Jeffrey Qin, Zhuangfei Gao, Wasu Top Piriyakulkij, Mia Radovanovic, Jessica Sommerville, Kevin Ellis, Marta Kryven
Children expertly construct mental models under uncertainty despite limited world knowledge. Which computational principles make this possible? We study this question in an interactive physical Box Task in which participants infer a latent cause through interaction with a stochastic and partially observed environment. The Box Task was originally designed to study children's puzzle-solving qualitatively. We contribute a computational analysis of behavior that formalizes the cognitive process by which children generate new hypotheses and respond to environmental uncertainty as inference unfolds. Our modeling framework is based on Bayesian particle-based inference, which maintains a small set of working hypotheses and continually generates new ones. We give two complementary implementations of hypothesis representations within this framework: (1) as constraints on evidence, and (2) as executable programs evaluated against evidence. Using the constraint-based formulation, we show that the model needs to account both for subjective reliability of evidence and online hypothesis generation to explain key signatures of children's behavior. Using the programmatic formulation, we show that hypotheses may take the form of partial compositional rules to guide information gathering when evidence interpretation is hard. The programmatic hypotheses are implemented using LLM-based program synthesis, evaluated across three prompt variants and several LLM backends, demonstrating robustness of our approach. Together, these results extend current models of children's inference to account for subjective reliability of evidence and open-ended hypothesis spaces, and provide a computational analysis of the form generated hypotheses may take in practice.
Simon Alford, Edward Gu, Omar Costilla-Reyes, Dan Tamayo, Miles Cranmer, Kevin Ellis
The problem of predicting when a multi-planet system will become dynamically unstable has defied analytical progress over the past three hundred years. Recent machine learning advances achieve high predictive performance of instability dynamics, but as black-box systems cannot be interpreted to connect to existing scientific understanding. Here we show analytic equations that predict when a multi-planet system will undergo instability. We discover these equations by first training a neural network on a dataset of N-body simulations, and then distilling its latent knowledge into closed-form algebraic expressions. Our two-stage pipeline first learns an interpretable variable basis, then searches for equations using symbolic regression. The resulting equations outperform existing analytic estimates of instability and apply across wide ranges of mass ratios, spacing, and orbital eccentricities. They capture structure in the prediction landscape with a small number of variables amenable to dynamical interpretation. These results demonstrate how symbolic learning can be combined with neural networks to extract scientific insight from complex dynamical systems.
Shuzhi Liu, Archana Warrier, Dat Nguyen, Chengqi Zheng, Kevin Ellis, Yewen Pu
Learning through exploration and using newly acquired knowledge to achieve goals are central capabilities of general intelligence. Understanding these capabilities requires tracing how learners build, use, and revise world models during interaction. We construct the first dataset that records how humans discover and use the mechanisms of novel environments, using ARC-AGI-3 as a testbed: 144 trajectories from 64 participants across 25 public games, each pairing time-synchronized actions with think-aloud audio, plus 250 trajectories from large language model (LLM) agents with and without harnesses on the same games. We annotate mechanism triggers and recognition, action purposes, and errors and recovery, linking changes in understanding to the observations and actions that support them. We analyze characteristics of human cognition and compare them with those of LLM agents. Both groups anticipate mechanisms and use familiar analogies. Qualitative representations are more common in successful human trajectories than in successful LLM trajectories (50.0% versus 14.3%). Humans more often explore unfamiliar situations without a concrete hypothesis, while hypothesis testing is common in both groups. We also trace how learners recover through belief revision, replanning, and execution correction. As LLMs with well-designed harnesses reach saturated performance on public ARC-AGI-3 games, our cognitive analyses motivate next-generation benchmarks that challenge familiar priors, require accumulated evidence and abstraction, and test planning through subgoals, experimentation, and recovery. Our dataset is available at [https://arc3-human-think-aloud.github.io/](https://arc3-human-think-aloud.github.io/).