标题： 探测语言模型中的算术错误 显示英文标题

标题： Probing for Arithmetic Errors in Language Models

摘要： 我们研究了语言模型中的内部激活是否可用于检测算术错误。 从一个受控的三位数加法设置开始，我们表明简单的探测器可以准确地从隐藏状态中解码模型的预测输出和正确答案，无论模型的输出是否正确。 在此基础上，我们训练了轻量级的错误检测器，以超过90%的准确率预测模型的正确性。 然后我们将分析扩展到仅加法的GSM8K问题的结构化思维链痕迹，并发现针对简单算术训练的探测器在这一更复杂的设置中表现良好，揭示了一致的内部表示。 最后，我们证明这些探测器可以引导对错误推理步骤的选择性重新提示，以最小的干扰提高任务准确性。 我们的研究结果表明，仅从内部激活就可以预见算术错误，并且简单的探测器为轻量级模型自我纠正提供了一条可行的路径。 显示英文摘要

摘要： We investigate whether internal activations in language models can be used to detect arithmetic errors. Starting with a controlled setting of 3-digit addition, we show that simple probes can accurately decode both the model's predicted output and the correct answer from hidden states, regardless of whether the model's output is correct. Building on this, we train lightweight error detectors that predict model correctness with over 90% accuracy. We then extend our analysis to structured chain-of-thought traces on addition-only GSM8K problems and find that probes trained on simple arithmetic generalize well to this more complex setting, revealing consistent internal representations. Finally, we demonstrate that these probes can guide selective re-prompting of erroneous reasoning steps, improving task accuracy with minimal disruption to correct outputs. Our findings suggest that arithmetic errors can be anticipated from internal activations alone, and that simple probes offer a viable path toward lightweight model self-correction.