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Large language models (LLMs) demonstrate impressive language understandingand contextual learning abilities, making them suitable for natural languageprocessing (NLP) tasks and complex mathematical reasoning. However, whenapplied to mathematical reasoning tasks, LLMs often struggle to generatecorrect reasoning steps and answers despite having high probabilities for thesolutions. To overcome this limitation and enhance the mathematical reasoningcapabilities of fine-tuned LLMs without additional fine-tuning steps, wepropose a method that incorporates Monte Carlo Tree Search (MCTS) and alightweight energy function to rank decision steps and enable immediatereaction and precise reasoning. Specifically, we re-formulate the fine-tunedLLMs into a Residual-based Energy Model (Residual-EBM) and employ noisecontrastive estimation to estimate the energy function's parameters. We thenutilize MCTS with the energy function as a path verifier to search the outputspace and evaluate the reasoning path. Through extensive experiments on twomathematical reasoning benchmarks, GSM8k and AQUA-RAT, we demonstrate theexceptional capabilities of our method, which significantly improves the pass@1metric of the fine-tuned model without requiring additional fine-tuning orreinforcement learning with human feedback alignment.

No Train Still Gain. Unleash Mathematical Reasoning of Large Language Models with Monte Carlo Tree Search Guided by Energy Function