arXiv subjects

Thomas Hou

Publications and source records attributed to Thomas Hou.

3 recordsLinked to original sources

arXiv2026

Think Twice Before You Act: Protecting LLM Agents Against Tool Description Poisoning via Isolated Planning

The integration of external tools has substantially expanded the capabilities of large language model (LLM) agents, but it also introduces new attack surfaces beyond prompt injection. In particular, cross-tool description poisoning can manipulate planner-visible tool metadata to steer an agent's trajectory, even if the poisoned tool itself is never chosen. To understand the effectiveness of existing defenses against this emerging threat, we first evaluate several prompt-injection defenses and find that they transfer poorly to cross-tool description poisoning. A key observation is that poisoned descriptions persist in the planning context across steps, enabling continuous influence over subsequent tool choices. Building on this insight, we propose Tool-Guard, a novel system-level defense based on a new concept called isolated planning, in which tool invocations that are detected as misaligned or suspicious cause the corresponding tool to be placed in a quarantined list (the influenced list), breaking further influence from poisoned descriptions. With this influence isolated, the tool can continue to be used to support the task, enabling a robust defense that preserves legitimate tool utility. Experiments on the AgentDojo and ASB benchmarks show that Tool-Guard substantially reduces attack success while maintaining high task utility. Our code is available at https://github.com/shishishi123/Tool-Guard.

cs.CR↗

arXiv2025

Nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes Equation

The nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes equations is one of the central open problems in mathematical fluid dynamics. In this paper, we provide, to our knowledge, the first rigorous computer-assisted proof demonstrating such nonuniqueness. Inspired by earlier works in this area, we construct a Leray-Hopf solution in the self-similar setting and then establish the existence of a second solution by analyzing the stability of the linearized operator around this profile, showing that it corresponds to an unstable perturbation. To achieve this, we develop an innovative numerical method that computes candidate solutions with high precision and propose a framework for rigorously establishing exact solutions in a neighborhood of these candidates. A key step is to decompose the linearized operator into a coercive part plus a compact perturbation, which is further approximated by a finite-rank operator up to a small error. The invertibility of the linearized operator restricted to the image of this finite-rank approximation is then rigorously verified using computer-assisted proofs. This certifies the existence of an unstable eigenpair and, consequently, yields a second solution - indeed, infinitely many Leray-Hopf solutions.

math.AP↗

arXiv2022

FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution operators in function spaces and leverages physics losses during training to penalize deviations from known physics laws. Spectral differentiation provides an efficient way to compute derivatives for the physics losses, but it inherently assumes periodicity. When applied to non-periodic functions, this assumption can lead to significant errors, including Gibbs phenomena near domain boundaries which degrade the accuracy of both function representations and derivative computations. To overcome this limitation, we introduce the FC-PINO (Fourier-Continuation-based Physics-Informed Neural Operator) architecture which extends the accuracy and efficiency of PINO and spectral differentiation to non-periodic and non-smooth PDEs. In FC-PINO, we propose integrating Fourier continuation into the PINO framework, and test two different continuation approaches: FC-Legendre and FC-Gram. By transforming non-periodic signals into periodic functions on extended domains in a well-conditioned manner, Fourier continuation enables fast and accurate derivative computations. This approach avoids the discretization sensitivity of finite differences and the memory overhead of automatic differentiation. We demonstrate that standard PINO fails (without padding) or struggles (even with padding) to solve non-periodic and non-smooth PDEs with high precision, across challenging benchmarks. In contrast, the proposed FC-PINO provides accurate, robust, and scalable solutions, substantially outperforming PINO alternatives, and demonstrating that Fourier continuation is critical for extending PINO to a wider range of PDE problems when high-precision solutions are needed.

cs.LG↗