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Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at \url{https://github.com/zhaoxlpku/SubgoalXL}.

Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks. However, there are increasing debates regarding whether these models truly understand and apply mathematical knowledge or merely rely on shortcuts for mathematical reasoning. One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly. This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations. We introduce the adversarial grade school math (GSM-Plus) dataset, an extension of GSM8K augmented with various mathematical perturbations. Our experiments on 25 LLMs and 4 prompting techniques show that while LLMs exhibit different levels of math reasoning abilities, their performances are far from robust. In particular, even for problems that have been solved in GSM8K, LLMs can make mistakes when new statements are added or the question targets are altered. We also explore whether more robust performance can be achieved by composing existing prompting methods, in which we try an iterative method that generates and verifies each intermediate thought based on its reasoning goal and calculation result., Comment: ACL 2024

Multimodal reasoning stands as a pivotal capability for large vision-language models (LVLMs). The integration with Domain-Specific Languages (DSL), offering precise visual representations, equips these models with the opportunity to execute more accurate reasoning in complex and professional domains. However, the vanilla Chain-of-Thought (CoT) prompting method faces challenges in effectively leveraging the unique strengths of visual and DSL representations, primarily due to their differing reasoning mechanisms. Additionally, it often falls short in addressing critical steps in multi-step reasoning tasks. To mitigate these challenges, we introduce the \underline{B}i-Modal \underline{B}ehavioral \underline{A}lignment (BBA) prompting method, designed to maximize the potential of DSL in augmenting complex multi-modal reasoning tasks. This method initiates by guiding LVLMs to create separate reasoning chains for visual and DSL representations. Subsequently, it aligns these chains by addressing any inconsistencies, thus achieving a cohesive integration of behaviors from different modalities. Our experiments demonstrate that BBA substantially improves the performance of GPT-4V(ision) on geometry problem solving ($28.34\% \to 34.22\%$), chess positional advantage prediction ($42.08\% \to 46.99\%$) and molecular property prediction ($77.47\% \to 83.52\%$)., Comment: Preprint

Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of subgoal-based methods, we propose a novel framework called \textbf{SE}quential sub\textbf{G}oal \textbf{O}ptimization (SEGO) to enhance LLMs' ability to solve mathematical problems. By establishing a connection between the subgoal breakdown process and the probability of solving problems, SEGO aims to identify better subgoals with theoretical guarantees. Addressing the challenge of identifying suitable subgoals in a large solution space, our framework generates problem-specific subgoals and adjusts them according to carefully designed criteria. Incorporating these optimized subgoals into the policy model training leads to significant improvements in problem-solving performance. We validate SEGO's efficacy through experiments on two benchmarks, GSM8K and MATH, where our approach outperforms existing methods, highlighting the potential of SEGO in AI-driven mathematical problem-solving. Data and code associated with this paper will be available at https://github.com/zhaoxlpku/SEGO, Comment: Preprint

Video-grounded dialogue understanding is a challenging problem that requires machine to perceive, parse and reason over situated semantics extracted from weakly aligned video and dialogues. Most existing benchmarks treat both modalities the same as a frame-independent visual understanding task, while neglecting the intrinsic attributes in multimodal dialogues, such as scene and topic transitions. In this paper, we present Video-grounded Scene&Topic AwaRe dialogue (VSTAR) dataset, a large scale video-grounded dialogue understanding dataset based on 395 TV series. Based on VSTAR, we propose two benchmarks for video-grounded dialogue understanding: scene segmentation and topic segmentation, and one benchmark for video-grounded dialogue generation. Comprehensive experiments are performed on these benchmarks to demonstrate the importance of multimodal information and segments in video-grounded dialogue understanding and generation., Comment: To appear at ACL 2023

Large language models~(LLMs) present an intriguing avenue of exploration in the domain of formal theorem proving. Nonetheless, the full utilization of these models, particularly in terms of demonstration formatting and organization, remains an underexplored area. In an endeavor to enhance the efficacy of LLMs, we introduce a subgoal-based demonstration learning framework, consisting of two primary elements: Firstly, drawing upon the insights of subgoal learning from the domains of reinforcement learning and robotics, we propose the construction of distinct subgoals for each demonstration example and refine these subgoals in accordance with the pertinent theories of subgoal learning. Secondly, we build upon recent advances in diffusion models to predict the optimal organization, simultaneously addressing two intricate issues that persist within the domain of demonstration organization: subset selection and order determination. Through the integration of subgoal-based learning methodologies, we have successfully increased the prevailing proof accuracy from 38.9\% to 44.3\% on the miniF2F benchmark. Furthermore, the adoption of diffusion models for demonstration organization can lead to an additional enhancement in accuracy to 45.5\%, or a $5\times$ improvement in sampling efficiency compared with the long-standing state-of-the-art method. Our code is available at \url{https://github.com/HKUNLP/subgoal-theorem-prover}.

With the availability of massive general-domain dialogue data, pre-trained dialogue generation appears to be super appealing to transfer knowledge from the general domain to downstream applications. In most existing work, such transferable ability is mainly obtained by fitting a large model with hundreds of millions of parameters on massive data in an exhaustive way, leading to inefficient running and poor interpretability. This paper proposes a novel dialogue generation model with a latent structure that is easily transferable from the general domain to downstream tasks in a lightweight and transparent way. Experiments on two benchmarks validate the effectiveness of the proposed model. Thanks to the transferable latent structure, our model is able to yield better dialogue responses than four strong baselines in terms of both automatic and human evaluations, and our model with about 22% parameters particularly delivers a 5x speedup in running time compared with the strongest baseline. Moreover, the proposed model is explainable by interpreting the discrete latent variables., Comment: To appear at EMNLP 2022 main conference

Knowledge-grounded conversation (KGC) shows excellent potential to deliver an engaging and informative response. However, existing approaches emphasize selecting one golden knowledge given a particular dialogue context, overlooking the one-to-many phenomenon in dialogue. As a result, the existing paradigm limits the diversity of knowledge selection and generation. To this end, we establish a multi-reference KGC dataset and propose a series of metrics to systematically assess the one-to-many efficacy of existing KGC models. Furthermore, to extend the hypothesis space of knowledge selection to enhance the mapping relationship between multiple knowledge and multiple responses, we devise a span-based variational model and optimize the model in a wake-sleep style with an ameliorated evidence lower bound objective to learn the one-to-many generalization. Both automatic and human evaluations demonstrate the efficacy of our approach., Comment: To appear at EMNLP 2022 main conference. The first two authors contributed equally

We study video-grounded dialogue generation, where a response is generated based on the dialogue context and the associated video. The primary challenges of this task lie in (1) the difficulty of integrating video data into pre-trained language models (PLMs) which presents obstacles to exploiting the power of large-scale pre-training; and (2) the necessity of taking into account the complementarity of various modalities throughout the reasoning process. Although having made remarkable progress in video-grounded dialogue generation, existing methods still fall short when it comes to integrating with PLMs in a way that allows information from different modalities to complement each other. To alleviate these issues, we first propose extracting pertinent information from videos and turning it into reasoning paths that are acceptable to PLMs. Additionally, we propose a multi-agent reinforcement learning method to collaboratively perform reasoning on different modalities (i.e., video and dialogue context). Empirical experiment results on two public datasets indicate that the proposed model can significantly outperform state-of-the-art models by large margins on both automatic and human evaluations., Comment: To appear at EMNLP 2022 findings

Grounding dialogue generation by extra knowledge has shown great potentials towards building a system capable of replying with knowledgeable and engaging responses. Existing studies focus on how to synthesize a response with proper knowledge, yet neglect that the same knowledge could be expressed differently by speakers even under the same context. In this work, we mainly consider two aspects of knowledge expression, namely the structure of the response and style of the content in each part. We therefore introduce two sequential latent variables to represent the structure and the content style respectively. We propose a segmentation-based generation model and optimize the model by a variational approach to discover the underlying pattern of knowledge expression in a response. Evaluation results on two benchmarks indicate that our model can learn the structure style defined by a few examples and generate responses in desired content style., Comment: Accepted by NAACL 2022 (main conference)

Knowledge-grounded conversation (KGC) shows great potential in building an engaging and knowledgeable chatbot, and knowledge selection is a key ingredient in it. However, previous methods for knowledge selection only concentrate on the relevance between knowledge and dialogue context, ignoring the fact that age, hobby, education and life experience of an interlocutor have a major effect on his or her personal preference over external knowledge. Without taking the personalization issue into account, it is difficult to select the proper knowledge and generate persona-consistent responses. In this work, we introduce personal memory into knowledge selection in KGC to address the personalization issue. We propose a variational method to model the underlying relationship between one's personal memory and his or her selection of knowledge, and devise a learning scheme in which the forward mapping from personal memory to knowledge and its inverse mapping is included in a closed loop so that they could teach each other. Experiment results show that our method outperforms existing KGC methods significantly on both automatic evaluation and human evaluation., Comment: Accepted by ACL 2022 (main conference). First two authors contributed equally

We study knowledge-grounded dialogue generation with pre-trained language models. To leverage the redundant external knowledge under capacity constraint, we propose equipping response generation defined by a pre-trained language model with a knowledge selection module, and an unsupervised approach to jointly optimizing knowledge selection and response generation with unlabeled dialogues. Empirical results on two benchmarks indicate that our model can significantly outperform state-of-the-art methods in both automatic evaluation and human judgment., Comment: Accepted by EMNLP 2020

Building an intelligent dialogue system with the ability to select a proper response according to a multi-turn context is a great challenging task. Existing studies focus on building a context-response matching model with various neural architectures or PLMs and typically learning with a single response prediction task. These approaches overlook many potential training signals contained in dialogue data, which might be beneficial for context understanding and produce better features for response prediction. Besides, the response retrieved from existing dialogue systems supervised by the conventional way still faces some critical challenges, including incoherence and inconsistency. To address these issues, in this paper, we propose learning a context-response matching model with auxiliary self-supervised tasks designed for the dialogue data based on pre-trained language models. Specifically, we introduce four self-supervised tasks including next session prediction, utterance restoration, incoherence detection and consistency discrimination, and jointly train the PLM-based response selection model with these auxiliary tasks in a multi-task manner. By this means, the auxiliary tasks can guide the learning of the matching model to achieve a better local optimum and select a more proper response. Experiment results on two benchmarks indicate that the proposed auxiliary self-supervised tasks bring significant improvement for multi-turn response selection in retrieval-based dialogues, and our model achieves new state-of-the-art results on both datasets., Comment: 10 pages

While neural conversation models have shown great potentials towards generating informative and engaging responses via introducing external knowledge, learning such a model often requires knowledge-grounded dialogues that are difficult to obtain. To overcome the data challenge and reduce the cost of building a knowledge-grounded dialogue system, we explore the problem under a zero-resource setting by assuming no context-knowledge-response triples are needed for training. To this end, we propose representing the knowledge that bridges a context and a response and the way that the knowledge is expressed as latent variables, and devise a variational approach that can effectively estimate a generation model from a dialogue corpus and a knowledge corpus that are independent with each other. Evaluation results on three benchmarks of knowledge-grounded dialogue generation indicate that our model can achieve comparable performance with state-of-the-art methods that rely on knowledge-grounded dialogues for training, and exhibits a good generalization ability over different topics and different datasets., Comment: Accepted by NeurIPS 2020

Responding with knowledge has been recognized as an important capability for an intelligent conversational agent. Yet knowledge-grounded dialogues, as training data for learning such a response generation model, are difficult to obtain. Motivated by the challenge in practice, we consider knowledge-grounded dialogue generation under a natural assumption that only limited training examples are available. In such a low-resource setting, we devise a disentangled response decoder in order to isolate parameters that depend on knowledge-grounded dialogues from the entire generation model. By this means, the major part of the model can be learned from a large number of ungrounded dialogues and unstructured documents, while the remaining small parameters can be well fitted using the limited training examples. Evaluation results on two benchmarks indicate that with only 1/8 training data, our model can achieve the state-of-the-art performance and generalize well on out-of-domain knowledge., Comment: Published in ICLR 2020

We present a document-grounded matching network (DGMN) for response selection that can power a knowledge-aware retrieval-based chatbot system. The challenges of building such a model lie in how to ground conversation contexts with background documents and how to recognize important information in the documents for matching. To overcome the challenges, DGMN fuses information in a document and a context into representations of each other, and dynamically determines if grounding is necessary and importance of different parts of the document and the context through hierarchical interaction with a response at the matching step. Empirical studies on two public data sets indicate that DGMN can significantly improve upon state-of-the-art methods and at the same time enjoys good interpretability.