Thermodynamic Focusing for Inference-Time Search: Practical Methods for Target-Conditioned Sampling and Prompted Inference

This paper introduces the Inverted Causality Focusing Algorithm (ICFA), a novel approach to address the challenge of finding rare but useful solutions in large candidate spaces, particularly relevant to language generation, planning, and reinforcement learning. ICFA leverages target-conditioned reweighting, reusing existing samplers and similarity functions to create a focused sampling distribution. The paper provides a practical recipe for implementation, a stability diagnostic, and theoretical justification for its effectiveness. The inclusion of reproducible experiments in constrained language generation and sparse-reward navigation strengthens the claims. The connection to prompted inference is also interesting, suggesting a potential bridge between algorithmic and language-based search strategies. The adaptive control of focusing strength is a key contribution to avoid degeneracy.