Gauge-compatible tensors on statistical manifolds: splitting and submanifold geometry
arXiv:2608.31145
2026
Architecture
1 ideas extracted · analyzed Sep 2, 2026
What the math gives to ML
The paper provides a concrete compatibility law between dual affine connections: when the tensor Θ is Levi-Civita-parallel, the statistical difference operator K must anticommute with Θ. This is transferable as a structured neural interaction in which hidden channels are split into two eigenspaces and learned couplings are forced to cross between them. The most direct experiment is a paired residual block with shared within-stream processing and an exactly off-diagonal cross-stream operator, measuring both optimization stability and the predicted gauge identity.
Ideas from this paper
Unverified
2026
Replace an unconstrained hidden-to-hidden interaction in an MLP or transformer feed-forward block by two gauge-related branches. Split channels with an orthogonal involution Θ, constrain the learned interaction K to anticommute with Θ, and use opposite signs of K in paired branches. This creates a testable inductive bias in which the learned interaction only transfers information between the two channel subspaces.
Useful6/10
Difficulty5/10
Novelty8/10