Induction and Inquiry via Probabilistic Reasoning over Language and Code

Real world decision-making requires constructing mental models under uncertainty over evidence, over the underlying causal rules, and over the state of the world itself. Which computational principles underpin human inference under such conditions, and do LLM-based agents exhibit similar behavior given matching constraints? We address these questions using an inductive inference Box Task in which participants, human children and LLM-based agents, infer a latent cause through sequential interaction with an uncertain environment. We formalize this task as program induction with Bayesian particle-based inference, admitting two complementary interpretations: (1) as a constraint satisfaction process over hypotheses, and (2) as a program synthesis problem in which hypotheses are executable programs evaluated against evidence. Using the constraint-based formulation, we show that children's behavior is best explained by a combination of subjective evidence reliability and online hypothesis generation, accounting for both their evidence-seeking patterns and their dissociation between task completion and rule generalization. Using the program synthesis formulation, we treat LLM-based agents as model organisms: controllable systems that allow systematic manipulation of task conditions. Across backends, LLM-based agents replicate children's responses to changes in evidence reliability and observability, including discounting unreliable evidence, seeking to resolve partial information, and dissociating between task completion and causal generalization. At the same time, LLM-based agents tend to over-observe and over-comply with instructions relative to children. These results suggest that while children and LLM-based agents adapt similarly to environmental structure, their information-seeking behavior exhibits distinct underlying costs and inductive biases.

Modern language models (LMs) can learn to perform new tasks in different ways: in instruction following, the target task is described explicitly in natural language; in few-shot prompting, the task is specified implicitly with a small number of examples; in instruction inference, LMs are presented with in-context examples and are then prompted to generate a natural language task description before making predictions. Each of these procedures may be thought of as invoking a different form of reasoning: instruction following involves deductive reasoning, few-shot prompting involves inductive reasoning, and instruction inference involves abductive reasoning. How do these different capabilities relate? Across four LMs (from the gpt and llama families) and two learning problems (involving arithmetic functions and machine translation) we find a strong dissociation between the different types of reasoning: LMs can sometimes learn effectively from few-shot prompts even when they are unable to explain their own prediction rules; conversely, they sometimes infer useful task descriptions while completely failing to learn from human-generated descriptions of the same task. Our results highlight the non-systematic nature of reasoning even in some of today's largest LMs, and underscore the fact that very different learning mechanisms may be invoked by seemingly similar prompting procedures.

Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable. Yet, many real-world reasoning problems are inductive: agents must infer uncertain beliefs from sparse, ambiguous observations. There are challenges to using standard fine-tuning methods for inductive reasoning, including difficulties in curating large-scale, high-quality labeled datasets and in handling targets that are inherently distributional. In this work, we introduce a novel approach, called Program-based Posterior Training (PPT), to address these limitations: we use an LLM to generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses to queries, and then fine-tune on these probabilistic soft labels. Using this approach, we fine-tune LLMs on 10,000 programmatically generated scenarios and evaluate on held-out motifs, human-labeled judgments, and external benchmarks. Overall, PPT substantially improves estimation accuracy on held-out inductive tasks, increases alignment with human judgments, and transfers to external benchmarks for estimation and calibration. Additionally, the gains in raw calibration are not subsumed by post-hoc temperature scaling, showing that the models have more deeply internalized uncertainty compared to output rescaling. Together, these results suggest that probabilistic-program-mediated fine-tuning is a promising approach for post-training LLMs to reliably perform approximate inductive inference.