Sen Song

Jinhao Li, Zhiyuan Ma, Xueqiao Han et al.

Electroencephalography (EEG) foundation models aim to learn reusable representations from large-scale unlabeled recordings. A common pretraining strategy is masked waveform reconstruction, but applying supervision directly to noisy EEG may encourage models to recover predictable background activity, acquisition effects, and artifacts rather than neural structure that transfers across tasks. This raises a central question: what should an EEG foundation model predict to learn transferable representations? We introduce EEG-JEPA a structured latent-prediction framework for EEG foundation modeling. Rather than reconstructing masked voltage samples, a masked context encoder and predictor infer contextual latent states produced by an exponential-moving-average target encoder that observes the complete input. EEG-JEPA organizes target design along three complementary dimensions: target content specifies what representation is predicted, target support specifies where prediction occurs over structured electrode--time regions through Neurotopology-Aware Multi-scale Electrode-Temporal Masking (N-MET), and target depth specifies at which encoder layers supervision is applied. Together, these designs shift EEG pretraining from recovering missing measurements to inferring latent states from structured electrode--time context. We evaluate EEG-JEPA through controlled objective comparisons, frozen multitask transfer, and full fine-tuning. Under the same backbone, pretraining corpus, and training duration, EEG-JEPA improves the 14-task frozen macro balanced accuracy from 40.49% to 50.42% over CBraMod-style masked waveform reconstruction. Multi-source continuation further raises this result to 52.94%, the highest average among the EEG foundation models evaluated on EEG-FM-Bench. Under protocol-matched full fine-tuning, EEG-JEPA also improves the nine-task average balanced accuracy from 68.98% to 70.65%.

Sen Song

All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al. (2021) proved causes representational rank to decay doubly exponentially with depth in pure self-attention stacks. We develop a theoretical framework that targets this structural limitation at the mathematical level by replacing the flat Euclidean metric with learned per-token Riemannian metrics. Our contributions are threefold. (1) We prove that Riemannian attention scores with heterogeneous per-token metrics are non-Gram---they cannot be factorized as QK^T with factorization dimension O(d). We are explicit that this is a structural observation, not a proof of rank preservation. (2) We establish that low-rank metric factors render all geometric operations tractable: geodesic distance in O(d*r) per token and metric inversion in O(d*r^2) via the Woodbury identity---both far below the O(d^3) cost of a general matrix---making Riemannian attention feasible at billion-parameter scale with negligible overhead. (3) We present the Fiber Bundle Transformer, a complete architecture specification in which each token position carries its own Riemannian metric, attention is geodesic distance computation, feed-forward updates use metric-preconditioned steps, and the connection carries explicit curvature and torsion proxies. We derive formal predictions about correctly implemented geometric architectures and identify the central open problem: proving or disproving that heterogeneous Riemannian metrics prevent the rank collapse that row-stochastic attention matrices otherwise cause. This paper presents theoretical analysis and architectural design; empirical validation is the subject of future work.