Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods (2502.01618v4)

Abstract: 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.

• The paper proposes recasting LLM inference-time scaling as a probabilistic inference task solved with particle-based Monte Carlo methods instead of traditional search optimization.
• Applying Particle Filtering empirically shows 4-16 times greater scaling efficiency compared to deterministic search on math reasoning tasks.
• This probabilistic approach enabled a smaller model (Qwen2.5-Math-1.5B) to outperform GPT-4o using only four computational rollouts, demonstrating potential for resource efficiency.

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

The paper explores the nuanced challenge of enhancing the performance of LLMs at inference time, by adopting a probabilistic inference framework. Traditionally, LLMs have exhibited remarkable gains in capability predominantly through scaling the models or datasets. However, the marginal improvements from merely increasing model sizes and data appear to diminish, especially when faced with complex tasks requiring substantial computational resources. The authors of this paper shift the approach by recasting inference-time scaling as a probabilistic inference task using particle-based Monte Carlo methods rather than conventional search optimization methods reliant on reward models.

A key argument presented is that existing inference-time scaling techniques, which formulate the task as a search problem using reward models, often succumb to reward hacking due to approximation inaccuracies in the models. This paper innovates by treating the inference-time scaling challenge within the context of a probabilistic framework, leveraging sampling-based techniques. In doing so, it aims to explore the typical set of the state distribution of a state-space model with an approximate likelihood, contrasting with the mode optimization of the distribution characteristic of search-based methods.

The researchers introduce a novel methodology applying particle-based Monte Carlo methods, specifically Particle Filtering (PF), to this task. Monte Carlo methods provide a mechanism of probabilistic inference that incorporates both diversity in exploration and boundary constraints that curtail reliance on potentially flawed reward models. The empirical results substantiate the efficacy of this probabilistic approach; the methods developed show a scaling efficiency 4--16 times greater than deterministic search counterparts on mathematical reasoning tasks. Significantly, the application of this method with the Qwen2.5-Math-1.5B-Instruct model achieves performance surpassing that of the GPT-4o with only four computational rollouts.

This work articulates a strong case for a paradigmatic shift in inference-time scaling for LLMs. There is a systematic alignment between probabilistic inference and scaling, enabling enhanced performance of smaller LLMs to match or exceed the capabilities of much larger models. By integrating the strengths of particle-based Monte Carlo methods, the paper establishes a connection between probabilistic inference and the scalability of LLMs, opening avenues for the development of more efficient and robust algorithms for AI systems.

The implications are manifold. Practically, the advancements promise more efficient utilization of computational resources, making high-performance AI accessible even with non-trivial hardware. Theoretically, bridging probabilistic inference with inference-time scaling presages a richer toolkit for cryptographic AI operations and, possibly, a pivot towards more dynamics-driven AI model training and deployment systems. Future research could explore further optimizations in Monte Carlo methods fine-tuned for diverse LLM architectures and extend the framework to encompass other model types and tasks beyond mathematical reasoning.

In conclusion, the paper sets forth a compelling proposition in AI research, especially in maximizing the utility of LLMs during inference. The innovations outlined here present a promising frontier in the pursuit of scalable, efficient AI systems, adapting fundamental principles from probabilistic modeling to potentially transformative effect in the performance of LLMs.