Axiomatizing Neural Networks via Pursuit of Subspaces
While deep neural networks have achieved remarkable success across a wide range of domains, their underlying mechanisms remain poorly understood, and they are often regarded as black boxes. This gap between empirical performance and theoretical understanding poses a challenge analogous to the pre-axiomatic stage of classical geometry. In this work, we introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic framework that formulates neural network behavior through a set of geometric postulates. These axioms, together with their derived consequences, provide a unified perspective on representation, computation, and generalization in both shallow and deep architectures. We show tha...
| Authors | Mehmet Yamac, Mert Duman, Ugur Akpinar et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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