arXiv:2605.24041v2 Announce Type: cross Abstract: Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), which augments pre-trained operators with a learned refinement module iteratively applied via fixed-point iteration. IRNO decomposes the prediction into a coarse initialization followed by successive residual corrections, paralleling classical numerical solvers. Under local assumptions, we establish contraction of the induced operator, ensuring convergence to a unique fixed point. To explicitly target high-frequency errors, we propose a progressive spectral loss that adaptively increases penalty on high-frequency components over refinement steps during training. Across physical systems, IRNO consistently lowers error, with up to 56.05% improvement on turbulent flow. On Active Matter, spectral analysis reveals that, relative to base operator, the normalized error ratios decrease to 27.72-36.10% in low-, 5.07-6.68% in mid-, and 1.48-2.04% in high-frequencies, remaining stable beyond the trained iteration count. Code is available at https://github.com/xiaotianliu-dartmouth/Iterative_Refinement_Neural_Operator

arXiv:2603.29232v1 Announce Type: cross Abstract: Large language models (LLMs) are widely applied to data analytics over documents, yet direct reasoning over long, noisy documents remains brittle and error-prone. Hence, we study document question answering (QA) that consolidates dispersed evidence into a structured output (e.g., a table, graph, or chunks) to support reliable, verifiable QA. We propose a two-pillar framework, LiteCoST, to achieve both high accuracy and low latency with small language models (SLMs). Pillar 1: Chain-of-Structured-Thought (CoST). We introduce a CoST template, a schema-aware instruction that guides a strong LLM to produce both a step-wise CoST trace and the corresponding structured output. The process induces a minimal structure, normalizes entities/units, aligns records, serializes the output, and verifies/refines it, yielding auditable supervision. Pillar 2: SLM fine-tuning. The compact models are trained on LLM-generated CoST data in two stages: Supervised Fine-Tuning for structural alignment, followed by Group Relative Policy Optimization (GRPO) incorporating triple rewards for answer/format quality and process consistency. By distilling structure-first behavior into SLMs, this approach achieves LLM-comparable quality on multi-domain long-document QA using 3B/7B SLMs, while delivering 2-4x lower latency than GPT-4o and DeepSeek-R1 (671B). The code is available at https://github.com/HKUSTDial/LiteCoST.

Nature, Published online: 01 April 2026; doi:10.1038/s41586-026-10364-3

A dual-symmetry-guided strategy is used to assemble a broad class of complex Archimedean lattices and two-dimensional quasicrystalline structures, providing a general and experimentally accessible route to complex-symmetry materials.