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Ge Yan

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2 published item(s)

preprint2026arXiv

LLM Agents Already Know When to Call Tools -- Even Without Reasoning

Tool-augmented LLM agents tend to call tools indiscriminately, even when the model can answer directly. Each unnecessary call wastes API fees and latency, yet no existing benchmark systematically studies when a tool call is actually needed. We propose When2Tool, a benchmark of 18 environments (15 single-hop, 3 multi-hop) spanning three categories of tool necessity -- computational scale, knowledge boundaries, and execution reliability -- each with controlled difficulty levels that create a clear decision boundary between tool-necessary and tool-unnecessary tasks. We evaluate two families of training-free baselines: Prompt-only (varying the prompt to discourage unnecessary calls) and Reason-then-Act (requiring the model to reason about tool necessity before acting). Both provide limited control: Prompt-only suppresses necessary calls alongside unnecessary ones, and Reason-then-Act still incurs a disproportionate accuracy cost on hard tasks. To understand why these baselines fail, we probe the models' hidden states and find that tool necessity is linearly decodable from the pre-generation representation with AUROC 0.89--0.96 across six models, substantially exceeding the model's own verbalized reasoning. This reveals that models already know when tools are needed, but fail to act on this knowledge during generation. Building on this finding, we propose Probe&Prefill, which uses a lightweight linear probe to read the hidden-state signal and prefills the model's response with a steering sentence. Across all models tested, Probe&Prefill reduces tool calls by 48% with only 1.7% accuracy loss, while the best baseline at comparable accuracy only reduces 6% of tool calls, or achieves a similar tool call reduction but incurs a 5$\times$ higher accuracy loss. Our code is available at https://github.com/Trustworthy-ML-Lab/when2tool

preprint2021arXiv

Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws

The paper describes the construction of entropy-stable discontinuous Galerkin difference (DGD) discretizations for hyperbolic conservation laws on unstructured grids. The construction takes advantage of existing theory for entropy-stable summation-by-parts (SBP) discretizations. In particular, the paper shows how DGD discretizations -- both linear and nonlinear -- can be constructed by defining the SBP trial and test functions in terms of interpolated DGD degrees of freedom. In the case of entropy-stable discretizations, the entropy variables rather than the conservative variables must be interpolated to the SBP nodes. A fully-discrete entropy-stable scheme is obtained by adopting the relaxation Runge-Kutta version of the midpoint method. In addition, DGD matrix operators for the first derivative are shown to be dense-norm SBP operators. Numerical results are presented to verify the accuracy and entropy-stability of the DGD discretization in the context of the Euler equations. The results suggest that DGD and SBP solution errors are similar for the same number of degrees of freedom. Finally, an investigation of the DGD spectra shows that spectral radius is relatively insensitive to discretization order; however, the high-order methods do suffer from the linear instability reported for other entropy-stable discretizations.