研究揭示 Transformer 算术学习的“破碎组合性”反直觉规律
Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic
AI 导读
一项 arXiv 研究在合成算术任务上训练 Transformer，发现其习得技能的顺序是反向或并行的，而非人类式的序列规则，作者称之为“破碎组合性”。研究认为，学习动态由与训练数据的相关性匹配塑造，而非因果或程序性组合，这导致部分习得的技能相互竞争，产生混合错误并在分布偏移下更脆弱。这种定性行为在现代 LLM 中同样存在，且无法通过单纯的模型扩展或 scratchpad 监督缓解。
正文 · 原文
Abstract:Large language models (LLMs) often achieve strong benchmark accuracy yet remain brittle under small distribution shifts. While recent mechanistic studies reveal the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill acquisition and the role of data distributions remain elusive. In this study, we train transformers on synthetic arithmetic tasks with black-box model-agnostic metrics for analyzing non-human skill compositions. We discover that transformers often acquire skills for arithmetic in reverse order or in parallel instead of human-like sequential rules--a phenomenon we refer to as shattered compositionality. To explain these behaviors, we provide evidence that correlational matching to the training data, rather than causal or procedural composition, shapes learning dynamics. As a consequence, this non-human acquisition creates competition between partially learned skills, producing characteristic mixing errors and weaker robustness under controlled distribution shifts. We further show that the same qualitative behavior persists in modern LLMs and is not mitigated by pure model scaling or scratchpad supervision. Our results highlight a mismatch between training-time skill acquisition and the human-like hierarchical compositions, with implications for reasoning reliability and out-of-distribution robustness.
| Comments: | 37 pages, 29 figures |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| ACM classes: | I.2.6; I.2.7 |
| Cite as: | arXiv:2601.22510 [cs.LG] |
| (or arXiv:2601.22510v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.22510 arXiv-issued DOI via DataCite |
Submission history
From: Xingyu Zhao [view email]
[v1]
Fri, 30 Jan 2026 03:38:54 UTC (5,693 KB)
[v2]
Sat, 8 Aug 2026 23:41:54 UTC (764 KB)
[v3]
Tue, 10 Nov 2026 21:38:03 UTC (966 KB)
来源：arXiv cs.AI · arxiv.org