Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as \textit{self-consistency}, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose \textbf{Self-Agreement}, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model's decoder to generate a \textit{diverse} set of reasoning paths, and subsequently prompts the language model \textit{one more time} to determine the optimal answer by selecting the most \textit{agreed} answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.

Recent advancements in large language models (LLMs) have demonstrated remarkable abilities in handling a variety of natural language processing (NLP) downstream tasks, even on mathematical tasks requiring multi-step reasoning. Meanwhile, we also constructed a small-scale Chinese primary school mathematics test set (named KMath), consisting of 188 examples to evaluate the correctness of the problem-solving process generated by the models. Empirical studies demonstrate that KwaiYiiMath can achieve stateof-the-art (SOTA) performance on GSM8k, CMath, and KMath compared with the similar size models, respectively. Recent advances in large language models (LLMs) have revolutionized the natural language processing (NLP) landscape Kenton & Toutanova (2019); Brown et al. (2020), where scaling up model size and the amount of data is one of the key ingredients Rae et al. (2021); Chowdhery et al. (2022); Anil et al. (2023); Touvron et al. (2023a;b). Surprisingly, recent progress suggests that LLMs also have the potential to solve reasoning problems Clark et al. (2020); Talmor et al. (2020); Suzgun et al. (2022); Wei et al. (2022b). In this report, we focus on how to enhance the mathematical reasoning capabilities of LLM through an alignment process that includes supervised fine-tuning (SFT) and reinforcement learning from human feedback (RLHF). Specifically, we introduce the KwaiYiiMath which is finetuned with human alignment techniques from KwaiYiiBase to tackle mathematical problems. Experimental results show that KwaiYiiMath outperforms many open-source models in similar sizes by a large margin and is approaching GPT-4 on three mathematical benchmarks including both English and Chinese, i.e., GSM8k Cobbe et al. (2021), CMath Wei et al. (2023), and a small-scale in-house dataset KMath. KwaiYiiBase is a large language model developed by Kuaishou https://github.com/kwai/KwaiYii/. Section 3 introduces the methodology of KwaiYiiMath including the process of supervised fine-tuning and human preference alignment. Additionally, it also describes details about the efforts in collecting large amounts of mathematical high-quality training data.