A Probabilistic Inference Approach to Inference-Time Scaling of LLMs
  using Particle-Based Monte Carlo Methods
Authors: name: Isha Puri, name: Shivchander Sudalairaj, name: Guangxuan Xu, name: Kai Xu, name: Akash Srivastava

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 and further information is available at
https://probabilistic-inference-scaling.github.io.