MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs

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 from a small-scale problem-solution dataset (denoted as seed data). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as MathGenieLM. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.

MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Typos-aware Bottlenecked Pre-Training for Robust Dense Retrieval

Current dense retrievers (DRs) are limited in their ability to effectively process misspelled queries, which constitute a significant portion of query traffic in commercial search engines. The main issue is that the pre-trained language model-based encoders used by DRs are typically trained and fine-tuned using clean, well-curated text data. Misspelled queries are typically not found in the data used for training these models, and thus misspelled queries observed at inference time are out-of-distribution compared to the data used for training and fine-tuning. Previous efforts to address this issue have focused on \textit{fine-tuning} strategies, but their effectiveness on misspelled queries remains lower than that of pipelines that employ separate state-of-the-art spell-checking components. To address this challenge, we propose ToRoDer (TypOs-aware bottlenecked pre-training for RObust DEnse Retrieval), a novel \textit{pre-training} strategy for DRs that increases their robustness to misspelled queries while preserving their effectiveness in downstream retrieval tasks. ToRoDer utilizes an encoder-decoder architecture where the encoder takes misspelled text with masked tokens as input and outputs bottlenecked information to the decoder. The decoder then takes as input the bottlenecked embeddings, along with token embeddings of the original text with the misspelled tokens masked out. The pre-training task is to recover the masked tokens for both the encoder and decoder. Our extensive experimental results and detailed ablation studies show that DRs pre-trained with ToRoDer exhibit significantly higher effectiveness on misspelled queries, sensibly closing the gap with pipelines that use a separate, complex spell-checker component, while retaining their effectiveness on correctly spelled queries.

Empowering Dual-Encoder with Query Generator for Cross-Lingual Dense Retrieval

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.

Lexicon-Enhanced Self-Supervised Training for Multilingual Dense Retrieval

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.

Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semantics

Trajectory Representation Learning (TRL) is a powerful tool for spatial-temporal data analysis and management. TRL aims to convert complicated raw trajectories into low-dimensional representation vectors, which can be applied to various downstream tasks, such as trajectory classification, clustering, and similarity computation. Existing TRL works usually treat trajectories as ordinary sequence data, while some important spatial-temporal characteristics, such as temporal regularities and travel semantics, are not fully exploited. To fill this gap, we propose a novel Self-supervised trajectory representation learning framework with TemporAl Regularities and Travel semantics, namely START. The proposed method consists of two stages. The first stage is a Trajectory Pattern-Enhanced Graph Attention Network (TPE-GAT), which converts the road network features and travel semantics into representation vectors of road segments. The second stage is a Time-Aware Trajectory Encoder (TAT-Enc), which encodes representation vectors of road segments in the same trajectory as a trajectory representation vector, meanwhile incorporating temporal regularities with the trajectory representation. Moreover, we also design two self-supervised tasks, i.e., span-masked trajectory recovery and trajectory contrastive learning, to introduce spatial-temporal characteristics of trajectories into the training process of our START framework. The effectiveness of the proposed method is verified by extensive experiments on two large-scale real-world datasets for three downstream tasks. The experiments also demonstrate that our method can be transferred across different cities to adapt heterogeneous trajectory datasets.

Bridging the Gap Between Indexing and Retrieval for Differentiable Search Index with Query Generation

The Differentiable Search Index (DSI) is a new, emerging paradigm for information retrieval. Unlike traditional retrieval architectures where index and retrieval are two different and separate components, DSI uses a single transformer model to perform both indexing and retrieval. In this paper, we identify and tackle an important issue of current DSI models: the data distribution mismatch that occurs between the DSI indexing and retrieval processes. Specifically, we argue that, at indexing, current DSI methods learn to build connections between long document texts and their identifies, but then at retrieval, short query texts are provided to DSI models to perform the retrieval of the document identifiers. This problem is further exacerbated when using DSI for cross-lingual retrieval, where document text and query text are in different languages. To address this fundamental problem of current DSI models we propose a simple yet effective indexing framework for DSI called DSI-QG. In DSI-QG, documents are represented by a number of relevant queries generated by a query generation model at indexing time. This allows DSI models to connect a document identifier to a set of query texts when indexing, hence mitigating data distribution mismatches present between the indexing and the retrieval phases. Empirical results on popular mono-lingual and cross-lingual passage retrieval benchmark datasets show that DSI-QG significantly outperforms the original DSI model.

Unsupervised Context Aware Sentence Representation Pretraining for Multi-lingual Dense Retrieval

Recent research demonstrates the effectiveness of using pretrained language models (PLM) to improve dense retrieval and multilingual dense retrieval. In this work, we present a simple but effective monolingual pretraining task called contrastive context prediction~(CCP) to learn sentence representation by modeling sentence level contextual relation. By pushing the embedding of sentences in a local context closer and pushing random negative samples away, different languages could form isomorphic structure, then sentence pairs in two different languages will be automatically aligned. Our experiments show that model collapse and information leakage are very easy to happen during contrastive training of language model, but language-specific memory bank and asymmetric batch normalization operation play an essential role in preventing collapsing and information leakage, respectively. Besides, a post-processing for sentence embedding is also very effective to achieve better retrieval performance. On the multilingual sentence retrieval task Tatoeba, our model achieves new SOTA results among methods without using bilingual data. Our model also shows larger gain on Tatoeba when transferring between non-English pairs. On two multi-lingual query-passage retrieval tasks, XOR Retrieve and Mr.TYDI, our model even achieves two SOTA results in both zero-shot and supervised setting among all pretraining models using bilingual data.

GroupLink: An End-to-end Multitask Method for Word Grouping and Relation Extraction in Form Understanding

Forms are a common type of document in real life and carry rich information through textual contents and the organizational structure. To realize automatic processing of forms, word grouping and relation extraction are two fundamental and crucial steps after preliminary processing of optical character reader (OCR). Word grouping is to aggregate words that belong to the same semantic entity, and relation extraction is to predict the links between semantic entities. Existing works treat them as two individual tasks, but these two tasks are correlated and can reinforce each other. The grouping process will refine the integrated representation of the corresponding entity, and the linking process will give feedback to the grouping performance. For this purpose, we acquire multimodal features from both textual data and layout information and build an end-to-end model through multitask training to combine word grouping and relation extraction to enhance performance on each task. We validate our proposed method on a real-world, fully-annotated, noisy-scanned benchmark, FUNSD, and extensive experiments demonstrate the effectiveness of our method.