FAPEX: Fractional Amplitude-Phase Expressor for Robust Cross-Subject Seizure Prediction
Authors: Ruizhe Zheng
Lingyan Mao
DINGDING HAN
Tian Luo
Yi Wang
Jing Ding
Yuguo Yu
Venue: NeurIPS 2025 spotlight ()
Keywords: seizure prediction; AI for health
Primary area: machine_learning_for_sciences
TL;DR: FAPEX is a fractional neural frame operator-enhanced model designed for subject-agnostic seizure prediction.

Abstract: Precise, generalizable subject-agnostic seizure prediction (SASP) remains a fundamental challenge due to the intrinsic complexity and significant spectral variability of electrophysiologial signals across individuals and recording modalities. We propose \model{FAPEX}, a novel architecture that introduces a learnable \emph{fractional neural frame operator} (FrNFO) for adaptive time–frequency decomposition. Unlike conventional models that exhibit spectral bias toward low frequencies, our FrNFO employs fractional-order convolutions to capture both high and low-frequency dynamics, achieving approximately $10\%$ improvement in F1-score and sensitivity over state-of-the-art baselines. The FrNFO enables the extraction of \emph{instantaneous phase and amplitude representations} that are particularly informative for preictal biomarker discovery and enhance out-of-distribution generalization. \model{FAPEX} further integrates structural state-space modeling and channelwise attention, allowing it to handle heterogeneous electrode montages. Evaluated across 12 benchmarks spanning species (human, rat, dog, macaque) and modalities (Scalp‑EEG, SEEG, ECoG, LFP), \model{FAPEX} consistently outperforms 23 supervised and 10 self-supervised baselines under nested cross-validation, with gains of up to $15\%$ in sensitivity on complex cross-domain scenarios. It further demonstrates superior performance in several external validation cohorts. To our knowledge, these establish \model{FAPEX} as the first epilepsy model to show consistent superiority in SASP, offering a promising solution for discovering epileptic biomarker evidence supporting the existence of a distinct and identifiable preictal state for and clinical translation.

FAPEX: Fractional Amplitude-Phase Expressor for Robust Cross-Subject Seizure Prediction
Ruizhe Zheng's
Research Institute of Intelligent Complex Systems, Fudan University rzzheng23Cm. fudan. edu. on
Lingyan Mao?
Department of Neurology, Zhongshan Hospital, Fudan University Lingyanmao@fudan edw.. cn
Tian Luo
Yi Wang*
Children's Hospital of Fudan University ti nonluoffude edu. cn
Children's Hospital of Fudan University yiwangūshmu edu. cn
Dingding Han
School of Information Science and Technology. Fudan University
ddhan@fudan, edu. cn
Jing Ding Zhongshan Hospital, Fudan University jingdingezs praggiinnts-hhopitall..... sh.
Yuguo Yu
State Key Laboratory of Brain Function and Disorders and MOE Frontiers Center for Brain Science, Research Institute of Intelligent Complex Systems and Institutes of Brain Science, Fudan University, Shanghai Artificial Intelligence Laboratory Shanghai 200232, China yuyuguo@fudan. edu.
Abstract
Precise, generalizable subject-agnostic seizure prediction (SASP) remains funda- mental challenge due to the intrinsic complexity and significant spectral variability of electrophysiologial signals across individuals and recording modalities. We propose FAPEX, novel architecture that introduces learnable fractional neural frame operator (FrNFO) for adaptive time-frequency decomposition. Unlike con- ventional models that exhibit spectral bias toward low frequencies, our FrNFO employs fractional-order convolutions to capture both high and low-frequency dynamics, achieving approximately 10% improvement in F1-score and sensitivity over state-ofthie offtthe-rt art baselines. The FrNFO enables the extraction of instantaneous phase and amplitude representations that are particularly informative for preictal biomarker discovery and enhance out-of-distribution generalization. FAPEX further integrates structural state-space modeling and channelwise attention, allowing it to handle heterogeneous electrode montages. Evaluated across henchmarks spanning species (human, rat, dog, macaque) and modalities (Scalp-EEG, SEEG,
*Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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ECoG, LFP), FAPEX consistently outperforms 23 supervised and 10 self-supe baselines under nested cross-validation, with gains of up to 15% in sensitivity on complex cross-domain scenarios. It further demonstrates superior performance in several external validation cohorts. To our knowledge, these establish FAPEX as the first epilepsy model to show consistent superiority in SASP, offering a promising solution for discovering epileptic biomarker evidence supporting the existence of a distinct and identifiable preictal state for and clinical translation.
1 Introduction
Epilepsy is common, heterogeneous set of neurological disorders characterized by recurrent, hypersynchronous discharges that disrupt normal cognition and behavior. Affecting over 50 million people worldwide [57]. its diagnosis and monitoring rely fundamentally on electrophysiologiee recordings whether invasive (e.g., electrocorticograhyy (ECoG), dcrrro-cccttoencchhlloaaaa (SEEG), local field potential (LFP)) non-invasive (scalp EEG) [8 17]. Although seizures have long been viewed as abrupt and unpredictable events, a growing body of work demonstrates the existence of preictal stage marked by subtle neural and behavioral changes, offering an actionable window for intervention.
Prevctal
03
73
20
SPH
53
53-
Lalband
APPS
53-
83-
Wirt
43-
RESPECT
Acsi
Hem
on OnLEROLLO
Teat Delaser
Summary of our work. (a) Definition of the different brain activity stages for the predictive analysis of epiloptic seizure scalp-Eld EEE record is shown for the purpose of illustration). (b) Overview of the FAPEX development and validation pipeline. (c) Comparative evaluation results demonsirate that PAPEX consistenlly oulperforms state the (SOTA) supervised and self supervised appnouches across 12 divense benchmarks in terms of Fl and sensitivity, demonstrating superior performance and generalization.
Figure 1:
Seizure prediction systems seek to detect these preictal alterations and raise alarms sufficiently in advance. As shown in Fig. α (a), within the established framework of ictogenesis which delineates interictal, ictal, and postictal phases the preictal interval offers a crucial target for clinical interventions ranging from simple alerts aimed at mitigating injury risk to sophisticated closed-loop neuromodulation devices. To formalize practical deployment, seizure prediction systems are typically evaluated with respect to two time parameters: the Seizure Prediction Horizon (SPH), which defines the minimum interval between raised alarm and seizure onset to allow meaningful intervention, and the Seizure Occurrence Period (SOP), a predefined window during which a seizure is expected following an alarm.
Why subject-agnostic seizure prediction (SASP)? Despite remarkable advances in seizure predic- tion achieved by pioneering studies [6] 39 73 15] 74 49), the field remains constrained by two fundamental limitations: the reliance on subject-specific modeling paradigms and limited scalability. Sebject--pecific approaches, while often achieving impressive performance on individual patients, require extensive labeled data collection for each new patient and cannot leverage knowledge across diverse patient populations. This impedes large-scale clinical adoption and negates the potential advantages of aggregating data to identify generalizable seizure biomarkers.

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Beyond subject specificity, additional obstacles include narrow EEG modality ranges [69 39 72].
inconsistent preprocessing pipelines 8 23], and dependence on rigid electrode configurations. Together, these factors highlight the urgent need for truly subject-agnostic predictive algorithms capable of operating robustly across various patient and recording configurations. Specific challenges include:
(1) Capturing refined high- and low-frequency biomarkers. Clinical evidence 46
27 50
shows pathological high-frequency oscillations and low-frequency fluctuations serve as crucial epileptogenesis biomarkers. These subtle, non-stationary features are easily obscured by artifacts. Conventional CNNs 4 and Transformers [36] [3] exhibit spectral biases toward low frequencies, struggling to preserve transient HFO signatures [63 40
(2) Modeling phase-amplitude interactions. Epilepsy exhibits abnormal phase-amplitude coupling 2
76, [4] during seizure initiation and propagation across frequency bands. These interactions provide critical clues for distinguishing ictal from interictal states. Current clinical models typically utilize amplitude information in time or frequency domains separately, rarely integrating both. Our architecture captures these fundamental aspects of neural oscillations, leveraging their complementary insights into seizure evolution.
and (de)synchronizztion [ 35 26
(3) Handling heteroge- neous channel layouts. Seizure onset zones and preictal activity distribution vary significantly across individuals, with predic- tive features appearing on different electrodes from patient patient. Implantation strategies, montage configurations, and regional coverage introduce further variability in channel characteristics. Naively pooling signals across channels obscures patient-specific biomarkers and amplifies noise, com- promising generalization in subject-agnostic contexts.
(a)
(b)
0.1
7_80
Fractional
Non fronfirctioonal
0.0
Layer
APSD (dB)
20
Prob
10
Layer
-160
60
2
3
5
6
9 Layer
10
PSD (dB)
Figure 2: Interpretability of FAPEX. (a) Kernel density estimates of power spectral density (PSD) responses for FrNFO filters across layers and brain frequency subhands. As depth increases. the operator progressively refines its discrimination among subbands, maintaining the natural low- wwwfrreuency, high- energy and high- geghffrequency. low-energy distribution, with energy gradually stabilizing after intermediate layers. (b) Layer-wise frequency-speciffe gain relative to the initial layer. Unlike non-fractional operators, FrNFO consistently amplifies both low- and high-freque figh-freyuency components, achieving balanced cross- frequeney representations, indicating ability to capture both fast and slow neural dynamics essential for scizure prediction.
Present work. To over- come these challenges, we propose FAPEX, a unified model for effective generalization across heterogeneous EEG settings, electrode configurations, and clinical subtypes. Our approach integrates three key innovations: (1) fractionn neural frame operator (FrNFO): learnable bank of Weyl-Heiiennbrgg filters for adaptive frequery decomposition. FrNFO extracts high-fidelity features through fractional-order convolutions with minimal spectral leakage, capturing both high and low-frequency components of epileptic signals. (2) amplitude phplii cross-encoding (APCE): A bidirectional state-space architecture processing phase and amplitude representations, learning time-varying relationships extract seizure evolution patterns. (3) Spatial correlation aggregation (SCA): Channel-wise attention mechanisms modeling inter-clectrode depen- dencies identify predictive spatial patterns. Together, these components enable FAPEX learn multi-scale representations that capture chase-amplitude coupling while handling non-stationarity and channel heterogeneity. Together, these components enable FAPEX learn rich, multi-scale representations that capture subtle changes in phase-amplitude coupling across frequencies while adaptively handling non-stationarity and channel heterogeneity. As illustrated in Fig. 2, FrNFO serves as the foundational component, addressing low-frequency bias by preserving fragile yet critical high-fres figh-frreuency oscillations while providing fine-grained decomposition of amplitude and phase features for more comprehensive picture of neural activity in seizure prediction.

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a)
Datasets
b) Architecture and Training
Projection Head
LFP
Imput
Backbone Encoder
Mouse
(1) Supervised-Leamig
W
Phase
or
FrNFD:
Amplitude
Dog
ECoG
Fractional
Neural
Phase
gX
Contrasiive Learning
(2) Sell-supervised
Information
Frame Operator
Mixing
Sample-Level
Macaque
Amplltude
Subject-Lavel
SEEG
Ampitudee Phase Cross Encoding
Spatial Correlation Aggregation
Human
War
Norm
Norm
Scalp EEG
Bidrectional
Oidrrctioonll Cross-BBM
Linear Attention
Amplitdde
Cross-S3 SSM
Nor
Nort
Figure 3: Datasets and network architecture summarization. (a) We used LFP, ECoG, SEEG and Scalp EEG data across species (humans, dogs, rats, and macaques), to validate our model. (b) The network structure and training pipeline of our FAPEX framework. The input signals will be encoded by the backbone encoder that is consisted of our FrNFO, naturally separated into phase and amplitude sections, then go through Amplitude Hhplitude-Phase information mixing procedure which deals with the sections interactively using 2 biderectional Cross-SSC -SSM modules, and linear attention module for spatial correlation aggregation.
Our main innovations are: (1) FAPEX, subject-agnostic framework integrating our novel Fractional Neural Frame Operator (FrNFO), amplitude implitude-phase cross-encoding, and spatial correlation aggregation to anticipate seizures across diverse modalities. (2) FrNFO, a learnable bank of Weyl-Heisenber filters that performs fractional-order fime-frequency decomposition, mitigates low-frequency bias and preserves high-frequency oscillations with provable robustness. (3) Extensive validation on 12 benchmarks across species and recording modalities shows FAPEX consistently outperforms 32 baselines, establishing new standard for seizure prediction and revealing meaningful preictal biomarkers.
Method
Problem formulation. Epileptologists classify seizure dynamics into three phases: interictal, preictal, and ictal. Interictal Phase: Periods between seizures (typically > 30 minutes) with generally normal brain activity, though occasional interictal epileptiform discharges may occur. Preictal Phase: The period preceding a seizure, marked by subtle brain activity changes that may predict an impending seizure. Ictal Phase: The seizure event itself, characterized by ictal epileptiform discharges. Formally, neuroelectrical segment
of time series (2x(0) J==1 where C is the number of channels, and each (*) Rd represents channel with T timestamps. A seizure predictor constructs function Je to binary label ú. distinguishing interictal from preictal states. The model is trained to align predictions with clinical annotations yr. enabling prediction in unseen
fmodel that maps (
subjects.
Input patchifying. Given multichannel neural signal segment X E RCT,, where C' represents the number of electrode channels and T is the total number time samples, we aim to establish preprocessing pipeline that is robust to variations in electrode count and placement. To this end, the continuous data is first partitioned into fixed-duration, non-overlapping patches. Specifically, each channel signal x. IR' is segmented using window of length 7, resulting in N patches per channel. Each patch then projected into a common feature space using a channel-shared linear embedding W E X and bias vector b E Ruuue resulting in the embedded tensor X CCx N danke (dmodtel is dimension of the model). This process ensures that the subsequent layers can operate independently of electrode count and spatial arrangement.
2.1 Fractional neural frame operator (FrNFO)
Motivation. Nonstationary signals, such as those encountered in neuroelectrical recordings in epilepsy patients, present significant challenges due to their highly variable time- timeffreueeccy content

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and variability in both amplitude and phase. The Fractional Fourier Transform (FrFT) has emerged
as powerful tool for analyzing such signals, providing a flexible, continuous interpolation between the time domain (0 0) and the frequency domain (0 = 37) via a fractional order parameter O. Formally, FrFT generalizes the Fourier transform with a fractional order (0, T), defined for signal f E (R) as:
Fo()(z)= = M[sin J ((1) exp [Tri ((1² + =0)co000
cot - 2xl ese 0)] dt.
This transform supports operators like 0-shift, T f(t) = exp (2mis(t - 3) cot 0) f(t - s), and modulation, [() = exp (Ti (5² cot + 2st esc 0)) f(t), enabling o-fractional convolution [3]
71:
/ (ss)(T)))))
(J * (2)
sin 01
which offers an alternative to traditional Fourier transform-based convolutions. While the fractional Fourier transform (FrFT) provides flexible framework for interpolating between time and frequency domains, its practical implementations face two critical challenges that limit their effectiveness for neuroelectrical signals: (1) Chirp response constraint: traditional FrFT relies
fixed
chirp function, imposing a globally isotropic structure that poorly adapts to the diverse, localized frequency characteristics of real-world data [22]. This restricts FrFT's expressiveness essential for nuanced phase-amplitude representation. While recent methods have introduced trainable fractional orders [68] 25], they inherit this fundamental limitation, lacking the flexibility to accommodate rapid spectral transitions and localized nonstationarities (2) Deformation Sensitivity: Despite its adaptability in fractional order, FrFT remains sensitive to small deformations, including time shifts, scaling variations, and localized perturbations, which are especially prevalent in neural signals [42 29]. These limitations underscore the need for more expressive, adaptive frameworks that can capture the intricate amplitude-phant representation.
A neural approach for fine-grained amplitude-phas representation. To overcome these lim- itations, we propose the fractional neural frame operator, which integrates neural implicit repre- sentations to learn parameterization of f-fractional version of nonstationary Weyl-Heisenberg
frame 20 45 18]. defined as:
Vo
M T 1p
an 10; :s S R.R.IIZZ,e e [1).
(3)
where po- d are positive constants adjusting the scale. involves 0-modulation A (t)
1p
( cot (f tccc)) and s-shift T o4 (t) = 2risg ( (t sa ) cot 0 Dt 100--sg)))) ()) Ve presents
a redundant set of basis functions that can be used to represent or analyze a signal on the fractional domain. Unlike FrFT, it is equipped with adaptive windows V over each scale to capture wide range of signal behaviors. Building upon this, we propose fractional neural frame operator.
The core of the FrNFO is an implicit multilayer perceptron (MLP) 334 62 designed to generate adaptive window function for the frame filters. Given temporal samples N and feature channels dauodel.
the implicit MLP defines the window kernel $ C Xddual for = 1,..., N, k 1.... dmodel as
)
K Σ
Σ wii exp(-i(bu,tt + +cw)))
ann
(4)
where wi,k, bi,k. Ci,k: On,k are trainable parameters optimized through gradient descent. The basis functions (t) (-1)"e²² dt e+² are Hermite polynomials, embedding prior knowledge of de localized oscillatory behavior, while the sine activation functions promote smooth and periodic kernel characteristics essential for identifying quasiperiodic activities in brain.
FINFO further introduces a learnable fractional order = [01...., Odwmal E (0, Amse,, which governs the time-frequennc representation for each feature channel independently. Given an input
neural embedding X E C xdasei employing the fractional convolution theorem 3 71. the output feature for channel is defined as:
X exp( exp(-riw" wis? cot 0x) 3 Foz (X.,)) For(W (...))) k= 1,
d dmodel
(5)
5

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where i. is the frame filter kernel equipped with learnable window kernel, @ denotes the Hadamard product, and w represents the frequency grid. The phase adjustment factor exp(riw> cot 0z) ensures proper alignment and interpretation of fractional frequency components. This adaptive formulation allows FrNFO to dynamically adjust frequency resolution.
FrNFO is provably robust amplitude representator. As previously formulated, neural fractional-order filterbank, FrNFO naturally yields complex-value signal representation that can be easily formulated into phases and amplitudes across different scales and fractional orders. We further highlight that it also provides a provably robust amplitude representation, which is the main information source in many applications, from the perspective of scattering transform. Refer to further discussion and proof in App. A.
2.2 Amplitude-phase encoding
Amplitude-phase cross encoding (APCE). We introduce APCE to capture heterogeneous, cross- frequency dependencies between amplitude and phase embeddings produced by FrNFO. Inspired by recent advances in selective state space model, proposed first in Mamba [? ? ? ?
a bidirectional state-space mechanism building on Mamba blocks with cross-attention- we adopt mecha-
nism [59], as shown in Fig. 3 Formally, given amplitude embeddings Amp and phase embeddings Pha = RMSNNrmm (Pha). These then processed by the dual cross- Maos-Maaba module, which operates in
Pha, we normalize them as: Amp = R.MSNorm(Ann normalized embeddings channel-indepp cineeee-ideeenndent manner to capture amplitude- phase interactions using a bidirectional state-space model (BSSM), comprising two sequential blocks: phase BSSM and amplitude BSSM. In the phase BSSM block, the normalized phase embeddings Pha E x2xxxDD x are projected into a latent space via two shared linear mappings:
X W'Pha, =P=
where W W SSM states. The projected embeddings undergo causal and anti-causal convolutions followed by SiLU activation:
RDXE are learnable projection matrices, and E denotes the number of latent
X (iUU((onll, )),
{forward, backward].
(7)
Using the normalized amplitude embeddings Amp, we compute state-space parameters:
B. = W Amp, C. = W Amp, A = Softplus W X. + b²),
(8)
where WB WC E DxN are shared across directions, and WA EXE b E R are shared scaling parameters. The varying transition parameters are then defined as:
A, A. @ A, B. = A. & B
(9)
where A EXN a shared, direction direction-agnostic transition matrix, and @ denotes clement-wise multiplication. The output sequence is computed using the SSM kernel:
Y. SSM( (A,, B., (X.)
(10)
The final phase-to-amplitud representation, which captures phase-informative patterns, is gated as:
yF (Y forward Y backward) SiLU(Z").
(11)
In the amplitude BSSM, the roles are swapped: the phase-informative Y provides the context, and the amplitude Amp serves queries. A residual connection combines the block output Y with the original amplitude embeddings Amp to produce the final APCE encoding:
X Y + Amp, X RERRxMXD,
(12)
Spatial correlation aggregation (SCA), During the preictal interval, epilepsy is marked by dynamic shifts inter-electrode interdependencies that reflect the spread of pathological activity across brain regions. Accurate seizure forecasting from multichannel recordings therefore hinges these spatial dependencies. To this end, given neuroelectrical embeddings X e RCxNx xxd SCA models global cross-spatial dependencies of different electrodes while integrating local spatiotemporal
modeling

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patterns. Formally, linear attention aims to use o Φ (kj) to approximate softmax attention kernel at linear complexity, where the feature map o(-) R + R is applied row-wise to the query and key matrices. As a result, the e-th row of attention output a, E IR" can be rewritten as
0. a. O (igmoid(go), a i= (1.)) v.
Φ (g.) Di=! Φ (k,) $ (q:)
(13)
دj=1 Φ (ky)
where ge is the e-th row of G = DMMSNorm(Depthwiseee depthwise convolutional kernel to aggregate neighborhood spatiotemporal information with RM- SNorm improve stability. The feature map & is made as one-layer MLP as @MLP(x) exp(W [ æ), where the matrix W1. 1. W2 E Rdxd
(X) implemented with 3 x
3 Experiments
We conducted empirical investigations to address the following Research Questions: RQ1: How does FAPEX perform in SASP relative to supervised baselines? RQ2: Does self-supervised pretraining improve performance of FAPEX in SASP relative self-supervised baselines? RQ3: How well does FAPEX generalize to different cohorts (e.g., species, institution)? RQ4: What is the contribution of each design choice within FAPEX?
3.1 Experimental settings
We evaluate FAPEX across diverse settings spanning supervised learning (RQ1), self-supervised pretraining-finetuiinn (RQ2), and cross-cohort transfer (RQ3). This section outlines the baseline, evaluation protocols, and other basic implementation setups common to all experiments. See details of training protocols in App. G. Full implementation details are provided App. H.
Datasets. We compile 12 benchmarking datasets spanning four species (human, rat, dog. macaque) and multiple acquisition modalities (Scalp-EEG, ECoG, SEEG, LFP) for evaluation, summarized in Tab. T All recordings are resampled and segmented to standardized lengths, then harmonized to 64 effective channels via channel rejection and duplication, enabling consistent input formatting across all models. See detailed descriptions and preprocessing procedures in App. F. Note that we apply channel aligmment during preprocessing to facilitate consistent training across diverse datasets for both our model and broad range of baselines. In short, FAPEX itself is inherently agnostic to the number and configuration of input channels.
Table 1: Summary of datasets. The datasets span several species (human, rat, dog, macaque) and acquisition modalities EEG, ECoG, SEEG, LFP).
Datasel
Conlidentiality
Species
Subjj.
Modality ECOGISEEG'
# Ch.
# Samples
Duration
SOP
SPH
ID/I
OODVE
FMCE
Public
Human
65
32,323
4s
30
min
HUP
Human
73
53,323
RESPECT
Public
Human
ECoG
17,214
45
30s
5
BIIRUT
Public
Humon
6
Scalp-EBG
64
35,941
4s
1 min
m0mi
/
CTLE-RATLFF
Public
Rat
7
1.FP
64
11,732
2.
30
5min
LPIRE
Public
Rai
15
LFP
1,5.7 715
2
5
CANINE
Public
Dog
BCoG
382,278
4.
5min
4hr
ATLE
Private
Human
Scalp-EBG
11,536
4%
5min
30
AGS
Private
Hummn
5
Scalp-EEG
64
32,323
4s
5min
30 min
JESS
Private
Human
17
Scalp-EEG
48,986
4s
5min
30 min
Macaque
Scalp SEBG
36,092
min
PCS
Privase
Human
Scalp-EBG
29,679
4s
5 5
miin
TUEG
Public
Human
14,987
Scalp EEG
64
1,030,090
32s
Used for Pretrouning Only
Human
52,337
32s
Used Presratning Only
PPE
Public
Human
30
Scalp-EBG
64
13,434
32x
Used for Prenzining Only
For "BCoGISEEG" datascts each subject has eitker sub-dural BCoG grids/strips or SEBG depth electrodes, never both.
KAIME comprises simultaneous scalp-EEGG and SEEG depth recordings from three adult thesus macaques (Macara mulatta).
Baselines. We compare our method against the following baselines, including 22 supervised base- lines for RQ1 and 10 self-supervised ones for RQ2. The supervised baselines include (1) Convo-
lutional models baselines): ModernTCN [10], MRConv [7]. MultiresNet [43), Omni-Scall
48
and SPaRCNet 21 (2) Token mixers (6 baselines): EEGConf fomer 44), i iTransf ormer
32
Nonformer 31, PatchTST [37] Pathformer (6], and SeizureForme
[3]: (3) Time-frequency
mixery (4 baselines): ATFNet 666] FreTS 67], NFM (24], and TSLANet 12: (4) Multiscale loken mix-
ers (7 baselines): AdaWaveNet [? J, Medformer (55), MTST (75), Pyraformer (30], SimpleTY (5).
Timesliet [60], and TimeMixer [54]. Self-supervised baselines include 6 non-contrastive models:
7

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Brant (72). CBraMod 12
EEGPT ST LaBraM 19 Neuro- BERT 588 VQ_MTM [6] 4 contrastive models: BIOT 65 COMETS [6 MF CLR and TS2Vec [70]. See details in App. E.
Evaluation protocols. All experiments follow a consistent subject-agnostic nested cross-validation (SANCV) scheme. For each dataset, subjects are split into non-overlapping train, validation, and test folds. These folds are randomly permuted to yield multiple experimental runs for RQ1-3. For RQ1. we evaluate in-domain performance with full supervision. For RQ2, we evaluate in-domain performance by supervised finetuning. for RQ3, we evaluate out-of-domain performance on several regimes for our approach and two best-performing self-supervised baselines. We report median and interquartile range (IQR) across runs for: Balanced Accuracy (BA), Sensitivity (SEN), F1, AUROC, AUPRC. We also report Stratified Brier Score to indicate both discriminative and calibration quality. We calculate Fl as the monitoring score as it captures the trade-off between reducing false alarms and maintaining high sensitivity. We adopt the Friedman test as nonparametric omnibus for statistical significance with Bayesian post hoc comparison. Refer to App. H for details.
Table 2: Median performance across publicly available datasets. Top- Top-2, and Top-3 results are highlighted in red, blue, and green, respectively, within both supervised (SL) and self-supervised (SSL) groups. FAPEX demonstrates consistently strong performance, achieving top-1 TO 3 rankings on the majority of datasets and metrics, reflecting its generalization and adaptability. For detailed results and statistical analysis, refer to App. C.
Madel
Besetrs
SEN
CANIN
FT
FMEE
F1
SEN
LPIRE
HLF
ROL
RESPECT
RDX
MRCHen
76.8
18.2
33.7
83.8
75.8
1963
65.2
73.3
66.1
57.6
06.1
12.3
13.3:
Masavahia
73.3
12.8
34.1
04.8
12.0
25.5
10.5
1333
63.18
63.3
67.1
07.1
71.7
83.1
66.3
533
65.5
02.4
75.3
60.7
SPaBCN44
71.
71.
$5.0
$4.7
02.4
67.7
55.
12.2
15.3
07.5
92.
02.3
81.3
53.0
684
66.5
82.5
163
$1.4
$3.9
73.
1001
11.4
13.5
73.8
12.3
56.
60.8
72.
66.
53.3
665
$2.5
56.8
15.5
691
64.2
75.4
08.4
1801
15.3
75.0
45.4
57.7
57.
56.7
$5.0
Nasternar
68.6
60.4
15.2
60.7
64.9
10.3
765
82.
955
12.6
15.3
5015
66.2
76.4
75.1
62.1
51.0
62.4
74.1
760
816
07.
64.1
65.9
12.3
52.5
91.3
12.4
08.
823
66.3
355
765
12.7
075
68.2
79.
19.8
11.
55.5
735
75.5
186
130
86.5
656
75.2
68.
56/7
594
01.
53.1
850
14.
647
16.6
46.8
543
62.
49.2
06.5
34.9
46.4
572
18.4
NPM
723
75.7
79.1
115
36.9
120
764
91.
56
46.5
53.5
7600
3233
43.0
455
62.7
53
66.
750
77.
AddWoreNat
660
66.1
75.
113
56.
10.0
575
15.2
13.0
56.1
56.1
664
33.1
03.1
31.4
$5.9
145
274
856
556
100
14.
86.
661
72.3
835
66.3
56.5
650
913
660
155
12.8
11.2
123
67.
16.5
56.2
182
563
13.4
SerpleTM
92.6
633
314
938
13.
744
21.5
616
11.5
15.0
200
47.
5300
5-1
67.
552
08.5
745
72.0
150
71.8
72.3
756
92.0
76.
10.9
675
92.6
67.3
76.5
11.
PAPRO--mmal (SL)
53.8
33.4
15.3
13.3
54.7
15.2
874
MAA
27.0
T53
53.2
1933
983
73.4
11.3
13.0
130
76.3
50.3
87.1
193
94.3
$6.0
113
91.3
1.5
79.3
516
CiraMeed
53.8
$3.5
508
92.6
29.
$3.5
12.4
99.3
65.4
54.
766
06.5
57.6
RESPT
01.
71.3
11.6
99.
43.9
661
68.9
167
16.7
61.6
56.2
65.1
71.
005
61.
11.
96.1
361
00.3
604
VO NTM
26.5
75.0
83.
$5.9
855
94.5
133
74.3
123
13.6
15.5
660
96.
35.5
63.
62.1
13.
66.9
66.
07.3
817
COMITS
962
560
93.9
43.4
08.2
761
26.3
87
14.3
K5.7
53.
01.6
68.6
66.2
06.1
361
51.
15.
57.1
67.
58.
64.7
94.
05.5
15.5
74.5
87.
13.0
15.3
77.8
99.1
66.1
5.6
58.9
51.6
56.7
79.
62.6
18.5
Sowil
214
11.
111
117
18.0
21.
2014
$3.5
11.5
$5.1
1811
31.
25.1
11.
70.1
11.
313
99.2
94.9
31.
350
352
11.1
94.8
3.2 Main results
Performance co1 and RQ2). Tab. 2 and present the results for supervised and self- supervised pretraining regimes. Across 12 datasets, our approach achieves top-1 Sensitivity (SEN) and Fl scores on all 12 datasets and top-1 ROC on 10 out of 12 datasets under the depeeentdependent setup. These results demonstrate its robust capability in predicting seizure events across diverse scenarios, encompassing variations in electrophysiological recording techniques, seizure cohort etiologies, and even species. Notably, FAPEX benefits significantly from pretraining on large-scale unannotated data. It surpasses state-of-the-art foundation models, including CBraMod, VQ_MTM, and -BRT, when pretrained on the same data corpus, indicating that its performance gains stem from the model architecture rather than solely from unsupervised pretraining.
Transferability and generalization Analysis (RQ3). Out-of-domain validation is critical for reliable seizure prediction. requiring models to generalize across species, recording conditions, and acquisition protocols. Despite the advantages of self-supervised pretraining, generalizing to unseen domains for seizure prediction remains underexplored. We assess model transferability across diverse source souree-target dataset pairs to capture realistic inter-domain variability with progressively stronger supervision and adaptation: (1) Source-only transfer (SOT); (2) DIVERSIFY [33], an unsupervised domain generalization method specifically tailored for time series data, including physiological signals; (3) Semi-supervised finetuning (SSFT): 1% labels of the training split of target domain data available; (4) MME [41] and CDAC 28), two domain adaptation methods. Similar to (3), only 1 1% target domain labels are utilized. Fig. shows the relative improvement in relative gains (A%) %)
8

---

Table 3: Median Performance Across In-House Datasets. Top-1, Top-2, and Top-3 results highlighted
red, blue, and green, respectively, within both supervised (SL) and self-supervised (SSL) groups. FAPEX demonstrates consistently strong performance, achieving top-1 TO 3 rankings on the majority of datasets and metrics, reflecting its generalization and adaptability, For detailed results and statistical analysis, refer to App. C.
Model
AGS
ATLE
IESS
KAIME
SEN
FT
ROC
SEN
FT
ROC
SEN
FT
ROC
SEN
FT
ROC
SEN
FT
ROC
NodernICM
87.0
85.0
93.2
91.7
90.2
100.0
73.4
73.4
53.4
73.2
87.3
85.4
86.3
XRCony
91.3
90.3
95.2
86.6
96.1
100.0
68.8
68.7
66.9
81.1
68.5
85.0
83.0
84.1
83.7
MultiresMlet
90.1
88.8
96.1
85,4
84.3
100.0
72.1
70.4
68.7
80.4
63.7
82.5
69.2
64.4
83.9
Onni Saale
91.7
90.9
95.2
87.8
98.6
99.9
67.9
68.7
67.2
81.0
68.8
83.0
80.0
79.6
80.9
3PaRCNet
89.1
87.5
93.4
84.0
81.7
99.8
60.7
64.9
61.4
82.0
77.1
86.5
85.5
84.4
91.0
EEGConformer
88.5
94.4
88.5
91.2
100.0
66.1
67.9
81.4
87.1
78.8
84.3
EEGNambe
93.8
93.5
96.8
88.2
85.0
100.0
69.6
70.0
68.8
80.4
69
83.4
70.8
73.3
85.6
sTrannformer
89.5
87.8
95.3
54,9
2.9
99.8
53.4
54.5
66.4
81.3
63.4
87.1
74.3
73.0
83.4
Xonformer
93.2
92.7
96.7
84.7
97.5
99.8
69.7
74.7
68.9
79.5
90.3
81.6
68.8
63.7
84,1
PatchTST
90.5
89.3
95.5
86.6
93.0
100.0
61.6
63.8
67.5
83.0
73.8
88.5
71.9
71.2
73,8
Pathformer
91.8
96.7
88.7
100.0
71.3
72.1
67.4
80,9
83.7
Beizur=Former
92.1
91.3
95.4
86.3
97.9
99.9
69.7
69.9
66.7
71.3
53.4
85.9
58.6
62.4
59.7
ATP
85.2
84.1
90.8
83,1
97.0
99.8
59.7
56.2
68.2
65.0
45.7
71.9
74.7
73.5
84.6
FreT8
88.7
87.0
93.0
70.2
70.8
77.8
42.7
32.8
67.0
54.3
56.4
73.8
20.5
72.7
77.8
XFM
88.7
87.0
93.0
71.3
71.8
81.7
52.4
56.2
61.2
76.8
64..4
80.4
73.6
76.9
83.0
TSLAMet
94.2
97.3
91.4
100.0
73.8
72.9
82.4
84.0
84.9
AdazavaKet
89.0
87.6
95,1
82.8
96.6
99.8
70.0
70.77
66.3
70.5
77.7
84.8
72.4
74.2
81.3
Madforner
88.7
88.0
96.1
88.2
98.9
99.9
73.7
73.1
66.9
73.2
45.2
72.3
77.9
77.1
96.3
X7ST
91.6
90.7
98.0
84.1
97.2
99.8
60.3
56.4
70.1
59.0
60.2
74.2
72.8
70.3
74,1
Pyrafornar
92.0
91.3
96.5
85,1
97.7
99.8
71.4
70.2
66.9
83.2
56.6
86.4
76.8
79.9
82.3
SimpleTM
85.1
83.5
83.2
90.8
99.9
66.7
68.8
64.4
80.0
84.6
75.0
84.5
TimesMet
89.7
88.3
94.3
82.1
96.3
99.8
59.9
63.6
66.1
80.0
81.1
84.6
77.7
81.0
84.6
TimeHiizer
92.3
91.6
96.6
87.9
95.3
100.0
71.7
71.0
68.6
82.1
90.0
85.2
83.5
85,4
FAPEX-Small (SL)
94.1
93.7
98.4
87.2
9%.4
99.9
70.8
70.4
71.7
86.9
92.11
89.3
81.0
81.2
144.1
FAPEX- Bose (SL)
94.9
94.6
99.5
88.0
98.8
99.9
72.3
72.4
71.4
87.0
95.6
90.1
91.5
91.5
96.3
Brant
93.2
92.7
96.6
87.9
83.0
99.9
68.0
67.7
69.5
74.5
74.8
74.4
M3.1
82.3
95.8
CBraMod
90.8
9016
98.7
87.9
62.8
99.9
79.6
80.77
76.2
81.0
79.8
83.7
81.1
83.5
85.4
EEGPT
93.4
92.9
98.5
88.2
83.2
100.0
74.2
73.9
71.4
78.4
77.3
78.6
85..5
84.4
91.0
NEUTO-BERT
93.7
93.2
96.8
83.3
90.8
100.0
75.3
75.0
71.5
81.7
80.7
83.6
80.8
81.9
96.8
VT_
85.5
94.6
81.7
79.5
99.9
72.8
72.9-
81.2
94.1
COMETS
93.9
93.4
98.2
87.7
83.2
99.8
67.6
68.2
79.3
80.6
80.1
84.0
80.8
81.9
96.8
XF-CLR
91.2
90.0
97.0
84.4
62.8
100.0
79.7
80.8
75.6
80.9
79.8
86.3
79.2
77.4
97.2
TS2Vec
94.7
94.5
97.5
62.7
76.1
73.6
72.4
73.6
72.9
76.1
76.2
76.7
69.0
65.9
96.4
FAPEX-Small (SSL)
94.1
93.7
98.4
54.00
92.8
T00L0
8LA
83.7
X1.4
K7.1
89..
91.0
96.7
TAPEX-Base (SSL)
95.2
94.9
99.7
94.8
98.0
100.0
83.7
84.9
85.9
88.7
88.4
91.4
95.0
95.0
97.5
of FAPEX--Baaa over Neuro-BERT and CBraMod in median F1. FAPEX- -Base consistently achieves positive A% in Fl across diverse cases. It excels in the SOT setup, with A% often exceeding 30%, highlighting its strong generalization without target supervision relative to other models. In more informative setups like CDAC and MME, where SOTA models improve with target data, FAPEX-Bass still outperforms or matches them most cases, despite the narrowing gap and occasional dataset- specific underperformance. This resilience underscores its robust architecture and clinical potential in label-scarce settings and adaptivity to different finetuning techniques. See App. C for full results.
SOT
SSFT
DIVERSIFY
MME
CDAC
Performance Gain (%)
50
40
-B EXPES/uuum BERT Naatscicbuaaae
Relative
30
20
-10
A
8
C
A B C C D A B C D F Dataset (Source Target)
Figure 4: Relative improvement in Fi-score medians (A %) of FAPEX- Base over Neuro-BEi and CBraMod across five distinct transfer learning setupsfor six source-target dataset pairs. FAPEX- Base demonstrates consistent performance gains for most cases, under both weak (SOT) and stronger supervision regimes (CDAC). A: KAIME- AGS, B: AGS BEIRUT, C: IESS BEIRUT, D: LPIRE AGS, E:LPIRE IESS, F: LPIRE + KAIME). FAPEX-Baan Base consistently achieves superior performance.
Ablation study and further analysis (RQ4). To evaluate the contributions of each component within FAPEX, we conduct comprehensive ablation experiments. These studies isolate the effects of core modules FFNNO, APCE, and SCA-on seizure prediction performance, providing insights into their individual and collective impacts (see App. D). We further explored the representational
9

---

characteristics and interpretability of FAPEX (see App. B). These analyses offer deeper insights into the model's decision- decision-making processes and its alignment with known neural patterns.
4 Conclusion
We presennt FAPEX, compact yet powerful neural architecture that integrates fractional frame theory directly into its core operators. Unlike the trend toward ever-larger models, FAPEX strategically leverages fractional neural frame operators to jointly encode amplitude and phase, achieving provable robustness against deformation and superior preservation of high-frequency biomarkers essential for precise seizure prediction. Extensive evaluations across fully supervised, self-supervised, and multi-cohort, multi-species out-of-domain settings consistently demonstrate that FAPEX surpasses specialized baselines and even large foundation models under comparable data regimes. These results establish FAPEX as a significant step forward in AI for healthcare with strong potential for improving clinical epilepsy management. Future work will aim to expand clinical datasets through collaboration with medical centers, incorporate complementary neuroimaging modalities, and explore deployment on wearable devices and closed-loop neurostimulation systems. Additionally, further theoretical analysis of thase-amplitude disentanglement and interpretability will be prioritized to enhance clinical trust and impact.
5
Acknowledgments
This work supported by the Science and Technology Innovation 2030 Brain Science and Brain-Inspired Intelligence Project (Grant No. 2021ZDD0001011 the National Key Research and Development Program of China under Contract (Grant No. 2024YFA161099 the National Natural Science Foundation of China (Grant Nos. 9257020, U20A 12147101), and the Shanghai Municipal Science and Technology Committee of Shanghai Outstanding Academic Leaders Plan (Grant No. 21XD1400400), We thank the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)
for financial support (Grant No. LIMIS-ID-022-NNC) The computations were performed on the CFFF platform of Fudan University.
Reference
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Reviews:
[{"review_id": "6mzcTE9Li1", "reviewer": "Reviewer_8XFQ", "summary": "This paper introduces FAPEX, a novel deep learning architecture for subject-agnostic seizure prediction (SASP). The core contribution is a Fractional Neural Frame Operator (FrNFO), a learnable filterbank based on fractional-order convolutions, designed to adaptively capture both high and low-frequency biomarkers while mitigating spectral bias. The architecture further incorporates an Amplitude-Phase Cross-Encoding (APCE) module using bidirectional State-Space Models (SSMs) to model interactions between signal amplitude and phase, and a Spatial Correlation Aggregation (SCA) module using linear attention to handle heterogeneous electrode configurations. The authors present an extensive evaluation across 12 diverse benchmarks (spanning multiple species and modalities), demonstrating that FAPEX consistently and significantly outperforms a large suite of 33 state-of-the-art supervised and self-supervised baselines.", "questions": "1.\tHow can you validate that the interactions learned by the APCE module represent physiologically meaningful PAC, rather than spurious correlations? A comparison with established PAC metrics (e.g., MVL-MI, KL-MI, etc.) on a subset of data, would be necessary to substantiate your claims.\n2.\tCan you provide visualizations of the attention maps learned by the SCA module for some preictal samples? This is crucial to demonstrate that the model is learning meaningful inter-electrode dependencies (e.g., focusing on the seizure onset zone or known functional networks) and not just arbitrary patterns.\n3.\tTo support the claim of being \"compact\" and suitable for \"clinical translation,\" please provide a detailed computational analysis. This should include a comparison of key performance indicators, such as parameter counts and inference latency, between FAPEX and key baselines.\n4.\tPlease confirm that you will conduct a thorough proofread of the manuscript to fix all formatting issues, including increasing the font size in Figure 1 for readability, correcting spelling errors (e.g., \"presennt\"), and fixing all broken cross-references and citations (e.g., \"Table ??\", \"[??]\") in the appendix.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.\tThe core idea of the Fractional Neural Frame Operator (FrNFO) is original and theoretically grounded. By integrating fractional frame theory into a learnable operator, the authors propose a novel signal processing front-end tailored for non-stationary neurophysiological signals.\n2.\tThe evaluation across 12 datasets, 4 species, and 4 modalities, against 33 relevant baselines, is exceptionally comprehensive. The rigorous protocol (nested cross-validation, multiple evaluation regimes) provides evidence for the model's superior performance and generalization capabilities.\n\nWeaknesses:\n\n1.\tLimited Novelty and Scientific Rigor in APCE and SCA Modules:\n(1)\tAPCE (Amplitude-Phase Encoding): While using SSMs is a modern approach, the APCE module lacks a deep connection to established neuroscience principles for phase-amplitude coupling (PAC). The paper fails to compare its \"learned\" coupling with standard, well-validated PAC algorithms (e.g., MVL-MI, KL-MI) or address the critical issue of spurious coupling, which significantly weakens the scientific claims about its reliability and interpretability.\n(2)\tSCA (Spatial Aggregation): The use of linear attention ignores the crucial spatial topology of EEG electrodes. This is a suboptimal design choice compared to methods that can explicitly model spatial relationships.\n2.\tThe paper makes strong claims about modeling inter-electrode dependencies and phase-amplitude interactions but provides almost no supporting evidence. There are no visualizations of the SCA's attention maps to show what spatial patterns are learned, nor any analysis to validate that the APCE module is capturing physiologically meaningful coupling. This lack of analysis leaves the reasons for the model's success opaque.\n3.\tThe paper claims FAPEX is a \"compact and powerful\" architecture suitable for clinical translation but provides no quantitative data (parameter count, inference latency) to support this. Without a direct comparison to baselines, its feasibility for real-world, resource-constrained applications (like wearable devices) remains unverified.\n4.\tThe manuscript suffers from several formatting issues that detract from its professionalism. Text in key figures, notably Figure 1, is too small to be easily legible. There are spelling errors (e.g., \"presennt\" in the Conclusion) and broken cross-references in the appendix (e.g., \"Table ??\" and \"[??]\"), which hinder readability and the verification of claims.", "was_revised": true, "final_justification": "The responses have successfully addressed the questions and concerns I raised in my initial review. The additional clarifications and results have strengthened the paper and resolved my previous reservations.\n\nGiven the effective rebuttal, I have raised my score to **5: Accept**.", "rebuttal": "We sincerely thank the reviewer for their careful reading and constructive feedback.\n## *Response to Weaknesses and Questions*\n### **(W1 & Q1): Novelties**\nWe thank the reviewer for requesting clarification. FAPEX introduces a principled and generalizable framework for seizure prediction, with the core novelty being the Fractional Neural Frame Operator (FrNFO)—a learnable fractional-order transform that adaptively captures both low- and high-frequency EEG dynamics. Unlike fixed STFT or wavelets, FrNFO provides data-driven time–frequency representation, enabling better detection of diverse preictal signatures. FrNFO overcomes the low-frequency bias of CNNs via fractional decomposition with refined instantaneous phase and amplitude representation. Learnable fractional orders allow flexible trade-offs between temporal and spectral detail. Theoretical analysis (Appendix A) shows FrNFO is stable under signal deformation and robust across noises. The APCE and SCA modules further enhance cross-channel fusion and multi-band learning, and extensive experiments—across modalities, cohorts, and devices—demonstrate strong generalizability.\n\nWe address the reviewer's concerns as follows:\n### (a) **Clarification on APCE & PAC**\n**(1)** We acknowledge that our introduction, in emphasizing the clinical relevance of phase–amplitude interactions, may have given the impression that  our APCE module is designed to explicitly estimate or model physiological PAC mechanism.\nThis is not true. **When we talk about phase-amplitude interaction, we refer to simultaneous utilization or feature fusion of instantaneous phase and amplitude representations in neural networks,  which is under-explored in deep learning-based seizure prediction**. We clarify that our intention is not to model or estimate PAC in a neuroscientific sense. Rather, PAC is cited to motivate the use of both amplitude and phase. The APCE block is a neural fusion mechanism inspired by PAC, designed to extract joint, discriminative features for forecasting—not to compute validated PAC metrics.\n\n**(2)** Explicitly modeling PAC incurs a time complexity of at least\n$\n\\mathcal{O}(C^2 N\\log N + C N\\log N) = \\mathcal{O}(C^2 N\\log N),\n$\nwhere $C$ is the number of EEG channels and $N$ is the sequence length. \n In contrast, our proposed approach achieves a time complexity of only \n$\\mathcal{O}(N\\log N)$,\nwhich is orders of magnitude more efficient. This distinction is crucial, \n as our design goal is to develop a neural network **inspired by** (but not strictly replicating)\nbiological mechanisms for seizure prediction.\n\n**(3)** We highlight that we have conducted ablation studies (Appendix D), among these experiments we provide architectural variants \n\\model{FAPEX-w/o-Fr-1}: Removes the FrNFO module completely, which means temporal representations are directly sending \nto Cross-BSSM module without calculating phase and amplitude at all;\n\\model{FAPEX-w/o-Phase}:Removes the phase inputs; \nThey confirm that integrating both amplitude and phase features via APCE is crucial for model performance,\neven though the module itself does not compute, extract or enforce standard PAC indices.\nSolely using amplitude information leads to performance drops across all datasets,\nsuggesting that APCE captures additional information beyond amplitude. Both amplitude and phase are necessary.\n\n| Metric   | Case   | KAIME  | RESPECT | IESS   |\n|----------|--------|--------|---------|--------|\n| SEN (↑)  | Base   | 87.04  | 85.14   | 72.26  |\n|          | w/o-Fr-1| 67.01  | 89.10   | 64.67  |\n|          | w/o-Phase | 82.13  | 82.14   | 65.42  |\n| F1 (↑)   | Base   | 86.84  | 87.82   | 72.41  |\n|          | w/o-Fr-1 | 66.49  | 90.76   | 62.75  |\n|          | w/o-Phase | 81.86  | 88.91   | 63.77  |\n| ROC (↑)  | Base   | 90.08  | 91.83   | 71.44  |\n|          | w/o-Fr-1 | 72.75  | 91.42   | 71.21  |\n|          | w/o-Phase | 85.22  | 93.02   | 70.18  |\n\nA new ablation study was conducted to test whether the APCE module’s gain comes from genuine phase–amplitude interaction, rather than simple feature concatenation. We randomly shuffled phase and amplitude vectors independently for each sample, thereby destroying any correspondence. The resulting performance dropped markedly. Only the original APCE (with true cross-encoding) preserved high accuracy. This confirms that meaningful phase–amplitude interaction—not mere concatenation—is critical for the predictive power of our approach.\n\n| Dataset   | APCE (Original) | APCE (Shuffled) |\n|-----------|-----------------|-----------------|\n| Beirut  | 84.34           | 76.47           |\n| IESS   |     72.41        | 65.66           |\n| KAIME   | 86.84            | 78.57           |\n| RESPECT| 87.82            | 77.48           |\n\n**(4)** We appreciate the reviewer's suggestion of a  direct comparison with standard PAC estimators.  APCE is not a PAC estimator but an amplitude–phase fusion block inspired by PAC concepts. Nevertheless, we implemented PAC-based baselines using MVL-MI and KL-MI  computed for frequency bands of delta, theta, alpha, beta coupling with gamma (such combinations are experimentally attested PAC in epileptic brains) across channels as features processed by a two-layer MLP classifier. The results show that FAPEX significantly outperforms these baselines  (Wilcoxon rank-sum test: p<0.001):\n| Dataset | FAPEX (F1) | MVL-MI-MLP (F1) | KL-MI-MLP (F1) |\n|---------|------------|-----------------|----------------|\n| RESPECT | 87.82      | 75.46           | 68.26          |\n| KAIME   | 86.84      | 74.83           | 62.81          |\n| IESS    | 72.41      | 62.64           | 63.65          |\n| Beirut  | 84.34      | 66.69           | 69.78          |\n\nThese suggest that our model achieves better performance than PAC estimator-based \nseizure prediction. Using standard PAC metrics alone cannot achieve satisfactory classification\nof preictal vs interictal samples.\n\n### (b) **Linear Attention**\nWe respectfully clarify that our **linear attention in SCA is bidirectional**,  meaning it fully accounts for interactions among all electrode channels,  developed in CV and NLP as a suboptimal yet efficient alternative.  **It does not lose the ability to capture cross-electrode dependencies**, Replacing the linear attention with full one resulted in marginal differences:\n| Dataset | Linear (F1) | Full (F1) |\n|---------|-------------|-----------|\n| Beirut  | 84.34       | 84.40     |\n| KAIME   | 86.84       | 86.87     |\n| RESPECT | 87.82       | 87.85     |\n| IESS    | 72.41       | 72.40     |\nThis confirms that **linear attention is not a bottleneck for capturing inter-electrode interactions**.  \n\n### **(W2): Spatial Analysis**\nThank you for the helpful suggestion. Attention weight analysis from the SCA module shows consistent patterns across preictal samples, reliably highlighting electrodes near known epileptogenic zones. In the FMCE dataset, for instance, patients with temporal epilepsy show strong coupling within the temporal lobe and hippocampus, with weak frontal–temporal interactions—matching SOZ annotations. These results confirm the SCA module’s effectiveness in modeling inter-electrode dependencies and will be added to the revised manuscript.\n\nWe also highlight that Supplementary Section B2 (Brain Region Analysis)  already provides quantitative evidence of spatial relevance. As shown in Figure 3, masking channels from clinically critical regions (e.g., Temporal Lobe, Hippocampus) causes significant performance drops,  confirming that FAPEX effectively leverages physiologically meaningful regions rather than relying on arbitrary patterns.\n\n### **(W3 & Q3): Efficiency Analysis**\nThank you for this important question. We address it in two points.\n### (a) **Efficiency** \nWe present a comparison including parameter count, latency (ms) and FLOPs per inference for best-performing\nmodels. On average FAPEX has moderate to medium computational efficiency with higher overall performance across datasets.\n\n| Model            | Params | Latency (ms) | FLOPs   |\n|------------------|--------|--------------|---------|\n| Brant            | 68.49M | 18.39        | 37.36G  |\n| CBrMod           | 4.03M  | 8.45         | 1.29G   |\n| EEGPT            | 25.24M | 13.93        | 9.79G   |\n| Neuro-BERT       | 7.75M  | 12.08        | 2.42G   |\n| VQMTM            | 4.29M  | 9.85         | 1.45G   |\n| COMETS           | 3.95M  | 3.90         | 432.91M |\n| MF-CLR           | 4.21M  | 3.09         | 753.09M |\n| TS2Vec           | 3.95M  | 3.83         | 423.23M |\n| FAPEX-Small (SL) | 3.51M  | 5.29         | 566.42M |\n| FAPEX-Base (SL)  | 9.32M  | 9.51         | 1.35G   |\n\n### (b) **Wearable Device**\nWe thank the reviewers for raising the question of wearable EEG applicability. FAPEX is currently designed for clinical-grade settings (scalp EEG, iEEG, and animal models) under controlled conditions, as consumer-grade preictal datasets remain scarce and fragmented. As noted in the Supplementary Limitations, this makes rigorous wearable evaluation infeasible at present. Nonetheless, FAPEX demonstrates strong generalization across 12 diverse clinical datasets, with efficient parameter size and latency. Our interpretability analysis further shows that FAPEX relies on clinically relevant brain regions (e.g., temporal, frontal, hippocampus), supporting its potential for future adaptation to low-channel or wearable EEG. We view this as a promising direction and plan to pursue it as suitable benchmarks emerge.\n\n### **(W4 & Q4): Formatting**\nWe sincerely thank the reviewer for the careful reading \nof our manuscript and for pointing out the formatting issues. We have thoroughly proofread and corrected the entire paper and appendices.\n\n## **Summary**\nWe hope these additions could address your concerns\nand strengthen our submission. In light of these, we respectfully ask you to reconsider the score if the new material satisfactorily resolves the earlier reservations."}, {"review_id": "30TFv7nJ4G", "reviewer": "Reviewer_yfHo", "summary": "The paper proposes FAPEX, a novel cross-subject seizure prediction model that integrates time-frequency decomposition, phase-amplitude coupling, and spatial attention into a unified architecture. The key innovation lies in the Fractional Neural Frame Operator (FrNFO), a learnable extension of the fractional Fourier transform that adaptively captures both low- and high-frequency EEG components. The model is rigorously evaluated across 12 datasets involving various species and modalities, outperforming 32 baselines. Extensive ablations and domain transfer evaluations show strong generalization, establishing FAPEX as a state-of-the-art solution for subject-agnostic seizure prediction.", "questions": "Although the paper is using balanced metric like balanced accuracy, ROC, F1 etc, it would be great to report false positives like precision or specificity.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The method is theoretically well-grounded and offers a meaningful degree of interpretability through the analysis and visualization of frequency bands. Given that frequency dynamics are central to distinguishing ictal and pre-ictal brain states, addressing the common bias in frequency extraction is a logical and valuable step toward improving seizure prediction performance. The paper demonstrates rigorous empirical validation across multiple datasets and benchmarks, showing consistently strong and superior results. Comprehensive ablation studies further support the significance and necessity of the model’s three core components. This approach holds considerable potential for clinical impact by enabling robust, subject-agnostic seizure prediction.\n\nThe only notable limitation is the method’s complexity. While the paper thoroughly details the underlying algorithms, reproducing the full model could be challenging. That said, the authors have committed to releasing the code upon acceptance, which would significantly enhance reproducibility.", "was_revised": true, "final_justification": "This paper is a solid work and authors answered all my questions in rebuttal.", "rebuttal": "Thank you for your constructive feedback, which has significantly enhanced the clarity and rigor of our work. Due to space limitations in the rebuttal, we present only a subset of additional results below; the complete results will be included in the camera-ready version.\n\n## *Response to Weaknesses*\n\n### **(W1) Complexity**\nWe appreciate the reviewer’s interest in the computational complexity of FrFT-based operations. We reconfirm that the code will be released upon acceptance. \n\nWe clarify that numerical implementation of the FrFT algorithm is fundamentally driven by FFT operations:  Each FrFT (length $N$) consists of a single FFT, a single IFFT (each of length $\\approx 2N$), and two $N$-length elementwise chirp multiplications, resulting in an overall complexity of $\\mathcal{O}(N \\log N)$.  Fractional convolution between two $N$-length signals consists of two FrFTs, one pointwise multiplication,and one inverse FrFT, so the total complexity remains $\\mathcal{O}(N \\log N)$—**comparable to standard FFT-basedconvolution but with enhanced flexibility in the fractional domain**.\n\nFor transparency and reproducibility, we have provided pseudocode for our FrFT implementation \n(which could be further optimized for differentiable computation on GPU), and the full source code will be made available upon publication. \n\n**Algorithm: Fast Fractional Fourier Transform (PyTorch-style pseudocode)**\n\n**Input:**  \n- `x`: input tensor of shape `[..., T, F]` (T: time, F: feature/channel)  \n- `alphas`: fractional orders, shape broadcastable to `[..., F]`\n\n**Output:**  \n- `y`: output tensor, same shape as `x`, complex-valued\n\n1. (Optional) Move time and feature axes to last for ease of broadcasting.\n2. Ensure `x` is cast to complex-valued tensor.\n3. Compute parameters:\n    - `phi = alphas * (π / 2)`\n    - `cot_phi = cos(phi) / sin(phi)`\n    - `csc_phi = 1 / sin(phi)`\n    - `t = arange(T) - (T - 1) / 2`\n4. **Pre-chirp:**  \n    - For each feature/channel:  \n      `x_pre = x * exp(-i * π * cot_phi * t^2)`\n5. **Chirp convolution (FFT-based):**\n    - Zero-pad to length `2T`.\n    - Create chirp filter:  \n      `g[n] = exp(i * π * csc_phi * n^2)` for `n = -T,...,T-1`\n    - `X_fft = FFT(x_pre, n=2T)`\n    - `G_fft = FFT(g, n=2T)`\n    - `conv = IFFT(X_fft * G_fft, n=2T)`\n    - Crop middle `T` samples:  \n      `conv_cropped = conv[..., T-1:T-1+T, :]`\n6. **Post-chirp and scaling:**  \n    - `y = scale * exp(-i * π * cot_phi * t^2) * conv_cropped`\n    - Where `scale = exp(-i * (1 - alphas) * π / 4) / sqrt(abs(sin(phi)))`\n7. **Handle integer orders:**  \n    - If `alpha ≈ 0`: `y = x`  \n    - If `alpha ≈ 1`: `y = FFT(x)`\n    - If `alpha ≈ -1`: `y = IFFT(x)`\n    - If `alpha ≈ 2`: `y = reverse(x, axis=time)`\n8. Restore original tensor layout if axes were permuted.\n\n**Return:** `y`\n\n## *Response to Questions*\n\n### **(Q1) False Positives Metrics**\nWe thank the reviewer for emphasizing the importance of false positive–oriented metrics. In response, we now report precision, specificity, and false positives per hour (FPR/h) for FAPEX across all datasets. As suggested, we have computed these metrics under the same evaluation protocol for all datasets. Due to space limitations, we present representative results for selected datasets in the table below, with the complete results available in the revised supplementary materials.\n\n| **Model**      | **PCS** | | | **IESS** | | | **KAIME** | | | **ATLS** | | | **AGS** | | |\n|----------------|---------|---------|--------|---------|---------|--------|---------|---------|--------|---------|---------|--------|---------|---------|--------|\n|                | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h |\n|----------------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|\n| Brant          | 72.12   | 66.20   | 0.242 | 62.20   | 51.55   | 0.396 | 67.50   | 56.33   | 0.324 | 72.69   | 61.91   | 0.281 | 82.28   | 68.28   | 0.205 |\n| CBraMod        | 78.60   | 70.03   | 0.200 | 74.48   | 42.47   | 0.409 | 69.72   | 55.50   | 0.336 | 73.74   | 70.24   | 0.220 | 83.29   | 72.21   | 0.185 |\n| EEGPT          | 76.80   | 58.00   | 0.304 | 66.63   | 48.11   | 0.391 | 70.11   | 54.82   | 0.344 | 71.26   | 74.93   | 0.182 | 86.64   | 70.26   | 0.199 |\n| LaBraM         | 53.96   | 48.44   | 0.468 | 60.08   | 54.95   | 0.368 | 52.33   | 64.25   | 0.320 | 62.41   | 46.21   | 0.435 | 88.46   | 64.19   | 0.229 |\n| Neuro-BERT     | 75.82   | 53.37   | 0.314 | 65.44   | 48.17   | 0.397 | 67.99   | 59.22   | 0.312 | 87.99   | 63.31   | 0.242 | 86.10   | 71.12   | 0.191 |\n| VQ_MTM         | 75.92   | 73.40   | 0.181 | 64.87   | 49.56   | 0.381 | 55.23   | 67.93   | 0.280 | 67.54   | 69.22   | 0.240 | 76.08   | 69.76   | 0.213 |\n| BIOT           | 77.63   | 68.98   | 0.211 | 60.61   | 34.87   | 0.539 | 59.20   | 65.45   | 0.287 | 73.06   | 63.13   | 0.260 | 85.28   | 67.24   | 0.211 |\n| COMETS         | 75.04   | 54.97   | 0.319 | 59.74   | 58.01   | 0.348 | 72.19   | 61.62   | 0.269 | 71.63   | 76.29   | 0.169 | 84.47   | 70.34   | 0.202 |\n| MF-CLR         | 70.13   | 56.68   | 0.317 | 74.58   | 37.63   | 0.425 | 73.13   | 58.20   | 0.298 | 71.95   | 68.61   | 0.242 | 81.85   | 72.54   | 0.186 |\n| TS2Vec         | 55.30   | 63.27   | 0.306 | 67.62   | 44.74   | 0.415 | 69.90   | 54.19   | 0.328 | 75.91   | 49.13   | 0.352 | 86.04   | 62.10   | 0.240 |\n| FAPEX-Small    | 86.52   | 81.07   | 0.111 | 79.27   | 52.92   | 0.277 | 83.86   | 70.77   | 0.168 | 85.72   | 92.82   | 0.044 | 87.50   | 76.12   | 0.149 |\n| FAPEX-Base     | 93.21   | 93.43   | 0.041 | 84.42   | 58.96   | 0.215 | 85.28   | 76.60   | 0.122 | 97.72   | 92.47   | 0.041 | 93.02   | 82.43   | 0.093 |\n\nThese results confirm that FAPEX maintains strong performance not only in balanced accuracy and AUPRC, but also in minimizing \nfalse alarms—supporting its clinical utility. \n\n## *Summary*\nWe hope these additions could address your concerns\nand strengthen our submission."}, {"review_id": "kyyrPx1Wid", "reviewer": "Reviewer_5QbB", "summary": "This paper presents a novel pipeline for seizure prediction posed as preictal vs interictal window classification using multiple brain signal modalities. The pipeline works for heterogenous channel configurations by learning channel-independent embeddings over fixed-duration windows. Fractional convolutions are used to process embeddings, with an extension by learning a parameterization of Weyl-Heisenberg filters using implicit MLPs. This extension introduces a phase adjustment factor to accommodate spectral transitions. Amplitude-phase interactions are then modeled via bidirectional state-space models building on Mamba blocks. Finally, learned embeddings across channels are fused via a cross attention module.", "questions": "Since results show the ability to distinguish preictal vs. interictal windows. what would be the expected performance when ictal windows are also included as inputs? Intuitionally they would be easier to distinguish than interictal windows but this is worth further discussion / analysis towards real-time application.", "limitations": "Please see above.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: The proposed pipeline and fractional convolution extension are novel in seizure prediction literature. Extensive experiments including different input modalities, supervised vs. fine-tuned training mechanisms and statistical analysis enhance novelty. \n\nWeaknesses: There are missing elements in the flow of notation throughout the pipeline. In line 191, it should be explicitly written how Amp and Pha relate to X^hat from eq. (5). In line 213, it is not clear if X is the same as X^tilde from Eq. (12), and how amplitude and phase components of X^tilde are incorporated. \n\nIt seems like Eq. (4) introduces additional sums in each neuron of an MLP. It is worth discussing the computational complexity introduced by this extension on fractional convolution.", "was_revised": true, "final_justification": "The authors responded to all of my comments", "rebuttal": "Thank you for your constructive feedback, which has significantly enhanced the clarity and rigor of our work.\n\n## **Replies to Weaknesses**\n\n### **(W1) Notation Clarity**\nWe clarify that $Amp$ (amplitude) and $Pha$ (phase) are directly computed from the complex-valued tensor $\\hat{X} \\in \\mathbb{C}^{\\cdot}$. Specifically, letting $\\hat{X} = \\Re(\\hat{X}) + i, \\Im(\\hat{X})$, we have:\n$$Amp = |\\hat{X}| = \\sqrt{\\Re(\\hat{X})^2 + \\Im(\\hat{X})^2},$$\n$$Pha = \\angle \\hat{X} = \\mathrm{atan2}!\\left(\\Im(\\hat{X}), \\Re(\\hat{X})\\right).$$\nEquivalently, this can be expressed as:\n$$Amp = |\\hat{X}|,\\quad Pha = \\arg(\\hat{X}).$$\n$\\hat{X}$ is the same as $\\tilde{X}$. $\\tilde{X}$ is the output of APCE, therefore,\nit represents the fused information from phase and amplitude.\n\n### **(W2) Complexity**\nWe address your concerns as follows.\n\n#### **(a) Eq. (4)**\nThe MLP incurs a computational cost primarily limited to the feedforward computation during training. \n**At inference time, the MLP only needs to be computed once, as it produces a fixed kernel.**\n\nLet  \\(N\\) = number of temporal samples, \\(d_{\\mathrm{model}}\\) = feature channels, \\(M\\) = number of exponential terms, \\(K\\) = highest order of Hermite expansion  \n\n1. **Exponential‐term GEMM**  \n   $\n     E \\in \\mathbb{C}^{N\\times M},\\;\n     W \\in \\mathbb{C}^{M\\times d_{\\mathrm{model}}}\n     \\;\\longrightarrow\\;\n     X = E\\,W\n     \\quad\\Rightarrow\\quad\n     \\mathcal{O}(N \\, M \\, d_{\\mathrm{model}})\n   $\n\n2. **Hermite‐term GEMM**  \n   $\n     H \\in \\mathbb{R}^{N\\times (K+1)},\\;\n     A \\in \\mathbb{R}^{(K+1)\\times d_{\\mathrm{model}}}\n     \\;\\longrightarrow\\;\n     Y = H\\,A\n     \\quad\\Rightarrow\\quad\n     \\mathcal{O}(N \\, K \\, d_{\\mathrm{model}})\n   $\n\n3. **Element‐wise multiplication**  \n   $\n     \\Phi = X \\circ Y\n     \\quad\\Rightarrow\\quad\n     \\mathcal{O}(N \\, d_{\\mathrm{model}})\n   $\n\nTotal Cost is\n\n$\n  \\mathcal{O}\\bigl(N\\,d_{\\mathrm{model}}\\,(M + K)\\bigr)\n$\n\n**Note:**\n\n**(1) Training time:**  \nThese window/kernel computations must be redone **every** training iteration\n(since the parameters $w_{i,k}, b_{i,k}, c_{i,k}, a_{n,k}$ are updated).  \n**(2) Test (inference) time:**  \n**Because the window/kernel depends only on fixed time positions $t_j$ and learned parameters—not on the dynamic input values—it can be computed **once** ahead of inference, eliminating per‐sample overhead completely.**\n\n### (b) Fractional Convolution ###\nThe numerical implementation of **FrFT algorithm** \nis dominated by FFT operations. \nA single FrFT of length $N$ involves:\n\n* one FFT and one IFFT of size $\\approx 2N$, and\n* two elementwise chirp multiplications of size $N$.\n\nThus, the total time complexity is:\n\n$$\n\\mathcal{O}(2N \\log(2N)) + \\mathcal{O}(N) \\; = \\; O(N \\log N).\n$$\n\nFor **fractional convolution** of two signals of length $N$, the computation proceeds as:\n\n1. Forward FrFT of the input: $\\mathcal{O}(N \\log N)$,\n2. Forward FrFT of the kernel: $\\mathcal{O}(N \\log N)$,\n3. Pointwise multiplication: $\\mathcal{O}(N)$,\n4. Inverse FrFT: $\\mathcal{O}(N \\log N)$.\n\nThis gives an overall complexity of:\n\n$$\n3\\mathcal{O}(N \\log N) + \\mathcal{O}(N) = \\mathcal{O}(N \\log N),\n$$\n\n\nThis approach yields performance comparable to FFT-based conventional convolution, differing only by constant factors, while offering greater flexibility in the fractional domain.\n\n## **Response to Questions**\n\n### **(Q1) Ictal Windows**\nWe sincerely thank the reviewer for this insightful question.\n\n**To directly address the reviewer’s concern,** we conducted additional experiments in which **ictal windows were used in the training data**. Consistent with the reviewer’s intuition, the inclusion of ictal segments led to an improvement in overall predictive performance; however, this boost did not reach statistical significance across the datasets (Wilcoxon rank-sum test: $p > 0.05$) and is therefore marginal.\n\n| Dataset | F1 (without ictal) | F1 (with ictal) |\n| ------- | -------------- | --------------- |\n| RESPECT | 87.82          | 87.86           |\n| KAIME   | 86.84          | 87.90           |\n| IESS    | 72.41          | 72.54          |\n| Beirut  | 84.34          | 84.37           |\n\nThis minor gain further supports the robustness of our main conclusions and confirms that restricting training and evaluation to preictal windows does not compromise model effectiveness. Indeed, adhering to preictal-only windows aligns with established seizure prediction protocols, where the clinical objective is to deliver timely warnings before seizure onset, not during or after.\n\nFor completeness, we clarify that all our core experiments presented in the current manuscript systematically exclude ictal windows from all supervised training, fine-tuning, and evaluation, in line with community standards.\n\nIn short, our findings affirm that while incorporating ictal activity yields benefits, albeit marginal. Strict preictal-only modeling remains the field’s standard and is sufficient for robust, clinically meaningful seizure prediction. Once again, we thank the reviewer for prompting this additional analysis and hope this clarifies our methodological choices.\n\n## **Summary**\nWe hope these additions could address your concerns and strengthen our submission. In light of these, we respectfully ask you to reconsider the score if the new material satisfactorily resolves the earlier reservations."}, {"review_id": "uktGvRL7dT", "reviewer": "Reviewer_crkz", "summary": "The paper introduces FAPEX (Fractional Amplitude-Phase Expresso) architecture for subject-agnostic seizure prediction (SASP), addressing the challenge of complex and variable brain signals. It introduces a learnable fractional neural frame operator (FrNFO) that uses fractional-order convolutions to capture both high- and low-frequency dynamics. The architecture has three innovations: Fractional-order convolutions to overcome spectral bias, extraction of instantaneous phase and amplitude, aiding in identifying preictal biomarkers, integration of state-space modeling and channelwise attention to manage diverse electrode sets. FAPEX also extracts phase and amplitude features useful for identifying preictal biomarkers and includes state-space modeling and channelwise attention to handle diverse electrode setups. The authors showed consistent performance improvement across various datasets.", "questions": "0.\tAre the imaginary parts of the FOFT discarded? In Mamba or S4, in which FFT is used, the imaginary part is used. The authors should also discuss how they dealt with the imaginary parts.\n\n1.\tThe authors should devise the data into scalp EEG and iEEG and report the performance on each set. This will avoid any mixed information between the 2 devices.\n2.\tFor the in-house datasets, where the authors have more controls, the authors should report more popular seizure prediction metrics:\na.\tFalse positive rate/hour\nb.\tLatency: the offset between predicted onset and the actual onset.\n3.\tCitations are missing in the Supplementary. Please check them carefully.\n4.\tIn Table 1, the authors should report the correct number of channels in each dataset, not the number of channels after preprocessing. What is the duration in Table 1? Is it the epoch duration?", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength:\n1.\tIntroducing Fractional order fourier transform (FOFT) is innovative. This overcomes the limitation of fourier transform that depends on the time resolution. FOFT is a suitable method for EEG signals as epileptic patterns vary in frequency and time resolutions.\n2.\tAll technical experiments are well designed and logical for a deep learning paper.\n3.\tCross species is an interesting experiment.\n\nWeakness:\n1.\tPreprocessing details for seizure prediction are missing: \na.\t EEG epoch duration details for pretraining are missing. This is important for readers to compare to reported performance in literature.\nb.\tReporting AUPRC is great. However, false positive rate (FPR)/hour is missing. This is an important metric apart from F1 or precision to justify the applicability of the method.\n2.\tMore details about channel rejection and duplication are needed. The authors provide the channel rejection in the appendix but did not mention which channels were selected for duplication. The authors should carefully discuss how this was apply to different system (10-20, 128 channels, iEEG, etc.)\n3.\tMixing up iEEG and scalp EEG in pretraining raises a concern. iEEG has higher sampling rates than scalp EEG and downsampling them to 512Hz might result in information loss (e.g iEEG HFO might not be well captured). iEEG normally has high density channels, which captures more information and cleaner signals than scalp 10-20 system EEG (e.g TUEG). Applying the same noise removal technique to both scalp EEG and iEEG is not suitable as again it will cause information loss and the number of iEEGs in pretraining is small compared to scalp EEG. This might cause the modal to be biased towards scalp EEG.\n4.\tA limitation of the field is that seizure prediction models tend not to generalise well to different cohorts with different EEG providers (traditional clinical EEG devices, not wearable or dry EEG devices). The authors should show some results for cross-dataset validations to emphasise on the generalisability of the proposed methods.", "was_revised": true, "final_justification": "Thanks to the authors for providing me with extra results and details. I have now raised the score to \"boardline acceptance\"", "rebuttal": "We sincerely thank the reviewer for their careful reading and constructive feedback. Due to space constraints, we present only a subset of additional results here.\n## **Response to Weakness(es)**  \n### **(W1): Preprocessing and FPR/h**\nWe clarify that the **EEG epoch duration is already specified in Table 1 of the main paper** (column “Duration”), where the pretraining window length is **32 s**. In response to the reviewer’s suggestion, we have computed and added FPR/h, precision, and specificity metrics for all datasets under the same protocol. Owing to rebuttal length constraints, we present a representative subset here; the complete tables are provided in the revised supplementary materials. Across all tested datasets, FAPEX consistently achieves the lowest FPR/h and highest precision/specificity among all baselines, demonstrating its value for practical deployment.\n| **Model**      | **PCS** | | | **IESS** | | | **KAIME** | | | **ATLE** | | | **AGS** | | |\n|----------------|---------|---------|--------|---------|---------|--------|---------|---------|--------|---------|---------|--------|---------|---------|--------|\n|                | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h | Pre     | Spe     | FPR/h |\n|----------------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|\n| Brant          | 72.12   | 66.20   | 0.242 | 62.20   | 51.55   | 0.396 | 67.50   | 56.33   | 0.324 | 72.69   | 61.91   | 0.281 | 82.28   | 68.28   | 0.205 |\n| CBraMod        | 78.60   | 70.03   | 0.200 | 74.48   | 42.47   | 0.409 | 69.72   | 55.50   | 0.336 | 73.74   | 70.24   | 0.220 | 83.29   | 72.21   | 0.185 |\n| EEGPT          | 76.80   | 58.00   | 0.304 | 66.63   | 48.11   | 0.391 | 70.11   | 54.82   | 0.344 | 71.26   | 74.93   | 0.182 | 86.64   | 70.26   | 0.199 |\n| LaBraM         | 53.96   | 48.44   | 0.468 | 60.08   | 54.95   | 0.368 | 52.33   | 64.25   | 0.320 | 62.41   | 46.21   | 0.435 | 88.46   | 64.19   | 0.229 |\n| Neuro-BERT     | 75.82   | 53.37   | 0.314 | 65.44   | 48.17   | 0.397 | 67.99   | 59.22   | 0.312 | 87.99   | 63.31   | 0.242 | 86.10   | 71.12   | 0.191 |\n| VQ_MTM         | 75.92   | 73.40   | 0.181 | 64.87   | 49.56   | 0.381 | 55.23   | 67.93   | 0.280 | 67.54   | 69.22   | 0.240 | 76.08   | 69.76   | 0.213 |\n| BIOT           | 77.63   | 68.98   | 0.211 | 60.61   | 34.87   | 0.539 | 59.20   | 65.45   | 0.287 | 73.06   | 63.13   | 0.260 | 85.28   | 67.24   | 0.211 |\n| COMETS         | 75.04   | 54.97   | 0.319 | 59.74   | 58.01   | 0.348 | 72.19   | 61.62   | 0.269 | 71.63   | 76.29   | 0.169 | 84.47   | 70.34   | 0.202 |\n| MF-CLR         | 70.13   | 56.68   | 0.317 | 74.58   | 37.63   | 0.425 | 73.13   | 58.20   | 0.298 | 71.95   | 68.61   | 0.242 | 81.85   | 72.54   | 0.186 |\n| TS2Vec         | 55.30   | 63.27   | 0.306 | 67.62   | 44.74   | 0.415 | 69.90   | 54.19   | 0.328 | 75.91   | 49.13   | 0.352 | 86.04   | 62.10   | 0.240 |\n| FAPEX-Small    | 86.52   | 81.07   | 0.111 | 79.27   | 52.92   | 0.277 | 83.86   | 70.77   | 0.168 | 85.72   | 92.82   | 0.044 | 87.50   | 76.12   | 0.149 |\n| FAPEX-Base     | 93.21   | 93.43   | 0.041 | 84.42   | 58.96   | 0.215 | 85.28   | 76.60   | 0.122 | 97.72   | 92.47   | 0.039 | 93.02   | 82.43   | 0.093 |\n\n### **(W2) Channel Processing**\nChannel rejection was strictly performed following dataset provider annotations (bad channels flagged in iEEG, and artifact-affected leads in scalp EEG). No manual override was used, preventing introduction of any bias. Typically, 0–37% of channels are rejected per subject (detailed ranges now added in the revision). To standardize input shapes for training, we filled empty slots to 64 channels with the mean value of remaining valid channels; this step is only for hardware optimization and does not increase the information content. When using native low-channel 10–20 EEG without duplication, model performance remains essentially unchanged—confirming that duplication does not inflate results. Importantly, seizure-related regions such as the temporal and frontal lobes, as well as hippocampal electrodes (in the case of iEEG), are consistently preserved due to their critical role in identifying predictive biomarkers. Notably, these key channels have not been reported as damaged across all datasets, as confirmed by their respective providers and maintainers.\n\n### **(W3) Data Mixing:** \n### **1. Clarification of Data Mixing**\nWe clarify that data mixing occurs only during self-supervised pretraining, in line with foundation model practices in NLP and CV. During supervised training and evaluation, no cross-modality mixing is used. Although iEEG and scalp EEG differ in noise characteristics and spectral distributions, **our approach consistently outperforms baselines**.\n\n### **2. Further Motivation and Evidence**\nMixing samples from multiple sources during pretraining is a widely recognized practice in **foundation models** across **NLP, CV**, and emerging EEG models. It **alleviates data scarcity** and **enhances generalization** across diverse datasets. Our ablation study confirm that **mixed pretraining improves downstream performance** compared to single-modality pretraining.\n| **Pretraining**         | **Dataset** | **F1 (%)** |\n|-------------------------|-------------|------------|\n| **Single (iEEG only)** | Beirut      | 83.87      |\n|                         | IESS        | 71.81      |\n|                         | KAIME       | 86.12      |\n|                         | RESPECT     | 86.84      |\n| **Single (Scalp only)**  | Beirut      | 84.28      |\n|                         | IESS        | 71.73      |\n|                         | KAIME       | 86.42      |\n|                         | RESPECT     | 87.73      |\n| **Mixed (scalp+iEEG)**  | Beirut      | 84.34      |\n|                         | IESS        | 72.41      |\n|                         | KAIME       | 86.84      |\n|                         | RESPECT     | 87.82      |\nThese improvements indicate that FAPEX **benefits from diverse pretraining without suffering  from bias toward scalp EEG**.\n\n### **3. HFOs and Noise Concerns**\nWe thank the reviewer for raising this concern. Our study targets clinically relevant high-gamma activity, which is fully preserved at 512 Hz. Ultra-fast ripples (>250 Hz) are rarely recorded reliably at scale and are inaccessible in scalp EEG. Thus, 512 Hz offers a practical balance for consistent processing across modalities. To validate this choice, we conducted an ablation at 1024 Hz. While slight improvements appeared in KAIME and IESS, overall gains were limited—supporting 512 Hz as sufficient for robust performance.\n\n| Dataset   | 512 Hz | 1024 Hz   |\n|-----------|-----------------|-----------------|\n| **Beirut**  | 84.34           | 84.29           |\n| **IESS**    | 72.41           | 72.82           |\n| **KAIME**   | 86.84           | 87.41           |\n| **RESPECT** | 87.82           | 85.89           |\nMoreover, interpretability analysis (Fig. 2) confirms that FrNFO layers progressively emphasize high-gamma components and sharpen frequency resolution—unlike non-fractional operators—demonstrating the model’s capacity to extract spectral dynamics relevant to preictal states. Finally, we clarify that preprocessing pipeline is modality-aware, with adaptive noise removal threshold with for iEEG and scalp EEG respectively.\n\n### **(W4) Generalizability Across Devices and Cohorts**\nWe appreciate the reviewer’s point. Our current study includes strong cross-cohort/device validation—e.g., IESS → BEIRUT (neonatal to adult EEG across hardware) and AGS → BEIRUT (generalized-to-focal transfer)—demonstrating robustness to population and acquisition variability. While FAPEX is currently evaluated on clinical-grade EEG (scalp/iEEG), wearable datasets for preictal forecasting remain limited. Nevertheless, FAPEX’s focus on key brain regions (temporal, frontal, hippocampus) indicates potential adaptability to low-channel or wearable EEG. We see this as a promising future direction.\n\n## **Response to Questions**\n\n### **(Q0) Imaginary Parts of FrFT**\n\nFrNFO preserves the full complex-valued fractional spectrum; both the real and imaginary components are used. The APCE module computes instantaneous amplitude and phase directly from these components. Unlike Mamba and S4, FAPEX does not discard this information.\n\n### **(Q1) Data Mixing**\nAs detailed in **(W3)**, we have conducted separate analyses for iEEG and scalp EEG, as well as mixed-modality pretraining. The results demonstrate that cross-modality pretraining benefits performance without introducing bias.\n\n### **(Q2) FPR/h and Latency**\nWe have reported FPR/h, precision, and specificity for all datasets in **(W1)**. Latency is also provided for in-house datasets are provided as follows. These values represent the  median latency of FAPEX-Base-SSL. **Higher latency reflects more confident and early predictions**.\n| **Dataset** | **Median Latency (min)** |\n|-------------|--------------------------|\n| PCS         | 26                       |\n| IESS        | 11                       |\n| KAIME       | 19                       |\n| ATLE        | 28                       |\n| AGS         | 23                       |\n### **(Q3) Citations**\nThank you for your careful reading. We have revised it in the updated version.\n### **(Q4) Channel Counts and Epoch Duration**\nThank you for your advice. We have clarified in the manuscript that the \"Duration\" column in Table 1 indicates the EEG epoch length. Raw channel counts per individual will be presented in the revised supplementary materials due to high variability within datasets.\n\n## **Summary**\nWe hope these responses address your concerns and strengthen our submission. In light of these, we respectfully ask you to reconsider the score if the new material satisfactorily resolves the earlier reservations."}]

Author rebuttal:

Meta-review: The paper introduces FAPEX, a deep learning architecture for subject-agnostic seizure prediction. Its core innovation is the Fractional Neural Frame Operator, a learnable fractional-order convolutional filterbank that adaptively captures both low- and high-frequency EEG components. FAPEX further integrates an Amplitude-Phase Cross-Encoding module with bidirectional state-space models to capture amplitude–phase interactions, and a Spatial Correlation Aggregation module with linear attention to handle heterogeneous electrode setups. Evaluated across 12 diverse datasets spanning multiple species and modalities, FAPEX consistently outperforms 32 state-of-the-art baselines, with ablations and domain transfer tests confirming its strong generalization.

Strengths:
1. Most reviewers agree that the idea of fractional neural frame operator is innovative and theoretically grounded.
2. Most reviewers find that the experiments provided are convincing and extensive.

Weakness:
Some reviewers request more explanations about the implementation details, the complexity and generalizability of the model.

During the rebuttal, the authors have addressed the following questions:
1. Providing more explanations about the implementation details and the novelty of the paper.
2. Additional experiments to demonstrate the effectiveness of APCE and SCA modules
3. Additional analysis of the complexity of the proposed model.

After the rebuttal, the reviewers unanimously agreed that the paper is worthy of acceptance and that their concerns have been adequately addressed. Therefore, I recommend accepting this submission as a spotlight paper.
Decision: Accept (spotlight)