让模型理解数学中的人类沟通意图，提升可解释性与自然性
Models Can and Should Embrace the Communicative Nature of Human-Generated Math
- 将数学视为人类交流的产物，而非纯符号系统
- 模型对等号的理解呈现人类式差异，不同表达生成不同应用题
- 模型偏好自然流畅的证明顺序，即使逻辑等价也更倾向人性表达
数学是人创作给人看的：如同语料库不仅反映命题，也体现语言使用者的交际意图，训练模型所用的数学数据也不仅包含理想化的数学对象，更蕴含丰富的沟通目的。尽管纯符号化处理数学有其优势，本文提出，将数学视为情境化的语言交流更为有益，而语言模型恰好适合这一目标，当前对其潜力认识尚不充分。通过两个案例验证：第一，实验发现语言模型以人类方式理解等号——对同一方程的不同排列生成系统性不同的应用题；第二，模型更偏好自然顺序的证明，即使其他顺序在逻辑上等价。我们主张，人工智能应学习并表征人类数学中的隐含沟通意图。
原文摘要 · Abstract (English)
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical entities but rich communicative intentions. While there are important advantages to treating math in a purely symbolic manner, we here hypothesize that there are benefits to treating math as situated linguistic communication and that language models are well suited for this goal, in ways that are not fully appreciated. We illustrate these points with two case studies. First, we ran an experiment in which we found that language models interpret the equals sign in a humanlike way -- generating systematically different word problems for the same underlying equation arranged in different ways. Second, we found that language models prefer proofs to be ordered in naturalistic ways, even though other orders would be logically equivalent. We advocate for AI systems that learn from and represent the communicative intentions latent in human-generated math.
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