Augmenting large language models (LLMs) with tools significantly enhances their problem-solving potential across multifaceted tasks. However, current tools automatically created by LLMs often serve as a mere summary of specific problems or solutions, which face two main issues: 1) Low reusability: The tools are overly problem-specific and struggle to handle new problems. 2) Limited diversity: The toolsets are too narrow, limiting their application to address a broader range of different problems. In this paper, we propose the Knowledge-grounded Tool Creation with Evolution (KTCE) framework, which aims to craft reusable and comprehensive toolsets for LLMs in a two-stage process. In the first stage (Knowledge-based Tool Creation), we conceptualize tools as a form of executable domain knowledge and propose a problem-knowledge-tool paradigm. Specifically, we leverage LLMs to abstract "knowledge" from "problems" and create a three-layer knowledge tree of topics, concepts, and key points. This hierarchical structure serves as a foundation for inducing atomic "tools" from "knowledge", grounding them in fundamental concepts and enhancing their usability. In the second stage (Tool Evolutionary Search), we evolve the toolsets through several actions including tool selection, mutation, and crossover. This stage mimics the biological evolution process, aiding toolsets in discovering new tools or updating existing ones, thereby increasing the diversity of the toolset. Experiments on challenging mathematical/tabular/scientific reasoning tasks demonstrate that our approach achieves substantial accuracy improvements ranging from 6.23% to 18.49% on average. Moreover, in-depth analyses reveal the superior characteristics of our toolkit, including high reusability, high diversity, and high generalizability on cross-data/LLM performance with low complexity.

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.

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.