Wild Guesses and Mild Guesses in Active Concept Learning
Anirudh Chari, Neil Pattanaik
TL;DR
Active concept learning with LLM-generated hypotheses faces a proposal bottleneck imposed by the generator's support. The authors formulate a neuro-symbolic Bayesian learner using a particle posterior and compare an approximate EIG strategy to a Positive Test Strategy (PTS). They show that EIG can cause proposal-support collapse in simple concepts, while PTS maintains proposal validity and accelerates convergence, highlighting a generator-induced stability benefit at the cost of optimal information gain. They identify a 'support-mismatch trap' and argue for generator-aware acquisition and meta-policies that switch strategies, linking cognitive notions of confirmation sampling to tractable inference in sparse open-ended hypothesis spaces with implications for robust neurosymbolic AI.
Abstract
Human concept learning is typically active: learners choose which instances to query or test in order to reduce uncertainty about an underlying rule or category. Active concept learning must balance informativeness of queries against the stability of the learner that generates and scores hypotheses. We study this trade-off in a neuro-symbolic Bayesian learner whose hypotheses are executable programs proposed by a large language model (LLM) and reweighted by Bayesian updating. We compare a Rational Active Learner that selects queries to maximize approximate expected information gain (EIG) and the human-like Positive Test Strategy (PTS) that queries instances predicted to be positive under the current best hypothesis. Across concept-learning tasks in the classic Number Game, EIG is effective when falsification is necessary (e.g., compound or exception-laden rules), but underperforms on simple concepts. We trace this failure to a support mismatch between the EIG policy and the LLM proposal distribution: highly diagnostic boundary queries drive the posterior toward regions where the generator produces invalid or overly specific programs, yielding a support-mismatch trap in the particle approximation. PTS is information-suboptimal but tends to maintain proposal validity by selecting "safe" queries, leading to faster convergence on simple rules. Our results suggest that "confirmation bias" may not be a cognitive error, but rather a rational adaptation for maintaining tractable inference in the sparse, open-ended hypothesis spaces characteristic of human thought.