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

TL;DR

This paper introduces ICFA, a practical framework for target-conditioned sampling that improves search efficiency in large candidate spaces across language generation and reinforcement learning tasks.

Contribution

The paper presents ICFA, a novel reweighting-based search method with adaptive focusing, theoretical insights, and practical implementations for various inference tasks.

Findings

ICFA reduces sample requirements in constrained language generation.

ICFA improves sparse-reward navigation performance.

Structured prompts can approximate ICFA's focusing mechanism.

Abstract

Finding rare but useful solutions in very large candidate spaces is a recurring practical challenge across language generation, planning, and reinforcement learning. We present a practical framework, \emph{Inverted Causality Focusing Algorithm} (ICFA), that treats search as a target-conditioned reweighting process. ICFA reuses an available proposal sampler and a task-specific similarity function to form a focused sampling distribution, while adaptively controlling focusing strength to avoid degeneracy. We provide a clear recipe, a stability diagnostic based on effective sample size, a compact theoretical sketch explaining when ICFA can reduce sample needs, and two reproducible experiments: constrained language generation and sparse-reward navigation. We further show how structured prompts instantiate an approximate, language-level form of ICFA and describe a hybrid architecture combining prompted inference with algorithmic reweighting.