No Train Still Gain. Unleash Mathematical Reasoning of Large Language Models with Monte Carlo Tree Search Guided by Energy Function
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Large language models (LLMs) exhibit impressive language understanding and in-context learning abilities including natural language processing (NLP) tasks and challenging mathematical reasoning. However, due to the lack of process-supervision, applying PLMs to mathematical reasoning tasks often fail to generate correct reasoning steps and final answer even though solutions have high probabilities. To unleash the mathematical reasoning of finetuned-LLMs without any further fineutuning steps, we propose a method to endow LLMs with immediate reaction and delicate reasoning system via Monte Carlo Tree Search(MCTS) and a light energy function to rank the decision steps. In particular, We first re-formalize the finetuned-LLMs to a Residual-based Energy Model (Residual-EBM) and apply noise contrastive estimation to estimate the parameters of energy function . Then we use MCTS with energy function as path verifier to search the output space and evaluating the reasoning path. Through extensive experiments on two mathematical reasoning benchmarks, namely GSM8k and MATH, we reveal the extraordinary capabilities of our method that improve the pass@1 of the finetuned-model without further finetuning or RLHF alignment by a substantial margin.
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