大模型用十进制数位独立表示数字，解释了其算术错误模式。
Language Models Encode Numbers Using Digit Representations in Base 10
- 通过探针实验发现模型以十进制数位方式存储数字
- 错误集中在答案的各个数位上，而非数值整体偏差
- 为分析大模型数值推理机制提供新视角
大型语言模型（LLMs）在处理简单数值问题时频繁出错，例如比较两个小数。一种自然假设是这些错误源于模型对数字的表示方式，特别是其表示是否捕捉了数值本身。我们基于观察：模型在数值任务上的错误常分布于答案的各位数上，而非围绕数值均值。通过一系列探针实验和因果干预，我们证明大模型内部以十进制每一位的独立环形表示来存储数字。这种按位表示方式，而非整体数值表示，解释了模型在涉及数值推理任务中的错误模式，并可作为未来研究模型数值机制的基础。
原文摘要 · Abstract (English)
Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether their representations of numbers capture their numeric values. We tackle this question from the observation that LLM errors on numerical tasks are often distributed across the digits of the answer rather than normally around its numeric value. Through a series of probing experiments and causal interventions, we show that LLMs internally represent numbers with individual circular representations per-digit in base 10. This digit-wise representation, as opposed to a value representation, sheds light on the error patterns of models on tasks involving numerical reasoning and could serve as a basis for future studies on analyzing numerical mechanisms in LLMs.
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