Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.

To enhance the reasoning capabilities of large language models (LLMs), self-consistency has gained significant popularity by combining multiple sampling with majority voting. However, the state-of-the-art self-consistency approaches consume substantial computational resources and lead to significant additional time costs due to the multiple sampling. This prevents its full potential from being realized in scenarios where computational resources are critical. To improve the inference efficiency, this paper introduces \textit{path-consistency}, a method that leverages the confidence of answers generated in earlier branches to identify the prefix of the most promising path. By dynamically guiding the generation of subsequent branches based on this prefix, the \textit{path-consistency} mitigates both the errors and redundancies from random or less useful sampling in self-consistency. As a result, it can significantly accelerate the inference process by reducing the number of tokens generated. Our extensive empirical evaluation shows that the \textit{path-consistency} achieves significant acceleration in inference latency ranging from $7.8\%$ to $40.5\%$, while maintaining or even improving task accuracy across different datasets, including mathematical reasoning, common sense reasoning, symbolic reasoning, and code generation.

As a way of communicating with users and any LLMs like GPT or PaLM2, prompting becomes an increasingly important research topic for better utilization of LLMs. Although simple prompting has great performance on single-step questions, it cannot always activate the correct knowledge path for multi-step reasoning tasks. The chain of thought (CoT), which often contains Zero-shot CoT and few-shot CoT, is a recently developed prompting method that is capable of explaining the reasoning process to the LLM and outperforms simple prompting in three challenging reasoning tasks, including arithmetic, symbolic, and common-sense reasoning. This paper proposes a code-level self-prompt Zero-shot CoT (SelfzCoT) that takes advantage of an entity node or reasoning path of representing knowledge to activate deeper knowledge of larger path lengths within LLM in a graph way. It is done with three iterative steps in the format of step-by-step reasoning that can be easily adjusted or extended to different kinds of tasks.

In the context of multi-step reasoning, e.g., with chain-of-thought, language models (LMs) can easily assign a high likelihood to incorrect steps. As a result, decoding strategies that optimize for solution likelihood often yield incorrect solutions. To address this issue, we propose Guiding chain-of-thought ReAsoning with a CorrectnEss Discriminator (GRACE), a stepwise decoding approach that steers the decoding process towards producing correct reasoning steps. GRACE employs a discriminator trained with a contrastive loss over correct and incorrect steps, which is used during decoding to score next-step candidates based on their correctness. Importantly, GRACE only requires sampling from the LM, without the need for LM training or fine-tuning. Using models from FLAN-T5 and LLaMA families, we evaluate GRACE over four math and two symbolic reasoning tasks, where it exhibits substantial performance gains compared to greedy decoding, verifiers, and self-consistency in most settings. When further combined with self-consistency, GRACE outperforms all the baselines by sizeable margins. Human and LLM evaluations over GSM8K show that GRACE not only improves the final answer accuracy but also the correctness of the intermediate reasoning. Our implementation can be accessed at \url{https://github.com/mukhal/grace}.

Reinforcement learning has seen wide success in finetuning large language models to better align with instructions via human feedback. The so-called algorithm, Reinforcement Learning with Human Feedback (RLHF) demonstrates impressive performance on the GPT series models. However, the underlying Reinforcement Learning (RL) algorithm is complex and requires an additional training pipeline for reward and value networks. In this paper, we consider an alternative approach: converting feedback to instruction by relabeling the original one and training the model for better alignment in a supervised manner. Such an algorithm doesn't require any additional parameters except for the original language model and maximally reuses the pretraining pipeline. To achieve this, we formulate instruction alignment problem for language models as a goal-reaching problem in decision making. We propose Hindsight Instruction Relabeling (HIR), a novel algorithm for aligning language models with instructions. The resulting two-stage algorithm shed light to a family of reward-free approaches that utilize the hindsightly relabeled instructions based on feedback. We evaluate the performance of HIR extensively on 12 challenging BigBench reasoning tasks and show that HIR outperforms the baseline algorithms and is comparable to or even surpasses supervised finetuning.