ToolMATH: A Math Tool Benchmark for Realistic Long-Horizon Multi-Tool Reasoning

We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution. It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability. \ToolMATH provides actionable diagnostic evidence of failure modes in tool-augmented agents, helping identify the control mechanisms required for robustness. \ToolMATH roughly contains 8k questions and 12k tools; we provide an additional hard-set \ToolMATHHard with questions and tools. Our evaluation reveals that the key failure factor is due to the inability to reason, leading to the accumulation of intermediate results' errors and constrain later decisions. Tool-list redundancy do not simply add noise, but amplify small early deviations into irreversible execution drift. The benchmark highlights that when the intended capability is missing, distractor tools can sometimes serve as partial substitutes in solution paths, yet they can also mislead models into ungrounded tool trajectories. Finally, comparisons between tool-use protocols emphasize that improvements come less from local action selection and more from long-range plan coherence and disciplined use of observations.

GRADE: Generating multi-hop QA and fine-gRAined Difficulty matrix for RAG Evaluation

Retrieval-Augmented Generation (RAG) systems are widely adopted in knowledge-intensive NLP tasks, but current evaluations often overlook the structural complexity and multi-step reasoning required in real-world scenarios. These benchmarks overlook key factors such as the interaction between retrieval difficulty and reasoning depth. To address this gap, we propose \textsc{GRADE}, a novel evaluation framework that models task difficulty along two orthogonal dimensions: (1) reasoning depth, defined by the number of inference steps (hops), and (2) semantic distance between the query and its supporting evidence. We construct a synthetic multi-hop QA dataset from factual news articles by extracting knowledge graphs and augmenting them through semantic clustering to recover missing links, allowing us to generate diverse and difficulty-controlled queries. Central to our framework is a 2D difficulty matrix that combines generator-side and retriever-side difficulty. Experiments across multiple domains and models show that error rates strongly correlate with our difficulty measures, validating their diagnostic utility. \textsc{GRADE} enables fine-grained analysis of RAG performance and provides a scalable foundation for evaluating and improving multi-hop reasoning in real-world applications.