Empowering large language models (LLMs) with effective tool utilization capabilities is crucial for enabling AI agents to solve complex problems. However, current models face two major limitations: (1) unreliable tool planning and invocation due to low-quality instruction datasets (e.g., widespread hallucinated API calls), and (2) weak tool reflection abilities (over 90% of errors cannot be corrected) resulting from static imitation learning. To address these critical limitations, we propose Tool-MVR, a novel Tool-Augmented LLM that achieves comprehensive System 2 reasoning through two key innovations. Specifically, we first introduce Multi-Agent Meta-Verification (MAMV), a systematic pipeline that rigorously validates APIs, queries, and reasoning trajectories to construct ToolBench-V, a new high-quality instruction dataset that addresses the limitation of unreliable tool planning and invocation. Second, we propose Exploration-based Reflection Learning (EXPLORE), which enhances tool reflection capabilities by leveraging tool feedback through a dynamic "Error → Reflection → Correction" learning paradigm, resulting in our reflection dataset ToolBench-R and addressing the critical weakness in tool reflection. Finally, we obtain Tool-MVR by finetuning open-source LLMs (e.g., Qwen-7B) on both ToolBench-V and ToolBench-R. Our experiments demonstrate that Tool-MVR achieves state-of-the-art performance on StableToolBench, surpassing both ToolLLM (by 23.9%) and GPT-4 (by 15.3%) while reducing API calls by 31.4%, with strong generalization capabilities across unseen tools and scenarios. Additionally, on our proposed RefineToolBench, the first benchmark specifically designed to evaluate tool reflection capabilities. Tool-MVR achieves a 58.9% error correction rate, significantly outperforming ToolLLM's 9.1%.

Math word problem (MWP) serves as a critical milestone for assessing the text mining ability and knowledge mastery level of models. Recent advancements have witnessed large language models (LLMs) showcasing remarkable performance on MWP. However, current LLMs still frequently exhibit logical errors, which highlights their inability to fully grasp the knowledge required for genuine step-by-step mathematical reasoning. To this end, in this paper, we propose a novel Knowledge-guided Solver (KNOS) framework that empowers LLMs to simulate human mathematical reasoning, whose core idea is toInvoke-Verify-Injectnecessary knowledge to solve MWP. We draw inspiration from the dual-process theory to construct two cooperative systems: aKnowledge Systemand anInference System. Specifically, theKnowledge Systememploys LLMs as the knowledge base and develops a novelknowledge invokerthat can elicit their relevant knowledge to support the strict step-level mathematical reasoning. In theInference System, we propose aknowledge verifierand aknowledge injectorto evaluate the knowledge rationality and further guide the step-wise symbolic deduction in an interpretable manner based on human cognitive mechanism, respectively. Moreover, to tackle the potential scarcity issue of mathematics-specific knowledge in LLMs, we consider an open-book exam scenario and propose an improved version of KNOS called EKNOS. In EKNOS, we meticulously designknowledge selectorsto extract the most relevant commonsense and math formulas from external knowledge sources for each reasoning step. This knowledge is utilized to assist theknowledge invokerin better stimulating LLMs’ reasoning abilities. Both KNOS and EKNOS are flexible to empower different LLMs. Our experiments with GPT3, ChatGPT, and GPT4 not only demonstrate their reasoning accuracy improvement but also show how they bring the strict step-wise interpretability of mathematical thinking.

Learning to answer multi-step complex questions requires machines to perform like a human to think and reason step by step, which is one of the core abilities of a question answering system. Recent advancements have revealed that large language models exhibit remarkable reasoning capabilities by generating intermediate chain-of-thought rationales. However, the completeness of their rationales lacks assurance as they are susceptible to omitting steps and making factual errors. In this paper, drawing inspiration from human-like reasoning processes in answering multi-step questions, we explicitly plan the rationales to ensure their completeness. We propose a two-stage Decomposition-Evaluation (Dec-Eval) framework including a step decomposition stage and a rationale generation stage. Specifically, in the first stage, we decompose the complex question into simpler sub-ones and simulate a human's ability to grasp logical clues to ensure the integrity of step planning. Then, in the second stage, based on the sub-questions, we generate and evaluate rationales step by step. Both stages work together organically, improving the completeness of rationales and the accuracy of the answer. To further control the question answering process, we propose a novel knowledge injection mechanism that incorporates external knowledge to guide both stages. Extensive experiments on three challenging multi-step QA datasets demonstrate that Dec-Eval can explicitly generate more logical rationales, and significantly improve the reasoning performances of different backbone models.

Unsupervised semantic hashing has emerged as an indispensable technique for fast image search, which aims to convert images into binary hash codes without relying on labels. Recent advancements in the field demonstrate that employing large-scale backbones (e.g., ViT) in unsupervised semantic hashing models can yield substantial improvements. However, the inference delay has become increasingly difficult to overlook. Knowledge distillation provides a means for practical model compression to alleviate this delay. Nevertheless, the prevailing knowledge distillation approaches are not explicitly designed for semantic hashing. They ignore the unique search paradigm of semantic hashing, the inherent necessities of the distillation process, and the property of hash codes. In this paper, we propose an innovative Bit-mask Robust Contrastive knowledge Distillation (BRCD) method, specifically devised for the distillation of semantic hashing models. To ensure the effectiveness of two kinds of search paradigms in the context of semantic hashing, BRCD first aligns the semantic spaces between the teacher and student models through a contrastive knowledge distillation objective. Additionally, to eliminate noisy augmentations and ensure robust optimization, a cluster-based method within the knowledge distillation process is introduced. Furthermore, through a bit-level analysis, we uncover the presence of redundancy bits resulting from the bit independence property. To mitigate these effects, we introduce a bit mask mechanism in our knowledge distillation objective. Finally, extensive experiments not only showcase the noteworthy performance of our BRCD method in comparison to other knowledge distillation methods but also substantiate the generality of our methods across diverse semantic hashing models and backbones. The code for BRCD is available at https://github.com/hly1998/BRCD.

Personalized learner modeling using cognitive diagnosis (CD), which aims to model learners' cognitive states by diagnosing learner traits from behavioral data, is a fundamental yet significant task in many web learning services. Existing cognitive diagnosis models (CDMs) follow theproficiency-response paradigm that views learner traits and question parameters as trainable embeddings and learns them through learner performance prediction. However, we notice that this paradigm leads to the inevitable non-identifiability and explainability overfitting problem, which is harmful to the quantification of learners' cognitive states and the quality of web learning services. To address these problems, we propose an identifiable cognitive diagnosis framework (ID-CDF) based on a novelresponse-proficiency-response paradigm inspired by encoder-decoder models. Specifically, we first devise the diagnostic module of ID-CDF, which leverages inductive learning to eliminate randomness in optimization to guarantee identifiability and captures the monotonicity between overall response data distribution and cognitive states to prevent explainability overfitting. Next, we propose a flexible predictive module for ID-CDF to ensure diagnosis preciseness. We further present an implementation of ID-CDF, i.e., ID-CDM, to illustrate its usability. Extensive experiments on four real-world datasets with different characteristics demonstrate that ID-CDF can effectively address the problems without loss of diagnosis preciseness. Our code is available at https://github.com/CSLiJT/ID-CDF.

The fundamental task of intelligent educational systems is to offer adaptive learning services to students, such as exercise recommendations and computerized adaptive testing. However, optimizing required models in these systems would always encounter the collection difficulty of high-quality interaction data in practice. Therefore, establishing a student simulator is of great value since it can generate valid interactions to help optimize models. Existing advances have achieved success but generally suffer from exposure bias and overlook long-term intentions. To tackle these problems, we propose a novel Direct-Adversarial Imitation Student Simulator (DAISim) by formulating it as a Markov Decision Process (MDP), which unifies the workflow of the simulator in training and generating to alleviate the exposure bias and single-step optimization problems. To construct the intentions underlying the complex student interactions, we first propose a direct imitation strategy to mimic the interactions with a simple reward function. Then, we propose an adversarial imitation strategy to learn a rational distribution with the reward given by a parameterized discriminator. Furthermore, we optimize the discriminator in adversarial imitation in a pairwise manner, and the theoretical analysis shows that the pairwise discriminator would improve the generation quality. We conduct extensive experiments on real-world datasets, where the results demonstrate that our DAISim can simulate high-quality student interactions whose distribution is close to real distribution and can promote several downstream services.

Math formulas (e.g., "distance = speed X time'') serve as one of the fundamental commonsense knowledge in human cognition, where humans naturally acquire and manipulate them in logical thinking for mathematical reasoning problems. However, existing reasoning models mainly focus on learning heuristic linguistics or patterns to generate answers, but do not pay enough attention on learning with such formula knowledge. Thus, they are not transparent (thus uninterpretable) in terms of understanding and grasping basic mathematical logic. In this paper, to promote a step forward in the domain, we first construct two datasets (Math23K-F and MAWPS-F) with precise annotations of formula usage in each reasoning step for math word problems. Especially, our datasets are refined on the benchmark datasets, and thus ensure the generality and comparability for relevant research. Then, we propose a novel Formula-mastered Solver (FOMAS) with the guidance of mastering formula knowledge to solve the problems. Specifically, we establish FOMAS with two systems drawing insight from the dual process theory, including a Knowledge System and a Reasoning System, to learn and apply formula knowledge, respectively. The Knowledge System accumulates the math formulas, where we propose a novel pretraining manner to mimic how humans grasp the mathematical logic behind them. Then, in the Reasoning System, we develop elaborate formula-guided symbol prediction and goal generation methods that retrieve the necessary formula knowledge from Knowledge System to improve both reasoning accuracy and interpretability. It organically simulates how humans conduct complex reasoning under the explicit instruction of math formulas. Experimental results prove that FOMAS has a stronger reasoning ability and achieves a more interpretable reasoning process, which verifies the necessity of introducing formula knowledge transparently.

Exploring how learners' knowledge states evolve during the learning activities is a critical task in online learning systems, which can facilitate personalized services downstream, such as course recommendation. Most of existing methods have devoted great efforts to analyzing learners' knowledge states according to their responses (i.e., right or wrong) to different questions. However, the significant effect of learners' learning behaviors (e.g., answering speed, the number of attempts) is omitted, which can reflect their knowledge acquisition deeper and ensure the reliability of the response. In this paper, we propose a Learning Behavior-oriented Knowledge Tracing (LBKT) model, with the goal of explicitly exploring the learning behavior effects on learners' knowledge states. Specifically, we first analyze and summarize several dominated learning behaviors including Speed, Attempts and Hints in the learning process. As the characteristics of different learning behaviors vary greatly, we separately estimate their various effects on learners' knowledge acquisition in a quantitative manner. Then, considering that different learning behaviors are closely dependent with each other, we assess the fused effect of multiple learning behaviors by capturing their complex dependent patterns. Finally, we integrate the forgetting factor with learners' knowledge acquisition to comprehensively update their changing knowledge states in learning. Extensive experimental results on several public datasets demonstrate that our model generates better performance prediction for learners against existing methods. Moreover, LBKT shows good interpretability in tracking learners' knowledge state by incorporating the learning behavior effects. Our codes are available at https://github.com/xbh0720/LBKT.

Automatically generating controllable and diverse mathematical word problems (MWPs) which conform to equations and topics is a crucial task in information retrieval and natural language generation. Recent deep learning models mainly focus on improving the problem readability but overlook the mathematical logic coherence, which tends to generate unsolvable problems. In this paper, we draw inspiration from the human problem-designing process and propose a Mathematical structure Planning and Knowledge enhanced Generation model (MaPKG), following the "plan-then-generate" steps. Specifically, we propose a novel dynamic planning module to make sentence-level equation plans and a dual-attention mechanism for word-level generation, incorporating equation structure representation and external commonsense knowledge. Extensive experiments on two MWP datasets show our model can guarantee more solvable, high-quality, and diverse problems. Our code is available at https://github.com/KenelmQLH/MaPKG.git

Social recommender systems play a key role in solving the problem of information overload. In order to better extract latent hierarchical property in the data, they usually explore the user-user connections and user-item interactions in hyperbolic space. Existing methods resort tangent spaces to realize some operations (e.g., matrix multiplication) on hyperbolic manifolds. However, frequently projecting between the hyperbolic space and the tangent space will destroy the global structure of the manifold and reduce the accuracy of predictions. Besides, decisions made by users are often influenced by multi-aspect potential preferences, which are usually represented as a vector for each user. To this end, we design a novel hyperbolic-to-hyperbolic user representation with multi-aspect social recommender system, namely H2HMSR, which directly works in hyperbolic space. Extensive experiments on three public datasets demonstrate that our model can adequately extract social information of users with multi-aspect preferences and outperforms hyperbolic and Euclidean counterparts.

Reasoning answers to mathematical problems requires machines to think and operate like a human to learn knowledge from mathematical data, which is one of the fundamental tasks for exploring general artificial intelligence. Most solutions focus on mimicking how humans understand problems, which generate the necessary expressions for answers. However, they are still far from enough since they ignore the core ability of humans to acquire knowledge from experience. In this paper, we propose a Cognitive Solver (CogSolver) that is capable of autonomously learning knowledge from scratch to solve mathematical problems, inspired by two cognitive science theories. Specifically, we draw one insight from the dual process theory to establish an intelligent BRAIN-ARM framework, and refer to another information processing theory to summarize the knowledge learning process into Store-Apply-Update steps. In CogSolver, the BRAIN system stores three types of mathematical knowledge, including semantics knowledge, relation knowledge, and mathematic rule knowledge. Then, the ARM system applies the knowledge in BRAIN to answer the problems. Specifically, we design a knowledge-aware module and a commutative module in ARM to improve its reasoning ability, where the knowledge is organically integrated into answer reasoning process. After solving the problems, BRAIN updates the stored knowledge according to the feedback of ARM, where we develop knowledge filters to eliminate the redundant ones and further form a more reasonable knowledge base. Our CogSolver carries out the above three steps iteratively, which behaves more like a human. We conduct extensive experiments on real-world math word problem datasets. The experimental results demonstrate the improvement in answer reasoning and clearly show how CogSolver gains knowledge from the problems, leading to superior interpretability. Our codes are available at https://github.com/bigdata-ustc/CogSolver.

Cognitive diagnosis, aiming at providing an approach to reveal the proficiency level of learners on knowledge concepts, plays an important role in intelligent education area and has recently received more and more attention. Although a number of works have been proposed in recent years, most of contemporary works acquire the traits parameters of learners and items in a transductive way, which are only suitable for stationary data. However, in the real scenario, the data is collected online, where learners, test items and interactions usually grow continuously, which can rarely meet the stationary condition. To this end, we propose a novel framework, Incremental Cognitive Diagnosis (ICD), to tailor cognitive diagnosis into the online scenario of intelligent education. Specifically, we first design a Deep Trait Network (DTN), which acquires the trait parameters in an inductive way rather than a transductive way. Then, we propose an Incremental Update Algorithm (IUA) to balance the effectiveness and training efficiency. We carry out Turning Point (TP) analysis to reduce update frequency, where we derive the minimum update condition based on the monotonicity theory of cognitive diagnosis. Meanwhile, we use a momentum update strategy on the incremental data to decrease update time without sacrificing effectiveness. Moreover, to keep the trait parameters as stable as possible, we refine the loss function in the incremental updating stage. Last but no least, our ICD is a general framework which can be applied to most of contemporary cognitive diagnosis models. To the best of our knowledge, this is the first attempt to investigate the incremental cognitive diagnosis problem with theoretical results about the update condition and a tailored incremental learning strategy. Extensive experiments demonstrate the effectiveness and robustness of our method.