Lightweight Transformer for EEG Classification via Balanced Signed Graph Algorithm Unrolling
Authors: Junyi Yao
Parham Eftekhar
Gene Cheung
Xujin Chris Liu
Yao Wang
Wei Hu
Venue: ICLR 2026 Poster (2026)
Keywords: balanced signed graph
spectral denoising
graph classification
Primary area: optimization

Abstract: Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. 
To differentiate epilepsy patients from healthy subjects using collected EEG signals, we build lightweight and interpretable  transformer-like neural nets by unrolling a spectral denoising algorithm for signals on a balanced signed graph---graph with no cycles of odd number of negative edges.
A balanced signed graph has well-defined frequencies that map to a corresponding positive graph via similarity transform of the graph Laplacian matrices.
We implement an ideal low-pass filter efficiently on the mapped positive graph via Lanczos approximation, where the optimal cutoff frequency is learned from data.
Given that two balanced signed graph denoisers learn posterior probabilities of two different signal classes during training, we evaluate their reconstruction errors for binary classification of EEG signals.
Experiments show that our method achieves classification performance comparable to representative deep learning schemes, while employing dramatically fewer parameters.

Published as a conference paper at ICLR 2026
LIGHTWEIGHT TRANSFORMER FOR EEG CLASSIFICA-
TION VIA BALANCED SIGNED GRAPH ALGORITHM UNROLLING
Junyi Yao
Parham Eftekhar York University e tftekaarryyoku.co
Gene Cheung York University
Peking University
2401112160@stu. wwt.stttuppuuu.oo...ouoo.. edu. en
genec8yorku.co
Xujin Chris Liu New York University x x13942@nyu.edd
Yao Wang
Wei Hu"
New York University
Peking University
yw523@nyu.edu
forhuwei θpku. edu. cn
ABSTRACT
Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. To differentiate epilepsy patients from healthy subjects using collected EEG signals, we build lightweight and interpretable transformer-lik neural nets by unrolling a spectral denoising algorithm for signals on balanced signed graph-graas graph with no cycles of odd number of negative edges. A balanced signed graph has well-defined frequencies that map corresponding positive graph via similarity transform of the graph Laplacian matrices. We implement an ideal low-pass filter efficiently on the mapped positive graph via Lanczos approximation, where the optimal cutoff frequency is learned from data. Given that two balanced signed graph denoisers learn posterior probabilities of two different signal classes during training, evaluate their reconstruction errors for binary classification of EEG signals. Experiments show that our method achieves classification performance comparable representative deep learning schemes, while employing dramatically fewer parameters.
INTRODUCTION
We study the classification of EEG signals in patients with epilepsy versus healthy control subjects. Compared classical model-based methods, such as k- NeNearsst Neighbors with dynamic time warping features (Tasci et al., 2023) and feature extraction from time frequency maps (Shen al.) (0024). deep learning (DL) models, such as CNN-based Shen et al. (2024), Bhaanaaee al. (2024) and Dicsli Lih et al. (202). have achieved state-of-the-an (SOTA) results (e.g., up to the 90% range). However, the transformer model consumes enormous number of parameters and functions as an uninterpretable black box. Thus, parameter reduction and interpretation of learning models is crucial towards practical implementation resource-constraieed EEG devices.
al. (2025) and more recent transformer-base
An alternative paradigm for data learning is algorithu unrolling (Monga al. 2021) 1): first design iterative optimization algorithm minimizing a mathematically-dehie objective, then "unroll" each iteration into a neural layer, and stack them back-to-back to compose feed-forward network for data- driven parameter learning. Notably, Yu el al. (203) recently unrolls an algorithm minimizing a sparse rate-reduction (SRR) objective into transformer-like neural net-called "white-box transformer". that achieves comparable performance as SOTA in image classification, while remaining 100% mathematical interpretable
*Corresponding author.
'Common in algorithm unrolling (Monga al. 2021). "interpretability" here means that each neural layer corresponds iteration of optimization algonthm minimizing mathematically-ddfnncd objective.

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Inspired by Yu et al. (2023), for the EEG signal classification problem also build transformers via algorithm unrolling, but from a unique graph signal processing (GSP) perspective (Ortega et al.)
2018: Cheung al. 2018). GSP studies mathematical tools such transforms, wavelets, and filters for discrete signals residing on irregular data kernels descrihed by graphs. Recently, Thuc et al. (024) shows that graph learning module with edge weight normalization plays the role of self-attention (Bahdanau et al. 2014), and thus unrolling a graph algorithm with graph learning modules inserted yields a transformer-like neural net. However, [Thuc et al. (2024) focuses solely on positive graphs that model simple pairwise positive correlations among neighboring pixels in static image.
For EEG signals, collected samples often exhibit pairwise anti correlatrsss which are effectively modeled by negative edges. Though frequencies for general signed graphs (with both positive and negative edges) are not well understood, Dinesh et al. (2025) shows that in the special case of balanced signed graphs-with no cycles of odd number of negative edges- frrossfcrreeeiiss can be rigorously defined: the Laplacian matrix _ of a balanced signed graph g is similarity transform of the Laplacian L of corresponding positive graph G (hence they share the same eigenvalues), and the spectra positive graphs are well understood and utilized in GSP (Ortega et al. (011)). Thus, widely studied filters for positive graphs (Onuki et al. 2016; SShmma 2020 can be readily reused for signals on balanced signed graphs (Yokota et al. 2025).
We leverage this fact to build EEG signal denoisers M as a pretext tast for later binary classifica- tion. Specifically, we first learn a balanced signed graph GB from EEG data; graph balance is ensured during signed edge weight assignment via a novel interpretation of the (CHT) (Harary 1953). Next, we construct an ideal low-pass (LP) cutoff frequency w- w-forr for the corresponding positive graph G minimize a denoising objective. The ideal LP filter is efficiently implemented via Lanczos approximation (Susnjara et al.) (013)), which we unroll into filter sub-network. The pair of LP filter graph learning module is repeated to build feed-forward network for sparse parameter learning (Thuc et al. 2024
's Theorem by the lone
Cai et al. 2025).
Having learned two denoisers Lo(-) and (-) trained on signals from two different classes 0 (healthy subjects) and 1 (epilepsy patients) thus capturing their respective posterior probabilities. we use their reconstruction errors on an input signal for binary classification. Experiments show that our classification method based on trained balanced signed graph denoisers achieves comparable performance as SOTA DL schemes, while employing drastically fewer parameters.
Summarizing, our key contributions are as follows:
1. Extending Thue et al. (2024) that focuses on positive graphs, we unroll a denoising algorithm for signals on balanced signed graphs with well-defined frequencies frequencies-learned directly from data via feature distance learning-
lightweight and interpretable transformer.
2. We implement ideal LP filter the positive graph G+ corresponding to each learned balanced signed graph GB (Dinesh et al. (2025) without eigen-decooposition in linear time via Lanezos approximation (Susnjara et al. 2015), where only the filter cutoff frequency w requires tuning from data.
3. We train two class- spesifc denoisers to learn two different posterior probabilities as a pretext task, then determine class assignment based on their reconstruction error.. This approach bridges generative modeling and discriminative classification in a novel manner- botth the algorithm-unrolle denoisers and the classification decision are casily interpretable.
4. Compared to SOTA DL methods, we achieve competitive classification performance on EEG signals distinguishing epilepsy patients from healthy subjects, while using significantly fewer parameters (e.g.. our scheme achieves 97.6% classification accuracy to transformer based model (Lih al. 2023 's 85.1%. while employing fewer than 1 1% of the parameters).
2 PRELIMINARIES
2.1 GRAPH SIGNAL PROCESSING DEFINITIONS
A graph (AV E, W) is defined by a node set N = (1,..., matrix W E N where Wa, way is the weight of edge (i,j) E & if it exists, and Wa,
"il...,N), N). an edge set E, and an adjacency
See Appendix A for related works.
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t-]
-1
1
D
2
2
2
3
a) Balanced signed graph
b) Positive graph
c) Positive product graph G
Example of balanced signed graph G in (a) and its corresponding positive graph G in (b). Red and blue nodes in G denote polarities -1 and 1, respectively. Positive graph can be extended to incorporate the time dimension via product graph g in (c) with temporal edges (red).
Figure 1:
otherwise. In this work, we assume that each edge weight wi, can positive or negative to denote positive negative correlations; G with both positive and negative edges is signed graph. We assume also that edges are bidirectional, and thus Wt, = W, and W is symmetric. A combinatorial graph Laplacian is defined as L - D - w = diag( W1) ) W. To account for self-loops, i.e., 3i, Wi, o O, a generalized graph Laplacian is typically used: L A D W + diag( (W) (Ortega et al. 2018 We use these Laplacian definitions for both positive and signed graphs.
2.2 GRAPH LAPLACIAN REGULARIZER
To quantify variation of signal over graph kernel G, the graph Laplacian regularizer (GLR) (Pang & Cheung 2017) is commonly used, defined using combinatorial Laplacian
x Lx = Σ
Wx, xz)²
(K,))E
From eq. 11. one can see that x Lx 2 0, Vx (L is positive semi-definite (PSD)) if L specifies
positive graph G i.e., Wi.j Vi,j.
2.3 BALANCED SIGNED GRAPHS
A balanced signed graph, denoted by GD, is a graph with no cycle of odd number of negative edges.
An equivalent definition of graph balance is through node polarities. Each node V is first assigned
a polarity 3; E (1,-13, By the Sartwright-Harayy 's Theorem (CHT) (Harary 1953). signed graph
balanced iff positive/negative edges always connect node oode-pairs of the same/opposite polarities. In
mathematical terms, a signed graph G is balanced if
8.3, sign(w;,).
v(i.j) E
(2)
Recently, Dinesh et al. (025 proved that there exists simple similarity transform from the (generalized) graph Laplacian L of a balanced signed graph g to graph Laplacian L of a corresponding positive graph i.e.
=
(3)
where T diag(3 (3) is diagonal matrix with diagonal entries equal node polarities f [B..... 3N in dD Thus, _ and L share the same cigenvalues, while L eigenvectors V TV+ are a linear transform of L+'s eigenvectors V+ As an example, consider the 3-node balanced signed graph nd in Fig. (a) and its corresponding positive graph g in (b). G is balanced since positive/negative edges connect node-pairs of same/opposite polarities. The balanced signed graph Laplacian LB and the corresponding positive graph Laplacian L are
1
2 -1
-1
C
1
2
-+
-2
(4)
-2
where T diag( -- 1 1)). Given that the graph frequencies of positive graphs are well established OOreea et al. 2018), the graph frequencies of balanced signed graphs also rigorously defined.
'Specifically, cigenvectors of positive graph Laplacian for increasing eigenvalues have non non-decreasing numbers of nodal domains that quantify signal variation across the graph kernel (Davies et al. 2000), and hence be rightfully interpreted frequency components (Fourier modes). See[Dinest et al. (2025) for details.
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3 BALANCED SIGNED GRAPH CONSTRUCTION & SIGNAL DENOISING
We first discuss construction of a balanced signed graph g in Section 3.1 which is mapped to positive graph G+ via similarity transform of Laplacian matrices. We describe denoiser (-) for signals on g based on ideal LP filtering in Section 3.2 Finally, we discuss how Lanczos approximation is used to efficiently implement& a LP filter in linear time.
3.1 BALANCED SIGNED GRAPH CONSTRUCTION
We construct a balanced signed graph G to connect nodes representing EEG sensors in an electrode array of size N. Typically, collected data at sensor i E V is time-series signal z [n], n E Σạ. We divide it into H chunks duration each, and consecutive chunks of the same sensor are connected in time using positive edges in product graph G of N x H nodes, as shown in Fig. c). For simplicity, we assume a single chunk in the sequel, focusing on ga.
Polarity Selection:
To ensure balance in G we first initialize polarity Bg for each node as follows. Given an empirical covariance matrix C I. NxNNN computed from collected EEG data, we select one row and initialize node i's polarity B < 1. Then, for each j. j # i, we initialize B3 + sign(C,,) i.e., node j has the same polarity as node i if Ct2y 0 (positively correlated), and opposite polarity otherwise.
At each subsequent graph learning module (see Section 4.1). polarities 3, s are updated. Given a set of computed edge weights {w.y}. J. for each node i, we first assume polarity 8; < {1. and flip signs of [We.5 Ji so that the graph balance condition eq. (2) is satisfied, resulting in balanced signed
graph Laplacian L (3:). Using set of training signals {x"] 1g 1. x. RNN, we select polarity 8 for node with the smaller GLR term eq. (T):
B = arg min
(xx))L"(33)))
(1,-1111 q=1
In words, eq. 5 chooses polarity 3 that results in (x" simmir concept as previous works that learn graph Laplacians from assumed smooth signals (Dong et al. 2016 Kalofolias 2016 Dong et al. 2019).
G more consistent / smooth with dataset
We update each node i's polarity and corresponding edge weight signs turn until convergence. The analysis of initialization statistics and the corresponding setup, including the update order, invocation strategy, and stopping criterion, are provided in detail in Appendix [ along with the pseudocode.
Feature Distance: Given polarities {B:). we compute signed edge weights {w., For each node
we assume that a feature function F E. + R (to be detailed in Section 4.1 computes fereesentttiveeeatreee where K E. Given f s, the Mahalanobis distance between nodes and j computed as
fow-dimensional representative feature vector f; = F' F(e,), f, E RK from input embedding e; E R
dr (f,
(f. (T)
-,),
(6)
where M E R is a PSD metric matrix, so that di,j 2 O, Vf, f3 For each edge (i.j) E E, we compute signed edge weight wt,j as
(Yang et al. 2022
exp( (pp(-d.,) exp( dr.) diy) o.w.
if 8, = 3,
Wi.j
We see that wa,j 2 0 (wi,j S 0) if nodes and j have the same (opposite) polarities; thus, by eq. eq. 7 ensures the constructed signed graph g is balanced. In either case, larger feature distance d, means smaller edge weight w.,j. Note that
the first to map non-negative learned feature distances d.j's 's to signed edge weights W 's of balanced signed graph.
Normalization: We perform the following normalization for weight wi, of each edge (i,1) E E:
W..
B.9;
V Eniauee www.nneeewwllyyy. Ie Whil
Σ Emlaanee exp(-dr.)) Ex ((K.))e exp(-
(8)
The resulting adjacency matrix WB eq. (8) is symmetric normalized variant of WBB
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h may not be PSD due to the presence of negative edges. To ensure PSDness, we leverage the Gershgorin Circle Theorem (GCT) (Varga 2004) and add self-loop of weight 1 6 to each node i, where å is computed
PSDness:
Combinatorial graph Laplaciar L D
min = min I B
Σ 1
8 max (->minn=)) 0)-
Xmin in eq. a symmetric real matrix P must reside inside at least one Gershgorin disc with center center; P.,
(9) is lower bound of the smallest eigenvalue Amin of by GCT: each eigenvalue À of
and radius r; = م | i.e., Di such that center; ri X I center; rú. A corollary is
that the smallest Gershgorin disc left-end-X in eq. (9) is lower bound for Xmin- Thus, eq. (9) implies that the eigenvalues of L are shifted up by via L = L + 5I to ensure L is PSD if Amin O. Note that - L + 8I and L share the same eigenvectors, and thus the self-loop
additions do not affect the spectral content of L
3.2 GRAPH SIGNAL DENOISING
We construct a signal denoiser, given an underlying balanced signed graph G specified by graph Laplacian _ To process signals on more convenient positive graph G+. we first perform similarity transform to obtain its corresponding positive graph Laplacian, L TC"T in eq. B where T diag(A). We employ the graph spectrum of L for ideal LPP filtering. Each target signal yB on G to be denoised is also pre-processed to y+ Ty as a signal on g+.
Denote by S. ( the low-frequency subspace spanned by the first eigenvectors (frequency components) V [vi; V2i.... Vw] RV of L corresponding to the w smallest eigenvalues.
To denoise observation y+ E R.,, we seek a signal x E IRN in (L++ closest to yt f2-norm
min xES
Ily - x112
(10)
Denote by z E R" the w GFT coefficients of x, i.e., x = Vaz. The optimal solution zz to eq.
(00 is
= (VV y (a) VIy+
(11)
x" = Vun" V. = (A
(12)
(C+)
where (a) is true since columns of V orthonormal by the Spectral Theorem (Hawkins 1975).
(C+ = V (A) is an ideal LP filter, and g (A) = diag((g (A.)...... 9- (AN))
has fre-
quency response Iu (Xx) defined
- (Ar) - 1 if
(13)
O.W.
Solution x* in eq. is an orthogonal projection of input y onto S_ Computing x" in eq. (2) requires computation of the first w eigenvectors V of L with complexity O(N3) for N. In implementation, the cutoff frequency w eq. (13) is made learnable by approximating the hard truncation with higmoid-based smooth low pass filter. Detailed formulations are provided in Appendix
Lanczos Low-pass Filter Approximation
Instead of an ideal LP filter eq. (13), we approximate via Lanezos approximation in complexity O(N) (Susnjara et al. 2015). In a nutshell, instead of cigen-decomposing large matrix L N via the Lanczos method we operate on a much smaller tri-diagonal matrix Hm E pm where < N is the dimension of the approximating Krylov space. We eigen-decompose H Zmng( A, m IT,, where 96 (A,) is the approximate LP frequency response for cutoff frequency & round which we tune from data after unrolling. See Appendix B for details.
signed graph Laplacian a D B where D Σ, [W:Bl. guaranteed to be PSD can be defined
instead (Dittrich & Matz 2020). but a corresponding LP filter would promote negative linear dependence rather than repulsions for negative edges during signal reconstruction. See Appendix for details.
An alternative is a maximon a posteriori (MAP) denoising formulation using GLR as a signal prior Pang
& Cheung 2017 Zeng et al. 2020 Dinesh et al. 2020). i.e., minx lly x1| + px _ However, Bai al. al.20))))) shows that the MAP prohlem- called the F-optimality criterion in optimal design- minimizes the worst-case signal reconstruction, while eq. (10) is the A-optimality criterion that minimizes the average case.
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back-propagation
loss function
+
BGL,
BGL2
LPF (14)
LPF (14)
LPF (14)
ground
truth
output
Unrolled Graph Signal Denoising Network. Low-pass filter (LPF) computing solution x" via eq. (12) is interleaved with balanced graph learning (BGL) module that updates balanced signed graph Laplacian L then transforms to L via eq. (3) ① and o are learned parameters.
Figure 2:
4 ALGORITHM UNROLLING
We implement the graph-based denoising procedure in eq. (22 and graph learning module re- peatedly; after a solution x" is obtained, representative features {f,} are updated (see Section 4.1). resulting in new feature distances {d.,} via eq. (6), new signed edge weights {w;,} via eq. 7 and new balanced signed graph Laplacian _ and positive graph Laplacian L via similarity transform eq. (3). The concept of iteratively filtering signals, with filter weights updated based on computed signals, is analogous to bilateral filter (BF) in image denoising (Tomasi & Manduchi [998).
4.1 GRAPH LEARNING MODULE
We unroll this repeated combo of low-pass filter graph learning module into neural layers compose a feed-forward network for data-driven parameter learning via back- pack-propagation; see Fig. 2 for an illustration. The key to our unrolled neural net is the periodic insertion of graph learning module BGL that updates Laplacian L for the next LP filter module LPF. Specifically, to compute feature vector I8 K for each node i, we define input embedding e; R as the recovered time series signal at node i, and implement a shallow CNN to compute f; CNN(e:) (e:), where K < E. Metric matrix M e TR. KxK in eq. (6) also optimally tuned. Together, the CNN parameters and M are the learned parameters D, for unrolled block BGL,, On the other hand, the optimal cutoff frequency w for the low-pass filter is learned per block, which constitutes parameters θ for LPF,.
4.2
MECHANISM
We review the classical self-attention mechanism in transformers (Vaswani et al.] 2017). First, given input embedding e; R for token i, affinity ei,j between tokens and j computed the scaled product of Kx, and Qx,. where K, Q E IR Ex are the key and query matrices, respectively. Using eij. non-negative and normalized attention weights ar 's are computed using the softmax operator:
exp(ei.)
Oi.j
exp(er.))
C. = (Qe,) (Ke:).
(14)
Finally, output embedding is computed as the sum of attention-weighted input embeddings multiplied by the value matrix V E EEXE.
y: Σ V.
(15)
A transformer concatenates self-attention operations both in series and in parallel (called multi-head).
Comparing eq. [14p to the right-hand side of eq. (b) we see that by interpreting negative dis- tance -d.,; as affinity ei.j. normalized edge weights Wa.j are essentially attention weights di.j- Thus, a graph learning module with normalized edge weights is a form of self-attention. In implementation. instead of learning dense and large key and query matrices K and Q, for normalized edge weights [w:,s} we learn only parameters for a shallow CNN to compute features (f,) and low-dimensional metric matrix M. Further, instead of learning dense and large value matrix V, we learn single cutoff frequency i of an ideal LP filter per block. Thus, our graph-base based implementation of self-attention yields substantial parameter savings compared to the classical self-attention mechanism.
Remark:

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5 USING GRAPH-BASED DENOISERS FOR CLASSIFICATION
By training two class-conditioned denoisers, vo(-) and V (-), using a squared-error loss function on signal classes corresponding healthy subjects and epilepsy patients, respectively, we training each network to compute the posterior mean of its corresponding class (though the networks are inspired by subspace projection); i.e. given noisy signal y and known class c, they compute
Po(y) = E[x y,c= 0j. L 1 = E[x y,c=
(16)
To accomplish eq. (1). the two denoisers must learn implicitly the posterior probabilities of the two classes. By the Bayes Theorem, the posterior probability Pr(xly, c) of signal x given observation proportional to the product of likelihood Pr(y|x, c) times prior Pr(x
Pr(xly, c) Pr(y|x, c) Pr(x|c).
(17)
Assuming zero-mean additive white Gaussian noise (AWGN) with variance o the likelihood is
1
Ily x1
Pr(y/x,c)
(2TO7) exp
(18)
20
Given our assumption that signal resides in low-frequency subspace Sw( the prior is
Pr(x/c) = { 1 if x x SL())
(19)
o.w.
Thus, given cutoff frequency w, the signal x that maximizes the posterior Pr(xly, c) is the signal x in (C+) closest in Euclidean distance y (so that Pr(x|c) and Pr(y)x, x, c) is maximized):
x" arg (Et)
min
Ily - -
(20)
i.e., the orthogonal projection of onto S. (C+) in eq. 12
Conversely, during supervised training of a denoiser L c.(:), given training pairs {(yo,): of class parameter set + (CNN parameters and cutoff frequency w) is tuned minimize the sum of distances between ground truths Xe, and projections (2+ of inputs Ye,; onto (x())):
min Σ [xx. )c
(21)
Thus, learning of parameter set d at different layers in unrolled network to minimize eq. (1 amounts to learning posterior Pr(xly, c). (Note that noisy signals y:'s with non-negligible noise variance of are necessary; a noiseless signal y, x, means that setting + N N-resulting in an all-pass
yield zero error in eq. (21). and thus no learning posterior Pr(xly,c).)
Once the two denoisers are trained, compute the following given input signal determine y's class membership:
arg min lly T T.(y)] (E(0,1)
(22)
The reasoning is follows: given that denoiser (y) computes the posterior mean E[x y, which is the minimum mean square error (MMSE) estimator, its error should be small when y indeed belongs class Hence, classification by reconstruction errors in eq. (22) is justified.
Modified Training Objective: To encourage discrimination of the two classes, we adopt a new loss function during denoiser training. We first identify pairs of signals (x.,).x1.;) from the two classes that are close in Fuclidean distance (and thus difficult to differentiate). We then train denoiser (o()) for class 0 with the following contrastive loss function (similar training procedure for L 1-)):
Σ | Vo(yo,))13 max (p- ||x1, Vo(yI.))1330)
(23)
where p > 0 a parameter, and ye,s is a noisy version of X Doing so means that Lo(+) captures signal statistics for class 0 that sufficiently different from class 1.
'I is also the maximum likelihond estimate (MLF).. See Appendix D for explanation.
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6 EXPERIMENTS
6.1 EXPERIMENTAL SETUP
Datasets and settings. We evaluate our model the Turkish Epilepsy EEG Dataset (Tasci et al. 2023), which is currently the largest publicly available dataset focused on epileptic seizures. The dataset comprises 10,356 EEG recordings collected from 121 participants, including 50 patients diagnosed with generalized epilepsy and 71 healthy controls. Each recording contains 35 channels of EEG signals sampled 500 Hz for a duration of 15 seconds. To mitigate artifacts typically observed at the beginning and end of recordings, we discard the first seconds and the last second.
As the default classification task setting, we follow (Tasci al., 2023 Lih et al. 2023; Shen et al. 2024 Bhhndagee et al., 2024 Dicsli et al,, 2025) and divide the dataset into training, validation, and test sets ratio of I: To assess the model's s generalization across different subjects, we also perform leave-one-out-subjeec (LOSO) classification task. In this setting, data from one subject is held out as the test set, while the remaining data is used for training and validation. The training and validation sets used for the denoising task, while the test set is reserved for classification.
For graph construction]] each remaining 6,000-point (12 second) sequence is segmented into non-overlapping chunks, resulting in temporal graph of length 6, where each node corresponds to 1000-dimensional feature vector. We employ three stacked blocks, each consisting of a BGL module with three convolutional layers followed by the LPF operation as shown in Figure [ The term block here refers to this BGL + LPF unit, which consistently used in the subsequent ablation studies. All models are trained on NVIDIA GeForce RTX 3090.
Baseline methods. We compare the proposed method with several competitive baselines, including both graph-based and non-graph-basee approaches. (Tasci al. 2023) use k-Nearest Neighbors (kNN) classifier combined with Multivariate Dynamic Time Warping (MDTW). The Transformer- based method of (Lih et al. 2023) models temporal dependencies in EEG time-series data for
classification. (Shen et al.] 2024) employ Regularized O-minus tensor network decomposition
(ROD) to extract features from time tome-freqeenyy (TF) maps. (Mohammadi Foumani et al.) 2024)
propose self-supervised masked reconstruction framework to learn robust temporal
BEG
representations. Convolutional Neural Networks (CNNs) are used by (Bhandage et al. 2024 Diesli
al. 2025) to extract discriminative features from EEG spectrograms, while (Pan et al. 2022) further
enhance feature quality by processing channel-wise embeddings on a Riemannian manifold. On the graph- based side, DGCNN (Song et al. 2018) and GIN (Zhang & Yao 2021) represent EEG
data as graphs to capture complex inter-channel relations, while EEGNet (Lawhern et al., 2018)
and FBCSPNet (Schirrmeister et al.) (017) incorporate graph-inspired operations to enhance feature
extraction and classification performance.
6.2
EXPERIMENTAL RESULTTS
6.2.1
MAIN RESULTS
T presents a detailed comparison of our method against several existing approaches, divided into two main categories: non-graph-ben based methods in the default task setting and graph-based methods in the leave-one-subee -usj---t-sub (LOSO) task setting.
In the default task setting, which involves training and testing on the same dataset split, our model outperforms most baselines in terms of accuracy, precision, specificity, and F1-score, achieving 97.57% 98.58%, 97. 97.45% and 98.01% % respectively, with only 14,787 parameters. This demonstrates the efficiency and effectiveness of our method. While (Bhandage et al.) (024) based on STFT and CNN achieves a higher accuracy of 99.299..00 99.20% and FI-score of 99.30% requires several orders of magnitude more parameters (over 11 11.5 million), making it computationally expensive and memory- inefficient.
In addition to the default setting, we also evaluate our model under the more challenging LOSO task setting, which tests the model's ability to generalize across different subjects. Here, our model demonstrates strong performance with 90.06% accuracy and 92.59% Fl-score, outperforming other based methods such as DGCNN, GIN, and EEGNet. This shows that our model not only excels
"ee Appendix P. for detailed configuration.
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Table Comparison of Performance Among Different Methods. We compare the performance of various non-graph and graph-based methods across several metrics. Our method, with a lightweight model, achieves state-of-the-ar (SOTA) results in most of the metrics, and comparable to larger models in terms of performance.
Accuracy (%)
Precision Recall Specificity Fi-score
Method
Params #
(%)
(%)
(%)
(%)
Non-graph-based Methods in Default Task Setting
MDTW + KNN Tasci
2023
87.78
89.39
81.32
92.68
85.16
TF ROD (Shen ct al.
2024
18,400
88.08
89.22
82.28
92.46
85.61
mAtt (Pan et al.
2022
46,542
92.00
95.27
85.68
96.78
90.22
EEG2Rep Mohammadi Foumani al. 2024
96,886
91.41
94.79
86.09
91.48
93.11
CWT DCNN (Diesli et al.
2025
143,297
95.91
94.55
96.98
96.06
95.30
Ours
14,787
97.57
98.58
95.98
97.45
98.01
Large model in Default Task Setting
Transformer
Lih et al.
2023
1,849,771
85.12
82.00
82.00
87.32
82.00
STFT CNN
Bhaandage al.
2024
11,533,928
99.20
99.14
99.46
98.98
99.30
Graph-based Methods LOSO Task Setting
DGCNN (Song al.
2018
149,466
76.74
69.56
62,74
84.60
65.97
GIN
Zhang Yao
2021
25,794
68.82
58.78
44.36
82.55
50.56
EEGNet Lawhern et al.
2018
9,170
78.78
81.26
53.25
93.11
64.34
FBCSPNet Schirrmeister
2017
98,242
81.76
92.80
53,40
97.67
67.79
Deep4Net Schirmeister 2017
321,227
78.62
73.06
64.20
86.72
68.34
Ours(LOSO)
14.787
90.06
93.48
86.10
91.70
92.59
in controlled, single-subject setting but also generalizes well to subjects, crucial aspect for real-world applications where the model needs to handle diverse and unknown data distributions. In this setting, our model maintains good balance between computational efficiency and high generalization capability, outperforming many larger models such as Deep4Net and FBCSPNet.
By constructing an interpretable, lightweight transformer through the unrolling of graph-based algorithms, we focus on learning only the identified unknown parameters outside the optimization framework, which specifically tailored for balanced signed graph signal denoising. This approach results in significant reduction in the number of parameters compared conventional "black-box' neural network models, which are often generic and lack interpretability.
6.2.2 ABLATION STUDIES
We evaluate the impact of graph type on classification performance by comparing the proposed balanced signed graph with two alternatiees: positive graph and an unbalanced signed graph. The positive graph assigns all edge weights positive, disregarding pairwise anti-correlation in data, while the unbalanced signed graph models pairwise anti- anti-correlations using negative edges, but does ensure graph balance, and thus graph frequencies are ill-defined. See Appendix [or details. As shown in Table 2 the balanced signed graph outperforms both alternatives, which highlights the importance of both signed edges and graph balance when modeling EEG signals and implementing LP graph filters for denoising.
In our ablation study on loss function design, we observe that using a standalone MSE loss for learning signal priors yields substantially weaker downstream classification performance compared with the contrastive MSE formulation defined eq. (33 As shown in Table 3, incorporating contrastive guidance consistently enhances all evaluation metrics, indicating that the margin- basedd based negative-sama penalty helps the denoiser preserve discrmmiiiiiiee structure that is critical for EEG classification.

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Table Ablation Study on Different Graph Types. We compare the performance of three graph types on the LOSO task. The results highlight the importance of signed edges and graph balance.
Setting
Accuracy (%)
Precision (%)
Recall (%)
Specificity (%) F1-score (%)
Positive Graph
84.30
88.49
76.88
86.00
87.23
Unbalanced
78.87
86.74
68.22
78.69
82.52
Signed Graph
Balanced
93.68
96.32
89.45
93.61
94.94
Signed Graph
Table 3: Classification Results with Denoisers Trained Using Different Loss Functions. We compare the classification performance of denoisers trained with standalone MSE loss and contrastive MSE loss. Incorporating contrastive guidance significantly improves all evaluation metries.
Accuracy (%)
Precision (%)
Recall (%)
Specificity (%)
F1-score (%)
Loss Function
Single MSE
81.44
77.36
97.67
99.32
86.97
Contrastive MSE
97.57
98.58
95.98
97.45
98.01
To assess whether enforcing graph balance during polarity optimization may inadvertently remove meaningful anti-correlations, we examined the signed graphs constructed directly from the empirical EEG covariance matrices. Each signal was segmented into six temporal chunks, forming product- graph structure identical to the Positive Product Graph in Fig. 1 of the main text. Edge signs were assigned based on covariance values, with threshold of -0.1 marking strongly negative relations. Across the resulting signed temporal graph, we observed only 6 odd negative basic cycles out of 1481 total cycles (a fraction of 0.004), and greedy approximation (Fontan et al. (2224) of the frustration index yielded merely 16 frustrated edges among 1322 edges. These metrics indicate that the empirical EEG graph already very close to a perfectly balanced signed structure, with sparse and highly consistent antiicorrelations. Consequently, enforcing balance makes only minimal adjustments while preserving the substantive anti-correlation patterns present in the data.
We also conducted further studies assess the robustness and generalizability of our method. These include ablation studies on model architecture, and signal feature distance computation (Appendix F), validation on the TUH Abnormal EEG Corpus (Obeid & Picone (016) (Appendix G), statistical significance tests for the default classification task and the LOSO task (Appendix(H), and a comparison of training and inference time for graph-based baselines (Appendix Tp.
7 CONCLUSION
To differentiate between EEG brain signals from epilepsy patients and those from healthy subjects, we unroll iterations of a balanced signed graph algorithm that minimizes a signal denoising objective into a lightweight and interpretable neural net. A balanced signed graph can capture pairwise anti- correlations data, while retaining the frequency notion for efficient spectral filtering. Via signed edge weight assignment that leverages the Cartwright-Harce when mapping from learned positive feature distances. Denoising achieved via a sequence of graph learning / ideal low-pass filtering modules, where the cutoff frequencies are learned from data. We show that our graph learning module with normalization plays the role self-attention, and thus our graph-based denoisers are transformers. Using two denoisers trained to learn posterior probabilities of two signal classes, our method achieves competitive binary classification as SOTA deep learning models, while requiring far fewer parameters. One limitation is that method is currently suitable only for binary classification. For future work, we consider an extension to build a multi-class classification tree from graph-based denoisers.
Theorem, graph balance is ensured
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8 ACKNOWLEDGEMENT
This work was supported in part by the Beijing Major Science and Technology Project under Contract no. Z251 100008125007 The work of G. Cheung was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-2025-06252.

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APPENDIX
LIGHTWEIGHT TRANSFORMER FOR EEG CLASSIFICATION VIA BALANCED SIGNED GRAPH ALGORITHM UNROLLING
A RELATED WORK IN DENOISERS AS PRETEXT TASK
Given that denoiser learn compact representations from sufficient training data, there existing works that train denoisers as a pretext task for other downstream applications (Ho et al. 2020 Wu et al.) 2023 Clark & Jaini 2023). Denoiser Diffusion Probabilistic Model (DDPM) (Ho et al. 2020) employs a learned denoiser in a reverse path to gradually remove Gaussian noise from a pure noise image, in order generate realistic image. Wu al. (2023) employs denoising masked autoencoder to learn latent representations from Gaussian-noise-commue
images, which can benefit downstream tasks such as classification. Clark & Jaini (2023) shows that denoiser-basse diffusion model can be repurposed for zero-shot classification. Our approach to binary EEG classification differs in the following aspects. First, we train one class-specific denoiser (e(+) per class c, so that the posterior probability distribution unique to that class is learned. Second, we use reconstruction errors of the two trained denoisers operating on an input signal to determine its class assignment. In so doing, we achieve model interpretability for both the denoising step and the classification step (the denoiser is built by unrolling graph- denoising algorithm), while minimizing the number of parameters used.
B LANCZOS LOW-PASS FILTER APPROXIMATION
Similarly done in Vu et al. (2021). we approximate a low-pass graph filter output g((+))))))))))))))))))))) via Lanezos approximation (Susnjara al. 2015) as follows. Denote by Um E R m N, matrix containing as columns orthonormal basis vectors of Krylov space K.m (C+ yt span (y, (y, Lt,,,.., (I+)m=ly] Um can be computed using the Lanezos method in O(m [8). Um. tri-diagonalizes L R NxN into HM E mmxm
i.e.
α1
82
82
0:2
83
Hm = U,
33
003
(24)
B.
3m
a'm.
We approximate a low-pass filter ((+)y++ as
x lly (m.
(25)
where e₁ is the first canonical vector. Eigen-decomposiitonn (HHm) Zmmg(Am))) can be com- puted in Omm²) ) for a tridiagonal, sparse and symmetric matrix, using a specialized algorithm such as the divide-and lirde-and-conee und-conquer eigenvalue algorithm (Cuppen 1980). Assuming m < N and the number of
edges El is O(N), complexity of eq. 25 is (N.).
C USE OF CONVENTIONAL GRAPH LAPLACIAN VERSUS SIGNED GRAPH LAPLACIAN
We show that the eigenvectors of the conventional graph Laplacian L D W better capture pairwise (dis)similarities (quantified by feature distance in equation 6 in our signed graph G for IP signal reconstruction than the signed graph Laplacian L A D W, where Di,- = Σ, W Dittrich & Matz, 2020). Eigenvectors {v.} of L are successive norm-one vectors that minimize the Rayleigh quotient:
Vi arg min
x =x=
Σ (NJEE
why - 22,2
(26)
v vi
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For Way < O. minimizing Lx promotes repulsion, Le., |2, xyl should be large, and æ; and z should be different / dissimilar.
In contrast, using the signed graph Laplacian L', the Rayleigh quotient is
L Σ (iJ)EE
|w, sign(ws,,)zzz)
(27)
If was < O, then Werl sign W/, sign(W,,))z))²= w zy)2 Thus, minimizing x L'xx promotes negative linear dependence, i.e. Io + -i] should be small and H; R -Ij. While negative linear dependence is a specifie structured form of repulsion, they are not the same. In our case, given that negative edge weights are encoding anti cotrecorrlatinns, anti-correlated samples i and j do not imply z; -2, f they have non-zero means. Experimentally, we found that using the conventional graph Laplacian L to define balanced signed graph frquencies outperforms using L in EEG signal denoising and classification.
We demonstrate also the importance of signed graph edges as well as graph balance in modeling EEG data with anti-correlations. A positive graph G+ with positive edges can have weights defined as Wa,j exp(-da,) given positive feature distance di in eq. (6). A general signed graph 9 can define signed edge weight way E [-1, 1] using shifted logistic function:
2
Wisj + (dh. +1.
(28)
where d² > 0 is parameter. Like eq. 7 eq. (28 states that edge weight wa,j has smaller weight for larger feature distance dz, but does not guarantee graph balance. Using the signed graph Laplacian definition L D W, one can then perform spectral low-pass filtering done previously. We
show Section that both positive graph and unbalanced signed graph are inferior to balanced signed graph in classification performance.
D JUSTIFICATION FOR THE RECONSTRUCTION ERROR METRIC
We provide an alternative explanation of why the reconstruction error criterion eq. 22 to determine class assignment for input signal y is reasonable. Given assumed AWGN noise model eq. 18
the signal x" that maximizes the likelihood term Pr(y x, c) is the one between xi = Vo(y and x V (y) that minimizes the numerator of the exponential function, i.e.
x arg
min
||y x = arg
max Pr(y x),c)
(29)
x (0)
x CE (0,1)
which is the reconstruction error criterion. Thus, our class assignment based on reconstruction error criterion equation 22 is also the maximum likelihood estimate (MLE).
E
MODEL SETUP
This section provides a detailed description of our model architecture and experimental configuration.
E.1
GRAPH CONSTRUCTION SETUP
Since EEG signals are computed between pairs of electrodes, model the basic spatial structure using a line graph derived from an undirected primary graph Go (N', where each vertex i e A corresponds to EEG electrode and each edge (i.j) E E" represents bipolar EEG channel (i.e., a signal computed between two electrodes). The line graph G = (N, E)) is then constructed such that each node l A corresponds
edge ex E Eo in the original graph Go. Two nodes k, I, E A in the line graph are connected by an edge (k, in & and only if the corresponding edges eg, el E" in the original graph share a common vertex. Formally,
N= E0 E = [(e,(( e2) E 8 x Ed nej + 0}-
(30)
This construction emphasizes the edge-centric structure of EEG signal representation, which naturally aligns with the properties of bipolar recordings. To capture temporal dynamics, we segment the EEG signal of length 6000 into 6 non-overlapping temporal windows, each of length 1000. A distinct line graph is instantiated for each window, resulting in a temporal graph composed of 6 time-specific subgraphs, effectively modeling time-evolving edge dependencies.
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E.2 BALANCED GRAPH LEARNING MODULES SETUP
Each Balanced Graph Learning (BGL) module is designed to extract local temporal features from EEG edge signals using lightweight convolutional architecture. Specifically, the module processes edge-level input through sequence of four convolutional blocks, each consisting of 2D convolution layer with kernel size (1,5) and stride (1, along the temporal dimension, followed by batch normalization and a LeakyReLU activation with a negative slope of 0.01. This gradually compresses the temporal length while preserving the spatial (node) dimension. A final 1 x convolution reduces the channel dimension one, and adaptive average pooling layer projects the output to fixed-size feature map of shape (N, d), where N = 210 is the number of nodes (6 time slices x 35 EEG channels) and d 63 is the feature dimension per node.
To construct the graph structure within each BGL module, we compute a sample-specific signed and normalized affinity matrix W R-N based on the extracted features f TR BxSNN
Mahalanobis-like distance is first evaluated as equation equation 6 where M = Q with Q: being a randomly initialized real matrix that is updated during training, yielding a symmetric positive semi-definite matrix M. The distances are normalized to [0, 1J per sample, and converted into affinities using a radial basis function: Wij = exp(-d.y), These affinities are then symmetrically normalized as W D-1//WDD 1/2 to obtain a stable and scale-invariant edge weight matrix.
E.3 LOW-PASS FILTER MODULES SETUP
To enable learnable frequency responses in the low-pass filter modules, we adopt a parameterized sigmoid function to approximate the ideal low-pass characteristic. Specifically, given the eigenvalues {A)) of the graph Laplacian L+ E RxS,, we define the frequency response function as:
g(A:) = a (a(w A,)),
(31)
where of-) denotes the sigmoid function, is steepness parameter set to 10 controlling the sharpness of the transition band, and is a learnable threshold representing the cutoff frequency. which allows the model to softly suppress high-frequency components (i.e., those with larger X,) while retaining low-frequency information in a differentiable and trainable manner. This formulation ensures smooth gradients during back- sock-propagation and avoids the non-differentiability of hard thresholding.
E.4 DENOISER TRAINING SETUP
All models trained for up 100 epochs using the Adam optimizer with an initial learning rate of x 10-3, A cosine annealing scheduler with warm restarts is applied to adjust the learning rate dynamically, with the first restart period set to To learning rate of 1 x 10-5, The parameter in the contrastive loss function equation 23 is fixed at 1.0. Training is conducted on single NVIDIA GeForee 3090 GPU with a batch size of Early stopping is implemented with patience of 10 epochs based on validation performance.
multiplier Tiuk 1, and a minimum
F MORE ABLATION STUDIES
In this section, we investigate the impact of different model design choices on classification perfor- mance. Specifically, we evaluate the effect of temporal sequence length, CNN block number, and distance metric selection on the overall model performance.
F.1 ABLATION STUDY ON TEMPORAL SEQUENCE LENGTH
We explore the influence temporal sequence length on the model's performance. As shown Table increasing the temporal sequence length from 3 to 10 consistently improves accuracy and other evaluation metrics, highlighting the model's 's ability to better capture temporal context. However, when the sequence length exceeds 10, performance improvements plateau, and the model's computational cost and memory consumption increase. These findings suggest diminishing returns with longer sequence lengths, emphasizing the need for balanced choice of sequence length.
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Table 4: Ablation study the temporal sequence length
Sequence Length
Accuracy (%)
Precision
Recall (%)
Specificity (%)
F1-score (%)
3
92.66
95.39
88.26
92.92
94.14
6
95.85
96.03
95.53
97.49
96.75
10
97.57
98.58
95.98
97.45
98.01
12
97.43
98.40
95.81
97.30
97.85
15
95.77
96,21
95.49
97.38
96.63
20
95,50
95.87
94.88
97.10
96.12
30
92,42
94.90
88.10
92.65
93.75
40
91.23
93.15
86.80
91.80
92.30
50
90.78
92.76
86.20
91.12
91.84
60
89.95
91.90
85.33
90.60
90.90
100
88.10
90.20
83.92
89.42
89.88
F.2 ABLATION STUDY ON CNN BLOCK NUMBER
We analyze the impact of varying the number of CNN blocks on model performance. As shown in Table increasing the number of CNN blocks leads to improved performance in terms of accuracy, precision, and F1-score. However, the performance improvements start to plateau after blocks, with further increases in depth providing diminishing returns. This suggests that deeper network helps improve feature extraction initially, but excessive depth increases computational complexity without significantly improving classification accuracy.
Table 5: Ablation study on the block number of CNN
Block Numbers
Accuracy (%)
Precision (%)
Recall (%)
Specificity (%)
F1-score (%)
65.15
29.12
92.45
74.50
41.87
94.31
96.57
90.62
94.37
95.46
4
96.12
96.00
94.10
96,20
95.02
6
97.57
98.58
95.98
97.45
98.01
9
97.44
98.40
96.00
97.40
97.90
12
97.42
98.35
95.95
97.38
97.85
F.3 ABLATION STUDY DISTANCE METRIC
We evaluate the influence of different distance metrics classification performance. Table 6howws the performance of four commonly used distance metrics: Mahalanobis Distance, Euclidean Distance, Cosine Similarity, and Manhattan Distance. The Mahalanobis Distance, which incorporates trainable parameters, provides the best performance in terms of accuracy, precision, and Fl -score,, with an accuracy 97.57%. precision of 98.58%, and F1-score of 98.01 %. However, requires longer convergence time (2 hours 14 minutes) compared to the simpler metrics such as Euclidean Distance, which achieves slightly lower accuracy of 96.80% and converges results highlight the trade-offs between performance and computational efficiency, with Mahalanobis Distance offering the best results the cost of increased computational overhead.
hour 55 minutes. These
Table 6: Ablation study on the distance metric
Distance Metric
Accuracy
Precision
Recall
Specificity (%)
Fl-score (%)
Convergence
(%)
(%)
(%)
Time
Mahalanobis Distance
97.57
98.58
95.98
97.45
98.01
2 min
Euclidean Distance
96.80
97.85
94.65
96.55
96.92
1 55 min
Cosine Similarity
96.40
97.60
94.80
96.70
96.90
h 40 min
Manhattan Distance
96.20
97.35
94.50
96.40
96.85
1 50 min
18

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Published as a conference paper at ICLR 2026
G CLASSIFICATION TASK ON TUH ABNORMAL EEG COUPUS DATASET
We also evaluated our method on the TUH Abnormal EEG Corpus (Obeid & Picone 2016), which is widely used in epilepsy detection. This dataset consists of 2,993 EEG segments from 2,329 patients, with 70% of the data used for training and 30% for testing, following the protocol in (Chen et al.) 2025 The comparison made with several baseline results from (Chen et al. (025). As shown in the model achieves accuracy of 90.69%, Fl-score of 92.60% and G-mean of 89.76%. These results are superior to several baseline methods. For instance, methods like BD-Deep4 and WaveNet-LSSTM have lower accuracies of 85.40% and 88. 78,,, respectively. Traditional approaches such as DWT + CSP + CatBoost also achieve 90.22% accuracy, but our method outperforms them by achieving higher Fl-scores and G-mean. Overall, our model demonstrates strong performance, surpassing a wide range of classical and deep learning methods, highlighting its effectiveness in detecting epileptic seizures in diverse datasets.
table
Table 7: Comparison of performance on TUH Abnormal EEG Corpus
Method
Accuracy (%)
F1-score (%)
G-mean (%)
BD-Deep4
85.40
82.52
84.08
AlexNet MLP
89.13
87.06
88.02
AlexNet + SVM
87.32
84.97
86.24
WaveNet-ISTMM
88.76
88.32
88.39
HT + RG
85.86
83.40
85.19
LSTM + Attention
79.05
79.00
79.00
WPD + CatBoost
87.68
86.06
87.24
Multilevel DWT KNN
87.68
86.07
87.24
WPD + CatBoost
89.13
87.60
88.60
DWT CSP + CatBoost
90.22
88.89
89.76
Ours
90.69
92.60
89.76
H STATISTICAL SIGNIFICANCE TESTING
To ensure the robustness and statistical significance of our results, we conducted extensive experi- ments, including t-tests and ANOVA.
We conducted 100 independent experiments across random data partitions, with each partition containing 10 runs, each initialized randomly. The mean classification accuracies (# standard deviation) of our method and three baseline models are presented in Table g Paired t-tests show that method outperforms all baselines significantly (p 0.001), demonstrating the effectiveness and robustness of our approach.
T-test:
Table 8: T-test Results for Performance Comparison
Model
Accuracy (mean + std)
p-value vs Ours
Ours
97.44 1 0.40
EEGNet
93.30 + 0.60
p p 0.0001
FBCSPNet
96.91 + 0.50
0.0001
Deep4Net
96.58 + 0.55
0.0001
ANOVA-test. In addition to the default evaluation, we also assess cross-subject generalization on the Turkish Epilepsy EEG Dataset. Since other seizure-focused datasets utilize different electrode montages, direct cross-dataset validation is not feasible. We adopted deave-one-subject-our (LOSO) protocol across all 121 subjects. Under this stricter data split, our model achieved 93.68% accuracy and 94.94% Fl-score, demonstrating strong performance across subjects. To further evaluate the consistency of performance across individuals, we performed one-way ANOVA on the per-subject LOSO accuracies and Fi-scores. The ANOVA results, shown in Table revealed no significant differences between subjects (Accuracy: F 0.85, p= 0.65; F1-score: F = 1.02, p = 0.42), confirming stable and consistent performance across different individuals.
19

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Published as a conference paper at ICLR 2026
Table 9: ANOVA Results for Per-Subject LOSO Evaluation
Metric
Mean + Std (%)
ANOVA F-value
p-value
LOSO Accuracy
93.68 1.20
0.85
0.65
LOSO Fl-score
94.94 = 1.10
1.02
0,42
I COMPUTATIONAL EFFICIENCY EVALUATION
To assess the computational efficiency of our method, we compared the training and inference times of our approach with three state-of-the-an baselines: EEGNet, FBCSPNet, and Deep4Net. Our method significantly outperforms these baselines in both training and inference times. Specifically, training our model takes only hours and 14 minutes, compared to 5 hours 33 minutes for EEGNet, 9 hours minute for Deep4Net, and 22 hours 19 minutes for FBCSPNet. Inference time is also considerably shorter, with our method requiring only 55 seconds, whereas EEGNet, FBCSPNet, and Deep4Net take 613 seconds, 396 seconds, and 455 seconds, respectively. These results demonstrate that our model offers substantial reductions in computational cost, making it more efficient for real-time applications while maintaining strong performance.
Table 10: Comparison of Training and Inference Times
Method
Training Time
Inference Time
EEGNet
5 hours 33 minutes
613 seconds
FBCSPNet
22 hours 19 minutes
396 seconds
Deep4Net
hours minute
455 seconds
Ours
2 hours 14 minutes
55 seconds
J RELIABILITY ANALYSIS OF THE POLARITY-SELECTION PROCEDURE
J.1 POLARITY OPTIMIZATION ALGORITHM
Algorithm 1: Polarity Optimization Procedure
Input: Initial polarity vector 3, validation sets Dj, D2, initial loss Lorig Output: Updated polarity vector /
for i = to N do
Randomly sample subset S C f1..... . with |S| (1.....5);
Construct proposal 8' by flipping signs of 33 on indices in S; Compute validation losses:
L
ValLoss(x),
L2
Σ zED2
ValLoss(z)
D
1D2
ZED1
L- L < Lorig then Accept proposal: B B¹, Lorig t- L;
else
Reject proposal;
return
During training, the polarity-optimizatio routine in Algorithm | is invoked once every two epochs, using only the validation dataset. To avoid unnecessary computation, we employ an carly-termination rule: if five consecutive invocations (corresponding to ten training epochs) result in accepted polarity update, the optimization considered converged. After this point, the polarity-selccton module is longer called for the remainder of training.
20

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Published as a conference paper at ICLR 2026
Each call to Algorithm iterates over all N nodes and evaluates one validation forward pass per proposal. In practice, the total runtime of one optimization call comparable to that of a single training epoch. This aligns with empirical measurements across all datasets and model variants.
J.2 STABILITY WITH RESPECT INITIALIZATION
We further examine the sensitivity of the procedure to initialization. Across different train/validation splits, the empirical covariance matrices computed from training data remain highly consistent with those computed from the full dataset. After normalization, the average Frobenius distance between the two covariance matrices 1.07 x 10-1, which negligibly small. Since only the signs of covariance entries are used to initialize node polarities, such minor variations do not affect the initialization. In particular, for LOSO settings where the training set constitutes approximately 99% the data, the covariance estimated from the training subset effectively identical to that of the entire dataset. Consequently, polarity initialization remains stable, and we observe no degradation in convergence behavior or final performance.
21


Reviews:
[{"review_id": "vxsQrAy4nR", "reviewer": "Reviewer_hLos", "summary": "The paper tackles binary classification of EEG signals. For each of the two classes, a graph-based signal denoiser is learnt from data. Denoising is done by applying a low-pass filter on the Laplacian of a learnt graph. For inference, the data point is denoised by both denoisers and the datapoint is classified as belonging to the class of the denoiser that best reconstructed the input signal. The model is then validated on real-world data where the authors highlight that it is competitive with SOTA, while employing fewer parameters.", "questions": "- Why are the large models in their own category in Table 1? \n- How does training time of your model compare to the large models (Li, Bhandage)?\n- Do you have empirical evidence on other datasets?\n- Can you comment on the error margins of the approaches?\n- Can you extract useful information from your models (Interpretability, Explainability)?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper investigates an interesting, real-world problem. Specifically in the medical domain, an interpretable model is often preferable to a stronger black box model. \n\n- The decisions made in the design of the approach are described nicely and backed by theory and literature references", "weaknesses": "- Notation is abused quite heavily throughout the paper. E.g.:\n  - $\\Psi_r$ are the parameters of the $r$-th block. At the same time $\\Psi_0(y)$ is the output of the denoiser for class $0$. Additionally, the parameters are $\\Phi_r$ in Figure 2.\n  - $x \\in \\mathbb{R}^N$ is the input signal. At the same time $x_i \\in \\mathbb{R}^E$ is the input embedding. \n  - $c_i$ is the center of the Gersgorin disk and $c$ is also the random variable referring to the class. \n\n- Table 1 (the main results table) is quite confusing. \n  - Why are the large models in their own category? \n  - The time needed for training is a much better metric for praticioners, even the 11mil model takes up less that 100MB of space, however, it will take considerably longer to train. \n  - You reference Li et. al in your main text, but surely ment Bhandage et. at.\n\n- The empirical evaluation is limited to one dataset (in two dífferent settings). The dataset that was used was essentially solved by Bhandage et. at. While the proposed method is competitive with the other baselines, there remains a gap to SOTA. In the LOSO problem setting, Bhandage et. at. are left out of the evaluation. The second experiment is quite weak in itself. Essentially, the hypothesis that \"being able to encode negative correlation is advantageous\" is empirically validated. This does little to strengthen the approach. No error margins are reported.\n\n- The idea of a interpretation of the model is only hinted at in the beginning and then left underexplored. In the life sciences, an explainable model often beats a stronger black-box model because it offers insight into the mechanisms at play. The paper has a strong entry point into such an analysis, as the approach actually constructs a model of the signal distribution for each class. That is, inspecting these models could lead to an analysis of what part of the signal is responsible for the distinction.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "J8LtrVsUFq", "reviewer": "Reviewer_zTYv", "summary": "The paper proposes a lightweight, interpretable “transformer-like” network for EEG seizure classification by unrolling a balanced signed-graph denoising algorithm. Key ideas: (i) learn a balanced signed graph of EEG channels, then map it via a similarity transform to an equivalent positive graph with well-defined frequencies; (ii) implement an ideal low-pass graph filter (cutoff learned from data) and interleave it with a balanced-graph learning (BGL) module; (iii) train two class-conditioned denoisers and classify by comparing reconstruction errors. On the Turkish Epilepsy EEG dataset the method attains 97.57% accuracy with only ~14.8k parameters, and shows strong leave-one-subject-out (LOSO) generalization.", "questions": "**I found that the main text exceeds the 9-page limit, which seems to violate the strict page requirements for submissions.**\n\nFor rebuttal, I hope the authors to answer the following questions:\n\nQ1: Please clarify whether the cutoff is implemented via explicit spectral truncation or via a smooth transfer function on eigenvalues (e.g., sigmoid). If both appear in the paper, which one produced the reported numbers, and why was it preferred?\n\nQ2: You ensure PSD by setting $L_B=\\bar L_B+\\delta I$. What is the empirical distribution of $\\delta$ across subjects/blocks? How does varying $\\delta$ shift the effective spectrum and the LP response (e.g., energy scaling)? \n\nQ3: How imbalanced are the learned signed graphs before enforcing balance (e.g., frustration index, fraction of odd negative cycles)? A short diagnostic could justify that hard balance enforcement does not wash out meaningful anti-correlations.\n\nQ4: Please provide pseudocode: update order, stopping criterion, and complexity per block for $\\beta_i\\in\\{\\pm1\\}$ updates. Do multiple random initializations converge to the same polarity assignment, or is there sensitivity? \n\nQ5: You mention covariance-based initialization. Can you confirm that statistics for initialization are computed only on training folds in LOSO/default splits? If not, could you re-run with train-only stats or provide a control showing negligible impact?\n\nQ6: Your normalized weights are symmetric and can be negative via polarities, unlike standard softmax attention. Could you either (a) provide a formal mapping/conditions when your weights behave like attention, or (b) present an ablation replacing your weight construction with softmax attention to show comparable behavior?\n\nQ7: For baseline speed/latency numbers: what hardware, precision , batch sizes, and dataloader settings were used? If possible, include on-device CPU or low-power GPU latency to substantiate the “lightweight” claim.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "S1. Principled modeling. The use of balanced signed graphs gives a rigorous frequency notion via a Laplacian similarity transform to a positive graph, enabling classical spectral filtering while still modeling anti-correlations that are common in EEG. This is technically neat and well-motivated.\n\nS2. Clear algorithm-unrolling design with interpretability. The network cleanly alternates LP filtering and BGL. Figure 2 makes the pipeline easy to follow。\n\nS3. Good parameter efficiency and competitive accuracy.", "weaknesses": "> W1. “Attention equivalence” is overstated.  \n\nThe normalized weights use\n    $$\\bar w_{ij}=\\beta_i\\beta_j\\frac{e^{-d_{ij}}}{\\sqrt{\\sum_\\ell e^{-d_{i\\ell}}\\sum_k e^{-d_{kj}}}},$$\n    which (a) can be negative via $\\beta_i\\beta_j$, (b) are *symmetric* rather than row-stochastic, and (c) need not satisfy $\\sum_j \\bar w_{ij}=1$. This differs materially from softmax attention\n    $$a_{ij}=\\frac{\\exp(e_{ij})}{\\sum_k \\exp(e_{ik})}\\ge 0,$$\n    so calling $\\bar w_{ij}$ “essentially attention weights” risks confusion.\n\n> W2. Possible leakage in polarity initialization.  \n\nInitializing polarities via an empirical covariance $\\bar C$ computed from “collected EEG data” is ambiguous: if $\\bar C$ uses the *entire* dataset, the train/test split is compromised. Clarify that initialization uses train-only statistics.\n\n> W3. Temporal modeling is inconsistent across sections. \n\nOne place “assumes a single chunk” and works on $G_B$, elsewhere the implementation uses a product graph with 6 windows (nodes $N=210=6\\times35$). It is unclear whether the experiments use the single-chunk simplification or the 6-slice product graph with temporal edges, and how this choice affects results.\n\n> W4. Feature metric is under-specified.  \n\nDistances use $d_{ij}=(f_i-f_j)^\\top M (f_i-f_j),\\quad M\\succeq0,$  but Appendix text suggests $M=Q_iQ_i^\\top$ selected from a candidate set. Is $M$ global, per-node, or per-block? How is the candidate set regularized to avoid degenerate metrics? What prevents collapse(e.g., rank-1 $M$) beyond the implicit CNN bottleneck?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XOzHri0wAH", "reviewer": "Reviewer_ZtHH", "summary": "The paper addresses the problem of EEG classification. The authors propose a discriminant\nanalysis model that predicts classes based on the smallest reconstruction error to a \nclass-wise autoencoder. The autoencoder represents the multivariate EEG time series\nas a graph where each node represents a segment of a univariate channel. \nConsecutive segments in the same channel are connected by edges, and concurrent\nchannel segments are connected by edges weighted by the correlation between their \nsegments. The autoencoder denoises by using a graph low-pass filter that uses only \nthe k eigen dimensions of the graph Laplacian with highest eigenvalue. The authors \naddress specifically the problem that some of the edge weights / correlations can \nbe negative, and then the graph Laplacian is no longer guaranteed to be positive\nsemidefinite. For this case they approximate the graph with a balanced signed \ngraph, flipping the signs of some edges; then a pos.semidef. Laplacian is guaranteed\nagain. In experiments on a large EEG dataset they show that their method outperforms\nseveral baselines, while reaching 98.4% of the performance of a way less\nparsimonious model with 1000 times more parameters.", "questions": "- q1. Can you compare the performance of your model with recent strong models\n  such as MAtt and EEG2Rep?\n- q2. As additional ablation study: how does the model perform w/o low-pass filtering?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- s1. denoising using the channel segment correlation graph is an interesting approach.\n- s2. finding a good balanced signed graph approximation is a novel idea in this context.\n- s3. very good results with a model with very few parameters.\n- s4. the method is well explained.", "weaknesses": "- w1. several strong baseline papers for EEG classification have been missed.\n- w2. an ablation study for low pass filtering is missing.\n- w3. experiments are hard to reproduce as no source code is provided and the method\n  is somewhat complex.\n\nmore details:\n\nw1. several strong baseline papers for EEG classification have been missed.\n- for example, MAtt [Pan et. al., NeurIPS 2022] is often compared to recently.\n- also the EEG foundation models such as EEG2Rep [Baeza-Yates et al., KDD 2024]\n  might be interesting models to compare to. They also report on TUAB\n  (like your appendix G), but way lower scores. Is the experimental protocol\n  the same?\n\nw2. an ablation study for low pass filtering is missing.\n- would the model deteriorate if you do not low-pass filter at all?\n- then your model is basically a graph attention neural network.\n- what is not clear to me: to softmax-like normalization of the \n  attention weights in eq. 8 should denoise already by pushing\n  the smaller weights close to zero. Low-pass filtering now sets them\n  to exactly zero. Why does this help?\n- you argue that your model does not use dense and large key,\n  value and query matrices K, V and Q, but the Mahalanobis kernel M \n  in eq. 6 you could interprete as say the key weights matrix Q.\n  Then you just choose the identity for K and V. \n\nw3. experiments are hard to reproduce as no source code is provided and the method\nis somewhat complex.\n- re-implementing all the different steps of your method will put a high burden on\n  researchers trying to work with your paper.\n\nsmaller points:\n- p1. the model's performance crucially depends on the contrastive loss (eq. 23), \n  but you do not mention this in the main paper. In ablation study F1, w/o \n  the constrastive loss your model performs worse than all your baselines \n  in tab. 1.\n  \n\nreferences:\n- Pan, Yue-Ting; Chou, Jing-Lun; Wei, Chun-Shu (NeurIPS 2022):\n  \"MAtt: a manifold attention network for EEG decoding.\"\n  Advances in Neural Information Processing Systems.\n\n- Baeza-Yates, Ricardo; Bonchi, Francesco; Nguyen, Nam; Foumani, Navid\n  Mohammadi; Salehi, Mahsa; Mackellar, Geoffrey; Ghane, Soheila; Irtza,\n  Saad (KDD 2024): \"EEG2Rep: Enhancing Self-supervised EEG\n  Representation Through Informative Masked Inputs.\"  Proceedings of the\n  30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD\n  2024, Barcelona, Spain, August 25-29, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "M2mT3uBhbo", "reviewer": "Reviewer_NKBD", "summary": "This paper proposed an EEG classification method based on unrolling a sequence of graph learning and low-pass graph filtering operations. At each step, the authors first learn a signed graph Laplacian, then cut off the high-frequency components for denoising. The authors interpret the final output as the posterior mean of the clean signal, and derive a classifier based on its distance to the noisy input. Experiments show that their method outperforms existing graph and non-graph EEG classification models in normal and LOSO settings.", "questions": "1. What is the justification for using the signed Laplacian? The total positivity of the combinatorial graph Laplacian is shown to be a useful bias for many problems. If both positive and negative correlations are allowed, one can just use eigenvectors of the empirical covariance matrix for denoising, essentially PCA. This is somewhat similar to the authors' choice, given their way of selecting the signs in the graph, but much simpler. Is there any ablation study on this?\n2. How did the authors select the cutoff value $\\omega$ for denoising?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper is well-written and easy to follow. More details are provided in the appendix.\n2. The authors interpret the graph learning and denoising as a form of transformers. The parameter space of the proposed model is substantially smaller than many existing methods, while the performance is stronger.", "weaknesses": "1. The graph construction is heuristic. Some design choices are not well-justified, e.g. the use of the Manhattan distance.\n2. The evaluation on the real dataset is on the weaker side. The authors only evaluate on two datasets, with one relegated to the appendix. More informative metrics such as PR-AUC should also be considered.\n3. The paper would benefit from some in-depth discussion about why the proposed model outperforms the competing ones.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)