Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods

TL;DR

This paper introduces a probabilistic inference approach using particle-based Monte Carlo methods to improve inference-time scaling of large language models, achieving significant efficiency gains over traditional search methods.

Contribution

It presents a novel probabilistic inference framework for LLM scaling at inference time, connecting probabilistic inference techniques with LLM optimization.

Findings

Achieves 4-16x better scaling than deterministic search methods.

Qwen2.5-Math-1.5B-Instruct surpasses GPT-4o accuracy in 4 rollouts.

Qwen2.5-Math-7B-Instruct reaches o1 accuracy in 32 rollouts.

Abstract

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code, videos, and further information available at https://probabilistic-inference-scaling.github.io.