Sheaf cohomology explains when predictive coding networks stall, NeurIPS paper shows

burny_tech · x · 2026-09-15

Jeffrey Seely's NeurIPS 2025 workshop paper reformulates linear predictive coding (PC) networks as cellular sheaves: the sheaf coboundary maps activations to edge-wise prediction errors, and PC inference is diffusion under the sheaf Laplacian. Sheaf cohomology then characterizes irreducible error patterns that inference cannot remove.

Key findings: recurrent feedback loops create internal contradictions producing prediction errors unrelated to supervision; Hodge decomposition determines when these contradictions stall learning; and the formalism doubles as a diagnostic tool and a design principle for weight initialization. In the thread, darthur praises the λi integration of the sheaf coboundary residual as a neat route to PI-controller behavior and asks about accelerating gluing dynamics with a local-rate derivative term.

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