Axiomatizing Neural Networks via Pursuit of Subspaces
Authors: Mehmet Yamac, Mert Duman, Ugur Akpinar et al.
Summary
arXiv:2605. 20534v1 Announce Type: cross 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.
Relevance
Read next because Axiomatizing Neural Networks via Pursuit of Subspaces overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: class, under, stage. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.20534v1 Announce Type: cross 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.