arXiv:2605.20534v1 Announce Type: new 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 c
The increasing complexity and pervasive application of deep neural networks necessitate a deeper theoretical understanding that extends beyond empirical successes, pushing researchers to develop foundational frameworks.
A foundational, axiomatic understanding of neural networks could unlock new capabilities, improve reliability, and accelerate development by moving beyond empirical trial-and-error.
The introduction of an axiomatic framework like Pursuit of Subspaces signals a potential methodological shift towards more theoretically grounded AI research, moving away from 'black box' intuitions.
- · AI researchers (mathematical AI)
- · AI ethics and safety organizations
- · Developers of provably robust AI
This work prompts further theoretical research into the geometric and algebraic foundations of neural network behavior.
Improved theoretical understanding could lead to the design of more efficient, interpretable, and reliable AI architectures.
A fully axiomatized neural network theory might enable formal verification of AI systems, expanding their use in safety-critical applications.
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Read at arXiv cs.LG