arXiv:2606.03645v1 Announce Type: new Abstract: Large Language Models exhibit paradoxical fragility in fundamental arithmetic, implying a disconnect between internal computation and discrete output. By analyzing the residual stream geometry during multi-operand addition, we identify the Iso-Raw-Sum Trajectory (IRST), a geometric structure where representations are anchored by semantic digits and modulated by continuous carry fibers. We propose the Noisy Quantization Model to explain this geometry, framing arithmetic errors as Geometric Slippages caused by internal neural noise pushing a contin
This research provides a foundational understanding of how complex neural networks process basic arithmetic, building on increasing scrutiny of LLM reliability and interpretability.
Understanding the internal mechanisms and failure modes of Large Language Models in fundamental tasks like arithmetic is crucial for improving their robustness, trustworthiness, and applicability to sensitive operations.
This research shifts the understanding of LLM arithmetic from a 'black box' problem to one with identifiable geometric structures and quantifiable error mechanisms, enabling more targeted improvements.
- · AI researchers
- · ML interpretability tools
- · LLM developers
- · AI safety researchers
- · Overly simplistic LLM development approaches
Improved debugging and fine-tuning techniques for LLMs related to numerical reasoning.
Development of more robust and auditable AI systems for domains requiring precise calculations.
Enhanced trust in AI systems for critical applications, potentially accelerating AI integration into finance or engineering more broadly.
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Read at arXiv cs.LG