Decoupling Time and Space: A Temporally Conditioned Refinement for EEG Source Imaging

Marco Morik; Jesse Palarus; Carmen Vidaurre; Klaus-Robert Müller; Shinichi Nakajima

cs.LGOct 5, 2026

Decoupling Time and Space: A Temporally Conditioned Refinement for EEG Source Imaging

Authors: Marco Morik, Jesse Palarus, Carmen Vidaurre, Klaus-Robert Müller, Shinichi Nakajima

Organizations: Berlin Institute for the Foundations of Learning and Data, Germany · Machine Learning Group, Technische Universität Berlin, Germany · Basque Center on Cognition, Brain and Language, Mikeletegi Pasealekua, Spain · Ikerbasque, Bizkaia, Spain · Department of Artificial Intelligence, Korea University, Seoul, Korea · Max Planck Institut für Informatik, Saarbrücken, Germany · RIKEN AIP, Tokyo, Japan

Abstract

Electroencephalography (EEG) offers millisecond temporal resolution, but inferring underlying neural sources is a severely ill-posed spatial inverse problem. While deep learning has advanced spatial reconstruction, current architectures face a critical dilemma: frame-by-frame models discard vital temporal context, whereas full 4D spatiotemporal networks introduce an architectural trade-off between reconstruction accuracy and inference cost. We propose a novel two-stream framework that explicitly decouples global temporal representation learning from per-time-point spatial refinement. A Transformer-based Temporal Condition Encoder processes the entire EEG sequence via factorized spatiotemporal attention, retaining sensor-resolved features. A fixed inverse then maps these features into source-indexed conditioning for a per-timestep Source-Space Transformer or volumetric convolutional refiner. Extensive evaluations on realistic synthetic data demonstrate that this temporal prior dramatically improves spatial localization, outperforming classical and spatiotemporal baselines, particularly in high-noise and multi-source regimes. Training across diverse leadfields and explicit operator mismatches improves transfer to unseen head geometries and brings template-based reconstruction closer to subject-specific inversion. Furthermore, we apply the model trained only on synthetic EEG data to real-world EEG. A logistic regressor fit on source power differences in eyes-open, eyes-closed conditions successfully decodes age groups.

Figures & tables

Panel of Figure 1 — Fig. 1 : Temporal conditioning for source refinement. The novel Temporal Conditioning (+TC) path (highlighted in blue) applies the Temporal Condition Encoder $g_{\theta}$ to the full EEG sequence, alternates temporal and sensor attention, and unpatches features to an aligned sequence of condition vectors $\mathbf{c}$ . At each time point, the subject-specific eLORETA-inverse $\mathbf{L}_{j}^{\dagger}$ transports the EEG slice and each condition feature into source space. The refiner $f_{\theta}$ fuses these two source-space inputs to predict the final sources $\hat{\mathbf{x}}_{t}$ .

Space	Head model	$M$	$S$	# (train/eval)
Surface	LEMON [ 53 ]	61	516	127/10
	IBP2021 [ 54 ]	62	516	11/5
	fsaverage [ 55 ]	16-62	516	2-3/1
Volume	fsaverage [ 55 ]	16-62	599	3/1
Volume	IBP2021 [ 54 ]	62	461-641	11/5

TABLE I : Lead-field pools.

M

S

denote sensor/source-location counts, the final column counts training/evaluation lead fields. Surface and volume spaces use oct4 and 14-mm grids, respectively.

Fig. 2 : Reconstructed magnitudes at one active patch center on an unseen IBP2021 head at

5\text{\,}\mathrm{dB}

SNR. SoST+TC (ours), SoST, DeepSIF, and eLORETA process the same sequence. The displayed 0-500 ms window is taken from the 512-sample, 256 Hz record.

Surface source space
Method	NMAE	NEMD	Spatial NEMD	Temporal NEMD	Cosine Error	Params. (M)	Latency (ms)
SoST	0.824	1.023	0.804	0.572	0.354	16.5	489.8
SoST+TC	0.645	0.701	0.652	0.255	0.219	17.4	504.8
SoST+TC+OM	0.577	0.641	0.593	0.232	0.185	17.4	505.9
Deep CB [ 39 ]	0.889	0.844	0.819	0.404	0.380	$<0.1$	50.2
DeepSIF [ 19 ]	0.860	0.937	0.873	0.728	0.399	7.4	19.3

TABLE II : Aggregate reconstruction errors (lower is better) and computational cost. Evaluation uses 200 simulated sequences per head (512 samples at 256 Hz), with SNR, active patch count, and patch standard deviation sampled uniformly from

[-10,30]

dB,

\{1,\ldots,20\}

, and

[5,40]

mm, respectively. Within each surface seed, errors are averaged over ten held-out LEMON and five held-out IBP2021 heads separately, then equally across datasets, taking the mean over three training seeds. Volume rows average five held-out IBP2021 heads for one training seed. Runtime protocol: FP32, batch size one, 512 time points per forward call, 50 timed runs on an NVIDIA A100 80GB.

Fig. 3 : Robustness to sensor noise and source multiplicity. Rows show NMAE, spatial NEMD, and temporal NEMD. The SNR sweep (left) draws source counts uniformly from 1-10, the source-count sweep (right) fixes SNR at 5 dB. Each point first averages 15 equally weighted held-out heads (ten LEMON, five IBP2021) within each seed, then reports the mean

\pm

sample SD over three training seeds. Our proposed SoST+TC retains lower errors across both the evaluated noise and source-count settings.

Fig. 4 : Conditioning interventions on one held-out IBP2021 head, with 64 paired simulations per difficulty. Left: spatial NEMD, right: temporal NEMD. Positive deltas indicate worse errors than the intact input. Boxes show medians and interquartile range, and points show individual simulations. Interventions are zero initial source estimate input, zero condition, and time-shuffled condition. Easy/medium/hard use 15/5/ $-5$ dB SNR and 1/1-5/5-10 active sources.

Fig. 5 : Head-model generalization. A: NMAE (lower is better) averages ten held-out LEMON or five held-out IBP2021 heads in the respective columns, then reports seed mean $\pm$ sample SD over three seeds. Parentheses identify single-pool training. Specialists transfer less accurately across datasets, mixed training reduces transfer loss. Additionally, Operator Mixing improves the template inverse performance. B: Maps show full-epoch source-vector RMS divided by one common ground-truth maximum. The mismatched specialist underestimates activity and misses one of three active regions.

Fig. 6 : LEMON age-group decoding on 10 unseen test subjects, whose geometries were held out from source-model training. A: Descriptive older-minus-younger Cohen’s $d$ maps from these ten participants, using pooled within-age SD within the 4-35 Hz frequency band. B: Test balanced accuracy of separate logistic classifiers trained on 115 participants using one indicated band or total-power reactivity (516 source features, 61 raw-EEG features where missing electrodes use training-fold mean imputation). SoST+TC shows great age-group decoding.

Explore similar work

EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution
May 28, 2026Alex Lazarovich, Ofir Itzhak Shahar, Gur Elkin +1Electroencephalography Mixtures
Stein Faculty of Computer and Information Science Ben-Gurion University of the Negev, Israel
Transformer Based Model for Spatiotemporal Feature Learning in EEG Emotion Recognition
Jun 9, 2026Xinglong Cui, Dian GuElectroencephalography Spatiotemporal Representations
Beijing Neurodeep Technology Co., Ltd, Beijing, 100176, China · University of Pennsylvania, Seattle, 98121, USA
Not All EEG Moments Are Equal: Position-Adaptive Time Scheduling for EEG Generation
Jul 25, 2026Boheng Liu, Ziyu Li, Chenghua Duan +2Electroencephalography Conditional Flow Matching
School of Computer Science and Technology Beijing Institute of Technology Beijing, China

May 28, 2026, cs.LGJ/K move · Enter open · S save

EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution

Alex Lazarovich, Ofir Itzhak Shahar, Gur Elkin, Ohad Ben-Shahar

Stein Faculty of Computer and Information Science Ben-Gurion University of the Negev, Israel

Electroencephalography Mixtures

Open paper AskPDF arXiv

High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of Anisotropic Gaussians), a differentiable framework that reconstructs HD-EEG signals from a sparse subset of low-density (LD) electrodes by representing brain electrical sources as a mixture of anisotropic 4D space-time Gaussians. EMAG places a mixture of multiple Gaussians at each point of a spherical brain grid, each parameterized by a full 4 x 4 precision matrix, enabling anisotropic spatial spreads and explicit coupling between spatial and temporal dimensions. The forward model renders scalp EEG via differentiable Gaussian field contributions at electrode locations, enabling end-to-end training without explicit source localization supervision. We evaluate EMAG on three public EEG benchmarks (Localize-MI, SEED, and SEED-IV) at super-resolution factors of 2x through 8/16x. EMAG outperforms the current state-of-the-art EEG super-resolution method at most super-resolution factors on three standard benchmarks (Localize-MI, SEED, SEED-IV). The explicit Gaussian parameterization further enables direct visualization and interpretability of learned brain source configurations, potentially opening avenues for clinical and neuroscientific applications, such as source localization or biomarker discovery.

Abstract

Explore similar work

EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution

Transformer Based Model for Spatiotemporal Feature Learning in EEG Emotion Recognition

Not All EEG Moments Are Equal: Position-Adaptive Time Scheduling for EEG Generation