
Accepted: yes
Keywords: EEG

graph

neuroscience

seizure

dynamic modeling

expressiveness
Abstract: Dynamic GNNs, which integrate temporal and spatial features in Electroencephalography (EEG) data, have shown great potential in automating seizure detection.
However, fully capturing the underlying dynamics necessary to represent brain states, such as seizure and non-seizure, remains a non-trivial task and presents two fundamental challenges.
First, most existing dynamic GNN methods are built on temporally fixed static graphs, which fail to reflect the evolving nature of brain connectivity during seizure progression. 
Second, current efforts to jointly model temporal signals and graph structures and, more importantly, their interactions remain nascent, often resulting in inconsistent performance.
To address these challenges, we present the first theoretical analysis of these two problems, demonstrating the effectiveness and necessity of explicit dynamic modeling and time-then-graph dynamic GNN method.
Building on these insights, we propose EvoBrain, a novel seizure detection model that integrates a two-stream Mamba architecture with a GCN enhanced by Laplacian Positional Encoding, following neurological insights.
Moreover, EvoBrain incorporates explicitly dynamic graph structures, allowing both nodes and edges to evolve over time.
Our contributions include 
(a) a theoretical analysis proving the expressivity advantage of explicit dynamic modeling and time-then-graph over other approaches, 
(b) a novel and efficient model that significantly improves AUROC by 23\% and F1 score by 30\%, compared with the dynamic GNN baseline, and 
(c) broad evaluation of our method on the challenging early seizure prediction task.

EvoBrain: Dynamic Multi-Channel EEG Graph Modeling for Time-Evolving Brain Networks

Abstract

Dynamic GNNs, which integrate temporal and spatial features in Electroencephalography (EEG) data, have shown great potential in automating seizure detection. However, fully capturing the underlying dynamics necessary to represent brain states, such as seizure and non-seizure, remains a non-trivial task and presents two fundamental challenges. First, most existing dynamic GNN methods are built on temporally fixed static graphs, which fail to reflect the evolving nature of brain connectivity during seizure progression. Second, current efforts to jointly model temporal signals and graph structures and, more importantly, their interactions remain nascent, often resulting in inconsistent performance. To address these challenges, we present the first theoretical analysis of these two problems, demonstrating the effectiveness and necessity of explicit dynamic modeling and time-then-graph dynamic GNN method. Building on these insights, we propose EvoBrain , a novel seizure detection model that integrates a two-stream Mamba architecture with a GCN enhanced by Laplacian Positional Encoding, following neurological insights. Moreover, EvoBrain incorporates explicitly dynamic graph structures, allowing both nodes and edges to evolve over time. Our contributions include (a) a theoretical analysis proving the expressivity advantage of explicit dynamic modeling and time-then-graph over other approaches, (b) a novel and efficient model that significantly improves AUROC by 23% and F1 score by 30%, compared with the dynamic GNN baseline, and (c) broad evaluations of our method on the challenging early seizure prediction task.

1 Introduction

Epileptic seizures are typically considered a network disorder (Burns et al., 2014a). The abnormal connections across brain regions often serve as markers of seizure events (Li et al., 2021b). As such, recent studies have leveraged graph neural networks (GNNs) to model these networks for automating seizure detection (Cai et al., 2023; Ho and Armanfard, 2023). Considering the unfolding time-course of brain dynamics, a recent trend models EEGs as a sequence of time-varying graphs. Temporal models, such as recurrent neural networks (RNNs), integrated with GNNs, known as dynamic GNNs, have been proposed to learn spatiotemporal features in EEGs (Tang et al., 2023). By modeling graphs at fine-grained time steps and their sequential representations, these methods can capture how graphs or brain states evolve over time, further enhancing seizure detection accuracy.

Theorem 2.

Temporal model

(RNN)

Graph model

(GNN)

Representation

time-then-graph model

Dynamic graph structure

Edge model

Edge feature

Temporal modeling

with two stream Mamba

Explicit dynamic modeling

Topology capturing with LapPE

Spatial modeling with GCN

Frequency

decomposition

Theorem 1.

Time

Frequency

Amplitude

Time

Frequency dynamics

Seizure

Time-evolving

Multi-channel

EEG signals

Brain networks

Pre-seizure

Normal

Change even within

the same state

Connectivity varies

across states

Graph

construction

M

However, effectively representing brain dynamics by integrating graph and temporal models remains non-trivial. In this paper, we study this critical problem in accurate seizure detection and prediction by learning dynamic representations from EEGs. In essence, we mainly face two challenges: ( 1 ) Representing EEG dynamics (Problem 1). We observe that although many existing methods are labeled as 'dynamic,' they often employ static graph structures (Ho and Armanfard, 2023; Tang et al., 2022). Typically, these methods construct a predefined graph based on EEG channel correlations from the initial snapshot, which is then fixed and shared across all subsequent EEG snapshots. This implicitly assumes that the spatial structure of brain activity remains constant over time. In contrast, seizures induce evolving patterns of neuronal synchrony and desynchrony across different brain regions (Rolls et al., 2021; Li et al., 2021b; Chen et al., 2025), as shown in Figure 1. ( 2 ) Effective Spatio-temporal Modeling (Problem 2). Dynamic GNNs can generally be categorized into time-then-graph , graph-then-time , and time-and-graph architectures, following the taxonomy of Gao and Ribeiro (2022) (A concise illustration is provided in Appendix Figure 7). The time-then-graph first model the temporal dynamics and then employ GNNs to learn spatial representations. The graph-then-time first applies GNNs to each EEG snapshot independently, and then learns temporal dynamics from the resulting graph features. The time-and-graph is a recurrent GNN to capture temporal interactions between EEG snapshots before performing graph learning at each time step. However, the independent GNNs in graph-then-time represent information at single time steps without accounting for dynamic interactions between time steps. While recurrent GNNs in time-and-graph capture graph interactions, they also rely heavily on the independent initial GNNs. Overall, an effective dynamic GNNs for integrating temporal and graph-based representations to model brain dynamics remains poorly understood.

Novelty and Contributions : We first analyze a theoretical foundation for designing dynamic graph structures and models that effectively represent brain dynamics. Building upon this foundation, we propose EvoBrain , which effectively learns Evo lving, dynamic characteristics in Brain networks for accurate seizure detection and prediction. Overall, we summarize our contributions as:

Theoretical Analysis. To tackle the first challenge, we propose and analyze dynamic graph structure that explicitly incorporate temporal EEG graph modeling (Theorem 1). To tackle the second challenge, we first theoretically analyze different dynamic GNNs approaches from EEG graph perspective (Theorem 2). We discuss the necessarily of dynamic GNNs at node-level, since the node similarity measures are key factors in determining EEG graph construction.

Novel Model Design. We hence propose a novel time-then-graph model, EvoBrain , which integrates a two-stream Mamba architecture (Gu and Dao, 2024) with a GCN enhanced by Laplacian Positional Encoding (Wang et al., 2022), following neurological insights. EvoBrain achieves up to 23% and 30% improvements in AUROC and F1 scores, respectively, compared with the dynamic GNN baseline. Also, EvoBrain is 17 × faster than the SOTA time-and-graph dynamic GNN.

Broad Evaluation. Unlike most seizure detection studies (Eldele et al., 2021; Cai et al., 2023; Ho and Armanfard, 2023), we evaluate the more challenging task of seizure prediction, which aims to identify the preictal state before seizures. This is critical for early intervention in clinical settings, and EvoBrain maintains performance, with a 13.8% improvement in AUROC.

2 Problem Setting

2.1 Notations

We define an EEG x with N channels and T snapshots as a graph G = ( A , X ) , where A = ( V , E ) and A ∈ R N × N × T are the adjacency matrices. V and E represent the channels (i.e., nodes) and edges. Notably, most existing work constructs a weighted adjacency matrix A ∈ R N × N as fixed across T meaning that all EEG snapshots share the same graph structure and only the node features H are computed iteratively at each snapshot. In this paper, each edge e i,j,t ∈ E represents pairwise connectivity between channels v i and v j , where i, j ∈ N . The feature vector x i,t ∈ R d captures the electrical activity of i -th channel during the EEG snapshot at time step t . If e i,j,t exists, a i,j,t is a non-zero value. a i,j,t ∈ R quantifies the connectivity strength between two channels for each snapshot. To represent temporal EEG graphs, we define the embedding of node v i at time step t as h node i,t ∈ R k , which captures both the spatial connectivity information from the edges and the temporal dynamics from previous node embeddings. The embedding of edge e i,j,t , denoted as h edge i,j,t ∈ R l , captures the temporal evolution of channel connectivity, reflecting changes in brain networks.

2.2 Problem - Dynamic GNN Expressivity in EEG Modeling

Brain networks in different states can manifest as distinct graph structures, as shown in Figure 1. We treat expressivity analysis as a graph isomorphism problem (Xu et al., 2019), where non-isomorphic EEG graphs represent different brain states, enabling the model to effectively distinguish between seizure and non-seizure graphs. We formulate the challenge of representing EEG dynamics as the distinction between implicit and explicit dynamic graph modeling in Problem 1. We further define the challenge of effective spatio-temporal modeling as the investigation of the expressivity of graph-then-time , time-and-graph , and time-then-graph (Gao and Ribeiro, 2022) in dynamic EEG graph analysis in Problem 2.

Definition 1 (Implicit Dynamic Graph Modeling - Static Structure) . This approach fixes a single adjacency matrix A ∈ R N × N across all time steps, although each node's feature vector x : ,t evolves across t . Formally, A : , : ,t = ̂ A , for each t ∈ { 1 , . . . , T } , where ̂ A is constant for all t . Hence, the spatial connectivity among EEG channels remains unchanged, and only node features capture the dynamic aspects.

Definition 2 (Explicit Dynamic Graph Modeling - Dynamic Structure) . In contrast to the implicit setting, here both node features x : ,t and the adjacency matrices { A : , : ,t } T t =1 can vary with time. Specifically, A : , : ,t ∈ R N × N at each snapshot t may be computed by a function f : A : , : ,t = f ( x : ,t ) , ∀ t ∈ { 1 , . . . , T } , thereby capturing the dynamic evolution of channel connectivity in addition to time-varying nodes.

Problem 1 (Implicit vs. Explicit Dynamic Graph Modeling) . We consider two approaches for capturing spatial relationships. In the implicit (static) approach, a single adjacency matrix A remains fixed across all time steps, so only the node features evolve. In the explicit (dynamic) approach, both node features and adjacency matrices { A : , : ,t } T t =1 can change with t , allowing for time-varying connectivities derived from the EEG data. Our goal is to compare the expressiveness of these two approaches in capturing spatiotemporal dependencies for dynamic EEG graph analysis.

Definition 3 (Graph-then-time) . This architecture first apply GNNs to learn spatial, graph information at each t independently, followed by the temporal processing (e.g., by RNNs) of the resulting node embeddings. The formal definition is given as:

where h node i,t (1 ≤ t ≤ T ) denotes the embedding of node i ∈ V , GNN L in ( X : ,t , a : , : ,t ) denotes graph learning on the current snapshot through L layer GNNs. The learned embeddings, h node i,t -1 , are then passed into the RNN cell to capture the temporal dependencies. The last step output h : ,T is considered the final representation Z .

Definition 4 (Time-and-graph) . This architecture alternately processes time and graph components, applying GNNs to each EEG snapshot, as formally defined by:

where we initialize H i, 0 = 0 . GNN L in encodes each x : ,t while GNN L rc encodes representations from historical snapshots H : ,t -1 , and RNN cell embeds evolution of those graph representations.

Definition 5 (Time-then-graph) . This architecture first models the evolution of node and edge attributes over time and then applies a GNN to the resulting static graph for final representation:

time-then-graph represents the evolution of h node and h edge using two sequential models RNN node and RNN edge , resulting in a new (static) graph, which is then encoded by a GNN L .

Problem 2 (Expressive Dynamic EEG Graph Architecture) . Determine which of these three architectures exhibits the highest expressiveness for dynamic EEG graph modeling, and characterize their relative representational power.

3 Theoretical Analysis for Dynamic EEG Graphs

In this section, we aim to provide a theoretical analysis of the two problems. To this end, we employ 1-Weisfeiler-Lehman (1-WL) GNNs, a standard tool for analyzing graph isomorphism, as detailed in Appendix B. In the context of dynamic EEG analysis, an expressive model should be able to distinguish between different brain states by identifying non-isomorphic graphs.

Remark. For Theorem 2, we follow the general GNN taxonomy proposed by Gao and Ribeiro (2022), but extend the analysis to EEGs, specifically focusing on node-level expressivity in dynamic EEG graphs. Their analysis partially targets edge- or structure-level representations using unattributed graphs, but it does not explicitly consider node features. In contrast, node features are essential in EEG analysis, as EEG graph construction typically relies on pairwise similarity between channels (Ho and Armanfard, 2023; Tang et al., 2022). To this end, we provide formal theorems and proofs that consistently incorporate node features throughout the expressivity analysis. We also discuss the necessity of jointly modeling both node and edge representations from the perspective of EEG graphs in Appendix C.1.

Theorem 1. [Implicit ⪵ Explicit Dynamic Graph Modeling.] Explicit dynamic modeling (dynamic adjacency matrices) is strictly more expressive than implicit dynamic modeling (static graph structures) in capturing spatiotemporal dependencies in EEG signals.

̸

Proof. Let F implicit and F explicit denote the function classes expressible by implicit and explicit dynamic models, respectively. Since an explicit model can replicate any implicit model by ignoring time variations in adjacency, it follows that F implicit ⊆ F explicit . To show strict separation, we construct two temporal EEG graphs that share identical node features but differ in adjacency at a single time step. An implicit model compresses adjacency into a static representation, potentially making these graphs indistinguishable, while an explicit model processes time-varying adjacency and can distinguish them. Thus, F implicit = F explicit , proving F implicit ⊂ F explicit . The full proof is provided in Appendix C.2.

Lemma 1. [graph-then-time ⪵ time-and-graph ] time-and-graph is strictly more expressive than graph-then-time representation family on T n,T, H eta as long as we use 1-WL GNNs.

Proof. By Definition 3, h i,t -1 is passed without this additional GNN (i.e., GNN L rc ( · ) ) to learn interactions between EEG snapshots. This results in a simpler form of temporal representation compared to time-and-graph : h i,t -1 ⊆ [ GNN L rc ( H : ,t -1 , A : , : ,t )] i . graph-then-time is a strict subset of time-and-graph in terms of expressiveness.

Lemma 2. [time-and-graph ⪵ time-then-graph ] time-then-graph is strictly more expressive than time-and-graph representation family on T n,T,θ , as time-then-graph outputs different representations, while time-and-graph does not.

In Appendix C.3, we prove Lemma 2 using both node and edge representation perspectives (based on Lemma 4 in Appendix C.1) to hold Theorem 2. Notably, we provide a synthetic EEG task where any time-and-graph representation fails, while a time-then-graph approach succeeds. time-then-graph learns node and edge features across time steps to capture temporal dependencies. This is done by encoding the temporal adjacency matrices A : , : , ≤ t and node features X : , ≤ t together, enabling the model to distinguish between graphs with distinct temporal structures. However, time-and-graph handles each time step independently, leading to identical representations across time.

Theorem 2. [Temporal EEG Graph Expressivity] Based on Lemmas 1 and 2, we conclude that graph-then-time is strictly less expressive than time-and-graph, and time-and-graph is strictly less expressive than time-then-graph on T n,T,θ , when the graph representation is a 1-WL GNN:

We confirm this conclusion in our experiments of both seizure detection and early prediction tasks.

4 Proposed Method - EvoBrain

Based on the above analysis, this section presents our EvoBrain , which is built on top of explicit dynamic modeling and time-then-graph architecture to represent temporal EEG structures.

4.1 Explicit Dynamic Brain Graph Structure

Based on Theorem 1, we propose to construct EEG graphs for each snapshot instead of constructing a single static graph from the entire EEG recording. We first segment an EEG epoch into short time durations (i.e., snapshots) at regular intervals and compute channel correlations to construct a sequence of graph structures. Specifically, for the t -th snapshot, we define the edge weight a i,j,t as the weighted adjacency matrix A , computed as the absolute value of the normalized cross-correlation between nodes v i and v j . To prevent information redundancy and create sparse graphs, we rank the correlations among neighboring nodes and retain only the edges with the topτ highest correlations.

where x i, : ,t and x j, : ,t represent v i and v j channels of t -th EEG snapshot. ∗ denotes the normalized cross-correlation operation. N ( v i ) denotes the set of topτ neighbors of v i with higher correlations. After computing this for T snapshots, we obtain a sequence of directed, weighted EEG graphs G to represent brain networks at different time points. In other words, the dynamic nature of the EEG is captured by the evolving structure of these graphs over time.

4.2 Dynamic GNN in Time-Then-Graph Model

Based on Theorem 2, we propose a novel time-then-graph model, where two-stream Mamba Gu and Dao (2024) learn the temporal evolution of node and edge attributes independently, followed by Graph Convolutional Networks (GCN) to capture spatial dependencies across electrodes in a static graph. This method effectively captures the temporal and spatial dynamics inherent in EEG data for seizure detection and prediction. Notably, the model input is not the raw EEG signals but their frequency representation. Here, clinical seizure analysis aims to identify specific frequency oscillations and waveforms, such as spikes (Khan et al., 2018). To effectively capture such features,

we apply a short-term Fourier transform (STFT) to the EEG signal, retaining the log amplitudes of the non-negative frequency components, following prior studies (Covert et al., 2019; Asif et al., 2020; Tang et al., 2022). The EEG frequency snapshots are then normalized using z-normalization across the training set. Consequently, an EEG frequency representation with a sequence of snapshots is formulated as X ∈ R N × T × d , serving N node initialization and dynamic graph construction.

4.2.1 Temporal Modeling with Mamba

We introduce a two-stream Mamba framework, with separate processes for node and edge attributes to capture their temporal dynamics. Given a dynamic EEG graph G , Mamba can be interpreted as a linear RNN with selective state updates, making it suitable for modeling brain dynamics that involve both short-term and long-term memory processes. In the brain, short-term memory maintains transient information over brief intervals, while long-term memory spans extended timescales, enabling the integration of past experiences into current processing.

For a traditional RNN processing sequence { x t } T t =1 , the hidden state update is: h t = σ ( Wh t -1 + Ux t ) , where the weight matrices W and U representing synaptic connectivity between neurons are fixed across time t . However, the synaptic weights are constantly changing, controlled in part by chemicals such as neuromodulators (Citri and Malenka, 2008). This limits the model's ability to evolve information over long sequences (Costacurta et al., 2024). In contrast, Mamba can be viewed as a linear RNN with input-dependent parameters for each element x e (node feature x i , t or weighted adjacency matrix a i , j , t ):

where f ∗ are learnable projections for important frequency bands or edge connectivity. The hidden state h e t encodes the evolving neural activity, serving as a substrate for both transient (working) memory and more persistent (long-term) memory traces. The softplus activation τ ∆ guarantees that the gating variable ∆ e t remains positive, thereby modulating the trade-off between retaining previous neural states and incorporating new inputs. Specifically, the forgetting term (1 -∆ e t · D ) implements a selective mechanism analogous to synaptic decay or inhibitory processes that diminish outdated or irrelevant information. Conversely, the update term ∆ e t · B e t mirrors neuromodulatory gating (e,g, via dopamine signaling) that selectively reinforces and integrates salient new information. The projection C e t translates the internal neural state into observable outputs. The final hidden states h node i = y node i,T and h edge ij = y edge ij,T capture the temporal evolution of nodes and edges.

4.2.2 Spatial Modeling with GCN and LapPE

We adapt Graph Convolutional Network (GCN) and Laplacian Positional Encoding (LapPE) (Wang et al., 2022) for efficiently modeling spatial dependencies in EEG signals.

Capturing Brain Network Topology. Recent studies of neuroscience reveal that particular functions are closely associated with specific brain regions (e.g., Neocortex or Broca's area) (Hawkins and Ahmad, 2016; Rubinov and Sporns, 2010). However, due to the fundamental computation of GNNs, nodes that are structurally equivalent under graph automorphism receive identical representations, effectively losing their individual identities (Wang et al., 2022). In order to reflect the spatial specificity of the brain within spatial modeling, we introduce Laplacian Positional Encoding (LapPE). Given edge feature H edge the normalized Laplacian L is defined as: L = I -( D -1 / 2 A ′ D -1 / 2 ) = UΛU ⊤ , A ′ = τ edge ( f edge ( H edge )) , where τ edge is the softplus function, f edge is the learnable projection, A ′ is a weighted adjacency matrix A ′ , and D is a degree matrix, diagonal with D = { ∑ j a ′ i,j } N i =1 . I ∈ R N × N is the identity matrix, and D -1 / 2 is the element-wise inverse square root of the degree matrix D . Performing an eigendecomposition on L yields. The columns of U ∈ R N × N are the eigenvectors of L , and Λ is a diagonal matrix containing the corresponding eigenvalues.

To capture the global geometry of the network, we select the first K eigenvectors corresponding to the smallest eigenvalues. For node i , its Laplacian-based positional encoding p i ∈ R K is given by p i = [ u 1 [ i ] , u 2 [ i ] , . . . , u K [ i ]] ⊤ , x node i = [ h node i ; p i ] , where u k [ i ] denotes the i -th component of the k -th eigenvector and [; ] indicates vector concatenation.

Modeling EEG Spatial Dynamics. We then adapt a GCN to learn spatial dependencies. These graph embeddings capture the temporal evolution of EEG snapshots, with each snapshot reflecting the brain state at that particular time. Each layer of the GCN updates the node embeddings by aggregating information from neighboring nodes and edges. The node embeddings are updated as follows:

h ( l +1) i = σ ( ( D -1 / 2 A ′ D -1 / 2 ) h ( l ) j Θ ( l ) ) , where h ( l ) i is the embedding of node i at layer l and h (0) i = x node i . Θ ( l ) is the learnable weight matrix at layer l , and σ is an activation function (e.g., ReLU). Afterward, we apply max pooling over the node embeddings, i.e., Z = h ( L ) i , followed by a fully connected layer and softmax activation for seizure detection and prediction tasks.

5 Experiments and Results

5.1 Experimental Setup

Tasks. In this study, we focus on two tasks: seizure detection and seizure early prediction.

Seizure detection is framed as a binary classification problem, where the goal is to distinguish between seizure and non-seizure EEG segments, termed epochs. This task serves as the foundation for automated seizure monitoring systems.

Seizure early prediction is the more challenging and clinically urgent task. It aims to predict the onset of an epileptic seizure before it occurs. Researchers typically frame this task as a classification problem (Burrello et al., 2020; Batista et al., 2024), where the goal is to distinguish between preictal EEG epochs and the normal state. Accurate classification enables timely patient warnings or preemptive interventions, such as electrical stimulation, to prevent or mitigate seizures. The seizure prediction task is defined as a classification problem between inter-ictal (normal) and pre-ictal states (Burrello et al., 2020). However, there is no clear clinical definition regarding its onset or duration of pre-ictal state (Lopes et al., 2023). So it is defined as a fixed duration before the seizure occurrence (Batista et al., 2024). This duration is chosen to account for the time required for stimulation by implanted devices (Cook et al., 2013) and to allow for seizure preparation. In this study, we define the pre-ictal state as one minute, providing adequate time for effective electrical stimulation to mitigate seizures or minimal preparation. Data labeled as seizures were discarded, and a five-minute buffer zone around the boundary data was excluded from the analysis. The remaining data were used as the normal state.

Datasets. We used the Temple University Hospital EEG Seizure dataset v1.5.2 ( TUSZ ) (Shah et al., 2018) to evaluate EvoBrain . Data description can be found in Appendix F. TUSZ is the largest public EEG seizure database, containing 5,612 EEG recordings with 3,050 annotated seizures. Each recording consists of 19 EEG channels. Additionally, we used the smaller CHB-MIT dataset, which consists of 844 hours of 22-channel scalp EEG data from 22 patients, including 163 recorded seizure episodes. For the TUSZ dataset, we followed the official data split, in which a subset of patients is designated for testing. Similarly, for the CHB-MIT dataset, we used randomly selected 15% of the patient's data for testing. Hyperparameters and augmentation strategies were set following prior studies and can be found in Appendix D. Preprocessing: For the early prediction task, we defined the one-minute period before a seizure as the preictal phase, implying the ability to predict seizures up to one minute in advance.

Baselines. We selected four dynamic GNNs studies as baselines: EvolveGCN-O (Pareja et al., 2020), which follows the graph-then-time architecture, and a time-and-graph work, DCRNN (Tang et al., 2022). time-then-graph approach, GRAPHS4MER (Tang et al., 2023) and GRU-GCN Gao and Ribeiro (2022) are time-then-graph architectures. We included EEG foundation models, BIOT (Yang et al., 2023a), LaBraM (Jiang et al., 2024), and EEGPT (Wang et al., 2024). LaBraM and EEGPT were fine-tuned from the publicly available base model checkpoint. We also evaluated LSTM (Hochreiter and Schmidhuber, 1997) and CNN-LSTM (Ahmedt-Aristizabal et al., 2020) as referenced in Tang et al. (2022) and conventional methods, Support Vector Machine (SVM) and Random Forest.

Metrics. We used the Area Under the Receiver Operating Characteristic Curve (AUROC) and F1 score as evaluation metrics. AUROC considers various threshold scenarios, providing an overall measure of the model's ability to distinguish between classes. The F1 score focuses on selecting the

best threshold by balancing precision and recall. All results are averaged over five runs with different random seeds. Experimental details are provided in Appendix E.

5.2 Results

Main Results. Table 1 presents a performance comparison of seizure detection and prediction for the TUSZ dataset using various models over 12-second and 60-second windows. EvoBrain consistently outperforms dynamic GNN baselines and achieves competitive performance to the large-scale foundation model, LaBraM, while using 30 times fewer parameters . For the seizure detection in a 12-second window data, EvoBrain shows a 14% increase in AUROC and 12% increase in F1 score compared with LaBraM. For the 60-second window data, EvoBrain shows a 23% increase in AUROC and 30% ( 0 . 670 → 0 . 865 ) increase in F1 score ( 0 . 340 → 0 . 483 ) compared with EvolveGCN. All time-then-graph models demonstrate relatively high performance, supporting our theoretical analysis and conclusion of Theorem 2 in Section 3.

Figure 2 shows the ROC curves results comparing EvoBrain with other dynamic GNN models on seizure detection task. In subfigure (a), for the TUSZ dataset, EvoBrain achieves an AUC of 0.88, outperforming DCRNN (0.81) and EvolveGCN (0.76). Our ROC curve is positioned higher, indicating a stronger ability to differentiate between seizure and non-seizure events. In subfigures (b) for the CHB-MIT dataset, EvoBrain achieves an AUC of 0.94, significantly higher than the 0.81 and 0.59 of time-and-graph and graph-then-time approaches, respectively. The results show the effectiveness of time-then-graph for identifying seizures.

Dynamic Graph Structure Evaluation. Figure 3 shows the effectiveness of our proposed dynamic graph structure (i.e,. explicit dynamic modeling) compared to the static graph structure (i.e., implicit dynamic modeling) commonly used in existing work (Ho and Armanfard, 2023; Tang et al., 2022). The purple bar shows the performance of the static graph structure, while the orange bar represents the results when the static graph is replaced with our dynamic graph structures. As seen, the improvements are not limited to our time-then-graph method but also enhance the performance of all dynamic GNNs approaches. The figure highlights the effectiveness and necessity of dynamic graphs in capturing brain dynamics. The results imply that

(a) TUSZ dataset

(b) CHB-MIT dataset

TruePositiveRate

PositiveRate

EvoBrain (AUC=0.88)

EvoBrain(AUC=0.94)

GRU-GCN (AUC=0.86)

True

GRU-GCN (AUC=0.90)

GRAPHS4MER (0.83)

GRAPHS4MER (0.82)

DCRNN (AUC = 0.81)

DCRNN (AUC = 0.81)

EvolveGCN (AUC =0.76)

EvolveGCN (AUC =0.59)

0

False Positive Rate

0

False Positive Rate

(a) TUSZ 12s

(b) TUSZ 60s

EvolveCGN

DCRNN

GRAPHS4MER

GRU-GCN

EvoBrain

EvolveCGN

DCRNN

GRAPHS4MER

GRU-GCN

EvoBrain

Dynamic graph structure

(Explicit dynamic modeling)

Static graph structure

(Implicit dynamic modeling)

0.88

0.86

AUROC

0.70

0.60

(b) Training time

(a) Inference time

TUSZ dataset

CHB-MIT dataset

CHB-MIT dataset

TUSZ dataset

200

DCRNN

Time

(sw)

100

S

m

e

200

200

EvolveGCN

GRAPH4MER

Test

100

GRU-GCN

EvoBrain

Average

50

100

100

Average

12

30

60

0

12

Input data length (s)

60

12

30

60

0

12

Input Data length (s)

60

(a) Architecture evaluation

(b) Node feature

(d) RNN layer

(c) GNN layer

modeling temporal dynamics in EEGs should incorporate various channel connectivity or structural information, supporting our theoretical analysis and conclusion of Theorem 1 in Section 3.

Computational Efficiency. To assess the computational efficiency of our method, we measured the training time and inference time. Dynamic GNNs require computation time that scales with the length of the input data (details are provided in Appendix D). Figure 4 (a) illustrates the average training time per step for dynamic GNNs with a batch size of 1 across various input lengths. In practice, while the RNN component operates very quickly, the GNN processing accounts for most of the computation time. Since our method performs GNN processing only once for each data sample, it is up to 17 × faster training time and more than 14 × faster inference time than DCRNN. Thus, our approach is not only superior in performance but also fast in computational efficiency.

Ablation Study. Figure 5 (a) shows the results of different architectures applied to the same GRU and GCN layers using the 12-second TUSZ dataset on the seizure detection task. Consistent with Theorem 1, the time-then-graph architecture achieved the best performance. Figure 5 (b) shows the results when the FFT processing or LapPE was removed. Figure 5 (c) illustrates that replacing the GCN with GIN yields nearly identical performance, whereas removing the GNN and using only the RNN leads to a performance drop. Figure 5 (d) shows results of replacing Mamba with GRU layers on the seizure detection task using the 60-second TUSZ dataset. The results demonstrates that Mamba provides performance benefits, especially for longer input sequences.

5.3 Clinical Analysis.

We show a case analysis of our constructed dynamic graphs from a neuroscience perspective. Figure 6 shows the top-10 edges with the strongest connections in the learned dynamic graphs , where the yellow color represents the strength of the connections. These edges are selected based on the highest values, indicating the most significant relationships captured by the model. In Figure 6 (a), a sample unrelated to a seizure shows weak, sparse connections spread across various regions over an extended period. Figure 6 (b) shows a pre-seizure sample, where some connections gradually strengthen. Figure 6 (c) shows the result of a focal seizure, a type of seizure that originates in a specific area, with sustained strong connections only in a specific region. In Figure 6 (d), a generalized seizure is

(b) Pre-seizure

(a) Normal

(c) Focal-seizure

(d) Generalized-seizure

Strong

Weak

?

C4

?

4

C4

?

2

2

C4

4

illustrated, characterized by strong connections across the entire brain.

Successful surgical and neuromodulatory treatments critically depend on accurate localization of the seizure onset zone (SOZ) (Li et al., 2021a). Even the most experienced clinicians are challenged because there is no clinically validated biomarker of SOZ. Prior studies have shown that abnormal connections across several channels may constitute a more effective marker of the SOZ (Scharfman, 2007; Burns et al., 2014b; Li et al., 2018). Our dynamic graph structures align with neuroscientific observations, successfully visualizing these abnormal connections and their changes. This offers promising potential for application in surgical planning and treatment strategies.

6 Conclusion

In this work, we propose a dynamic multi-channel EEG graph modeling approach, EvoBrain . By adopting a time-then-graph strategy together with explicit dynamic modeling, EvoBrain captures the evolving nature of brain networks. Our theoretical analysis establishes the expressivity advantages of both explicit dynamic graphs and the time-then-graph paradigm over alternatives, providing a principled foundation for the design choices. EvoBrain yields substantial empirical gains, including improvements of 23% in AUROC and 30% in F1 over a strong dynamic GNN baseline, and strong performance on early seizure prediction. Case clinical analyses further highlight potential clinical utility by revealing network changes consistent with seizure progression. Taken together, these results suggest EvoBrain is a practical and theoretically grounded step toward reliable, clinically meaningful EEG-based seizure analysis.

Limitations and Social Impacts. In seizure prediction, pre-ictal patterns are typically weaker and more spatially diffuse. While EvoBrain achieves the best performance among lightweight GNN-based models, LaBraM benefits from more parameters and pretraining on large-scale multiple EEG corpora, which enhances its ability to generalize under limited and noisy pre-seizure data conditions. While we focus our evaluation on the seizure task, generalization to other tasks remains a challenge of future work. Regarding potential negative societal impacts, we recognize key risks such as bias and system malfunction. Specifically, models trained on EEG data from specific demographic groups may exhibit biased performance when applied to broader populations, potentially leading to unequal diagnostic accuracy. Additionally, miscalibrated early seizure prediction could lead to false alarms, causing unnecessary interventions or patient distress. These challenges highlight promising directions for future work, where incorporating fairness assessments, demographic audits, and human-in-the-loop strategies can lead to more robust and trustworthy EEG-based systems.

Acknowledgments

The authors would like to sincerely thank the anonymous reviewers for their valuable comments and helpful suggestions. This work was supported by JST BOOST, Japan Grant Number JPMJBS2402, 'Program for Leading Graduate Schools' of The University of Osaka, JSPS KAKENHI Grantin-Aid for Scientific Research Number JP24K20778, JST CREST JPMJCR23M3, JST START JPMJST2553, JST CREST JPMJCR20C6, the Japan Science and Technology Agency (JST) AIP Acceleration Research (JPMJCR24U2, TY), Japan Agency for Medical Research and Development (AMED, JP19dm0307103, HK, JP24wm0625207, TY), the Japan Science and Technology Agency (JST) Moonshot R &D-MILLENNIA Program (JPMJMS2012, TY), AIP Acceleration Research (JPMJCR24U2, TY), JST K Program JPMJKP25Y6, JST COI-NEXT JPMJPF2009, JST COI-NEXT JPMJPF2115,Future Social Value Co-Creation Project - The University of Osaka.

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Appendix

graph-then-time

Theorem 2.

Temporal model (RNN)

Graph model (GNN)

Representation

time-and-graph

Edge model

time-then-graph model

Dynamic graph structure

Explicit dynamic modeling

Implicit dynamic modeling

Static graph structure

Fixed

Theorem 1.

Time

(a) Two graph structures

(b) Three dynamic graph architectures

A Related Work

Automated Seizure Analysis. The automated detection or prediction of seizures has been a longstanding challenge (Zhang et al., 2024b; Kotoge et al., 2024). Deep learning has shown great achievements in automating EEG feature extraction and detection, using convolutional neural networks (CNNs) (Fukumori et al., 2022b; Ahmedt-Aristizabal et al., 2020; Asif et al., 2020; Saab et al., 2020), RNN-based models (Fukumori et al., 2022a; Ahmedt-Aristizabal et al., 2020; Rasheed et al., 2021), Transformers (Eldele et al., 2021; Yang et al., 2023b; Jiang et al., 2024; Yi et al., 2023), and brain-inspired models (Rich et al., 2020; Burelo et al., 2022; Chen et al., 2023; Costa et al., 2024).

Spatial Relationships in EEG Networks. A seizure is fundamentally a network disease, and detection typically relies on the ability to determine abnormalities in EEG channels (Burns et al., 2014a; Li et al., 2021b; Rolls et al., 2021). Many multi-channel methods have been proposed for capturing spatial information in channels (Jiang et al., 2024; Yi et al., 2023; Zhang et al., 2023; Mohammadi Foumani et al., 2024). Among them, recent studies have proposed GNNs to capture further the non-Euclidean structure of EEG electrodes and the connectivity in brain networks (Covert et al., 2019; Sun et al., 2021; Li et al., 2022b; Chen et al., 2022; Klepl et al., 2022; Demir et al., 2022). These methods form EEGs as graphs, embedding each channel into the nodes and learning spatial graph representations (Demir et al., 2021; Ho and Armanfard, 2023). However, they do not explicitly model temporal relationships, relying instead on convolutional filters or conventional linear projections for node embeddings.

Dynamic GNNs for EEG Modeling. Dynamic GNN is effective in learning temporal graph dynamics, achieving promising results in tasks such as dynamic link prediction (Tian et al., 2024), node classification (Zhang et al., 2024a), and graph clustering (Liu et al., 2024). Recently, some studies have focused on dynamic GNNs aimed to enhance temporal and graph representations for EEG-based seizure modeling. Tang et al. (2022) proposes a time-and-graph model , which uses frequency features from FFT as node features and applies GNN and RNN processing simultaneously for each sliding window. Cai et al. (2023) adopts a graph-then-time model that combines GCN and RNN for seizure detection. However, these studies construct static graphs with fixed structures across temporal learning. Hou et al. (2022) propose time-then-graph model, BiLSTM-GCNNet, which uses RNNs to construct static graph from node feature. GRAPHS4MER (Tang et al., 2023) is also proposed as a time-then-graph method. This work learns dynamic graphs using an internal graph structure learning model. Similarly, both Asadzadeh et al. (2022) and Li et al. (2022a) internally learn dynamic graph structures. However, its input for graph structure learning is still based on the static Euclid distance or similarity of the entire data sample (e.g., 12 or 60 seconds) rather than individual snapshots. Our work differs by defining dynamic graph structures that more effectively capture the temporal evolution of brain connectivity in EEGs.

B Graph Isomorphism and 1-WL Test

Graph isomorphism refers to the problem of determining whether two graphs are structurally identical, meaning there exists a one-to-one correspondence between their nodes and edges. This is a crucial challenge in graph classification tasks, where the goal is to assign labels to entire graphs based

on their structures. A model that can effectively differentiate non-isomorphic graphs is said to have high expressiveness, which is essential for accurate classification. In many cases, graph classification models like GNNs rely on graph isomorphism tests to ensure that structurally distinct graphs receive different embeddings, which improves the model's ability to classify graphs correctly.

1-Weisfeiler-Lehman (1-WL) test is a widely used graph isomorphism test that forms the foundation of many GNNs. In the 1-WL framework, each node's representation is iteratively updated by aggregating information from its neighboring nodes, followed by a hashing process to capture the structural patterns of the graph. GNNs leveraging this concept, such as Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs), essentially perform a similar neighborhood aggregation, making them as expressive as the 1-WL test in distinguishing non-isomorphic graphs (Xu et al., 2019). Modern GNN architectures adhere to this paradigm, making the 1-WL a standard baseline for GNN expressivity. In our work, we also use 1-WL-based GNNs, leveraging their proven expressiveness for dynamic brain graph modeling.

C Proofs of Expressivity Analysis

C.1 Expressiveness with Node and Edge Representations

Lemma3. [Necessity of Node Representations] Edges alone (Gao and Ribeiro, 2022) are insufficient to uniquely distinguish certain temporal EEG graphs. Specifically, there exist pairs of temporal EEG graphs that have identical edge features across all time steps but different node features, making them indistinguishable based solely on edge representations. Therefore, incorporating node representations is necessary to achieve full expressiveness in EEG graph classification tasks.

̸

Proof. Given G (1) and G (2) , with the same sets of V and E , for ∀ t , the edge features satisfy: a (1) i,j,t = a (2) i,j,t ∀ ( v i , v j ) ∈ E , ∀ t ∈ { 1 , 2 , . . . , T } . However, suppose there exists at least one node v k ∈ V and one time step t ′ such that: x (1) k,t ′ = x (2) k,t ′ . Since a (1) i,j,t = a (2) i,j,t , any GNN architecture that relies solely on edge features will produce identical embeddings for G (1) and G (2) , ∀ t .

Lemma 4. [Expressiveness with Node and Edge Representations] When both node and edge representations are incorporated, a GNN can uniquely distinguish any pair of temporal EEG graphs that differ in either node features or edge features at any time step, provided the GNN is sufficiently expressive (e.g., 1-WL GNN).

Proof. Given G (1) = ( A (1) , X (1) ) and G (2) = ( A (2) , X (2) ) , suppose they differ in at least one node feature or edge feature at some time step t . An expressive GNN can produce different embeddings for these graphs by capturing the differences in node and/or edge features. Specifically:

̸

If X (1) : ,t = X (2) : ,t for some t , then the node embeddings h (1) i,t and h (2) i,t will differ for at least one node v i .

̸

If a ( 1 ) i , j , t = a ( 2 ) i , j , t for some edge ( v i , v j ) and some t , then the edge embeddings h (1) ij,t and h (2) ij,t will differ for that edge.

Since the GNN aggregates information from both node and edge embeddings, any difference in either will propagate through the network, resulting in distinct final representations Z (1) and Z (2) . Thus, the GNN can uniquely distinguish between G (1) and G (2) .

C.2 Implicit and Explicit Dynamic Modeling

Theorem 1. [Implicit ⪵ Explicit Dynamic Graph Modeling.] Explicit dynamic modeling (dynamic adjacency matrices) is strictly more expressive than implicit dynamic modeling (static graph structures) in capturing spatiotemporal dependencies in EEG signals.

Proof. Let F implicit be the family of functions (e.g., representations or classifiers) expressible by an implicit dynamic graph model that compresses all adjacency snapshots { A : , : ,t } T t =1 into a single

adjacency matrix ̂ A , and let F explicit be the family of functions expressible by an explicit dynamic graph model that uses the full time-varying adjacency { A : , : ,t } T t =1 . We prove

̸

Subset Relationship. It can be interpreted as any implicit dynamic model aggregates the set of adjacency matrices { A : , : ,t } T t =1 into a single, static ̂ A by some function f ( · ) (e.g., averaging, summation, thresholding):

Such a model uses ̂ A for all time steps, disregarding changes in edges across t . In contrast, an explicit dynamic model directly processes the full sequence { A : , : ,t } T t =1 . To see that F implicit is contained in F explicit , observe that any function f imp ∈ F implicit can be mimicked by an explicit model that simply ignores the time-specific variability in adjacency and substitutes f ( { A : , : ,t } ) = ̂ A as if it were the adjacency for every t . Hence,

(2) Strict Separation by Counterexample. To show that F implicit = F explicit , we construct two temporal EEG graphs, G (1) = { X : ,t , A (1) : , : ,t } T t =1 and G (2) = { X : ,t , A (2) : , : ,t } T t =1 , such that

Their node features match at every time step:

Their adjacency differs only at one time step t ′ :

̸

̸

Under implicit dynamic modeling, the function f ( { A : , : ,t } T t =1 ) may yield the same compressed adjacency ̂ A for both G (1) and G (2) . Hence, any implicit model would treat the two graphs identically , failing to separate them because the single ̂ A cannot preserve the difference at t ′ .

̸

In contrast, the explicit dynamic model processes { A ( k ) : , : ,t } T t =1 without discarding the time-stepspecific variations. Consequently, it does see A (1) : , : ,t ′ = A (2) : , : ,t ′ , and can therefore distinguish G (1) from G (2) . Thus, there exist inputs in the domain of temporal EEG graphs that are indistinguishable by any implicit dynamic model but distinguishable by an explicit dynamic model. This proves

̸

and in view of the subset argument, we conclude

explicit dynamic modeling is strictly more expressive than implicit dynamic modeling.

C.3 time-and-graph and time-then-graph

Lemma 2. [time-and-graph ⪵ time-then-graph ] time-then-graph is strictly more expressive than time-and-graph representation family on T n,T,θ , as time-then-graph outputs different representations, while time-and-graph does not.

Gao and Ribeiro (2022) prove that a time-then-graph representation that outputs the same embeddings as an arbitrary time-and-graph representation. Thus, time-then-graph is as expressive as time-andgraph . To prove Lemma 2 we also provide a EEG graph classification task where any time-and-graph representation will fail while a time-then-graph would work, which then, added to the previous result, proves that time-then-graph is strictly more expressive than time-and-graph .

i.e., implying

̸

Time

Edge feature

1

2

Dynamic EEG graph

[1, 1]

[0, 1]

[1, 0]

X

Proof. We now propose a synthetic EEG task, whose temporal graph is illustrated in Figure 8. The goal is to differentiate the topologies between two 2-step temporal graphs. Each snapshot is a static EEG graph with 8 attributed nodes, denoted as C 8 , 1 and C 8 , 2 .

Two temporal graphs differ in their second time step t 2 . If the graphs have the same features, any 1-WL GNN will output the same representations for both C 8 , 1 and C 8 , 2 . We use a ( top ) to represent the adjacency matrix of dynamics in the top left of Figure 8, and a ( btm ) for dynamics in the bottom left of Figure 8. Note that X ( top ) = X ( btm ) since the temporal graph has the same features.

Hence, for a time-and-graph representation:

Then, when we apply Equation (2) at the first time step, for the top graph:

for the bottom graph:

For the second time step:

̸

Despite A ( top ) : , : , 2 = A ( btm ) : , : , 2 , the 1-WL GNN will output the same representations h ( top ) i , 2 = h ( btm ) i , 2 for both C 8 , 1 and C 8 , 2 .

Therefore:

̸

̸

concluding our proof.

Thus, time-and-graph will output the same final representation Z ( top ) = Z ( btm ) for two different temporal graphs in Figure 8.

For the time-then-graph representation, we apply Equation (3). First, for the node representations:

Since X ( top ) = X ( btm ) , we have h node(top) i = h node(btm) i for all nodes i .

Now, for the edge representations:

̸

Here, a ( top ) i , j , ≤ 2 = a ( btm ) i , j , ≤ 2 for some ( i, j ) pairs, because the graph structures differ at t 2 . Therefore, h edge(top) i , j = h edge(btm) i , j for these pairs. Finally, we apply the GNN:

Since h edge(top) = h edge(btm) , and 1-WL GNNs can distinguish graphs with different edge attributes, we have:

̸

̸

Thus, time-then-graph outputs different final representations Z ( top ) = Z ( btm ) for the two temporal graphs in Figure 8, successfully distinguishing them.

Finally, we conclude:

The time-then-graph is at least as expressive as the time-and-graph ;

The time-then-graph can distinguish temporal graphs not distinguishable by time-and-graph .

Thus, time-then-graph is strictly more expressive than time-and-graph . More precisely,

D Computational Complexity

In this section, we provide the computational complexities of the three architectures: graph-then-time , time-and-graph , and time-then-graph . We demonstrate that the time-then-graph architecture has the lowest computational complexity among them.

Let T be the number of time steps, V be the number of nodes, E t be the number of edges at time t , ∑ t E t be the total number of edges across all time steps, E agg be the number of edges in the aggregated graph (i.e., the union of all edges across time steps), and d be the dimension of the node and edge representations.

D.1 graph-then-time Architecture

In the graph-then-time architecture, at each time step t , a GNN is applied to the snapshot graph ( X : ,t , a : , : , t ) to capture spatial relationships. Subsequently, an RNN processes the node embeddings over time to capture temporal dependencies.

The computational complexity per time step t is dominated by:

where V d 2 accounts for node-wise transformations (e.g., linear layers), and E t d accounts for message passing over edges.

Over all time steps, the total complexity for the GNN computations is:

The RNN processes the node embeddings over time with complexity:

Therefore, the overall computational complexity of the graph-then-time architecture is:

D.2 time-and-graph Architecture

In the time-and-graph architecture, temporal dependencies are integrated into the GNN computations. At each time step t , two GNNs are applied:

GNN L in processes the current snapshot inputs ( X : ,t , a : , : , t ) .

GNN L rc processes the representations from the previous time step ( h : , t -1 , a : , : , t ) .

The computational complexity per time step t is:

due to the node-wise transformations and edge-wise message passing with updated representations.

Over all time steps, the total complexity for the GNN computations is:

The RNN (or any recurrent unit) further processes the node embeddings with complexity:

Therefore, the overall computational complexity of the time-and-graph architecture is:

D.3 time-then-graph Architecture

In the time-then-graph architecture, temporal evolutions of node and edge attributes are modeled first using sequence models (e.g., RNNs). A GNN is then applied to the resulting static graph with aggregated temporal information.

The computational complexities are as follows:

Node Sequence Modeling. For each node i ∈ V , an RNN processes its temporal features X i, ≤ T :

Edge Sequence Modeling. For each edge ( i, j ) ∈ E agg, an RNN processes its temporal adjacency features a i , j , ≤ T :

GNN over Aggregated Graph. A GNN is applied once to the static graph with updated node and edge representations:

Therefore, the overall computational complexity of the time-then-graph architecture is:

D.4 Comparison of Complexities

To compare the computational complexities, we consider the dominant terms in Equations (7), (8), and (9).

· graph-then-time :

time-and-graph :

time-then-graph :

By comparing these computational complexities, the time-then-graph method is superior under the aggregated number of edges E agg is smaller than the total sum of edges over all time steps, i.e., E agg ≪ ∑ T E t .

E Experimental details and implementation

Model training. Training for all models was accomplished using the Adam optimizer (Kingma and Ba, 2014) in PyTorch on NVIDIA A6000 GPU and Xeon Gold 6258R CPU.

Data augmentation. During the training process, we applied the following data augmentation techniques, following prior studies (Tang et al., 2022; Eldele et al., 2021): randomly scaling the amplitude of the raw EEG signals by a factor between 0.8 and 1.2.

Implementation details. We used binary cross-entropy as the loss function to train all models. The models were trained for 100 epochs with an initial learning rate of 1e-4. To enhance efficiency and sparsity, we set τ = 3 and the top-3 neighbors' edges were kept for each node. The dropout probability was 0 (i.e., no dropout). EvoBrain has two Mamba consisting of two stacked layers and a two-layer GCN with 64 hidden units, resulting in 114,794 trainable parameters. We release GitHub repository ( https://github.com/Kotoge/EvoBrain ).

Implementation of baselines. For baselines, DCRNN (Tang et al., 2022), EvolveGCN (Pareja et al., 2020), and LSTM (Hochreiter and Schmidhuber, 1997), we used the number of RNN and GNN layers and hidden units in our EvoBrain . For BIOT, we use the same model architecture described in Yang et al. (2023a), i.e., four Transformer layers with eight attention heads and 256-dimensional embedding. For LaBraM, we used the official checkpoint provided by Jiang et al. (2024). For CNNLSTM, we use the same model architecture described in Ahmedt-Aristizabal et al. (2020), i.e., two stacked convolutional layers (32 3 × 3 kernels), one max-pooling layer ( 2 × 2 ), one fully-connected layer (output neuron = 512), two stacked LSTM layers (hidden size = 128), and one fully connected layer. Table 2 shows a comparison of trainable parameters, with our EvoBrain achieving the best performance using the relatively few parameters.

F Data description

Tabel 3 shows the details of TUSZ dataset.

G Memory Efficiency

Figure 4 shows memory efficiency comparisons across dynamic GNNs in both training and inference settings with a batch size of 1. While DCRNN and EvolveGCN exhibit the lowest memory usage, EvoBrain achieves over 10× faster computation compared to these baselines, making it a compelling choice for time-critical applications. Among the three time-then-graph models, EvoBrain demonstrates the best balance between memory consumption and computational speed, with significantly lower memory requirements than GRAPHS4MER and comparable usage to GRU-GCN.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the issue of existing so-called Dynamic GNN models that are actually built on temporally static graphs, thus failing to reflect the evolving nature of brain connectivity specifically in the applied field of seizure prediction. The paper is included in a broader theoretical framework in which this new model named EvoBrain is defined as a \"time-then-graph\" approach. This new model is used for seizure detection and integrates a two-stream Mamba architecture with a GCN enhanced by Laplacian Positional Encoding, significantly improving metrics like AUROC and F1-score across different baselines and task complexity.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\nOverall, I find this paper to be well organised, with its contributions clearly framed within the broader literature and showing potential impact on clinical seizure prediction. Although I do not work with seizure applications and with dynamic graph modelling (and thus I cannot fully validate some of the novelty claims), I still believe the paper stands out in several key areas, namely: (1) good results in seizure prediction at 60s before seizure onset, as opposed to 20s supposedly more commonly used in previous literature, (2) superior and consistent results demonstrated in table 1, and (3) the use of evolving dynamic graph structures over time, which the authors contrast with the static graphs adopted in earlier studies. These strengths are further reinforced by a theoretical framework analysing different parts of the method and method's motivation.\n\nIn my view, the novelty of this work comes from a novel combination of existing approaches to address previously known limitations, resulting in what appears to be a very successful model. This makes the ability to predict seizures up to a minute in advance not only clinically meaningful, but also a computationally efficient solution supported by solid theoretical grounding. \n\nBased on the significance of these strengths I'm leaning towards acceptance of this work; however, I'm only scoring it as borderline accept for now mostly given some points I need to clarify during the rebuttal period, as well as some weaknesses that I'll identify.\n\n\n## Weaknesses\n\nI have three main concerns about the experimental settings and problem definition. \n\nFirstly, I have the impression that the authors are mixing together two different claims: one thing is the dynamic graph creation at each timestep, and the other is the indication that the \"time-and-graph\" method is the most expressive representation. This taxonomy seemingly introduced by Gao and Ribeiro (2022) is new to me, but from section 2.2 it seems to me that all three representations could be used with only static graphs generated beforehand, as well as with a new graph being created at each timestep. In this way, I believe the *experimental* claim that time-then-graph is better than the others was not fairly evaluated because it seems that the method also included a dynamic graph creation on top of the time-then-graph framework, mixing claims. Thus, I believe a fairer comparison would include a dynamic graph creation in the baselines. \n\nSecondly, no traditional ML model was used. The authors seem to claim that this work could be useful for clinicians, but an important step of such thing is to present them what they currently use, assuming not so much deep learning. Baselines with proper hyperparameter search like for instance RandomForests/XGBoost/SVM would be important to report.\n\nFinally, and this is not as important as my previous two weaknesses given the final results, the paper only uses a GCN as \"the\" graph neural network model. I'm sure a straightforward GCN model helps in bringing the fast results claimed in the paper, but with so many GNN models currently in literature, it would be interesting to understand how a couple of other more GNN models would influence the performance and at what time/parameter cost (and as I mention in Questions, it would also be important to ablate this specific step).\n\n\nOther small suggestions:\n1. Typo in abstract: \"GMN\"\n2. I'm not sure the use of \"nascent\" in the abstract is clear. What does that mean, \"recent\"? How does that fit with the interactions claim?\n3. In section 4.1, it would be good to specify how the threshold to rank the correlations is defined, and maybe ablated.\n4. In section 4.1, it is not clear how the creation of the sparse graphs prevent information redundancy.\n5. In Figure 4, one would expects some measure of variation when comparing running times across different models, instead of showing only the averaged values.\n\nQUESTIONS:\nAs I mentioned, I am leaning towards acceptance of this work given the strengths of the paper; however, given the weaknesses I have identified, I can only recommend borderline accept at the moment. I will be happy to increase my scores if the authors satisfactorily tackle the weaknesses I have identified, as well as help me better understand some of the claims of the paper, which I leave in the following bullet points for easier identification:\n\n1. Shouldn't the application of the GCN layer at the end of the model be also ablated? The way the paper is written it seems that this so-called two-stream Mamba handling of the different graphs at different snapshots seems to be able to generate a very rich spatial model of the evolution of the different graph structures throughout time. In this sense, wouldn't it make sense to directly apply a fully connected layer on this spatial representation?\n2. To better evaluate the claimed novelty of the experiments, could the authors be more specific about the challenging task of seizure prediction at 60s before onset? Is it that they are the first ones using this timestep, or just that most works only use the 20s timestep?\n3. The dataset seems particularly imbalanced, which I'm sure is a common thing in this area. Did the authors use techniques to account for this for example by using a weighted loss function? This tends to help in these situations, but I'm not sure the authors considered it. In this sense, the AUROC and F1 scores are definitely good choices, but I believe the paper would benefit from having more fine-grained metrics like sensitivity and specificity in appendix.\n\nLIMITATIONS:\nThe checklist says that limitations as well as potential negative societal impacts of the work were discussed, but I don't see them anywhere. Could the authors please clarify where these points are located?", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose EvoBrain to capture both temporal and spatial dynamics in multi-channel EEG data for accurate seizure detection. By explicitly constructing and integrating dynamic graphs, the model effectively learns the evolving characteristics of brain networks. Experiments show the effectiveness of the proposed methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The manuscript is clearly written, and the idea of constructing and utilizing dynamic graphs is interesting and compelling.\n2. The study offers an in-depth exploration of the issues in the field.\n\nWeaknesses:\n1. The problem definition and data description are unclear. For example, in line 39, the terms 'initial snapshot' and 'subsequent EEG snapshots' are not easy to understand, as it is not clear which parts of Figure 1 they refer to. A detailed description and visualization of the data and task would make the article more accessible to a wider audience.\n2. The novelty of the proposed method appears limited, as Graph Convolutional Networks and Laplacian Positional Encoding are well-established and general techniques. Could you clarify which components of your model are specifically tailored to this task? Additionally, it would be useful to highlight the differences between your approach and existing models in the literature.\n3. The comparison methods in the experiments seem outdated, which mostly consists of approaches from 2022 and 2023. Could you consider including comparisons with more recent methods from the past two years? This would provide a more comprehensive evaluation of the effectiveness of your approach.\n4. The evaluation metrics used are not comprehensive. For medical tasks, recall and precision are also essential. Why were these not analyzed in the comparative and ablation studies? F1 and AUC may not always fully reflect the clinical performance of the model.\n\nQUESTIONS:\nSee Weaknesses\n1. A detailed description and visualization of the data and task would make the article more accessible to a wider audience.\n2. Could you clarify which components of your model are specifically tailored to this task? Additionally, it would be useful to highlight the differences between your approach and existing models in the literature.\n3. You are strongly recommended to include comparisons with more recent methods from the past two years (2024-2025). This would provide a more comprehensive evaluation of the effectiveness of your approach.\n4. Why were recall and precision scores not analyzed in the comparative and ablation studies? F1 and AUC may not always fully reflect the clinical performance of the model.\n\nLIMITATIONS:\nThe description of limitations in line 365 is rather superficial, making it difficult for readers to fully grasp the future directions. The authors should carefully discuss the limitations and highlight them in the checklist.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-24"}

comments: SUMMARY:
The authors provide a¡ framework for EEG seizure detection and pre-seizure identification using Graph Neural Networks. They demonstrate that dynamic representations of the graph, as well as temporal modeling of the graph using Mamba exhibits a better representation of the dynamics of the brain network. They demonstrate how its model outperforms some of the existing models, with a similar performance but an improvement in AUROC.

STRENGTHS AND WEAKNESSES:
The manuscript presents a solid mathematical foundation for their claims. They showcase how their model outperform other models. It is a strong manuscript.

The manuscript lacks of a discussion about the limitation of the model. For instance in Table 1 it is shown that for prediction of seizures LaBraM outperforms their method. A deep discussion about this is needed. Also generally a faster computation is achieve by an increased burden in memory. Then a discussion about the memory consumption for the training of the model is lacking. In general the manuscript lacks a discussion about the limitations of their approach.

QUESTIONS:
I wonder about the limitation of their approach and a deep discussion about the limitations of this model. Also a discussion of why LaBraM outperformed EvoBrain in the prediction of seizures.

LIMITATIONS:
There is a lack of discussion about limitations, please refer to my prior comments.
TITLE: Official Review
CLARITY: 4
IMPACT: 4
ORIGINALITY: 4
DATE: 2025-06-30

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes EvoBrain, a dynamic multi-channel EEG modeling framework for seizure detection and prediction. The authors identify two key gaps in existing dynamic GNN-based EEG models: (1) the overuse of static graph structures, which fail to capture evolving brain connectivity, and (2) insufficiently expressive spatio-temporal modeling architectures. EvoBrain addresses these issues through (a) an explicit dynamic graph structure that updates both nodes and edges over time, and (b) a time-then-graph modeling approach using a two-stream Mamba architecture for temporal dynamics, followed by GCNs with Laplacian Positional Encoding for spatial modeling. Theoretical analysis demonstrates the expressivity advantages of this approach. Experiments on large public datasets (TUSZ, CHB-MIT) show clear gains in AUROC and F1, with higher computational efficiency than previous baselines.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n* The motivation is well-defined, focusing on the clinical importance of modeling the evolving connectivity in EEG for seizure prediction.\n* The paper provides solid theoretical analysis, rigorously comparing different spatio-temporal dynamic graph architectures, and establishes the superiority of time-then-graph with explicit dynamic graphs.\n* The method is evaluated on strong baselines and large, realistic datasets, with results showing significant improvements in both performance and efficiency.\n* Engineering details, ablation, and neuroscientific interpretability are well-addressed, supporting clinical relevance.\n\n**Weaknesses:**\n\n* The core contribution is primarily an integration and refinement of known components: dynamic graphs, GNNs, and sequence models—rather than a fundamentally new paradigm.\n* The “explicit dynamic graph” idea is conceptually logical and increasingly common in recent GNN+EEG works; the main difference here is in more rigorous theoretical justification and cleaner engineering.\n* The method focuses mainly on standard seizure detection/prediction. Generalizability to more diverse EEG tasks (multi-class classification, cross-patient generalization, multi-modal fusion) is not explored.\n* Some implementation choices (two-stream Mamba, LapPE) feel like plug-and-play improvements, and the overall novelty is incremental relative to the field’s direction. not big innovation.\n\nQUESTIONS:\nno\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}