Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we introduce MathGenie, a novel method for generating diverse and reliable math problems by leveraging the ground-truth solutions of the seed data. We augment these ground-truth solutions and use a specially finetuned model to translate these augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for these questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based verification for filtering. Then, we finetune various pretrained models, ranging from 7B to 70B, on the newly curated data, resulting in a family of models known as MathGenie. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenie-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score.

In infilling tasks, sub-tokens, representing instances where a complete token is segmented into two parts, often emerge at the boundaries of prefixes, middles, and suffixes. Traditional methods focused on training models at the token level, leading to sub-optimal performance in character-level infilling tasks during the inference stage. Alternately, some approaches considered character-level infilling, but they relied on predicting sub-tokens in inference, yet this strategy diminished ability in character-level infilling tasks due to the large perplexity of the model on sub-tokens. In this paper, we introduce FIM-SE, which stands for Fill-In-the-Middle with both Starting and Ending character constraints. The proposed method addresses character-level infilling tasks by utilizing a line-level format to avoid predicting any sub-token in inference. In addition, we incorporate two special tokens to signify the rest of the incomplete lines, thereby enhancing generation guidance. Extensive experiments demonstrate that our proposed approach surpasses previous methods, offering a significant advantage. Code is available at https://github.com/SenseLLM/FIM-SE.

Recent multilingual pre-trained models have shown better performance in various multilingual tasks. However, these models perform poorly on multilingual retrieval tasks due to lacking multilingual training data. In this paper, we propose to mine and generate self-supervised training data based on a large-scale unlabeled corpus. We carefully design a mining method which combines the sparse and dense models to mine the relevance of unlabeled queries and passages. And we introduce a query generator to generate more queries in target languages for unlabeled passages. Through extensive experiments on Mr. TYDI dataset and an industrial dataset from a commercial search engine, we demonstrate that our method performs better than baselines based on various pre-trained multilingual models. Our method even achieves on-par performance with the supervised method on the latter dataset.

In monolingual dense retrieval, lots of works focus on how to distill knowledge from cross-encoder re-ranker to dual-encoder retriever and these methods achieve better performance due to the effectiveness of cross-encoder re-ranker. However, we find that the performance of the cross-encoder re-ranker is heavily influenced by the number of training samples and the quality of negative samples, which is hard to obtain in the cross-lingual setting. In this paper, we propose to use a query generator as the teacher in the cross-lingual setting, which is less dependent on enough training samples and high-quality negative samples. In addition to traditional knowledge distillation, we further propose a novel enhancement method, which uses the query generator to help the dual-encoder align queries from different languages, but does not need any additional parallel sentences. The experimental results show that our method outperforms the state-of-the-art methods on two benchmark datasets.