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Large language models (LLMs) have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. We demonstrate that with carefully designed prompts, LLMs can accurately carry out key calculations in research papers in theoretical physics. We focus on a broadly-used approximation method in quantum physics: the Hartree-Fock method, requiring an analytic multi-step calculation deriving approximate Hamiltonian and corresponding self-consistency equations. To carry out the calculations using LLMs, we design multi-step prompt templates that break down the analytic calculation into standardized steps with placeholders for problem-specific information. We evaluate GPT-4’s performance in executing the calculation for 15 papers from the past decade, demonstrating that, with the correction of intermediate steps, it can correctly derive the final Hartree-Fock Hamiltonian in 13 cases. Aggregating across all research papers, we find an average score of 87.5 (out of 100) on the execution of individual calculation steps. We further use LLMs to mitigate the two primary bottlenecks in this evaluation process: (i) extracting information from papers to fill in templates and (ii) automatic scoring of the calculation steps, demonstrating good results in both cases.
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Two Failures of Self-Consistency in the Multi-Step Reasoning of LLMs
Large language models (LLMs) have achieved widespread success on a variety of in-context few shot tasks, but this success is typically evaluated via correctness rather than consistency. We argue that self-consistency is an important criteria for valid multi-step reasoning in tasks where the solution is composed of the answers to multiple sub-steps. We propose two types of self consistency that are particularly important for multi-step reasoning – hypothetical consistency (a model’s ability to predict what its output would be in a hypothetical other context) and compositional consistency (consistency of a model’s final outputs when intermediate sub-steps are replaced with the model’s outputs for those steps). We demonstrate that multiple variants of the GPT-3/-4 models exhibit poor consistency rates across both types of consistency on a variety of tasks.
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- Award ID(s):
- 2046556
- PAR ID:
- 10542787
- Publisher / Repository:
- OpenReview
- Date Published:
- Journal Name:
- Transactions on machine learning research
- ISSN:
- 2835-8856
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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