Large language models (LLMs) have achieved remarkable performance across various reasoning tasks. However, many LLMs still encounter challenges in reasoning, especially for LLMs with fewer parameters or insufficient pre-training data. Through our experiments, we identify that noise accumulation across layers often leads to unstable token predictions during reasoning. We find that contrasting the probability distributions across layers effectively mitigates this interference. Building on this insight, we propose Adaptive Layer-Wise contrastive decoding (ALW), a novel framework that enhances reasoning ability by dynamically disentangling noise in shallow layers from critical signals in deep layers. Extensive experiments on several reasoning benchmarks demonstrate that ALW consistently improves answer accuracy across multiple LLMs while maintaining inference efficiency. For example, we achieve a 48% improvement on the Gsm8k using the LLaMA-7B model and an absolute accuracy increase of 5.2 points on the BBH evaluation benchmark with the LLaMA-65B model.

Large language models (LLMs) have demonstrated exceptional performance in reasoning tasks with dedicated Chain-of-Thought (CoT) prompts. Further enhancing CoT prompts with exquisite exemplars can significantly improve reasoning performance.However, the effectiveness of CoT prompts may fluctuate dramatically with different choices of in-context examples. Additionally, manual construction of rationale steps can be time-consuming, presenting challenges for the widespread adoption of CoT prompting. In this work, we propose a novel approach by introducing information entropy (IE) as a criteria on for CoT prompt selection. We extend this criterion to the CoT generation and inference stages, automatically generating CoT prompts with higher information entropy scores and adaptively determining the number of samples. These three stages together form our proposed information- entropy-based multi-step reasoning for large language models, named INFORM. Our experiments across seven reasoning benchmarks utilizing two language models(GPT-3.5-Turbo and text-davinci-003) demonstrate the superiority of INFORM both in performance and efficiency.