Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Multilingual translation supports multiple translation directions by projecting all languages in a shared space, but the translation quality is undermined by the difference between languages in the text-only modality, especially when the number of languages is large. To bridge this gap, we introduce visual context as the universal language-independent representation to facilitate multilingual translation. In this paper, we propose a framework to leverage the multimodal prompt to guide the Multimodal Multilingual neural Machine Translation (m3P), which aligns the representations of different languages with the same meaning and generates the conditional vision-language memory for translation. We construct a multilingual multimodal instruction dataset (InstrMulti102) to support 102 languages. Our method aims to minimize the representation distance of different languages by regarding the image as a central language. Experimental results show that m3P outperforms previous text-only baselines and multilingual multimodal methods by a large margin. Furthermore, the probing experiments validate the effectiveness of our method in enhancing translation under the low-resource and massively multilingual scenario.

Recent advancements in Text-to-SQL methods employing Large Language Models (LLMs) have demonstrated remarkable performance. Nonetheless, these approaches continue to encounter difficulties when handling extensive databases, intricate user queries, and erroneous SQL results. To tackle these challenges, we present \textsc{MAC-SQL}, a novel LLM-based multi-agent collaborative framework designed for the Text-to-SQL task. Our framework comprises three agents: the \textit{Selector}, accountable for condensing voluminous databases and preserving relevant table schemas for user questions; the \textit{Decomposer}, which disassembles complex user questions into more straightforward sub-problems and resolves them progressively; and the \textit{Refiner}, tasked with validating and refining defective SQL queries. We perform comprehensive experiments on two Text-to-SQL datasets, BIRD and Spider, achieving a state-of-the-art execution accuracy of 59.59\% on the BIRD test set. Moreover, we have open-sourced an instruction fine-tuning model, SQL-Llama, based on Code Llama 7B, in addition to an agent instruction dataset derived from training data based on BIRD and Spider. The SQL-Llama model has demonstrated encouraging results on the development sets of both BIRD and Spider. However, when compared to GPT-4, there remains a notable potential for enhancement. Our code and data are publicly available at https://github.com/wbbeyourself/MAC-SQL.

Dialogue summarization involves a wide range of scenarios and domains. However, existing methods generally only apply to specific scenarios or domains. In this study, we propose a new pre-trained model specifically designed for multi-scenario multi-domain dialogue summarization. It adopts a multi-stage pre-training strategy to reduce the gap between the pre-training objective and fine-tuning objective. Specifically, we first conduct domain-aware pre-training using large-scale multi-scenario multi-domain dialogue data to enhance the adaptability of our pre-trained model. Then, we conduct task-oriented pre-training using large-scale multi-scenario multi-domain "dialogue-summary" parallel data annotated by ChatGPT to enhance the dialogue summarization ability of our pre-trained model. Experimental results on three dialogue summarization datasets from different scenarios and domains indicate that our pre-trained model significantly outperforms previous state-of-the-art models in full fine-tuning, zero-shot, and few-shot settings.

Retrieval-enhanced text generation has shown remarkable progress on knowledge-intensive language tasks, such as open-domain question answering and knowledge-enhanced dialogue generation, by leveraging passages retrieved from a large passage corpus for delivering a proper answer given the input query. However, the retrieved passages are not ideal for guiding answer generation because of the discrepancy between retrieval and generation, i.e., the candidate passages are all treated equally during the retrieval procedure without considering their potential to generate a proper answer. This discrepancy makes a passage retriever deliver a sub-optimal collection of candidate passages to generate the answer. In this paper, we propose the GeneRative Knowledge Improved Passage Ranking (GripRank) approach, addressing the above challenge by distilling knowledge from a generative passage estimator (GPE) to a passage ranker, where the GPE is a generative language model used to measure how likely the candidate passages can generate the proper answer. We realize the distillation procedure by teaching the passage ranker learning to rank the passages ordered by the GPE. Furthermore, we improve the distillation quality by devising a curriculum knowledge distillation mechanism, which allows the knowledge provided by the GPE can be progressively distilled to the ranker through an easy-to-hard curriculum, enabling the passage ranker to correctly recognize the provenance of the answer from many plausible candidates. We conduct extensive experiments on four datasets across three knowledge-intensive language tasks. Experimental results show advantages over the state-of-the-art methods for both passage ranking and answer generation on the KILT benchmark.

Existing knowledge-grounded conversation systems generate responses typically in a retrieve-then-generate manner. They require a large knowledge base and a strong knowledge retrieval component, which is time- and resource-consuming. In this paper, we address the challenge by leveraging the inherent knowledge encoded in the pre-trained language models (PLMs). We propose Knowledgeable Prefix Tuning (KnowPrefix-Tuning), a two-stage tuning framework, bypassing the retrieval process in a knowledge-grounded conversation system by injecting prior knowledge into the lightweight knowledge prefix. The knowledge prefix is a sequence of continuous knowledge-specific vectors that can be learned during training. In addition, we propose a novel interactive re-parameterization mechanism that allows the prefix to interact fully with the PLM during the optimization of response generation. Experimental results demonstrate that KnowPrefix-Tuning outperforms fine-tuning and other lightweight tuning approaches, and performs comparably with strong retrieval-based baselines while being $3\times$ faster during inference.

Most current multi-modal summarization methods follow a cascaded manner, where an off-the-shelf object detector is first used to extract visual features, then these features are fused with language representations to generate the summary with an encoder-decoder model. The cascaded way cannot capture the semantic alignments between images and paragraphs, which are crucial to a precise summary. In this paper, we propose ViL-Sum to jointly model paragraph-level \textbf{Vi}sion-\textbf{L}anguage Semantic Alignment and Multi-Modal \textbf{Sum}marization. The core of ViL-Sum is a joint multi-modal encoder with two well-designed tasks, image reordering and image selection. The joint multi-modal encoder captures the interactions between modalities, where the reordering task guides the model to learn paragraph-level semantic alignment and the selection task guides the model to selected summary-related images in the final summary. Experimental results show that our proposed ViL-Sum significantly outperforms current state-of-the-art methods. In further analysis, we find that two well-designed tasks and joint multi-modal encoder can effectively guide the model to learn reasonable paragraphs-images and summary-images relations.

Large-scale Language Models (LLMs) are constrained by their inability to process lengthy inputs. To address this limitation, we propose the Self-Controlled Memory (SCM) system to unleash infinite-length input capacity for large-scale language models. Our SCM system is composed of three key modules: the language model agent, the memory stream, and the memory controller. The language model agent iteratively processes ultra-long inputs and stores all historical information in the memory stream. The memory controller provides the agent with both long-term memory (archived memory) and short-term memory (flash memory) to generate precise and coherent responses. The controller determines which memories from archived memory should be activated and how to incorporate them into the model input. Our SCM system can be integrated with any LLMs to enable them to process ultra-long texts without any modification or fine-tuning. Experimental results show that our SCM system enables LLMs, which are not optimized for multi-turn dialogue, to achieve multi-turn dialogue capabilities that are comparable to ChatGPT, and to outperform ChatGPT in scenarios involving ultra-long document summarization or long-term conversations. Additionally, we will supply a test set, which covers common long-text input scenarios, for evaluating the abilities of LLMs in processing long documents.~\footnote{Working in progress.}\footnote{\url{https://github.com/wbbeyourself/SCM4LLMs}}

Retrieval augmented methods have shown promising results in various classification tasks. However, existing methods focus on retrieving extra context to enrich the input, which is noise sensitive and non-expandable. In this paper, following this line, we propose a $k$-nearest-neighbor (KNN) -based method for retrieval augmented classifications, which interpolates the predicted label distribution with retrieved instances' label distributions. Different from the standard KNN process, we propose a decoupling mechanism as we find that shared representation for classification and retrieval hurts performance and leads to training instability. We evaluate our method on a wide range of classification datasets. Experimental results demonstrate the effectiveness and robustness of our proposed method. We also conduct extra experiments to analyze the contributions of different components in our model.\footnote{\url{https://github.com/xnliang98/knn-cls-w-decoupling}}

Pretrained language models (PLMs) have shown marvelous improvements across various NLP tasks. Most Chinese PLMs simply treat an input text as a sequence of characters, and completely ignore word information. Although Whole Word Masking can alleviate this, the semantics in words is still not well represented. In this paper, we revisit the segmentation granularity of Chinese PLMs. We propose a mixed-granularity Chinese BERT (MigBERT) by considering both characters and words. To achieve this, we design objective functions for learning both character and word-level representations. We conduct extensive experiments on various Chinese NLP tasks to evaluate existing PLMs as well as the proposed MigBERT. Experimental results show that MigBERT achieves new SOTA performance on all these tasks. Further analysis demonstrates that words are semantically richer than characters. More interestingly, we show that MigBERT also works with Japanese. Our code and model have been released here~\footnote{https://github.com/xnliang98/MigBERT}.