In plain words: Instead of doing the math itself, the language model writes a short program that lays out the reasoning, and a computer runs it to get the answer. Across math and finance question sets, this beat the usual step-by-step approach by about 12% on average.
Abstract · Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks
Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought' process. To disentangle computation from reasoning, we propose `Program of Thoughts' (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github https://github.com/wenhuchen/Program-of-Thoughts
Wenhu Chen, Xueguang Ma, Xinyi Wang, William W. Cohen
arXiv:2211.12588 · cs.CL, cs.AI · submitted Nov 22, 2022 · updated Oct 23, 2023
abstract · pdf · html · Published at TMLR 2023
I think the intuition that lots of people jumped to early about how "specs are the new code" was always correct, but at the same time it was absolutely nuts to think that specs can be represented in good ways with natural language and bullet-lists in markdown. We need chain-of-spec that's leveraging something semi-formal and then iterating on that representation, probably with feedback from other layers. Natural-language provides constraints, guess-and-check code generation is sort at the implementation level, but neither are actually the specification which is the heart of the issue. A perfect intermediate language will probably end up being something pretty familiar that leverages and/or combines existing formal methods from model-checkers, logic, games, discrete simulations, graphs, UML, etc. Why? It's just very hard to beat this stuff for compression, and this is what all the "context compaction" things are really groping towards anyway. See also the wisdom about "programming is theory building" and so on.
I think if/when something like that starts getting really useful you probably won't hear much about it, and there won't be a lot of talk about the success of hybrid-systems and LLMs+symbolics. Industry giants would have a huge vested interest in keeping the useful intermediate representation/languages a secret-sauce. Why? Well, they can pretend they are still doing something semi-magical with scale and sufficiently deep chain-of-thought and bill for extra tokens. That would tend to preserve the appearance of a big-data and big-computing moat for training and inference even if it is gradually drying up.