Utilizing large language models (LLMs) for data augmentation has yielded encouraging results in mathematical reasoning. However, these approaches face constraints in problem diversity, potentially restricting them to in-domain/distribution data generation. To this end, we propose **ControlMath**, an iterative method involving an equation-generator module and two LLM-based agents. The module creates diverse equations, which the Problem-Crafter agent then transforms into math word problems. The Reverse-Agent filters and selects high-quality data, adhering to the “less is more” principle. This approach enables the generation of diverse math problems, not limited to specific domains or distributions. As a result, we collect ControlMathQA, which involves 190k math word problems. Extensive results prove that combining our dataset with in-domain datasets like GSM8K can help improve the model’s mathematical ability to generalize, leading to improved performance both within and beyond specific domains.

Currently, learning better unsupervised sentence representations is the pursuit of many natural language processing communities. Lots of approaches based on pre-trained language models (PLMs) and contrastive learning have achieved promising results on this task. Experimentally, we observe that the over-smoothing problem reduces the capacity of these powerful PLMs, leading to sub-optimal sentence representations. In this paper, we present a Simple method named Self-Contrastive Learning (SSCL) to alleviate this issue, which samples negatives from PLMs intermediate layers, improving the quality of the sentence representation. Our proposed method is quite simple and can be easily extended to various state-of-the-art models for performance boosting, which can be seen as a plug-and-play contrastive framework for learning unsupervised sentence representation. Extensive results prove that SSCL brings the superior performance improvements of different strong baselines (e.g., BERT and SimCSE) on Semantic Textual Similarity and Transfer datasets

To present, multilingual language models trained using various pre-training tasks like mask language modeling (MLM) have yielded encouraging results on a wide range of downstream tasks. Despite the promising performances, structural knowledge in cross-lingual corpus is less explored in current works, leading to the semantic misalignment. In this paper, we propose a new pre-training task named Structural Contrast Pretraining (SCP) to align the structural words in a parallel sentence, enhancing the models’ ability to comprehend cross-lingual representations. Concretely, each structural word in source and target languages is regarded as a positive pair in SCP. Since contrastive learning compares positive and negative pairs, an increase in the frequency of negative pairings could enhance the performance of the resulting model. Therefore, we further propose Cross-lingual Momentum Contrast (CL-MoCo) to increase the number of negative pairs by maintaining a large size of the queue. CL-MoCo extends the original Moco approach into cross-lingual training and jointly optimizes the source-to-target language and target-to-source language representations, resulting in a more suitable encoder for cross-lingual transfer. We conduct extensive experiments to validate the proposed approach on three cross-lingual tasks across five datasets such as MLQA, WikiAnn, etc, and results prove the effectiveness of our method.