Spectral Considerations on Unsupervised Time-domain EEG Representation Learning with Deep Networks
Authors: David Aquilué-Llorens, Abel Puigseslloses, Angel Blanco, Claire Braboszcz, Aureli Soria-Frisch
Organizations: Starlab Barcelona S.L., Neuroscience Business Unit, Barcelona, Spain · Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
Electroencephalography (EEG) is a non-invasive, scalable source of quantitative biomarkers for the early diagnosis of brain disorders, and deep representation learning has become a powerful paradigm for extracting information-rich latent features from raw signals. However, neural networks tend to under-represent high-frequency information, a concern that is especially acute for EEG given its oscillatory nature and characteristic 1/fχ power decay, which risks masking disease-relevant high-frequency signatures. In this study, we systematically investigate the spectral constraints of unsupervised time-domain feature extraction across three autoencoder architectures (LSTMVAE, VAEEG, Transformer) and a state-of-the-art EEG foundation model. Using synthetic experiments and empirical validation, we show that while autoencoders capture macro-scale shifts such as alpha slowing, they remain biased against higher frequencies due to a magnitude-driven masking effect induced by the Mean Squared Error loss under 1/f-decaying spectra. Increasing latent dimensionality mitigates this attenuation but sacrifices latent compactness and generative stability. We argue that, as the field advances toward large-scale foundation-level feature extractors, it is imperative to move beyond simple time-domain reconstruction and to integrate spectral-domain loss terms and gradient-balancing techniques, so that the subtle high-frequency transients critical for diagnosing complex brain disorders are preserved in the latent representation.
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Figure 1: Performance Evaluation on Synthetic EEG Datasets. (a) Characterization of Synthetic Datasets: The upper (middle) panels display the group-specific Power Spectral Density (PSD), averaged across channels and subjects within the validation partition for the α ( β/γ ) datasets. The lower panels show representative 2-second EEG segments for the three simulated midline channels across both datasets. (b) Reconstruction Fidelity across Latent Dimensions: Model performance is reported as 1−MSE (where 1 indicates perfect reconstruction) on the held-out test partition. Results are shown for the LSTMVAE (upper), VAEEG (middle), and Transformer (lower) architectures as a function of the latent space dimensionality ( NLS ) and dataset type. (c) Latent Space Discriminative Power: Classification accuracy on the held-out test partition of a non-linear MLP trained to predict diagnostic group (HC, SCD, MCI, AD) from the latent embeddings. Accuracy is reported for the LSTMVAE, VAEEG, Transformer, and REVE (top to bottom), across varying latent dimensions. (d) provides a detail-view of REVE’s high accuracy. Theoretical chance accuracy (25%) is denoted by the horizontal red dashed line. Error bars indicate 95% confidence interval.
Figure 2: UMAP Projections of Latent Space Embeddings ( NLS=50 ). Two-dimensional UMAP visualizations of the latent manifolds learned by the LSTMVAE (left), VAEEG (middle), and Transformer (right) architectures. The upper row displays projections for the α slowing dataset, while the lower row represents the β/γ slowing dataset. Each point corresponds to a multi-channel EEG segment from the held-out test partition, color-coded by the synthetic diagnostic group (HC, SCD, MCI, AD) to illustrate the degree of class-wise clustering and separability within the learned latent space.
Figure 3: Spectral Learning Order Synthetic experiment adapted from Rahaman et al. [ 44 ] illustrating the evolution of frequency learning as a function of training progress. The heatmaps represent spectral fidelity, defined as the ratio between the reconstructed and target amplitudes for each frequency component ( f∈{5,10,…,50} Hz). A ratio of 1 (yellow) indicates successful reconstruction (hence encoding), while a ratio of 0 (blue) indicates the component has not yet been captured. Two scenarios are compared across the three architectures (LSTMVAE, VAEEG, and Transformer) with NLS=50 : the equal-amplitude condition ( Ai=1 , upper panels), isolating architectural bias; and the decaying-amplitude condition ( Ai∝1/fi0.75 , lower panels), simulating the power distribution of empirical EEG to observe magnitude-driven masking effects.
Figure 4: Spectral Organization of the LSTMVAE Latent Space for the held-out test partition of the BBHI Dataset. (a) UMAP projections of the latent embeddings color-coded by the grand-average (average over all channels) relative power within standard EEG frequency bands: theta ( 4−8 Hz), alpha ( 8−13 Hz), and beta ( 13−30 Hz). (b) Topographically resolved UMAP projections of alpha relative band power for the LSTMVAE (upper) and REVE (lower) models. Color-coding alpha band power is the result of averaging alpha band power over different sets of channels: Frontal (F7, F3, Fz, F4, F8), Temporal (T7, T8), and Central (C3, Cz, C4). These projections aim to illustrate the emergence of spectral and spatial representational structure within the unsupervised latent manifold.
Figure 5: Frequency-resolved spectral decay across reconstruction autoencoders as a function of latent space dimension ( NLS ), evaluated on the held-out test partition of the BBHI dataset. Power spectral densities (PSDs) of target 2-second EEG windows from the BBHI dataset (black) are compared against the PSDs of reconstructed outputs for the LSTMVAE (top, red gradient), VAEEG (middle, blue gradient), and Transformer (bottom, green gradient) models. Three latent space dimensions are shown, NLS={50,250,500} , with color intensity increasing from lighter to darker shades as NLS increases. Higher NLS improves high-frequency reconstruction fidelity, particularly for the Transformer architecture.
Figure 6: UMAP Projections of Latent Space Embeddings ( NLS=250 ). Two-dimensional UMAP visualizations of the latent manifolds learned by the (left to right) LSTMVAE, VAEEG, Transformer, and REVE architectures. The upper row displays projections for the α slowing dataset, while the lower row represents the β/γ slowing dataset. Each point corresponds to a multi-channel EEG segment from the held-out test partition, color-coded by the synthetic diagnostic group (HC, SCD, MCI, AD) to illustrate the degree of class-wise clustering and separability within the learned latent space.
Figure 7: Spectral Learning Order - Reconstruction Examples Evolution of reconstructed segments in the synthetic experiment adapted from Rahaman et al. [ 44 ] illustrating the evolution of frequency learning as a function of training progress in the equal-amplitude condition ( Ai=1 ) across three architectures: LSTMVAE (upper panels), VAEEG (middle panels), and Transformer (lower panels), all with NLS=50
Figure 8: UMAP projection of LS embeddings for LSTMVAE NLS=50 , coloured by demographic information (sex, age, and cognitive performance measured with MMSE)
Figure 9: UMAP projection of LS embeddings for REVE Base NLS=512 , coloured by demographic information (sex, age, and cognitive performance measured with MMSE)
Figure 10: Spectral Learning Order Study on REVE . For Figure details, refer to Figure 3 in the manuscript.
Figure 11: Spectral Learning Order Study on LSTMVAE and Transformer reconstruction autoencoders with a modified masked autoencoding objective . For Figure details, refer to Figure 3 in the manuscript.
Figure 12: Topographical Mapping of Spectral Decay in the held-out test partition of the BBHI Dataset for LSTMVAE (upper left), VAEEG (upper right), and Transformer (lower). Regional distribution of band-specific spectral attenuation ( ΔPdB ) as a function of increasing latent space dimensionality ( NLS ). Results are shown for the delta, theta, alpha, beta, and gamma bands across the scalp. Lighter hues indicate minimized attenuation (higher reconstruction fidelity), whereas darker hues denote regions of significant power loss, highlighting the spatial and spectral dependencies of the LSTMVAE. reconstruction process.
Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen, China · Omni-Intelligence, Shenzhen, China · College of Design and Engineering, National University of Singapore, Singapore +4
Ming Hsieh Department of Electrical and Computer Engineering1 University of Southern California · Thomas Lord Department of Computer Science2[cs.LG] University of Southern California · Department of Mathematical Sciences3 Aalborg University