Axiomatizing Neural Networks via Pursuit of Subspaces
The paper introduces the Pursuit of Subspaces (PoS) hypothesis, an axiomatic framework for understanding neural networks. This framework aims to bridge the gap between the empirical success of deep learning and its theoretical foundations. By formulating neural network behavior through geometric postulates, the authors provide insights into representation, computation, and generalization in neural architectures.
- ▪The PoS hypothesis offers a unified perspective on neural network behavior.
- ▪It formulates neural network behavior through a set of geometric postulates.
- ▪The framework addresses fundamental questions in deep learning, including representation structure and generalization behavior.
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Computer Science > Machine Learning arXiv:2605.20534 (cs) [Submitted on 19 May 2026] Title:Axiomatizing Neural Networks via Pursuit of Subspaces Authors:Mehmet Yamac, Mert Duman, Ugur Akpinar, Felix Rojas Casadiego, Serkan Kiranyaz, Marcel van Gerven, Moncef Gabbouj View a PDF of the paper titled Axiomatizing Neural Networks via Pursuit of Subspaces, by Mehmet Yamac and 6 other authors View PDF HTML (experimental) 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.
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