小模型算术推理靠抄最后数字,逻辑步骤其实没用。
The Readout Shortcut: Positional Number Copying Dominates Arithmetic CoT Readout in Small Language Models
- 模型直接复制答案前最后一个数,不看推理过程。
- 正确率54-92个百分点来自抄答案,95-96%的错误也抄最后数。
- 适合评估算术推理模型时警惕位置作弊,别信表面逻辑。
小语言模型进行算术推理需链式思考(CoT)提示,但打乱步骤后性能几乎不变。在三个1-3B指令微调模型上,我们通过前缀补全分离出答案读取阶段,发现存在位置捷径:模型总是复制答案分隔符前的最后一个数字,无论中间推理是否正确。真实答案出现贡献了54-92个百分点的准确率(占各模型教师强制上限的89-92%);即使在错误样本中,最终答案与最后一个推理数匹配率达95-96%。复制通道优先于上下文补全:替换最后一个数为错误值会导致准确率跌至接近零,即便中间步骤正确;而移除该数后,准确率仍能回升5-32个百分点——哪怕单步算术本可正常完成,只要存在可复制数字,就会被抑制。Qwen和Llama会87-95%地复制新干扰项;Gemma则选择性屏蔽。头级消融显示不同架构有特定头部参与;该现象在GSM-Symbolic上复现。非算术BBH任务中,打乱保留率急剧下降;7-8B模型开始出现内容选择性屏蔽。步骤级忠实度评估可能将位置传输出错误判为真实计算,是基于CoT监督的失效模式。
原文摘要 · Abstract (English)
Chain-of-thought (CoT) prompting is necessary for arithmetic in small language models, yet shuffling its steps preserves most performance. What does CoT contribute if not logical sequencing? In three 1-3B instruction-tuned LMs on GSM8K, we isolate the answer-readout stage via prefix completion and identify a positional shortcut: the model copies whichever number occupies the trailing position before the answer delimiter, regardless of intermediate reasoning. Gold-answer presence accounts for 54-92 pp of accuracy (89-92% of each model's teacher-forcing ceiling); even on incorrect items, the final answer matches the last CoT number 95-96% of the time. The copy channel takes precedence over retained-context completion: replacing the trailing number with a wrong value collapses accuracy to near-zero despite correct intermediates, yet removing it recovers 5-32 pp above that floor--even single-step arithmetic the model can otherwise perform is suppressed when a copyable number is present. Qwen and Llama copy novel distractors 87-95% of the time; Gemma gates selectively. Head-level ablation implicates architecture-specific head sets; the effect replicates on GSM-Symbolic. On non-arithmetic BBH tasks, shuffle retention drops sharply; at 7-8B, content-selective gating emerges. Step-level faithfulness evaluations risk conflating positional answer transport with genuine computation--a failure mode for CoT-based oversight.
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