HALT: Hallucination Assessment via Latent Testing

Hallucination in large language models (LLMs) can be understood as a failure of faithful readout: although internal representations may encode uncertainty about a query, decoding pressures still yield a fluent answer. We propose lightweight residual probes that read hallucination risk directly from intermediate hidden states of question tokens, motivated by the hypothesis that these layers retain epistemic signals that are attenuated in the final decoding stage. The probe is a small auxiliary network whose computation is orders of magnitude cheaper than token generation and can be evaluated fully in parallel with inference, enabling near-instantaneous hallucination risk estimation with effectively zero added latency in low-risk cases. We deploy the probe as an agentic critic for fast selective generation and routing, allowing LLMs to immediately answer confident queries while delegating uncertain ones to stronger verification pipelines. Across four QA benchmarks and multiple LLM families, the method achieves strong AUROC and AURAC, generalizes under dataset shift, and reveals interpretable structure in intermediate representations, positioning fast internal uncertainty readout as a principled foundation for reliable agentic AI.

From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs

Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems-often formulated as partial differential equations (PDEs)-has garnered increasing attention. While most existing research concentrates on theoretical properties (such as well-posedness, regularity, and continuity) of the solutions, alongside direct AI-driven methods for solving PDEs, the challenge of uncovering symbolic relationships within these equations remains largely unexplored. In this paper, we propose leveraging large language models (LLMs) to learn such symbolic relationships. Our results demonstrate that LLMs can effectively predict the operators involved in PDE solutions by utilizing the symbolic information in the PDEs. Furthermore, we show that discovering these symbolic relationships can substantially improve both the efficiency and accuracy of the finite expression method for finding analytical approximation of PDE solutions, delivering a fully interpretable solution pipeline. This work opens new avenues for understanding the symbolic structure of scientific problems and advancing their solution processes.