AI 与机器学习2024arxiv.org编辑精选
理解 LLM 中数学推理的局限性
Understanding the Limitations of Mathematical Reasoning in LLMs
入门 · 约 45 分钟读完前置知识：大语言模型基础、GSM8K 基准的了解
导读
这篇论文（Apple 团队的 GSM-Symbolic 研究）系统检验了大模型在小学数学应用题上的"推理"是否稳健：仅把题目中的人名、数字替换成同分布的变体（GSM-Symbolic），各模型准确率就明显下滑；再插入与解题无关、但看似相关的句子（GSM-NoOp），性能进一步大幅下降（论文报告的降幅可达数十个百分点）。作者据此认为当前模型做的是模式匹配而非真正的形式推理，并提出应关注推理的稳健性而非单一基准分数。
HN 关注点：它用简单的扰动实验直击"LLM 到底会不会推理"这一争议话题，且结论与许多人的日常使用体验相呼应。
后来怎么样
GSM-Symbolic 成为评估大模型数学推理稳健性的常用基准，被后续大量论文引用，'模式匹配而非真正推理'的结论引发广泛讨论。
HN 评论精选
这几条评论里：质疑 1 补充 2 亲历 1
补充以教学经验类比：多步串联和无关信息同样会拖垮人类学生，LLM 的表现约等于中等水平的高中毕业生。
我不对 LLM 是否真的在"推理"表态，但我要说这种性能下降和我在大一学生身上看到的情况很像（我目前在教微积分，近一半学生高中修过 AP 微积分）。他们做简单题没问题，但要求把多步——哪怕每步都很简单——串起来，准确率就下降、方差变大（我没有数据判断这种下降是否像论文假设的那样随步数线性变化）。往题目里加入无关信息时也是类似：很多学生被训练成必须用上题目给的所有信息，如果漏用 instructor 给的条件，那大概说明你漏了重要步骤。所以我不评判 LLM 做的算不算推理，但我确实认为 GPT-4o 这类 SOTA 模型的表现大约相当于智力中等的美国高中毕业生。也就是说，普通美国人在推理上的局限和好模型相似。这让我对人类表现有点失望，但对 LLM 算是好消息——它们做不了研究生级别的研究，却已经能帮到很大一部分人。
parsimo2010查看英文原文
I won't take a strong stance on whether or not LLMs actually do reasoning, but I will say that this decrease in performance is similar to what I see in college freshmen (I'm currently teaching a calculus course in which almost half of the students took AP calc in high school). They perform well on simple questions. Requiring students to chain multiple steps together, even simple steps, results in decreased accuracy and higher variance (I have no data on whether this decrease is linear or not, as the paper assumes that the decrease should be linear with the number of steps). We see similar results with adding unrelated statements into a problem- many students are trained to make sure to use all given information in solving a problem- if you leave out something that the instructor gives you, then you probably forgot to do something important. So while I don't take a stance on what an LLM does should be considered reasoning, I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence. In other words, average Americans exhibit similar limitations on their reasoning as good LLMs. Which on the one hand is a little disappointing to me in terms of the human performance but is kind of good news for LLMs- they aren't doing graduate-level research but they are already capable of helping a large portion of the population.
质疑质疑结论：题目出现无关/反常信息时，人类也会合理假设是笔误而非严格照字面推理，因此这不算 LLM 的致命缺陷。
这篇论文的发现之一是：给基础代数题加上无关信息后，LLM 的表现会急剧恶化。例子像这样："John 周一摘了 43 个猕猴桃，周二摘了 24 个。周三他摘的猕猴桃里有 5 个比平常小。周一到周三他总共摘了 87 个。他周三摘了多少个？"其中"周三有几个偏小"是无关信息，但加入这类内容后，GPT-4o 在某流行基准上的成绩从 95% 掉到 77%。我不觉得很了不起。先不谈 LLM：假设你自己读到这种带无关信息的题，你必须考虑两种可能——这句无关信息本可以不写，或者题目写错了、那句其实本该是相关的。后一种完全有可能，我认为假定它正确并不算严重失败。坦白说，看到有些人给 LLM 出的"整蛊题"——把经典逻辑题的条件反过来——我觉得我自己也会答"错"，不是因为我没理解题意，而是没有上下文时我会以为反转是笔误。
woopwoop查看英文原文
This paper, among other things, shows that LLMs have dramatically worse performance on basic algebra questions when you add in irrelevant information. The examples are things like "John picked 43 kiwis on Monday, 24 kiwis on Tuesday. On Wednesday, 5 of the kiwis he picked were smaller than usual. Altogether, on Monday, Tuesday, and Wednesday, John picked 87 kiwis. How many kiwis did John pick on Wednesday?" In this question, the remark about some of the kiwis on Wednesday being small is irrelevant, but adding things like this reduces performance on a popular benchmark from 95% to 77% for GPT-4o, for example. I don't find this very impressive. Forget LLMs for a second. Let's say _you_ read a question of that kind with some bit of irrelevant information. There are two possibilities you have to consider: the question may as well have excluded the irrelevant information, or the question was miswritten and the irrelevant information was meant to be relevant. The latter is a perfectly live possibility, and I don't think it's a dramatic failure to assume that this is correct. I have to confess that when I read some people's LLM gotcha questions, where they take some popular logic puzzle and invert things, I think I would get them "wrong" too. And not wrong because I don't understand the question, but wrong because with no context I'd just assume the inversion was a typo.
补充追问合成数学数据是否已被大规模用于训练、以及是否真正有效。
为数学生成海量合成数据似乎极其容易。有人在做吗？有效吗？
dr_dshiv查看英文原文
It seems incredibly easy to generate an enormous amount of synthetic data for math. Is that happening? Does it work?
亲历亲历验证：给经典逻辑谜题换一个本体（狼换成牛），模型能说清规则却解不出。
我实测过 LLM，结果类似。比如经典的农夫带卷心菜、山羊和狼过河的谜题，至少从 GPT-2 起模型就能解；但如果把狼换成牛，GPT-4o 虽然能正确推断出谜题的规则，却解不出来。
yk查看英文原文
I test llms actually similar. For example there is a well known logic puzzle were a farmer tries to cross a river with a cabbage a goat and a wolf. Llms can solve that since at least GPT-2, however if we replace the wolf with a cow, gpt-o does correctly infer the rules of the puzzle but can't solve it.
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