Stochastic Separability of Embedding Manifolds
Neurobiological studies and representation learning have observed that representations of objects belonging to the same category in high-dimensional neural spaces exhibit low-dimensional object manifold characteristics, and different object manifolds are linearly separable in these neural spaces. However, these experimentally observed phenomena lack rigorous theoretical validation to date. This paper proposes a new stochastic separability theorem for embedding manifolds of two different object categories. First, we establish a projection measure concentration theorem for embedding manifolds under general conditions. We develop a new two-layer measure concentration analysis technique, whic...
| Authors | Liqing Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 24 August 2026 |
| Last updated at source | 24 August 2026 |
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