Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model’s distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt.

Introduction. Humans tend to think for longer on difficult problems to reliably improve their decisions [9, 17, 18]. Can we instill a similar capability into today’s large language models (LLMs)? More specifically, given a challenging input query, can we enable language models to most effectively make use of additional computation at test time so as to improve the accuracy of their response? In theory, by applying additional computation at test time, an LLM should be able to do better than what it was trained to do. In addition, such a capability at test-time also has the potential to unlock new avenues in agentic and reasoning tasks [28, 34, 47]. For instance, if pre-trained model size can be traded off for additional computation during inference, this would enable LLM deployment in use-cases where smaller on-device models could be used in place of datacenter scale LLMs. Automating the generation of improved model outputs by using additional inference-time computation also provides a path towards a general self-improvement algorithm that can function with reduced human supervision.

Discussion / Conclusion. In this work, we conducted a thorough analysis of the efficacy of different techniques that aim to either improve search against a verifier or to refine an LLM’s proposal distribution, for scaling test-time compute for math reasoning. In general, we found that the efficacy of a given approach heavily correlates with the difficulty of the problem from the perspective of the base LLM’s capabilities. This motivated us to introduce the notion of “compute-optimal” scaling of test-time computation, which prescribes a adaptive, prompt-dependent strategy to improve performance under a given test-time compute budget. By applying such a compute-optimal scaling strategy, we find that can improve the efficiency of test-time compute scaling by a factor of 2 −4×.