EvoBrain: Dynamic Multi-Channel EEG Graph Modeling for Time-Evolving Brain Networks
Authors: Rikuto Kotoge
Zheng Chen
Tasuku Kimura
Yasuko Matsubara
Takufumi Yanagisawa
Haruhiko Kishima
Yasushi Sakurai
Venue: NeurIPS 2025 spotlight ()
Keywords: EEG
graph
neuroscience
seizure
dynamic modeling
expressiveness
Primary area: neuroscience_and_cognitive_science
TL;DR: EvoBrain, a theoretically grounded and efficient dynamic GNN that models temporal and evolving spatial EEG patterns for seizure analysis.

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
Rikuto Kotoge' Zheng Chen'
Tasuku Kimura!
Yasuko Matsubara' Yasushi Sakurai'
Takufumi Yanagisawa
Haruhiko Kishima²
SANKEN, The Univerity of Osaka, Japan
DDpartment of Neurosurgery, Graduate School of Medicine, The University of Osaka, Japan IIntitttee for Advanced Co- Creation Studies, The University of Osaka, Japan
(rikuto88, chenz, tasuku, yasuko, yasushi (attushi@@sssseeee A.sankem. osaka-u. ac. ?(tyanagisawa, hkishima) @nsurg med osaka-u.ac..p
Abstract
Dynamic GNNs, which integrate temporal and spatial features in Electroen- cephalography (EEG) data, have shown great potential in automating seizure detection. However, fully capturing the underlying dynamics necessary to repre- sent brain states, such as seizure and non-seizure, remains non-trivial task and presents two fundamental challenges. First, most existing dynamic GNN methods are built temporally fixed static graphs, which fail reflect the evolving nature brain connectivity during seizure progression. Second, current efforts to jointly model temporal signals and graph structures and, more importantly, their inter- actions 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-grape -eghhh dynamic GNN method. Building on these insights, we propose EvoBrain, a novel seizure detection model that integrates a two-stream Mamba architecture with GCN enhanced by Laplacian Positional Encoding. following neurological insights. Moreover, EvoBrain incorporates explicitly dynamic graph structures, allowing both nodes and edges 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 the challenging early seizure prediction task.
Introduction
Epileptic seizures typically considered network disorder (Burns al. 2014a). The abnormal connections across brain regions often serve as markers 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, recent trend models EEGs sequence of miryingying 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 time, further enhancing seizure detection accuracy.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Multi-channel EEG signals
Time-evolving
Normal
Pre-seizure
Seizure
Change even the same state
Connesiviiy varies across states
Brain networks
Frequency dynamics
Theorem
Theorem 2.
Explieit dynamiic modeling
time-theu--ee -ggaapp model
Represestation
decomposition
Frequency
construction
Graph
modelling GCN
AE
Gruph (GNN)
Topology capnaring with LapPl
Terppnr model (RNN)
Nauplituee
Fresuei
Dynamic graph structure
Edgg featuro
Nodlo model
Temporal modellng with streaue Manch
Time
The brain network evolves over time, and changes occurring during seizures and im- mediately before them in the pre-seizure phase, especially within specific zones, are clinically important. These changes are captured using dynamic graphs derived from multi-channel EEG signals. EvoBrain incorporates explicit dynamic graph modeling and time-then- graph architecture.
Figure 1:
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. essence, we mainly face two challenges:
(1) Representing EEG dynamics (Problem I.. 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 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 al. 2021 Li et al. 2021b Chen al. (025). shown in Figure I
2) Effective Spatio-temporee temporal Modeling (Problem2) 2}. Dynamic GNNs can generally be categorized into time-then-graph, graph-then-time, and time-and-grapl architectures, following the taxonomy of Gao and Ribeiro (002)) (A concise illustration is provided in Appendix Figure 7 The time-then-gruyy 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 recurrent GNN to capture temporal interactions between EEG snapshots before performing graph learning at each time step. However, the independent GNNs in then--itee--tme represent information at single time steps without accounting for dynamic interactions between time steps. While recurrent GNNs in time-and ann--an--raah capture graph interactions, they also rely heavily on the independent initial GNNs. Overall, an effective dynamic GNNs for integrating temporal and graph-based based representations to model brain dynamics remains poorly understood.
Novelty and Contributions: We first analyze theoretical foundation for designing dynamic graph structures and models that effectively represent brain dynamics. Building upon this foundation, we propose EvoBrain, which effectiivlyy learns Evolving, 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 I]. To tackle the second challenge, we first theoretically analyze different dynamic GNNs approaches from EEG graph perspective (Theorem P). We discuss the necessarily of dynamic GNNs at node-level, since the node similarity measures are key factors in determining EEG graph construction.

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Novel Model Design. We hence propose novel time-then graenh 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 AUROC and F1 scores, respectively, compared with the dynamic GNN baseline. Also, EvoBrain is 17 x faster than the SOTA time-and-gran 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 scizure prediction, which aims to identify the preictal state before seizures. This is critical for early intervention in clinical settings, and EvoBrain maintains performance, with 13.8% improvement in AUROC.
2 Problem Setting
2.1 Notations
We define an EEG a with N channels and I"' snapshots as a graph G = (A, where A= (V,, and A E N are the adjacency matrices. V and & represent the channels (i.e., nodes) and edges. Notably, most existing work constructs a weighted adjacency matrix A E NxN 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 Eigi. E & represents pairwise connectivity between channels U; and Vij, where i. E N. The feature vector Li, E Rdd captures the electrical activity of i-th channel during the EEG snapshot time step f. If Ci.j.t exists, atj. is a non-zero value. di.j.t E R quantifies the connectivity strength between two channels for snapshot. To represent temporal EEG graphs, we define the embedding of node eú at time step as higdde E R² which captures both the spatial connectivity information from the edges and the temporal dynamies from previous node embeddings. The embedding of edge Ci.i. denoted as h edge R', 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 I We treat expressivity analysis as 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 [ We further define the challenge of effective spatio-temporal modeling as the investigation of the expressivity of
gruph-then-time, time-and-gen gruph, and time-then- then-graph (Gao and Ribeiro 2022) in dynamic EEG
graph analysis in Problem
Definition 1 (Implicit Dynamic Graph Modeling Static Structure). This approach fixes a single adjacency matrix A E NxN across all time steps, although each node's 's feature vector x. evolves across t. Formally, A...t = for each t E E',,...,YY 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 B.,z and the adjacency matrices {A. can vary with time. Specifically, A.,. E RNNNN each snapshot t may be computed by a function f: A...t. (I.,1), Vt E {1,...,T), TT,, thereby capturing the dynamic evolution of channel connectivity in addition to time-varying nodes.
Problem (Implicit vs. Explicit Dynamic Graph Modeling). We consider two approaches for capturing spatial relationships. In the implicit (static) approach, 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_
change with t, allowing for tare-na 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 independently followed by the temporal processing (e.g., by RNNs) of the resulting node embeddings. The formal definition is given as:
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hgge Cell (X.,, A...)
{[ONN
h -
Z
H.T Vi V,
(I)
where he (1 St S T) denotes the embedding of node E V, GNN a.,..)) denotes graph learning the current snapshot through I. layer GNNs. The learned embeddings, h hg then passed into the RNN cell to capture the temporal dependencies. The last step output h is considered the final representation Z.
Definition 4 (Time-and-ae -ndd-aah--rg........ This architecture alternately processes time and graph components, applying GNNs to each EEG snapshot, as formally defined by:
mode = -Cel (CONN (X.,, 1,t
A.t.)) [GNN" ( (H...I.A...))) Z Hmode .T
Vi E V, (2)
where we initialize H4,0 O. GNN!, encodes each v,, while GNN encodes representations from historical snapshots 1, and RNN cell embeds evolution of those graph representations.
Definition -hee--thn--rapph. This architecture first models the evolution of node and edge
attributes over time and then applies GNN the resulting static graph for final representation:
h pode RNNuode (X,ST), VIEV,
edge hj
RNNNiee (aI,.TT) v(i,5) E
= GNN (Hrade Hodge).
time-then-graph represents the evolution of hode and de using two sequential models RNN and RNNddse resulting in new (static) graph, which is then encoded by GNN".
Problem 2 (Expressive Dynamic EEG Graph Architecture). Determine which of these three architec- tures 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 theoretical analysis of the two problems. To this end, we employ Seisfeiler-Lehmane (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 (0022) 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 pairwise similarity between channels (Ho and Armantard 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.I
Theorem 1. [Implicit 3 Explicit Dynamic Graph Modeling. Explicit dynamic modeling (dynamic ad- jacency matrices) is strictly more expressive than implicit dynamic modeling (static graph structures) in capturing spatiotemporal dependencies in EEG signals.
Proof. Let Fimplicit and Fexplicit 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 Fimplicit C Fexplicit To show strict separation, we construct two temporal EEG graphs that share identical node features but differ adjacency at single time step. An implicit model compresses adjacency into static representation, potentially making these graphs indistinguishable, while an explicit model processes time-varying adjacency and can distinguish them. Thus, Fimplicit o Fexplicits proving Fimplicit C Fexplicit. The full proof is provided in Appendix

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Lemma 1. Igraph-then-tie 3 time-and-en woadgraph/ ] time-and- graph is strictly more expressive than graph-then-ting representation family on TT,T,Mots as long as we use 1-WL GNNs.
Proof. By Definition h is passed without this additional GNN (i.e., G.) to learn interactions between EEG snapshots. This results in simpler form of temporal representation compared to time-and- -rand::pph: hi S [GNN (H (H, (H.))) graph-then-timg time is strict subset of time-and -add-aa--raph in terms expressiveness.
Lemma 2. [time-ande graph ž fine-then-graph ] time-then graph is strictly more expressive than time-and- -nd-gpap-- representation family on Tn,T.0- as time-then graph outputs different representations, while time-an time-and- -ad--gradd-- does not.
we prove Lemma using both node and edge representation perspectives (based on Notably, we provide a synthetic EEG task where any time-and- graph representation fails, while time-then-gruuh approach succeeds. fime-then- graphh learns node and edge features across time steps to capture temporal dependencies. This is done by encoding the temporal adjacency matrices ,,,,t and node features <; together, enabling the model to distinguish between graphs with distinct temporal structures. However, time-and- graph handles each time step independently, leading identical representations across time.
In Appendix C.3
Lemma iin Appendix C.T to hold Theorem _
Theorem 2. [Temporal EEG Graph Expressivity] Based on Lemmas ! and 2 conclude that
graph-then-ting strictly less expressive than time-and unndgraph, and time-and graph is strictly less expressive than time-then-ge graph on Tn,,,0 when the graph representation is I-WL GNN:
gruph-then-lime TT.... time-and-graph zTn,7,9 time-then-graple
(4)
We confirm this conclusion our experiments of both seizure detection and early prediction tasks.
Proposed Method - EvoBrain
Based on the above analysis, this section presents our EvoBrain, which is built top of explicit dynamic modeling and time-then-grape architecture to represent temporal EEG structures.
4.1 Explicit Dynamic Brain Graph Structure
Based on Theorem D 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 sequence graph structures. Specifically, for the f-th snapshot, we define the edge weight agj,t as the weighted adjacency matrix A, computed the absolute value of the normalized cross-correlation between nodes v, and Uy. To prevent information redundancy and create sparse graphs, we rank the correlations among neighboring nodes and retain only the edges with the top-r highest correlations.
at,j, |x,, * I,,al.
if E (wx), else O,
where Fi.., and Fy. represent 02 and by channels of t-th EEG snapshot. denotes the normalized cross-correlation operation. NW(;;) denotes the set of top-r neighbors of with higher correlations. After computing this for snapshots, we obtain a sequence of directed, weighted EEG graphs to represent brain networks different time points. In other words, the dynamic nature of the EBG is captured by the evolving structure of these graphs over time.
4.2 Dynamic GNN in Thme-Then-Graph Model
Based on Theorem 2 we propose a novel time-then- pihen-grapl. 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 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,
5

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we apply 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 HBG frequency snapshots are then normalized using 7-normalization across the training set. Consequently, an EEG frequency representation with a sequence of snapshots is formulated as X' E IR. NxTxd 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 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-ter -erg-termmmm 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 traditional RNN processing sequence {xt )= the hidden state update is: h, = a (WWh - Ux,), 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 s ability to evolve information over long sequences (Costacurta et al. 2024). In contrast, Mamba can be viewed as linear RNN with input-dependent parameters for each element x" (node feature X1,t or weighted adjacency matrix a:j,e):
A (x(
= fExx),
Ci = fE(x),
h (1 (1-4: D) h A.
xi, yi C,
(5)
selective forgetting
selective update
where f. are learnable projections for important frequency bands or edge connectivity. The hidden state hy encodes the evolving neural activity, serving as a substrate for both transient (working) memory and more persistent (long-term) memory traces. The softplus activation TA guarantees that the gating variable A remains positive, thereby modulating the trade-off between retaining previous neural states and incorporating new inputs. Specifically, the forgetting term (1 A, D) implements a selective mechanism analogous to synaptic decay or inhibitory processes that diminish outdated irrelevant information. Conversely, the update term A B; mirrors neuromodulatory gating (e.g, via dopamine signaling) that selectively reinforces and integrates salient new information. The projection C translates the internal neural state into observable outputs. The final hidden states mode mode and h = Yj..r capture the temporal evolution of nodes and edges.
edge
4.2.2 Spatial Modeling with GCN and LapPE
We adapt Graph Convolutional Network (GCN) and Laplacian Positional Encoding (LapPE) (Wang ct 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 '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).
order to reflect the spatial specificity of the brain within spatial modeling, introduce Laplacian Positional Encoding (LapPE). Given edge feature Hedge the normalized Laplacian L is defined as: L L=
UAU T A' = Tedge( (H where Tedge is the softplus function, fedge is the learnable projection, A' is a weighted adjacency matrix A', and D is a degree matrix, diagonal with D (Σ, a' M I E R.NN 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 E NxN the eigenvectors of L, and A is 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. E RK is given by
p; = [u [i]. (i),)).... ux| ux]) xnode mode; pt]. where nn [i) denotes the i-th component of the k-th eigenvector and [:] indicates vector concatenation.

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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 ((+1) (D=1)) (1) ( where h is the embedding of node i at layer I and
(0) x-rode ( is the learnable weight matrix at layer I, and a is an activation function (e.g..
h
ReLU). Afterward, we apply max pooling over the node embeddings, i.c., Z = h!"), followed by fully connected layer and softmax activation for seizure detection and prediction tasks.
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 classification problem (Burrello et al. 2020; Batista et al., 2024), where the goal is to distinguish between pre- ictal 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., (020)) However, there no clear clinical definition regarding its onset or duration of pre-ictal state (Lopes et al., (023). So it is defined as a fixed duration before the seizure occurrence (Batista et al., 2024). This duration 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 scizures 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, consists of 844 hours of 22-chamnel scalp EEG data from 22 patients, including 163 recorded seizure episodes. For the TUSZ dataset, we followed the official data split, in which subset of patients 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 seizure the preictal phase, implying the ability to predict seizures up to one minute in advance.
used the smaller CHB-MIT dataset, which
Baselines. We selected four dynamic GNNs studies as baselines: EvolveGCN-O (Pareja et al. 2020), which follows the graph-then-tin architecture, and a time-and-grane graph work, DCRNN (Tang ct al. 2022). time-then-ge graph approach, GRAPHS4MER (Tang et al. 2023) and GRU-GCN Gao and Ribeiro (2022) are time-then-greut graph architectures. We included EEG foundation models, BIOT (Yang et al. 2023a LaBraM (Jiang 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 KAhmedt-Aristizabae
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 Fl score focuses on selecting the
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Table 1: Performance comparison of TUSZ dataset on seizure detection and prediction for 12s and 60s. The best and second best results are highlighted.
Detection
Prediction
12x
60s
60s
Method
AUROC
Fl
AUROC
F1
AUROC
Fl
AUROC
Fi
SVM
10.004
0.369
0.720
0.390
:0.019
0.566 :0.016
0.320 100037
0.561 10.025
10.029
Random Forest
0.778 +00004
0.354 40.005
0.739 +0,31
0.386 +0.03
0.566 +0.032
0.344 +0.037
0,550 +0.057
0.330
+0.057
LSTM
0,794 10.006
0.381 10.019
0.720 10 014
0.392 10.012
0.572 10.024
0.353 10.011
0.559 10.026
0.393
10.025
CNN-LSTM
0,754 30.009
0.356 50 0008
0.680 50 007
0.331 200016
0,621 20.018
0.389 10.010
0.528 +0.020
0,316 20.028
BIOT
0.726
0.320 10.018
0.651
10 024
0,280 s0.013
0.576
0.425 10.016
0.574 20.006
10.008
LaBraM
0.825 10.003
0.472 10:013
0.793 10.002
0.469 10.010
0.661 10 003
0.482 10.010
0.669 10.014
0.413 10.020
EEGPT
0.803 +0.005
0.415 #0.011
0.743 +0 003
0.406 #0.012
0.672 +0 005
0.465 #0.012
0.610 #0.018
0.396 #0.022
EvolveGCN
0.757 10.004
0.343 10.012
0.670 10.017
0.340 10.015
0,622 00.006
0.437 10010
0.531 40,020
0.344 10019
DCRNN
0.817 +0.008
0.415
0.808 +0.014
0.435 #0,019
0.634
0.401
0.601
+0,029
GRAPHS4MER
0.833 +0.005
0.413 +0.017
0.778 40 021
0.439 e0,012
0.632
=0.02 021
0.438 +0.022
0.638 +0.025
0.355 10.031
GRII-GNN
0.856 +19
0.505 +0.009
0.822 +0.011
0.438 +0,014
0.659 +0.020
0.453 +0.012
0.601 +0,028
0.392 +0.077
EvoBrain (Ours)
0.877 +0.005
0.539 #0.009
0,865 10,009
0.483 #0.006
0.675 #0.015
0,470 +0.000
0,651 +0.023
0.401 40023
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 D 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 Fl score compared with LaBraM. For the 60-second window data, EvoBrain shows 23% increase in AUROC and 30% (0.670 - 0.865) increase in Fl 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 compar- ing 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, in- dicating 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-gee graph for identifying seizures.
Ine Pestrve B31:
EvoBiratn (ATIC-A31)
Evottratn (AUC
DUBNN LAUL -usi]
(ADC 0.80
BaikeGCN (ADC
BelnsKNN (ABIE 6,99)
Fulic Pooiie Iaa:c (a) TUSZ dataset
File Rudive Rate (b) CHB-MIT dataset
Figure 2: ROC curve results for the 12-second seizure detection task on two datasets.
Dynamic graph structure (Explicit dynamic modelngg)
Statie gnaph structure (Imppicit dynamic modeling)
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., im- plicit dynamic modeling) commonly used in ex- isting work (Ho and Armanfard [2023; Tang et al. 2022). The purple bar shows the performance of the static graph structure, while the orange bar rep- resents the results when the static graph is replaced with our dynamic graph structures. As seen, the im- provements are not limited to our time-then-gent graph method but also enhance the performance of all dy- namic GNNs approaches. The figure highlights the effectiveness and necessity of dynamic graphs in capturing brain dynamics. The results imply that
FvdeeCUN
DCRAW GRAPHSIMER
GRU-GEN
EvnBraia
Erotee
GRA GRAPHSAMER
DURAW
GEULDON
ExoBrain
(a) TUSZ 12s
(b) TUSZ 60s
Figure 3: Comparison of the proposed dynamic graph structure and the static structure.
8

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CHB-MIT datasct
TUSZ. datasct
CHB-MIT dataset
TUSZ datasct
200
Averae Training Time (mm)
Avenge Tea Time (imee(m))
100
200
EvalveGCN
GRAPHAMER
GRU-GCN
EvoBrain
100
12
30
60
12
Inpur data length (5) 60
12
30
12
Ippun Dama length (5)
60
(a) Inference time
(b) Training time
Figure 4: (a) Inference and (b) training time vs, input data length on CHB-MIT and TUSZ datasets.
Our model achieves to 17x faster training times and 14x faster inference times than its competitors, demonstrating scalability.
The Positive Rate
time-tbes-graph ((LT)
Frequency wi (0.88)
GCN (0.8)
time-and- graph (0.44
Frequency (8.66)
GIN (087)
Mamba (AUC - 0.8%) GRU 0.84)
graph-than-time (0.80)
(0.77)
GNN (8,85)
False Positive Rate (d) RNN layer
(a) Architecture evaluation
(b) Node feature
(c) GNN layer
Figure 5: (a) Architecture evaluation using same GNN and RNN layers. (b) Results using raw EEG instead of sequuency-oomali features. (c) GNN and (d) RNN layer evaluation.
modeling temporal dynamics in EEGs should incorporate various channel connectivity or structural information, supporting our thcoretical analysis and conclusion of Theorem in Section
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 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 17x faster training time and more than 14x faster inference time than DCRNN. Thus, approach is not only superior in performance but also fast in computational efficiency.
Ablation Study. Figure shows the results of different architectures applied 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 shows the results when the FFT processing or LapPE was removed. Figure 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 (d) shows results of replacing Mamba with GRU layers 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 case analysis of our constructed dynamic graphs from a neuroscience perspective. Figure shows the top-10 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), sample unrelated to a seizure shows weak, sparse connections spread across various regions over an extended period. Figure 6 (b) shows pre-seizure sample, where some connections gradually strengthen. Figure 6 (c) shows the result focal seizure, a type of seizure that originates in a specific area, with sustained strong connections only in specific region. In Figure X (d), a generalized seizure is

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Strong
(a) Normal
(b) Pre-seizure
Weak
(c) Focal-seizure
(d) Generalized-seizure
Figure Learned graph structure visualizations. The yellow color of the edges indicates the strength of the connections. In (a) Normal state, the dark shows weak connections. In (b) Pre-seizure state, the connections in specific regions strengthen over time. In (c) Focal seizure, which occurs only in specific area of the brain, strong connections are consistently present in a particular region. In (d) Generalized seizure, strong connections are observed across the entire brain.
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 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 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 dynamic multi- multi-channel EEG graph modeling approach, EvoBrain. By adopting a rime-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-graet then-graph paradigm over altematives, providing principled foundation for the design choices. EvoBrain yields substantial empirical gains, including improvements of 23% in AUROC and 30% in Fl over a strong dynamic GNN baseline, and strong performance 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 practical and theoretically grounded step toward reliable, clinically meaningful BEG-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-basee models, LaBraM benefits from more parameters and pretraining large-scale multiple EEG corpora, which enhances its ability to generalize under limited and noisy pre-seizure data conditions. While we focus evaluation the seizure task, generalization other tasks remains challenge of future work. Regarding potential negative societal impacts, we recognize key risks such as bias and system malfunction. Specifically, models trained 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 false alarms, causing unnecessary interventions or patient distress. These challenges highlight promising directions for future work, where incorporating fairness assessments, demographie audits, and human-in-Hee -n-tee--oo strategies can lead to more robust and trustworthy BEG-based systems.
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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 Grant- in-Aid for Scientific Research Number JP24K20778, JST CREST JPMJCR23M3, JST START JPMJST2553, JST CREST JPM,CR20C6, the Japan Science and Technology Agency (JST) AIP Acceleration Research (JPMICR24U2, TY), Japan Agency for Medical Research and Development (AMED, JP19dm0307103, HK, JP24wm0625207, TY), the Japan Science and Technology Agency (IST) Moonshot R <D-MILLENNIA Program (JPMJMS2012, TY), AIP Acceleration Research (JPMJCR2422, TY). JST K Program JPMJKP25Y6, JST COI-NEXT JPMJPF2009, JST COI-NEXT JPMJPF21155 1,, Future Social Value Co-Creation Project The University of Osaka.
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Appendix
Theorem 1.
Theurem
Explicit dpnumic modeling
Implicit dynamii modeling
fine-thet-ggrah model
grapb-dien-fime
dime-and-gruph
Facd
Fdgg
Dynamic graph structure
graph structure
Graph aodel (CNN)
Tespocal (RNN))
Repeccnnaions
(a) Two graph structures
(b) Three dynamic graph architectures
Figure 7: We compare (a) explicit dynamic modeling with implicit dynamic modeling and (b) time-then- thee--rhn-gggphhhhh graph with
graph graph-then- then-time and graph-and aaaphhand-inng time architectures.
A Related Work
Automated Seizure Analysis. The automated detection or prediction of seizures has been long- standing 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 net-
works (CNNs) (Fukumori et al., (0226) Ahmedd-Aristizabal et al. 20200 Asif et al. 2020 [aab et al.
2020
RNN-based models (Fukumori al.
[022a] Ahhmedt-Arisizzabe et al.
2020 Rasheed et
2021
Transformers (Eldele et al. [222 Yang et al. 2023b
Jiang et al.
2024
Yi et al. 2023)) ) and
brain-inspired models (Rich al., 2020 Burelo et 2022 Chen al.
2023 Costa et al. 2024).
Spatial Relationships in EEG Networks. A seizure is fundamentally a network disease, and detection typically relies the ability determine abnormalities in EEG channels (Burns al. 2014a Li et al., 2021b Rolls et al.) (021). Many multi-channe chinneh methods have been proposed for capturing spatial information in channels (Jiang al.) 2024 Yi al., 2023 Zhang et al. 2023 Mohammadi Foumani et al. (2024). Among them, recent studies have proposed GNNs to capture
Turther 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. [221 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 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 time-and and-graph model, , which uses frequency features from FFT as node features and applies GNN and RNN processing simultaneously for each sliding window. [Ca et al. (023) adopts a graph-ther seaph-then-time 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. (0022) propose time-then graph model, BiL.STM-GCNNG which uses RNNs to construct static graph from node feature. GRAPHS4MES (Tang et al., 2023) is also proposed as a time- time-then-gres 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 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.
EEG-based seizure modeling. (Tang et al. (2022) proposes
B Graph Isomorphism and 1-WL Test
Graph isomorphism refers to the problem of determining whether two graphs are structurally identical, meaning there exists one-to-one correspondence between their nodes and edges. This is erucial challenge in graph classification tasks, where the goal is to assign labels to entire graphs based
22

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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 s ability to classify graphs correctly.
1- Weisteiler-Lehmas (L-WL) test is a widely used graph isomorphism test that forms the foundation of many GNNs. In the I-WL framework, each node's representation is iteratively updated by aggregating information from its neighboring nodes, followed by 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 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-WLL-based GNNs, leveraging their proven expressiveness for dynamic brain graph modeling.
C Proofs of Expressivity Analysis
C.1 Expressiveness with Node and Edge Representations
Lemma 3. [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 achieve full expressiveness in EEG graph classification tasks.
Proof. Given g()) and (( with the same sets of V and E, for A t, the edge features satisfy: (1) (2)
1,g. aija Vi,, eÿ) E E, 21,2.... ..... T). However, suppose there exists least node (2) Va V and one time step t' such that: Fg, # i Since a a'j.et any GNN architecture that relies solely on edge features will produce identical embeddings for (1)) and G(2), Vt.
Lemma 4. [Expressiveness with Node and Edge Representations] When both node and edge rep- resentations are incorporated, a GNN can uniquely distinguish any pair of temporal EEG graphs that disfer in either node features or edge features at any time step, provided the GNN is sufficiently expressive (e.g., 1-WL. GNN).
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:
Proof. Given (()) (A(), x()) and g(2) (A(2),
1. If X A +x(?) for some t, then the node embeddings (1) and n will differ for at least node U/..
2. If a i.j.t A aijtt for some edge (vi, vz) and some I, then the edge embeddings n and ligh 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 (1)) and (22 Thus, the GNN can uniquely distinguish between (1) and (()).
C.2 Implicit and Explicit Dynamic Modeling
Theorem 1. [Implicit & Explicit Dynamic Graph Modeling.] Explicit dynamic modeling (dynamic ad- jacency matrices) is strictly more expressive than implicit dynamic modeling (static graph structures) capturing spatiotemporal dependencies EEG signals.
Proof. Let Fimplicit be the family of functions (e.g., representations classifiers) expressible by an implicit dynamic graph model that compresses all adjacency snapshots (A,,,,) into a single
23

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adjacency matrix A, and let Fexplicit be the family of functions expressible by explicit dynamic graph model that uses the full time-varying adjacency {A.. We prove
Fumplicit
Fexplicit
and Fimplicit # Fexplicit:
i.e.,
Fimplicit C; Cj
(1) Subset Relationship. It can be interpreted as any implicit dynamic model aggregates the set of adjacency matrices {A.,,)) into a single, static A by some function f(-) (e.g., averaging, summation, thresholding):
A (((A...)T)))
Such model uses Å for all time steps, disregarding changes in edges across l. In contrast, explicit dynamic model directly processes the full sequence (A.... To see that Fimplici is contained in Fexplicit observe that any function fimp Fimplicit can be mimicked by explicit model that simply ignores the time-specific variability adjacency and substitutes f((AA...)) = as if were the adjacency for every l. Hence,
fimp E &mmplliit fimp Fexplicit
implying
Fimplicit C Fexplicit-
(2) Strict Separation by Counterexample. To show that Fimplicit * F Fexplicits we construct two temporal EEG graphs, g()) (X.,, A Aither and G( (X.,,, A (2) 17 such that
1. Their node features match every time step:
x x(2) AEE (I.
2. Their adjacency differs only at one time step t::
(1)
and A (1) A (2) And VILI.
Under implicit dynamic modeling, the function (((A...))))) 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 Å cannot preserve the difference at L'.
In contrast, the explicit dynamic model processes {A (k)
{A(0) 17
f-- without discarding the time-step- (2)
specific variations. Consequently, does see !!! * A ",,,t" and can therefore distinguish (()) 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
Fimplicit * Fexplicits
and in view of the subset argument, we conclude
Fipplict C
Fexplicit
explicit dynamic modeling is strietly more expressive than implicit dynamic modeling.
C.3 time-and-graph and time-then-graph
Lemma 2. [time-and and-graph Σ time-then-graph ] time-then-graph strictly more expressive than time-and- graph representation, family on Tn,,,9, as time-then-grapy outputs different representations, while time-and graph does not.
Gao and Ribeiro (2022) prove that a teime-then-gaaphe representation that outputs the same embeddings as an arbitrary time-and- graph representation. Thus, time-then-gree trrppphhe-ggphhh is as expressive as time-and- graph. To prove Lemma 2 we also provide EEG graph classification task where any fime-und-gran representation will fail while time-then- graph would work, which then, added to the previous result, proves that time-then- graph is strictly more expressive than time-ane and--aadd

---

[1. 1]
Time
10, 1]
[1. 0]
Dynamic EEG graph
Edge feature
Figure 8: A synthetic EEG task where only time-then-graph is expressive. The top and bottom 2-time temporal graphs on the left side have snapshots of different structure time i2 (denote by C2 and 1) The top and bottom temporal graphs the left show different dynamic-graph structures. The right side shows their aggregated versions, where edge attributes indicate whether they existed (1) not (0) over time, using different colors. The goal is distinguish the structural differences between the top and bottom graphs. time-and and-grapp-- has the same node representation neighbors in both snapshots, indistinguishable. time-then- graph aggregates the dynamic graphs into different node representations and succeeds in distinguishing them.
Proof. We propose synthetic EEG task, whose temporal graph is illustrated in Figure g The goal is to differentiate the topologies between two 2-step temporal graphs. Each snapshot a static EEG graph with 8 attributed nodes, denoted as Cs,1 and C2
Two temporal graphs differ their second time step 12. If the graphs have the same features, any 1-WL GNN will output the same representations for both Cg,1 and Cz.2. We use (!op) to represent the adjacency matrix of dynamics in the top left of Figure 8 and (bim) for dynamics in the bottom left of Figure Note that X X (him) since the temporal graph has the same features.
Hence, for time-and-grann graph representation:
GNN in
[x
(top)
(top)) ...1
GNN!.
X (top)
(top)
,,1
:..22
GNNL
x (bim)
A (btm)
GNN
(bun)
(bam)
111
.22
:..2
GNN L
H
(tp)
(tep)
GNN
H (btm)
(bum)
:.0
..1
GNN rc
H
ttp)
(top))
GNN /
(htm)
(htm)
...2
Then, when we apply Equation
at the first time step, for the top graph:
h tep)
Cell [GNN1 (X/T) (X(T) (top) A (TT)
}}, [GNN' (h. (n
AA... A
for the bottom graph:
(hum) Cell [GNNN (x.(hm)) (btm) A (hm)) ) [GNN' (h.))mm) A.A.!. ( )))
h
Since (up) X (bim)
A. (top)
A. (bum)
.all and h
(top)
h (bum)
..11
we have: h (top)
h (bmm)
h
1.1
25

---

For the second time step:
h (tup)
Cell
[GNN X ( A ( |
(lup)
GNN (h. (top)
A (lup)
11,)
1.2
1,2
(btm)
Cell
(GNN (X. (x(22))
(bun)
(bmn)
GNN (h. (bum)
(bum))
Despite A (Uup) both C3,1 and C8,2-
A (bim)
A.22 the 1-WL GNN will output the same representations
h
(lup)
h
(hum)
for
Therefore:
Z (1p)
h
h12
(hrm)
(btm)
Thus, time-and -graph will output the same final representation (top)) temporal graphs in Figure 8
(btm) for two different
For the time-then-grest tareenggppphh representation, we apply Equation
First, for the node representations:
h
mode(top) Rode
(top) 2,52
(top) ((tp))) RNNmode mode ([x xx1,2
h
nade(bum)
mode
(bmm) 22
RNNNole ([x x,2
(btm) (bam)
Since ((op) X (bkm), we have h node(top)
h
nnde(bam) for all nodes i.
Now, for the edge representations:
edgettop)
(top) RNNedge
RNNelge
(tap) (laffg.) alj
LJ
h ij
edgetbim)
RNNodge
(him) 1.
RNNodge
(la aij.z
(bim) (bam)
Here, ai * aij.g2 for some (i,j) pairs, because the graph structures differ at l2. Therefore,
(top)
(him)
edgethim) for these pairs. Finally, apply the GNN: edgectopi # hjj
h
Z (top) GNN H moddectop) Hrogectop)),
Z (hm)) GNN mode((hh) Hadgethi)).
Since hodettlop) edgethhmm) and 1-WL GNNs can distinguish graphs with different edge attributes. we have:
Z [top) +f (bem)
(6)
Thus, time-then-graph outputs different final representations (to)) + (btm) for the two temporal graphs in Figure 8 successfully distinguishing them.
Finally, we conclude:
1. The time-then- graph is at least as expressive as the time-and-graph
2. The time-then hime-then-greet graph can distinguish temporal graphs not distinguishable by time-and graph.
Thus, lime- graph is strictly more expressive than site--and-rrahh: More precisely, time-and gran- ΣTuTT time-then Sine-then-graphe graph,
concluding our proof.
26

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D Computational Complexity
In this section, we provide the computational complexities of the three architectures: graph-then thett---ee-tmee time-and- graphg and time-then-ge graph. We demonstrate that the fime-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, be the number of edges at time E: Eg be the total number of edges across all time steps, Eagg be the number of edges in the aggregated graph (i.e., the union of all edges across time steps), and be the dimension of the node and edge representations.
D.I graph-then-time Architecture
In the graph-then-time architecture, at each time step 4, a GNN is applied to the snapshot graph (X a.,tt) capture spatial relationships. Subsequently, RNN processes the node embeddings over time to capture temporal dependencies.
The computational complexity per time step t is dominated by:
o (v + E,d),
where Vd accounts for wise transformations (e.g., linear layers), and Edd accounts for message passing over edges.
Over all time steps, the total complexity for the GNN computations is:
o TV + E,d
EEd
t=1
The RNN processes the node embeddings over time with complexity:
O (VTd²).
Therefore, the overall computational complexity of the graph-then-ting architecture is:
VTd +
=EEd E,d
D.2 time-and-graph Architecture
In the time-and-grann graph architecture, temporal dependencies are integrated into the GNN computations. At each time step two GNNs are applied:
GNNL in processes the current snapshot inputs (X.,., a...)).
GNNL processes the representations from the previous time step (h. a..,)).
The computational complexity per time step f is:
O (Vd + E.d))
due to the node-wise transformations and adge-wise message passing with updated representations.
Over all time steps, the total complexity for the GNN computations is:
T
o
&
Edd
27

---

The RNN (or any recurrent unit) further processes the node embeddings with complexity:
O (
Therefore, the overall computational complexity of the time-and-grann architecture is:
O
VTd + Σ Eyde
(8)
t=1
D.3 time-then-graph Architecture
In the time-then-graph then- 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 follows:
Node Sequence Modeling. For each node i E V, RNN processes its temporal features X S
O (VTd²).
Edge Sequence Modeling, For each edge (i,j) E Eage, an RNN processes its temporal adjacency features ajjSTi
O Edgg
GNN over Aggregated Graph.
A GNN is applied once to the static graph with updated node and
edge representations:
O (Vd² =)
Therefore, the overall computational complexity of the time time-then- graph architecture is:
O ((V Eagg) Td*).
(9)
D.4 Comparison of Complexities
To compare the computational complexities, we consider the dominant terms in Equations and O
8
graph-then-tine
T o VT& + Σ Eid
time-and-graph:
o VTd2 + Σ Exe
time-then-graph:
O ((V Faage) Td)).
By comparing these computational complexities, the time-then-eee -hhahh method is superior under the aggregated number edges Eage smaller than the total sum of edges over all time steps, i.c.,
Eage < ET E..
28

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E
Experimental details and implementation
Model training. Training for all models was accomplished using the Adam optimizer (Kingma and Ba 2014) in PyTTrrc on NVIDIA A6000 GPU and Xeon Gold 6258R CPU.
Data augmentation. During the training process. applied the following data augmentation techniques, following prior studies (Tang et al.) 2022 Eldele et al. 2021): randomly scaling the amplitude of the EEG signals by 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 le-4. To enhance efficiency and sparsity, we set r = and the top-3 neighbors' edges were kept for each node. The dropout probability was 0 (i.c., a two-layer GCN with 64 hidden units, resulting in 114,794 trainable parameters. We release GitHub repository (https: / gi thub. com http://Kooogge/eBBaaaaee
dropout). EvoBrain has two Mamba consisting of two stacked layers and
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 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 CNN- the same model architecture described in AlteedttArrsttzaabae et al. (2020), i.c., two stacked convolutional layers (32 x 3 kernels), one max-pooling layer (2 x 2), one fully-connected layer (output neuron 512), two stacked LSTM layers (hidden size 128), and one fully connected layer. Table D shows a comparison of trainable parameters, with our EvoBrain achieving the best performance using the relatively few parameters.
LSTM,
Table 2: Comparison of trainable parameters.
EveBrain
GRU-GCN
DCRNN
EvolveGCN
EEGPT
LaBraM
BIOT
CNN-LSTM
LSTM
Trainable Parameters
183,834
114,794
280,769
200,301
51,221,121
5,803,137
3,187,201
5,976,033
536,641
F Data description
Tabel ssoows the details of TUSZ dataset.
Table 3: Number of EEG data samples and patients in the train, validation, and test sets TUSZ dataset. Train, validation, and test sets consist of distinct patients.
EEG Input
Train Set
Validation Set
Test Set
Length
EFG samples
HFG samples
EEG samples
Task
Patients
Patients
Patients
(Sees)
% (Pre-) Seizure
% (Pre-) Seizure
% (Pre-) Seizure
Seizure
60-s
38,613 (9.3%)
530
5,503 (1 (11.4%)
61
8,848 (14.7%)
45
Detection
12-s
196,646 (6.9%
531
28,057 (8.7%)
44,959 (10.9%)
45
Seizure
60-s
7,550 (9.9%)
530
999 (12.0%)
1,277 (24.4%)
Prediction
12-s
40,716 (12.8%)
531
5,439 (16.0%)
6,956 (27.6%)
G
Memory Efficiency
Figure 4 shows memory efficiency comparisons across dynamic GNNs in both training and inference settings with batch size of 1. While DCRNN and EvolveGCN exhibit the lowest memory usage, EvoBrain achieves over 10x faster computation compared to these baselines, making it compelling choice for time-critical applications. Among the three time-then-grapp models, EvoBrain demon- strates the best balance between memory consumption and computational speed, with significantly lower memory requirements than GRAPHS4MER and comparable usage GRU-GCN.
29

---

Table 4: GPU memory consumption during training and inference. memory efficiency compared to baselines.
EvoBrain offers competitive
Model
Training (MB)
Inference (MB)
EvoBrain
51.35
46.64
GRU-GCN
54.61
52.09
GRAPHS4MER
369.46
93.02
DCRNN
21.10
20.54
EvolveGCN
22.06
20.07
30


Reviews:
[{"review_id": "EfMCOEclYh", "reviewer": "Reviewer_Ma49", "summary": "The 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.", "questions": "no", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**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.", "was_revised": true, "final_justification": "I think the authors have addressed my concern.  It is enough to accept.", "rebuttal": "We thank Reviewer Ma49 for recognizing our **well-defined motivation, solid theoretical analysis, strong baselines, large realistic dataset experiments, and neuroscientific interpretability**. We appreciate your time and constructive comments. Below, please find our point-by‑point responses to your concerns and questions, and we hope our clarifications below can address your concerns and raise your rating of the paper.\n\n**W1: The core contribution is primarily an integration and refinement of known components, rather than a fundamentally new paradigm**.  \nThank you for the discussion. Our contribution lies in the **theoretical foundation for modeling brain dynamics**, along with the proposal of **novel seizure detection models based on this foundation**.  \nAs you mentioned, this work is to first investigate and provide theoretical analyses for EEG modeling using dynamic graph neural networks. From a technical perspective, while EvoBrain is not a fundamentally new paradigm, it is a first time-then-graph architecture that combines explicit dynamic modeling for seizure tasks, guided by our theoretical foundation, that effectively captures evolving brain network dynamics.\n\n**W2: The main difference here is in more rigorous theoretical justification and cleaner engineering**.  \nWe hope that moving from intuitive modeling to a theoretically guided and clearly structured approach can provide a foundation for future research on GNN-based seizure modeling.  \nSeveral recent works (e.g., GRAPHS4MER) learn explicit dynamic graphs internally; however, they begin with a temporally fixed input graph. In contrast, our method computes the graph structure initially and directly based on individual temporal snapshots (e.g., 1 second) from the beginning.\n\n**W3: Generalizability to more diverse EEG tasks**.   \nThank you for your discussion. Our results already demonstrate the effectiveness of our method in terms of cross-patient generalization. We would like to clarify that training and test sets are composed of entirely different patients, and we will explicitly state this in Line 268 of the revision.    \nWe also appreciate your insightful comments. We will expand the discussion to include diverse EEG tasks and multi-modal fusion modeling in the Discussion Section.\n\n\n**W4: 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**.  \nOur model design is fundamentally guided by brain dynamics.\nThe choice of the two-stream Mamba architecture is grounded in our time-then-graph design, which separates the temporal modeling of node and edge attributes for explicitly modeling dynamics. This architecture incorporates a selective mechanism that mirrors the neurobiological processes of selectively retaining relevant information and adaptively integrating new stimuli. In addition, we incorporate LapPE to preserve brain region specificity. We hope that EvoBrain introduces a new architectural perspective to seizure detection research.  \nWe will further clarify these points in the subsequent vision of the paper."}, {"review_id": "h8Bh0Vp0d4", "reviewer": "Reviewer_qoYr", "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.", "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.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "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.\n\nThe 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.", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate Reviewer qoYr for recognizing the **solid mathematical foundation** and **acknowledging this as a strong manuscript**. We appreciate your time and constructive comments. Below, please find our point-by‑point responses to your concerns and questions. We hope our clarifications below can address your concerns and raise your rating of the paper.\n\n\n**W1: LaBraM outperforms ours on seizure prediction task**.  \nThank you for your comments, and we will discuss this in the final version as a limitation. Below is our intended discussion:  \nIn seizure detection, our method demonstrates superior performance due to its ability to highlight strong, localized network changes with high representational power. These changes are indicative of seizure onset and are effectively captured by our dynamic graph modeling.   \nHowever, in seizure prediction, where pre-ictal patterns are typically weaker and more spatially diffuse. While EvoBrain achieves the best performance among lightweight GNN-based models, LaBraM benefits from having approximately 30 times more parameters and pretraining on large-scale multiple EEG corpora, which enhances its ability to generalize under limited and noisy pre-seizure data conditions. \n\n\n**W2: Memory**.  \nWe appreciate the reviewer’s insightful comment regarding memory consumption and limitations. As suggested, we have measured the maximum GPU memory usage with a batch size of 1 for all GNN models. \n\n\n| Model       | Training (MB) | Inference (MB) |\n|-------------|---------------------------|-----------------------------|\n| EvoBrain    | 51.35 | 46.64                     |\n| GRU-GCN     | 54.61                   | 52.09                     |\n| Graphs4mer  | 369.46                    | 93.02                     |\n| DCRNN       | 21.10                     | 20.54                           |\n| EvolveGCN   | 22.06                     | 20.07                           |\n\nWhile DCRNN and EvolveGCN are indeed more memory-efficient , our EvoBrain achieves over 10× faster compared to these baselines as shown in the figure 4. \nAmong the three time-then-graph models, EvoBrain is the fastest and provides a well-balanced trade-off between memory usage and computational speed.  \nWe will include these points in the final version of our paper."}, {"review_id": "UcnRTwSzL0", "reviewer": "Reviewer_SFyk", "summary": "The 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.", "questions": "See 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.", "limitations": "The 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.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "Most of my concerns have been addressed during rebuttal. I will thus increase my scores.", "rebuttal": "We appreciate Reviewer SFyk for recognizing the **paper presentation, motivation,** and **in-depth theoretical exploration**. We appreciate your time and constructive comments. We hope our clarifications below can address your concerns and raise your rating of the paper.\n\n**W1 and Q1: Problem definition, data and task descriptions**.  \nThank you for your comments. We would like to clarify that the problem definition is provided in Section 2.2, and the data and task description are detailed in Section 5.1 and Appendices F and G. The term \"EEG snapshot\" refers to each short segment (i.e. 1-second) of EEG data that is extracted by sliding a window over the continuous EEG signal, serving as the input to the RNN-based model (as illustrated in Figure 1). \nWe will revise the final version to include a more detailed description and updated visualizations.\n\n**W2 and Q2: Novelty and components specifically tailored to this task**.  \nOur time-then-graph architecture and explicit dynamic graph structure are specifically tailored to EEG tasks. That is, our model design is fundamentally guided by brain dynamics.\nThe choice of the two-stream Mamba architecture is grounded in our time-then-graph design, which separates the temporal modeling of node and edge attributes for explicitly modeling brain dynamics. This architecture incorporates a selective mechanism that mirrors the neurobiological processes of selectively retaining relevant information and adaptively integrating new stimuli. In addition, we incorporate LapPE to preserve brain region specificity. We propose explicit dynamic graph structures for each EEG snapshot rather than using a single static graph, enabling it to capture transient connectivity changes of brain state, such as seizures. We hope that EvoBrain introduces a new architectural perspective to seizure research.\nThank you for your insightful comments, we will highlight this discussion more clearly in the revised version and relate it to the relevant literature.\n\n\n**W3 and Q3: Recent models**.  \nThank you for your comments. \nWe compared our method against LaBraM (ICLR'24), one of the most recent and powerful EEG foundation models. LaBraM is pretrained on large-scale datasets across multiple domains and possesses a larger number of parameters.  \nMoreover, we include two new baseline comparisons: **EEGPT (NeurIPS’24)** and **AMAG (NeurIPS’24)**. EEGPT is a recent foundation model for EEG, while AMAG is a deep graph model focused on neural dynamics.\nSimilar to LaBraM, EEGPT is pretrained on large-scale EEG datasets across multiple domains and contains 50 million parameters—approximately 277× larger than our EvoBrain model.\nOn the 12-second seizure detection task, EEGPT and AMAG achieve AUROC scores of 80.4 and 81.7, respectively, while our EvoBrain model achieves 87.7. This further supports the effectiveness of the proposed method.  \nWe will include all results in the final version.\n\n**W4 and Q4: Evaluation metrics**.  \nIn seizure tasks, seizure periods are typically much shorter than non-seizure periods, and our dataset reflects this class imbalance. In such cases, accuracy can be misleading, as a model that always predicts the majority class (i.e., non-seizure) may achieve high accuracy but provide little clinical value.\nIn contrast, F1 score balances precision and recall, making it more appropriate when positive (seizure) instances are rare but important to detect. Similarly, AUC (Area Under the ROC Curve) evaluates the model’s ability to distinguish between classes across different thresholds and is less affected by class imbalance.  \nOur experimental settings are fully aligned with the reference work DCRNN [1] and GRAPHS4MER [2]. We will also include precision and recall metrics in the final version, following your suggestion.\n\n- [1] Self-Supervised Graph Neural Networks for Improved Electroencephalographic Seizure Analysis, ICLR, 2022.\n- [2] Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models. CHIL, 2023.\n\n**Limitations**.  \nThank you for your comments and for pointing out this aspect, and we will enhance the discussion of limitations in the final version of our paper. Below is our intended discussion:  \nIn seizure prediction, where pre-ictal patterns are typically weaker and more spatially diffuse. While EvoBrain achieves the best performance among lightweight GNN-based models, LaBraM benefits from having approximately 30 times 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, which is particularly critical and life-threatening among various EEG applications, generalization to other tasks remains a limitation of our work."}, {"review_id": "T298uH7N0u", "reviewer": "Reviewer_w1Ha", "summary": "This 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.", "questions": "As 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.", "limitations": "The 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?", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "## 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.", "was_revised": true, "final_justification": "The rebuttal period was extremely useful and I thank the authors availability to answer my questions. As a result I have increased the score to Accept, and indeed I think this is a very interesting work!", "rebuttal": "We appreciate Reviewer w1Ha for recognizing the **paper organization, clear contributions, experiments** and **solid theoretical grounding**. We appreciate your time and constructive comments. We hope our clarifications below can address your concerns and raise your rating of the paper.\n\n\n**W1: Two different claims**.  \nAs you correctly pointed out, our contributions include two distinct components: (1) a dynamic graph creation and (2) a time-then-graph model. All three model variants (graph-then-time, time-and-graph, and time-then-graph) are compatible with either static or dynamic graph inputs.  \nTo ensure a fair comparison, we applied our dynamic graph structure to all GNN baselines across three model variants, as shown in Figure 3. Our time-then-graph model consistently outperforms the others even when all models use the static or our dynamic graph structures. Moreover, applying our dynamic graph to baseline architectures also improves their performance.\n\n\n**W2: No traditional ML model was used**.  \nWe have conducted experiments using Random Forests and SVM on the 12-second seizure prediction task. The AUROC scores were 0.778 for Random Forests and 0.765 for SVM. \nWe will include all results of these traditional baselines in the final version.\n\n**W3: Other GNN models**.  \nThank you for your comments.\nWe conducted additional experiments replacing the GCN layers with a more expressive Graph Isomorphism Network (GIN). The GCN layers contain 24,441 parameters, whereas the GIN layers increase the parameter count to 39,016.\nIn the 12-second seizure detection task, GIN achieved an AUROC of 87.2, which is slightly lower than the 87.7 obtained by the GCN. The excessive model complexity may overfit to transient or noisy patterns rather than capturing stable dynamics.   \nBased on our experiments, we observed that how different components are integrated (i.e., time-then-graph) is more critical for effective dynamic EEG modeling rather than the complexity of individual modules. \nWe will include these additional findings in the final version of the paper.\n\n\n\n**S1: Typo**.  \nThank you for your suggestion.\n\n**S2: Nascent**.  \nThank you for your thoughtful comment regarding the use of the term \"nascent\". Our intention was to emphasize that while there have been emerging efforts to model temporal signals and graph structures jointly, the modeling of their interactions remains at an early and underdeveloped stage. These methods are often exploratory and lack consistent theoretical or empirical grounding, leading to unstable performance across tasks.\n\n**S3: Threshold to rank the correlations**.  \nIn our experiment, the value of τ (number of top neighbors) is set to 3 following prior work on EEG functional connectivity modeling. We additionally conducted experiments with τ = 5 and τ = 7, and observed less than 1% variation in performance, suggesting that most connections beyond the top-3 are not informative. \nWe will include these results and relevant discussion in the final version.\n\n\n\n**S4: Sparse graphs**.  \nThank you for the discussion. By retaining only the top-τ most correlated neighbors for each node, we eliminate weak or noisy correlations that may not reflect meaningful functional connectivity. This sparsification reduces redundant or task-irrelevant information and improves both interpretability and performance.\n\n**S5: Variation in running times**.  \nThank you for your comments, and we will report the variation across multiple runs in the final version.\n\n**Q1: Ablation of GCN**.  \nWhile the two-stream Mamba effectively captures the temporal dynamics of node activity and edge strength independently, it lacks mechanisms to jointly model the interactions between node representations and their evolving connectivity patterns. Given that seizures are a network-level phenomenon, it is essential to capture not only which nodes are active, but also how their activity propagates through dynamic, task-relevant connections. The GCN layer explicitly fuses node features with their neighboring context, enabling the model to learn spatiotemporal patterns such as synchronized activation or pathological propagation across brain regions.   \nFrom our theoretical perspective of time-then-graph modeling, GCN complements the two-stream backbone by capturing cross-modal interactions between node activity and edge-defined structure.   \nWe conducted an ablation study, removing the GCN layer and concatenating node and edge features, then applying a linear classifier. This setup yielded an AUROC of 84.7 on the 12-second seizure detection task, which is notably lower than the 87.7 achieved with the GCN layer.\nWe will include this ablation along with the GIN comparison in the final version.\n\n**Q2: Seizure prediction**.  \nThank you for the constructive comments.\nCompared to seizure detection, the prediction task holds greater clinical value, as it enables early intervention by clinicians.\nSeizure prediction is inherently more difficult than detection, as it requires identifying subtle pre-ictal patterns rather than overt seizure activity. Longer prediction windows (such as 60s vs. 20s) contain less seizure-indicative information, making the task even more challenging and demanding greater model capacity.  \nTo the best of our knowledge, this is the first work to conduct seizure prediction on the large-scale TUSZ dataset, which involves a substantial number of patients and supports long prediction windows up to 60 seconds before seizure onset.\nThis setting is more challenging than those considered in most prior studies, which typically focus on shorter prediction windows.\nWe will address these points in the experimental setup section of the revision.\n\n**Q3: Imbalanced dataset**.  \nThank you for your suggestion.\nTo ensure a fair evaluation, we did not apply techniques such as weighted loss functions. Instead, we focused on balanced and robust metrics, F1 score, and AUROC.\nWe will include sensitivity and specificity in the appendix in the final version.\n\n**Limitations and negative social impacts**.  \nThank you for pointing out this important aspects. We will explicitly state these concerns as part of the limitations and broader societal impacts in the final version. Below is our intended discussion:\n\nIn seizure prediction, where pre-ictal patterns are typically weaker and more spatially diffuse. While EvoBrain achieves the best performance among lightweight GNN-based models, LaBraM benefits from having approximately 30 times 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, which is particularly critical and life-threatening among various EEG applications, generalization to other tasks remains a limitation of our work.  \nRegarding 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 the importance of incorporating fairness assessments, demographic audits, and human-in-the-loop strategies in future development and deployment stages."}]

Author rebuttal:

Meta-review: EvoBrain: Dynamic Multi-channel EEG Graph Modeling for Time-evolving Brain Network
 
The authors propose a Dynamic GNNs, to seamlessly integrate temporal and spatial features in Electroencephalography (EEG) data with a goal of detecting seizures. The primary challenge they address is that of the dynamics underlying these two states which reflect the brain evolving connectivity during a seizure. They proposed EvoBrain, as a novel seizure detection model by integrating a two-stream Mamba architecture with a GCN enhanced by Laplacian Positional Encoding, following neurological insights. Their integration of dynamic graph structures in EvoBrain, allows for the time evolution of both nodes and edges over time.  Their theoretical analysis shows the expressivity advantage of explicit dynamic modeling and time-then-graph over other approaches. Their evaluation of the novel and efficient model shows a significant improvement of AUROC by 23% and F1 score by 30%, in comparison with the dynamic GNN baseline. All the reviewers agreed that the explicit techniques exploited in the proposed methodology were not novel (i.e., G. Conv. Net. With temporal evolution) or as one reviewer succinctly described as a plug-and-play, and they also agreed that the theoretical analysis developed for the method is useful in that it provides insight into the functionality and the resulting improvement. Satisfactorily numerous experiments were conducted, and one reviewer insisted upon an explicit claim of a “first 60s ahead seizure prediction” (if that was the case, which the authors confirmed) and hence a first experimental breakthrough.
Despite some minor critiques, the reviewers evidently all agreed that it was a solid paper with the majority ranking of an outright “accept”.
Given the reviews and upon a quick reading of the paper,  the AC is recommending acceptance for publication.
The AC checked the provided source code location for anonymity, the link is non-operational : \url{https://anonymous.4open.science/r/EvoBrain-FBC5}
Decision: Accept (spotlight)