arXiv:2607.01010 2026 Architecture 2 ideas extracted · analyzed Aug 30, 2026
The paper replaces the usual general-position assumption in hyperplane capacity calculations with geometry-sensitive bounds based on intrinsic subspaces and supports. Its transferable asset is a way to estimate classification capacity from the effective dimension of learned representations rather than their ambient width. A practical neural-network use is to regularize or gate intermediate features so that their Cover-style separability capacity is sufficient for the task but not unnecessarily large. The paper also defines an ambiguity probability for query points, which can become a geometry-aware uncertainty or boundary regularizer.
Regularize an intermediate neural representation according to its estimated low-dimensional separability capacity instead of its ambient feature width. Learn feature gates or subspace assignments, estimate the union of active supports, and penalize representations whose Cover capacity exceeds a task-dependent target.
Estimate how often a representation lies on a separating hyperplane for alternative separable dichotomies, and use this quantity as a boundary-concentration penalty. Unlike a single classifier margin, the score measures whether many admissible separators consider the point ambiguous.