Title: FAPEX: Fractional Amplitude-Phase Expressor for Robust Cross-Subject Seizure Prediction
Venue: NeurIPS 2025
Accepted: yes
Keywords: seizure prediction; AI for health
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

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 FAPEX , a novel architecture that introduces a learnable 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 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 12 benchmarks spanning species (human, rat, dog, macaque) and modalities (Scalp-EEG, SEEG,

ECoG, LFP), 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 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 a 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 electrophysiological recordings-whether invasive (e.g., electrocorticography (ECoG), stereo-electroencephalography (SEEG), local field potential (LFP)) or non-invasive (scalp EEG) [38, 17]. Although seizures have long been viewed as abrupt and unpredictable events, a growing body of work demonstrates the existence of a preictal stage marked by subtle neural and behavioral changes, offering an actionable window for intervention.

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Fractional Neural Frame Operator

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Subject-Agnostic Model Development & Evaluation

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FMCE

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Seizure prediction systems seek to detect these preictal alterations and raise alarms sufficiently in advance. As shown in Fig. 1 (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 a 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 prediction achieved by pioneering studies [61, 39, 73, 9, 15, 74, 49], the field remains constrained by two fundamental limitations: the reliance on subject-specific modeling paradigms and limited scalability. Subject-specific 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.

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:

Capturing refined high- and low-frequency biomarkers. Clinical evidence [46, 14, 27, 50, 47] 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, 53] exhibit spectral biases toward low frequencies, struggling to preserve transient HFO signatures [63, 40].

Modeling phase-amplitude interactions. Epilepsy exhibits abnormal phase-amplitude coupling and (de)synchronization [1, 35, 26, 2, 76, 64] 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.

Handling heterogeneous channel layouts. Seizure onset zones and preictal activity distribution vary significantly across individuals, with predictive features appearing on different electrodes from patient to 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, compromising generalization in subject-agnostic contexts.

Present work. To overcome these challenges, we propose FAPEX , a unified

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model for effective generalization across heterogeneous EEG settings, electrode configurations, and clinical subtypes. Our approach integrates three key innovations: (1) fractional neural frame operator (FrNFO): a learnable bank of Weyl-Heisenberg filters for adaptive time-frequency 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-phase cross-encoding (APCE): A bidirectional state-space architecture processing phase and amplitude representations, learning time-varying relationships to extract seizure evolution patterns. (3) Spatial correlation aggregation (SCA): Channel-wise attention mechanisms modeling inter-electrode dependencies to identify predictive spatial patterns. Together, these components enable FAPEX to learn multi-scale representations that capture phase-amplitude coupling while handling non-stationarity and channel heterogeneity. Together , these components enable FAPEX to 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-frequency oscillations while providing fine-grained decomposition of amplitude and phase features for a more comprehensive picture of neural activity in seizure prediction.

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Our main innovations are: (1) FAPEX, a subject-agnostic framework integrating our novel Fractional Neural Frame Operator (FrNFO), amplitude-phase cross-encoding, and spatial correlation aggregation to anticipate seizures across diverse modalities. (2) FrNFO, a learnable bank of Weyl-Heisenberg filters that performs fractional-order time-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 a new standard for seizure prediction and revealing meaningful preictal biomarkers.

2 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, a neuroelectrical segment is a set of time series { x ( i ) } C i =1 , where C is the number of channels, and each x ( i ) ∈ R T represents a channel with T timestamps. A seizure predictor constructs a function f model that maps { x ( i ) } C i =1 to a binary label ˆ y i , distinguishing interictal from preictal states. The model is trained to align predictions with clinical annotations y i , enabling prediction in unseen subjects.

Input patchifying. Given a multichannel neural signal segment X ∈ R C × T , where C represents the number of electrode channels and T is the total number of time samples, we aim to establish a 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 c ∈ R T is segmented using a window of length τ , resulting in N = ⌊ T τ ⌋ patches per channel. Each patch is then projected into a common feature space using a channel-shared linear embedding W ∈ R d model × τ and bias vector b ∈ R d model , resulting in the embedded tensor ˜ X ∈ R C × N × d model ( d model 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-frequency content

and variability in both amplitude and phase. The Fractional Fourier Transform (FrFT) has emerged as a powerful tool for analyzing such signals, providing a flexible, continuous interpolation between the time domain ( θ = 0 ) and the frequency domain ( θ = π 2 ) via a fractional order parameter θ . Formally, FrFT generalizes the Fourier transform with a fractional order θ ∈ (0 , π ) , defined for a signal f ∈ L 2 ( R ) as:

This transform supports operators like θ -shift, T θ s f ( t ) = exp (2 πis ( t -s ) cot θ ) f ( t -s ) , and θ -modulation, M θ s f ( t ) = exp ( πi ( s 2 cot θ +2 st csc θ )) f ( t ) , enabling θ -fractional convolution [3, 71]:

which offers an alternative to traditional Fourier transform-based convolutions. While the fractional Fourier transform (FrFT) provides a 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 on a 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-phase representation.

A neural approach for fine-grained amplitude-phase representation. To overcome these limitations, we propose the fractional neural frame operator , which integrates neural implicit representations to learn a parameterization of θ -fractional version of nonstationary Weyl-Heisenberg frame [20, 45, 18], defined as:

where p j 0 , q j 0 are positive constants adjusting the scale. It involves θ -modulation M θ lp ( j ) 0 ( t ) = e πi (( lp ( j ) 0 ) 2 cot θ +2 lp ( j ) 0 t csc θ ) and θ -shift T θ sq ( j ) 0 ( t ) = e 2 πisq ( j ) 0 ( t -sq ( j ) 0 ) cot θ Φ j ( t -sq ( j ) 0 ) . Ψ θ 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 Ψ j over each scale j to capture a 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) [34, 62] designed to generate adaptive window function for the frame filters. Given temporal samples N and feature channels d model, the implicit MLP defines the window kernel Φ ∈ C N × d model for j = 1 , . . . , N, k = 1 , . . . , d model as

where w i,k , b i,k , c i,k , a n,k are trainable parameters optimized through gradient descent. The basis functions H n ( t ) = ( -1) n e t 2 d n dt n e -t 2 are Hermite polynomials, embedding prior knowledge of localized oscillatory behavior, while the sine activation functions promote smooth and periodic kernel characteristics essential for identifying quasiperiodic activities in brain.

FrNFO further introduces a learnable fractional order θ = [ θ 1 , . . . , θ d model ] ∈ (0 , π ) d model , which governs the time-frequency representation for each feature channel independently. Given an input neural embedding X ∈ C N × d model , employing the fractional convolution theorem [3, 71], the output feature for channel k is defined as:

where Ψ : ,k is the frame filter kernel equipped with learnable window kernel, ⊙ denotes the Hadamard product, and ω represents the frequency grid. The phase adjustment factor exp( πiω 2 cot θ k ) ensures proper alignment and interpretation of fractional frequency components. This adaptive formulation allows FrNFO to dynamically adjust frequency resolution.

FrNFO is a provably robust amplitude representator. As previously formulated, as a neural fractional-order filterbank, FrNFO naturally yields complex-valued 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, crossfrequency dependencies between amplitude and phase embeddings produced by FrNFO. Inspired by recent advances in selective state space model, proposed first in Mamba [ ? ? ? ? ], we adopt a bidirectional state-space mechanism building on Mamba blocks with cross-attention-like mechanism [59], as shown in Fig. 3. Formally, given amplitude embeddings Amp and phase embeddings Pha , we normalize them as: Amp = RMSNorm( Amp ) , Pha = RMSNorm( Pha ) . These normalized embeddings are then processed by the dual cross-Mamba module, which operates in a channel-independent 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 ∈ R B × M × D are projected into a latent space via two shared linear mappings:

where W x , W z ∈ R D × E are learnable projection matrices, and E denotes the number of latent SSM states. The projected embeddings undergo causal and anti-causal convolutions followed by a SiLU activation:

Using the normalized amplitude embeddings Amp , we compute state-space parameters:

where W B , W C ∈ R D × N are shared across directions, and W ∆ ∈ R E × E , b ∆ ∈ R E are shared scaling parameters. The time-varying transition parameters are then defined as:

where A ∈ R E × N is a shared, direction-agnostic transition matrix, and ⊗ denotes element-wise multiplication. The output sequence is computed using the SSM kernel:

The final phase-to-amplitude representation, which captures phase-informative patterns, is gated as:

In the amplitude BSSM, the roles are swapped: the phase-informative Y P provides the context, and the amplitude Amp serves as queries. A residual connection combines the block output Y A with the original amplitude embeddings Amp to produce the final APCE encoding:

Spatial correlation aggregation (SCA). During the preictal interval, epilepsy is marked by dynamic shifts in inter-electrode interdependencies that reflect the spread of pathological activity across brain regions. Accurate seizure forecasting from multichannel recordings therefore hinges on modeling these spatial dependencies. To this end, given neuroelectrical embeddings X ∈ R C × N × d , SCA models global cross-spatial dependencies of different electrodes while integrating local spatiotemporal

patterns. Formally, linear attention aims to use ϕ ( q i ) ϕ ( k j ) ⊤ to approximate softmax attention kernel at linear complexity, where the feature map ϕ ( · ) : R d ↦→ R d is applied row-wise to the query and key matrices. As a result, the c -th row of attention output a t ∈ R d can be rewritten as

where g c is the c -th row of G := RMSNorm[DepthwiseConv2d( X )] implemented with a 3 × 3 depthwise convolutional kernel to aggregate neighborhood spatiotemporal information with RMSNorm to improve stability. The feature map ϕ is made as a one-layer MLP as ϕ MLP ( x ) := exp( W ⊤ 1 x ) , where the matrix W 1 , W 2 ∈ R d × d .

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 to 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-finetuning ( 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 in 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, as summarized in Tab. 1. 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 alignment during preprocessing to facilitate consistent training across diverse datasets for both our model and a broad range of baselines. In short, FAPEX itself is inherently agnostic to the number and configuration of input channels.

1 For 'ECoG/SEEG' datasets each subject has either sub-dural ECoG grids/strips or SEEG depth electrodes, never both.

Baselines. We compare our method against the following baselines, including 22 supervised baselines for RQ1 and 10 self-supervised ones for RQ2 . The supervised baselines include (1) Convolutional models (5 baselines): ModernTCN [10], MRConv [7], MultiresNet [43], Omni-Scale [48], and SPaRCNet [21]; (2) Token mixers (6 baselines): EEGConformer [44], iTransformer [32], Nonformer [31], PatchTST [37], Pathformer [6], and SeizureFormer [13]; (3) Time-frequency mixers (4 baselines): ATFNet [66], FreTS [67], NFM [24], and TSLANet [12]; (4) Multiscale token mixers (7 baselines): AdaWaveNet [ ? ], Medformer [55], MTST [75], Pyraformer [30], SimpleTM [5], TimesNet [60], and TimeMixer [54]. Self-supervised baselines include 6 non-contrastive models:

Brant [72], CBraMod [52], EEGPT [51], LaBraM [19], Neuro-BERT [58], VQ_MTM [16]; 4 contrastive models: BIOT [65], COMETS [56], MF-CLR [11], 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 F1 as the monitoring score as it captures the trade-off between reducing false alarms and maintaining high sensitivity. We adopt the Friedman test as a nonparametric omnibus for statistical significance with Bayesian post hoc comparison. Refer to App. H for details.

Model

BEIRUT

CANINE

FMCE

CTLE-RATLFP

HUP

RESPECT

SEN

F1

ROC

SEN

F1

ROC

SEN

F1

ROC

SEN

F1

ROC

SEN

F1

ROC

SEN

F1

ROC

SEN

F1

ROC

ModernTCN

83.4

83.1

85.0

84.8

84.0

73.4

79.6

89.3

88.7

69.2

74.0

89.5

68.7

72.6

80.3

71.3

70.3

67.3

70.0

75.0

80.0

MRConv

78.6

78.2

83.5

83.7

83.8

72.6

78.8

89.9

88.2

73.0

76.4

73.0

60.5

68.4

68.7

69.1

67.8

66.1

71.1

72.7

73.8

MultiresNet

73.3

72.8

74.7

64.8

72.0

70.8

75.8

82.5

83.3

63.0

68.8

87.1

67.1

71.7

80.1

65.3

63.8

65.5

62.4

75.2

61.7

Omni-Scale

72.6

71.5

83.1

65.3

71.9

73.2

79.1

84.1

83.7

75.8

78.3

72.5

51.9

65.1

75.7

70.7

68.7

67.1

69.2

73.3

75.7

SPaRCNet

71.1

71.6

79.1

85.9

84.7

74.0

60.4

67.7

65.9

72.2

75.5

67.5

43.6

48.2

50.8

61.6

60.2

62.8

73.7

81.3

63.0

EEGConformer

68.4

66.5

82.5

79.3

81.4

52.9

73.0

85.0

81.4

73.5

76.8

72.3

58.5

65.8

70.2

64.6

63.3

64.6

82.5

84.6

86.5

EEGMamba

70.0

68.5

82.6

79.6

81.2

53.2

68.9

95.5

85.7

62.0

68.0

89.5

63.7

70.7

80.7

63.2

61.3

62.8

79.6

80.0

73.0

iTransformer

70.6

69.2

82.8

64.2

70.4

71.2

68.4

80.0

78.3

56.2

62.6

75.6

40.9

46.0

49.4

58.3

57.7

57.4

80.5

84.7

87.9

Nonformer

68.6

63.4

75.2

60.7

64.9

70.3

74.9

82.6

86.5

72.6

76.3

80.9

64.2

74.4

76.1

62.1

61.9

62.4

74.1

78.7

81.6

PatchTST

71.9

72.5

79.3

77.6

80.6

72.8

74.2

91.8

86.6

73.3

76.5

72.0

50.2

50.4

52.6

70.8

69.3

67.5

86.5

86.9

82.2

Pathformer

67.6

64.1

81.7

65.9

72.3

71.8

77.9

91.2

88.9

80.4

81.3

82.8

68.7

73.0

80.1

65.7

65.2

66.3

76.9

79.9

82.7

SeizureFormer

67.0

60.2

79.8

78.8

81.8

53.5

73.6

78.8

79.3

56.6

63.0

84.5

65.6

73.2

68.2

59.7

59.4

61.0

83.1

85.0

74.3

ATFNet

76.0

74.6

79.4

62.8

70.9

71.3

73.4

81.3

82.7

54.1

60.7

78.2

40.0

44.9

50.0

64.5

60.4

63.6

78.4

82.9

85.7

FreTS

64.7

58.6

81.8

46.8

54.3

69.5

62.0

68.3

61.4

49.2

56.5

68.5

34.9

38.6

49.4

62.6

50.1

57.2

64.0

72.5

78.4

NFM

77.3

75.7

79.7

71.5

76.9

72.0

74.4

91.8

86.4

46.5

52.5

74.0

37.3

43.0

48.8

62.7

63.4

64.4

75.0

77.0

80.8

TSLANet

83.4

83.1

85.0

85.7

84.4

73.0

74.2

91.8

86.6

65.3

70.7

88.9

68.6

72.2

79.9

67.9

66.5

67.5

74.3

78.7

76.2

AdaWaveNet

68.0

66.1

82.7

79.8

81.3

52.9

76.6

82.6

87.3

55.2

61.4

83.6

54.1

66.2

76.2

64.0

63.2

64.4

78.2

84.1

66.6

Medformer

83.8

83.1

84.4

85.9

84.5

74.1

77.8

83.6

88.6

70.0

74.3

86.7

66.7

72.3

80.6

64.8

64.3

65.0

59.7

68.0

70.5

MTST

80.3

78.4

84.1

68.0

74.5

72.5

75.5

89.3

87.7

70.8

74.7

69.5

45.3

49.6

50.4

65.9

64.4

66.2

79.4

82.9

82.2

Pyraformer

82.8

81.7

85.4

80.8

82.3

72.7

67.0

96.3

79.8

60.9

66.9

86.5

60.2

72.1

76.2

60.5

58.2

58.9

64.0

72.5

78.4

SimpleTM

82.6

82.0

83.4

82.8

83.3

72.5

74.4

80.5

80.6

72.5

76.0

70.9

47.5

52.0

51.1

67.8

65.2

68.5

74.5

77.7

70.0

TimesNet

70.3

70.6

78.4

67.3

74.1

72.3

67.0

74.6

73.4

63.4

69.0

74.2

47.1

49.4

51.5

65.9

61.7

65.4

64.2

63.4

76.9

TimeMixer

71.8

72.3

79.0

76.6

80.0

73.0

78.8

82.9

84.5

69.0

73.8

87.9

66.2

72.0

80.6

67.1

66.2

67.3

72.1

76.5

81.9

FAPEX-Small

(SL)

83.9

83.8

85.2

85.8

84.7

74.2

87.4

90.6

97.0

76.9

80.2

89.9

69.3

73.4

81.2

72.6

72.0

78.3

86.2

87.1

89.3

FAPEX-Base

(SL)

84.7

84.3

85.8

86.0

84.7

74.5

88.8

90.7

97.2

81.8

83.2

91.2

71.7

76.1

81.0

73.7

72.5

79.3

92.3

92.3

91.6

Brant

71.0

71.7

78.9

93.2

92.7

96.6

75.2

74.7

86.8

72.1

76.3

83.6

56.8

68.6

75.8

64.0

63.2

63.9

70.6

70.4

76.0

CBraMod

83.9

83.5

85.5

90.8

90.6

98.7

79.2

79.9

88.8

82.0

81.9

82.8

69.3

74.9

68.4

56.5

54.4

79.6

62.1

69.5

67.6

EEGPT

63.9

73.3

71.9

93.4

92.9

98.5

68.8

68.9

74.7

58.7

64.6

86.2

65.1

71.5

80.5

61.3

58.8

58.8

76.8

82.2

60.4

Neuro-BERT

85.4

85.2

86.9

93.7

93.2

96.8

77.9

78.1

87.7

72.7

76.8

85.5

68.6

73.8

81.5

56.5

54.4

79.6

67.3

74.6

82.4

VQ_MTM

74.5

75.0

82.7

87.9

85.5

94.6

73.7

74.3

82.3

72.6

75.8

69.7

50.7

55.5

63.7

62.1

63.5

64.9

66.8

67.3

81.7

COMETS

86.2

86.0

87.3

93.9

93.4

98.2

76.1

76.3

87.1

74.2

77.4

83.7

53.4

61.6

68.6

65.2

64.1

66.4

76.3

81.5

75.6

MF-CLR

78.2

76.5

83.8

91.2

90.0

97.0

79.5

80.1

88.5

66.6

71.8

88.5

47.6

51.3

50.6

67.1

66.2

67.3

76.3

82.2

76.8

TS2Vec

57.1

67.0

58.7

94.7

94.5

97.5

75.5

74.5

87.7

72.0

75.3

77.8

59.7

64.1

51.8

58.9

51.6

56.7

79.6

82.6

78.5

FAPEX-Small

87.5

86.7

90.0

94.1

93.7

98.4

89.5

89.6

97.5

84.8

86.2

90.4

72.0

75.8

81.2

72.0

72.1

79.4

79.0

82.3

89.8

FAPEX-Base

87.8

87.3

89.9

95.2

94.9

99.7

91.5

91.5

98.0

85.2

86.5

90.6

78.9

83.7

75.2

77.1

77.2

81.1

93.1

94.6

95.2

3.2 Main results

Performance comparison.(RQ1 and RQ2). Tab. 2 and 3 present the results for supervised and selfsupervised pretraining regimes. Across 12 datasets, our approach achieves top-1 Sensitivity (SEN) and F1 scores on all 12 datasets and top-1 ROC on 10 out of 12 datasets under the subject-dependent 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 Neuro-BERT , 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-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 is available; (4) MME [41] and CDAC [28], two domain adaptation methods. Similar to (3), only 1% target domain labels are utilized. Fig. 4 shows the relative improvement in relative gains ( ∆ %)

of FAPEX -Base over Neuro-BERT and CBraMod in median F1. FAPEX -Base consistently achieves positive ∆ %in F1 across diverse cases. It excels in the SOT setup, with ∆ %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 -Base still outperforms or matches them in most cases, despite the narrowing gap and occasional datasetspecific 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.

Relative

Performance Gain (%)

Dataset (Source   Target)

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-FrNFO, APCE, and SCA-on seizure prediction performance, providing insights into their individual and collective impacts (see App. D). We further explored the representational

characteristics and interpretability of FAPEX (see App. B). These analyses offer deeper insights into the model's decision-making processes and its alignment with known neural patterns.

4 Conclusion

We presennt FAPEX , a 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 phase-amplitude disentanglement and interpretability will be prioritized to enhance clinical trust and impact.

5 Acknowledgments

This work was supported by the Science and Technology Innovation 2030 - Brain Science and Brain-Inspired Intelligence Project (Grant No. 2021ZD0201301), the National Key Research and Development Program of China under Contract (Grant No. 2024YFA1610900), the National Natural Science Foundation of China (Grant Nos. 9257020, U20A20221, 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. SIMIS-ID-2025-NC). The computations were performed on the CFFF platform of Fudan University.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\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.\n\nQUESTIONS:\n0.\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?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: 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.\n\nQUESTIONS:\nSince 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.\n\nLIMITATIONS:\nPlease see above.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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.\n\nQUESTIONS:\nAlthough the paper is using balanced metric like balanced accuracy, ROC, F1 etc, it would be great to report false positives like precision or specificity.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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.\n\nQUESTIONS:\n1.\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.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}