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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. 

The recent striking success of deep neural networks in machine learning raises profound questions about the theoretical principles underlying their success. For example, what can such deep networks compute? How can we train them? How does information propagate through them? Why can they generalize? And how can we teach them to imagine? We review recent work in which methods of physical analysis rooted in statistical mechanics have begun to provide conceptual insights into these questions. These insights yield connections between deep learning and diverse physical and mathematical topics, including random landscapes, spin glasses, jamming, dynamical phase transitions, chaos, Riemannian geometry, random matrix theory, free probability, and nonequilibrium statistical mechanics. Indeed, the fields of statistical mechanics and machine learning have long enjoyed a rich history of strongly coupled interactions, and recent advances at the intersection of statistical mechanics and deep learning suggest these interactions will only deepen going forward.