Axiomatizing Neural Networks via Pursuit of Subspaces
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Computer Science > Machine Learning
Title:Axiomatizing Neural Networks via Pursuit of Subspaces
Abstract: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 that this framework yields geometric explanations for fundamental questions in deep learning, including representation structure, architectural mechanisms, and generalization behavior, offering a principled step toward a coherent theoretical foundation.
| Comments: | 43 pages, 25 figures. Code and additional materials will be released |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2605.20534 [cs.LG] |
| (or arXiv:2605.20534v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.20534
arXiv-issued DOI via DataCite (pending registration)
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