Separable Yet Inseparable: An EEG-oriented Head for Transformer-based Time-Series Generative Adversarial Networks

Technical Summary: Separable Yet Inseparable: An EEG-oriented Head for Transformer-based Time-Series Generative Adversarial Networks

Problem Statement
Synthetic electroencephalography (EEG) data offers a solution to critical challenges in neuroscience research, including data scarcity, class imbalance, and privacy constraints. However, existing generative models often fail to produce high-fidelity EEG signals that accurately reflect physiological characteristics. Current approaches frequently rely on architectures designed for generic time series or images, lacking specific mechanisms to model the spatiotemporal dynamics of brain activity. Furthermore, the evaluation of these models often utilizes metrics derived from natural image processing (e.g., Fréchet Inception Distance on time-frequency images), which the authors argue fail to capture the physiological discrepancies and noise characteristics inherent to EEG signals.

Methodology
The authors propose EEGGAN-SepH, an extension of the transformer-based Time Series Generative Adversarial Network (EEGGAN). The core innovation is the Separable Output Head (SepH), a lightweight module designed to convert the transformer's latent tokens into synthetic EEG trials while preserving physiological fidelity.

The SepH module consists of three sequential components:

1. Spatial Projection: The transformer output (embedding dimension $E$) is projected via a 2D convolution into $D \times C$ intermediate channels (where $C$ is the number of EEG channels). Crucially, this stage employs Group Normalization instead of Batch Normalization to prevent cross-sample dependencies during generation, followed by LeakyReLU activation.
2. Separable Convolution: Inspired by EEGNet, this block applies a depthwise convolution (kernel size 3) along the temporal dimension to learn local dynamics for each channel, followed by a pointwise convolution (kernel size 1) to mix information across channels and capture spatial dependencies.
3. Learnable Temporal Smoothing: To suppress high-frequency noise introduced by the generative process, a depthwise, learnable temporal smoothing filter is applied. The final output is a residual mix of the smoothed signal and the pre-smoothing signal ($x' = \alpha x_{smooth} + (1-\alpha)x$), where $\alpha$ is learned during training to balance noise suppression with signal preservation.

Evaluation Pipeline
The study introduces a rigorous evaluation pipeline that moves beyond standard image-based metrics. It computes the Fréchet Distance (FD) and Maximum Mean Discrepancy (MMD) on features extracted from:

• EEG-specific models: xDAWN (spatial filtering for evoked responses), EEGNet (task-discriminative features), and REVE (foundation model representations).
• Image-based models: Inception-v3 and CLIP (applied to Short-Time Fourier Transform images).

To validate the reliability of these metrics, the authors perform a Gaussian noise injection test, adding noise to real EEG trials and measuring the sensitivity of the metrics. A reliable metric should increase monotonically with noise levels.

Key Results
Experiments were conducted on two Event-Related Potential (ERP) datasets: a Reinforcement Learning (RL) dataset and the BCIAUT-P300 dataset.

• Generative Fidelity: EEGGAN-SepH consistently outperformed the baseline EEGGAN and its autoencoder-based variants across nearly all fidelity metrics. On the RL dataset, FD scores based on EEGNet features dropped by more than half (e.g., from 0.1297 to 0.0569 for the "Win" class against the test set). Qualitative analysis showed that EEGGAN-SepH produced cleaner Event-Related Potentials (ERPs) and spectra with significantly fewer high-frequency spikes compared to the baseline.
• Metric Sensitivity: The noise injection test revealed that standard FID computed on time-frequency images was largely insensitive to mild Gaussian noise. In contrast, FD and MMD computed on EEG-specific features (particularly EEGNet and REVE) responded consistently to noise levels, validating their use for synthetic EEG evaluation.
• Utility in Downstream Tasks: In a transfer learning setting on the BCIAUT-P300 dataset, pre-training on EEGGAN-SepH synthetic data improved classification performance (balanced accuracy and AUC) compared to pre-training on baseline EEGGAN data, particularly in low-data regimes (e.g., increasing balanced accuracy from 62.58% to 68.66% with limited fine-tuning data).
• Ablation Findings:
  • Replacing Group Normalization with Batch Normalization severely degraded performance, confirming the necessity of Group Normalization for generation stability.
  • Removing the learnable temporal smoothing filter improved image-based metrics (Inception/CLIP) but degraded EEG-specific metrics, highlighting a discrepancy between generic and domain-specific feature spaces.
  • The use of an auxiliary autoencoder (compressing signals before generation) degraded fidelity, suggesting that direct generation via SepH is superior for this architecture.

Significance and Claims
The paper claims that the proposed work addresses two primary gaps in the field:

1. Architectural Gap: It demonstrates that adding an EEG-oriented output head (SepH) to a transformer-based GAN significantly improves the physiological plausibility of synthetic data by modeling local temporal dynamics and suppressing high-frequency noise with minimal parameter overhead.
2. Evaluation Gap: It provides evidence that standard image-based metrics are insufficient for evaluating synthetic EEG. The authors advocate for the adoption of FD and MMD computed on features from EEG-specific models (like EEGNet and REVE) as the primary fidelity metrics, as they are more sensitive to noise and better reflect the physiological nature of the signal.

The authors conclude that EEGGAN-SepH generates synthetic data that effectively extends datasets for analysis and supports foundation model pre-training, though they acknowledge that a performance gap with real data persists and that future work should explore diffusion models and multi-channel spatial capabilities.