DRIFT: Detecting Representational Inconsistencies for Factual Truthfulness

LLMs often produce fluent but incorrect answers, yet detecting such hallucinations typically requires multiple sampling passes or post-hoc verification, adding significant latency and cost. We hypothesize that intermediate layers encode confidence signals that are lost in the final output layer, and propose a lightweight probe to read these signals directly from hidden states. The probe adds less than 0.1\% computational overhead and can run fully in parallel with generation, enabling hallucination detection before the answer is produced. Building on this, we develop an LLM router that answers confident queries immediately while delegating uncertain ones to stronger models. Despite its simplicity, our method achieves SOTA AUROC on 10 out of 12 settings across four QA benchmarks and three LLM families, with gains of up to 13 points over prior methods, and generalizes across dataset shifts without retraining.

ReSearch: A Multi-Stage Machine Learning Framework for Earth Science Data Discovery

The rapid expansion of Earth Science data from satellite observations, reanalysis products, and numerical simulations has created a critical bottleneck in scientific discovery, namely identifying relevant datasets for a given research objective. Existing discovery systems are primarily retrieval-centric and struggle to bridge the gap between high-level scientific intent and heterogeneous metadata at scale. We introduce \textbf{ReSearch}, a multi-stage, reasoning-enhanced search framework that formulates Earth Science data discovery as an iterative process of intent interpretation, high-recall retrieval, and context-aware ranking. ReSearch integrates lexical search, semantic embeddings, abbreviation expansion, and large language model reranking within a unified architecture that explicitly separates recall and precision objectives. To enable realistic evaluation, we construct a literature-grounded benchmark by aligning natural language intent with datasets cited in peer-reviewed Earth Science studies. Experiments demonstrate that ReSearch consistently improves recall and ranking performance over baseline methods, particularly for task-based queries expressing abstract scientific goals. These results underscore the importance of intent-aware, multi-stage search as a foundational capability for reproducible and scalable Earth Science research.

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.

FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction

Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing neural network-based approaches typically require training a separate model for each case. To overcome these limitations, we introduce a novel multi-modal foundation model for large-scale simulations of differential equations: FMint-SDE (Foundation Model based on Initialization for stochastic differential equations). Based on a decoder-only transformer with in-context learning, FMint-SDE leverages numerical and textual modalities to learn a universal error-correction scheme. It is trained using prompted sequences of coarse solutions generated by conventional solvers, enabling broad generalization across diverse systems. We evaluate our models on a suite of challenging SDE benchmarks spanning applications in molecular dynamics, mechanical systems, finance, and biology. Experimental results show that our approach achieves a superior accuracy-efficiency tradeoff compared to classical solvers, underscoring the potential of FMint-SDE as a general-purpose simulation tool for dynamical systems.

Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains

Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive representations for traditional numerical methods and lead to difficult optimization landscapes for machine learning-based approaches. In this work, we introduce an enhanced Finite Expression Method (FEX) designed to address these challenges with improved accuracy, interpretability, and computational efficiency. The proposed framework incorporates three key innovations: a symbolic spectral composition module that enables FEX to learn and represent multiscale oscillatory behavior; a redesigned linear input layer that significantly expands the expressivity of the model; and an eigenvalue formulation that extends FEX to a new class of problems involving eigenvalue PDEs. Through extensive numerical experiments, we demonstrate that FEX accurately resolves oscillatory PDEs on domains containing multiple holes of varying shapes and sizes. Compared with existing neural network-based solvers, FEX achieves substantially higher accuracy while yielding interpretable, closed-form solutions that expose the underlying structure of the problem. These advantages, often absent in conventional finite element, finite difference, and black-box neural approaches, highlight FEX as a powerful and transparent framework for solving complex PDEs.

Efficient Kilometer-Scale Precipitation Downscaling with Conditional Wavelet Diffusion

Effective hydrological modeling and extreme weather analysis demand precipitation data at a kilometer-scale resolution, which is significantly finer than the 10 km scale offered by standard global products like IMERG. To address this, we propose the Wavelet Diffusion Model (WDM), a generative framework that achieves 10x spatial super-resolution (downscaling to 1 km) and delivers a 9x inference speedup over pixel-based diffusion models. WDM is a conditional diffusion model that learns the learns the complex structure of precipitation from MRMS radar data directly in the wavelet domain. By focusing on high-frequency wavelet coefficients, it generates exceptionally realistic and detailed 1-km precipitation fields. This wavelet-based approach produces visually superior results with fewer artifacts than pixel-space models, and delivers a significant gains in sampling efficiency. Our results demonstrate that WDM provides a robust solution to the dual challenges of accuracy and speed in geoscience super-resolution, paving the way for more reliable hydrological forecasts.

OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents

Optimization plays a vital role in scientific research and practical applications, but formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce \textbf{OptimAI}, a framework for solving \underline{Optim}ization problems described in natural language by leveraging LLM-powered \underline{AI} agents, achieving superior performance over current state-of-the-art methods. Our framework is built upon four key roles: (1) a \emph{formulator} that translates natural language problem descriptions into precise mathematical formulations; (2) a \emph{planner} that constructs a high-level solution strategy prior to execution; and (3) a \emph{coder} and a \emph{code critic} capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in $5.8\times$ and $3.1\times$ drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional $3.3\times$ productivity gain. Our design emphasizes multi-agent collaboration, allowing us to conveniently explore the synergistic effect of combining diverse models within a unified system. Our approach attains 88.1\% accuracy on the NLP4LP dataset and 71.2\% on the Optibench (non-linear w/o table) subset, reducing error rates by 58\% and 50\% respectively over prior best results.

LLMs Meet Finance: Fine-Tuning Foundation Models for the Open FinLLM Leaderboard

This paper investigates the application of large language models (LLMs) to financial tasks. We fine-tuned foundation models using the Open FinLLM Leaderboard as a benchmark. Building on Qwen2.5 and Deepseek-R1, we employed techniques including supervised fine-tuning (SFT), direct preference optimization (DPO), and reinforcement learning (RL) to enhance their financial capabilities. The fine-tuned models demonstrated substantial performance gains across a wide range of financial tasks. Moreover, we measured the data scaling law in the financial domain. Our work demonstrates the potential of large language models (LLMs) in financial applications.

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.

Parsing the Language of Expression: Enhancing Symbolic Regression with Domain-Aware Symbolic Priors

Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression method that integrates symbol priors from diverse scientific domains - including physics, biology, chemistry, and engineering - into the regression process. By systematically analyzing domain-specific expressions, we derive probability distributions of symbols to guide expression generation. We propose novel tree-structured recurrent neural networks (RNNs) that leverage these symbol priors, enabling domain knowledge to steer the learning process. Additionally, we introduce a hierarchical tree structure for representing expressions, where unary and binary operators are organized to facilitate more efficient learning. To further accelerate training, we compile characteristic expression blocks from each domain and include them in the operator dictionary, providing relevant building blocks. Experimental results demonstrate that leveraging symbol priors significantly enhances the performance of symbolic regression, resulting in faster convergence and higher accuracy.