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Human language offers a powerful window into our thoughts -- we tell stories, give explanations, and express our beliefs and goals through words. Abundant evidence also suggests that language plays a developmental role in structuring our learning. Here, we ask: how much of human-like thinking can be captured by learning statistical patterns in language alone? We first contribute a new challenge benchmark for comparing humans and distributional large language models (LLMs). Our benchmark contains two problem-solving domains (planning and explanation generation) and is designed to require generalization to new, out-of-distribution problems expressed in language. We find that humans are far more robust than LLMs on this benchmark. Next, we propose a hybrid Parse-and-Solve model, which augments distributional LLMs with a structured symbolic reasoning module. We find that this model shows more robust adaptation to out-of-distribution planning problems, demonstrating the promise of hybrid AI models for more human-like reasoning., Comment: Originally accepted to the 2022 Cognitive Science (CogSci) conference

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search., 17 pages, 6 figs, replaced to match accepted NeurIPS version