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Compression-Driven Abstraction Under Limited Inference: A Resource-Rational Account of Rules, Chunks, and Symmetries

Creative Commons 'BY' version 4.0 license
Abstract

Humans can show abrupt gains in learning and problem solving, e.g., discovering a rule or forming a chunk. We propose a process-level account in which an agent selects among representation families by minimizing a two-part minimum description length (MDL) objective augmented with an explicit inference-cost penalty. Bounded inference is modeled as budgeted search with sparse top-k routing (limited consideration), yielding a retained-mass diagnostic _k that predicts when truncation changes choices. The framework yields simple threshold conditions for when rules, macros, and symmetry codes become worthwhile, predicting step-like changes as experience accumulates under fixed resources. Minimal simulations reproduce key signatures, including compute–coverage tradeoffs and symmetry-threshold scaling with group size. Large language model (LLM) experiments further show a semantic–exact dissociation in symmetry learning and candidate-set bottlenecks consistent with limited consideration.