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home / papers / 2022 / Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Written for the Research library (claude-opus-5-5) from the paper text, in our own words: the license "arXiv — non-exclusive license to distribute" does not allow redistributing the text itself. Original — arxiv.org/pdf/2211.12588v4

Summary

Program of Thoughts (PoT) is a prompting method in which a large language model (mainly Codex, code-davinci-002) writes a short Python program instead of a verbal chain of reasoning. An interpreter then does the computation, using SymPy for equations when needed. The model is responsible only for breaking the problem into steps, while arithmetic, iteration and equation solving are handed to an exact executor. PoT rests on two principles. The first is multi-step decomposition: the program breaks an expression into intermediate variables. The second is semantic binding: the variables have meaningful names. There are few-shot and zero-shot variants. In the zero-shot variant, the "#" token is suppressed so the model does not drift into writing comments. PoT can also be combined with self-consistency, and a two-stage PoT→CoT mode is used for AQuA. The method is evaluated on five MWP datasets (GSM8K, AQuA, SVAMP, TabMWP, MultiArith) and three financial ones (FinQA, ConvFinQA, TATQA). For the subtask tree, the paper is a strong argument for our design: the model builds the structure of steps, and a separate exact core computes the numbers. The ablations show that both step decomposition and naming intermediate quantities give a substantial gain.

Key points

  • Features: the problem text; tables are linearized (columns separated by "|", rows by line breaks); named intermediate variables carry meaning.
  • Architecture: no training; a few-shot (4–8 examples) or zero-shot prompt to an LLM, followed by Python execution; self-consistency by voting.
  • Few-shot greedy results (Table 2): PoT-Codex — GSM8K 71.6, AQuA 54.1, SVAMP 85.2, TabMWP 73.2, FinQA 64.5, ConvFinQA 64.6, TATQA 69.0; Codex CoT — 63.1 / 45.3 / 76.4 / 65.2 / 40.4 / 45.6 / 61.4.
  • Results with SC: PoT-SC-Codex — GSM8K 80.0, AQuA 58.6, SVAMP 89.1, TabMWP 81.8; Codex CoT-SC — 78.0 / 52.0 / 86.8 / 75.4. With GPT-4: PoT — GSM8K 97.2, AQuA 84.4, SVAMP 97.4.
  • Zero-shot (Table 3): PoT — GSM8K 57.0, AQuA 43.9, SVAMP 70.8, TabMWP 66.5, MultiArith 92.2; zero-shot CoT (GPT-3) — 40.5 / 31.9 / 63.7 / 53.5 / 79.3.
  • Ablations (Table 6): on GSM8K, without variable names 60.2, direct equation generation 45.8, vs. 71.6; compared with PaL (Table 5) — SVAMP 85.2 vs 79.4, ASDiv 85.2 vs 79.6. Small open models (codegen-16B, xgen-7B) reach only 8–13 on GSM8K.
  • Limitations: errors on TATQA are 47% incorrect value grounding and 33% incorrect logic; AQuA remains hard; a sandbox is required for code execution.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Mathematics & statistics

Cited by

547 papers of our library cite it (of the 140673 whose bibliographies we read); 46 of them have a page here, 501 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2211.12588 · arXiv 2211.12588

@misc{chen2022program,
  title = {{Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks}},
  author = {Chen, Wenhu and Ma, Xueguang and Wang, Xinyi and Cohen, William W.},
  year = {2022},
  doi = {10.48550/arxiv.2211.12588},
  eprint = {2211.12588},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2211.12588}
}

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