arXiv:2601.21601v2 Announce Type: replace Abstract: Neural networks adapt through first-order parameter updates, yet it remains unclear whether such updates preserve logical coherence. We investigate the geometric limits of the Linear Propagation Assumption (LPA), the premise that local updates coherently propagate to logical consequences. To formalize this, we adopt relation algebra and study three core operations on relations: negation flips truth values, converse swaps argument order, and composition chains relations. For negation and converse, we prove that guaranteeing direction-agnostic
The paper investigates fundamental limitations in neural network dynamics at a time when 'autonomous' AI systems are being deployed, making the robustness of their underlying logic critical.
Understanding the geometric limits of logical coherence in neural networks is crucial for developing truly reliable and agentic AI systems, impacting their safety and efficacy.
This research shifts focus from simply training powerful models to scrutinizing the foundational assumptions of how these models learn and maintain logical consistency during adaptation.
- · AI safety researchers
- · Developers of provably robust AI
- · Formal methods in AI
- · Developers of unverified autonomous AI
- · Approaches relying solely on empirical performance
- · Overly simplistic interpretations of AI learning
Further research will be spurred into the theoretical underpinnings of neural network logical propagation and stability.
This could lead to new architectural designs or training methodologies that explicitly account for and preserve logical coherence.
The development of highly reliable, complex AI agents, underpinning the next generation of autonomous systems, could be significantly advanced or limited by these foundational insights.
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Read at arXiv cs.LG