← 研踪 PaperTrailarXiv:2610.38634 · v1
"Close enough?" An investigation into multiplication errors in LLMs
首次提交 2026-10-28 18:51
版本更新 2026-10-28 18:51
雷达观测 2026-10-30 10:22
摘要
Large language models (LLMs) frequently fail at multi-digit arithmetic, but the underlying mechanisms governing these failures remain poorly understood. While recent work demonstrates that addition errors follow a "noisy quantisation" model localised around carry boundaries, whether this framework generalises to multiplication remains an open question. In this work, we evaluate multiplication capabilities across several small base LLMs on a dataset of 16,991 problems spanning varied operand lengths. We show that multiplication errors do not conform to the addition-style noisy quantisation model. Instead, we uncover a novel error regime in small Qwen models: errors in lower-order columns predominantly preserve parity. Conversely, higher-order digit errors shift toward off-by-one carry failures. Our findings suggest that arithmetic computation in LLMs relies on distinct, multi-periodic internal representations where parity is tracked more robustly than exact digit identity, providing new mechanistic insights into numerical reasoning in transformers.
作者备注：Accepted to Neurips 2026 NewInML workshop
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v1 · 2026-10-28 18:51 · 最新观测版本
"Close enough?" An investigation into multiplication errors in LLMs
Large language models (LLMs) frequently fail at multi-digit arithmetic, but the underlying mechanisms governing these failures remain poorly understood. While recent work demonstrates that addition errors follow a "noisy quantisation" model localised around carry boundaries, whether this framework generalises to multiplication remains an open question. In this work, we evaluate multiplication capabilities across several small base LLMs on a dataset of 16,991 problems spanning varied operand lengths. We show that multiplication errors do not conform to the addition-style noisy quantisation model. Instead, we uncover a novel error regime in small Qwen models: errors in lower-order columns predominantly preserve parity. Conversely, higher-order digit errors shift toward off-by-one carry failures. Our findings suggest that arithmetic computation in LLMs relies on distinct, multi-periodic internal representations where parity is tracked more robustly than exact digit identity, providing new mechanistic insights into numerical reasoning in transformers.
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