arXiv subjects

Chenghan Wu

Publications and source records attributed to Chenghan Wu.

7 recordsLinked to original sources

arXiv2026

Chain of Operators: An Inference-Time Harness for In-Context Operator Learning

While scientific foundation models show immense promise in accelerating physical simulations and numerical forecasting, they remain notoriously brittle when encountering out-of-distribution (OOD) scenarios. Adapting these generalist models to complex OOD tasks typically requires expensive parameter fine-tuning. In linguistic AI, this bottleneck is bypassed using "harnesses", which serve as external scaffolding such as reasoning chains and tool use to adapt frozen weights to complex tasks, yet designing an equivalent harness for physical domains remains an open frontier. To bridge this gap, we introduce Chain of Operators (CHOP), a framework that guides a frozen foundation model through complex OOD tasks without updating a single weight. By exploiting the in-context learning capability of In-Context Operator Networks (ICON), CHOP systematically decomposes unfamiliar problems into a sequence of explicit, closed-form mathematical operations and multiple model calls, translating OOD queries back into the model's learned operating regime. Across diverse benchmarks, including canonical PDE problems and real-world air-quality forecasting, CHOP consistently and substantially reduces inference errors compared to direct model evaluation. Crucially, these modular operator chains remain fully interpretable and can generalize across entirely distinct families of physical equations. Ultimately, this work demonstrates how frozen scientific models can adapt through programmable inference, establishing a modular, potential paradigm for agentic scientific computing.

cs.LG↗

arXiv2026

A foundation model of numerical intelligence with cross-disciplinary generalization

Intelligence is commonly understood as the ability to acquire and apply knowledge, adapt to unfamiliar situations and solve new problems. Large language models exhibit this capacity by inferring task-relevant knowledge from textual context and applying it to new tasks. Yet intelligence need not be confined to language. For scientific and social systems, we need models that acquire and apply knowledge from numerical context-an ability we call numerical intelligence. Here we introduce UNified In-Context Operator Networks (UNICON), a foundation model that exhibits numerical intelligence across disciplines. Using graph-based examples from a system as context, UNICON infers the predictive relation shared across them and applies it to queries from the same system. Across scientific and social systems, including those from disciplines absent from training, the same model approaches specialist performance without retraining. Combining UNICON with language-model agents to perform contextual ensemble learning (CEL) yields further gains, enabling it to surpass state-of-the-art specialists in a discipline unseen during training. We further show that training-corpus diversity improves generalization to unseen disciplines. Together, these results establish UNICON as a foundation model of numerical intelligence and position it as a building block for a broader ecosystem of artificial intelligence.

cs.AI↗

arXiv2026

Self-Improving Neural-Guided Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed bundling models capture this structure but become computationally intractable because the number of candidate bundles grows exponentially with the number of products. We develop a graph neural network (GNN)-guided pruning-then-optimization framework for bundle pricing with (non-)additive valuations. The method represents each instance as a compact segment-product graph, predicts segment-product inclusion probabilities, and accordingly prunes the exponential bundle space into a small candidate family; the final prices and bundle offerings are obtained by solving the mixed bundling formulation over the retained bundles, possibly refined by a GNN-guided local search. Because exact labels are available only at small scales, we further propose an iterative self-improvement procedure: the current GNN policies generate high-quality solutions on large-scale instances, which serve as near-optimal labels for training a stronger model at larger scales. Theoretically, we show that under mild conditions the proposed edge-output GNN class is expressive enough to represent the optimal product-assignment mapping, justifying the edge-level learning target. Numerical experiments show that the fastest proposed policy delivers 13-21% higher profit than bundle-size pricing on instances with up to 100 products at about 2% of its runtime.

cs.LG↗

arXiv2026

Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction

In-context operator learning enables neural networks to infer solution operators from contextual examples without weight updates. While prior work has demonstrated the effectiveness of this paradigm in leveraging vast datasets, a systematic comparison against single-operator learning using identical training data has been absent. We address this gap through controlled experiments comparing in-context operator learning against classical operator learning (single-operator models trained without contextual examples), under the same training steps and dataset. To enable this investigation on real-world spatiotemporal systems, we propose GICON (Graph In-Context Operator Network), combining graph message passing for geometric generalization with example-aware positional encoding for cardinality generalization. Experiments on air quality prediction across two Chinese regions show that in-context operator learning outperforms classical operator learning on complex tasks, generalizing across spatial domains and scaling robustly from few training examples to 100 at inference.

cs.LG↗

arXiv2025

A Survey of LLM-based Agents in Medicine: How far are we from Baymax?

Large Language Models (LLMs) are transforming healthcare through the development of LLM-based agents that can understand, reason about, and assist with medical tasks. This survey provides a comprehensive review of LLM-based agents in medicine, examining their architectures, applications, and challenges. We analyze the key components of medical agent systems, including system profiles, clinical planning mechanisms, medical reasoning frameworks, and external capacity enhancement. The survey covers major application scenarios such as clinical decision support, medical documentation, training simulations, and healthcare service optimization. We discuss evaluation frameworks and metrics used to assess these agents' performance in healthcare settings. While LLM-based agents show promise in enhancing healthcare delivery, several challenges remain, including hallucination management, multimodal integration, implementation barriers, and ethical considerations. The survey concludes by highlighting future research directions, including advances in medical reasoning inspired by recent developments in LLM architectures, integration with physical systems, and improvements in training simulations. This work provides researchers and practitioners with a structured overview of the current state and future prospects of LLM-based agents in medicine.

cs.CL↗

arXiv2024

Geometric Proof of the Irrationality of Square-Roots for Select Integers

This paper presents geometric proofs for the irrationality of square roots of select integers, extending classical approaches. Building on known geometric methods for proving the irrationality of sqrt(2), the authors explore whether similar techniques can be applied to other non-square integers. They begin by reviewing well-known results, such as Euclid's proof for the irrationality of sqrt(2), and discuss subsequent geometric extensions for sqrt(3), sqrt(5), and sqrt(6). The authors then introduce new geometric constructions, particularly using hexagons, to prove the irrationality of sqrt(6). Furthermore, the paper investigates the limitations and challenges of extending these geometric methods to triangular numbers. Through detailed geometric reasoning, the authors successfully generalize the approach to several square-free numbers and identify cases where the method breaks down. The paper concludes by inviting further exploration of geometric irrationality proofs for other integers, proposing potential avenues for future work.

math.HO↗

arXiv2023

Wafer-scale Graphene Electro-absorption Modulators Fabricated in a 300mm CMOS Platform

Graphene-based devices have shown great promise for several applications. For graphene devices to be used in real-world systems, it is necessary to demonstrate competitive device performance, repeatability of results, reliability, and a path to large-scale manufacturing with high yield at low cost. Here, we select single-layer graphene electro-absorption modulators as test vehicle and establish their wafer-scale integration in a 300mm pilot CMOS foundry environment. A hardmask is used to shape graphene, while tungsten-based contacts are fabricated using the damascene approach to enable CMOS-compatible fabrication. By analyzing data from hundreds of devices per wafer, the impact of specific processing steps on the performance could be identified and optimized. After optimization, modulation depth of 50 $\pm$ 4 dB/mm is demonstrated on 400 devices measured using 6 V peak-to-peak voltage. The electro-optical bandwidth is up to 15.1 $\pm$ 1 1.8 GHz for 25$μ$m-long devices. The results achieved are comparable to lab-based record-setting graphene devices of similar design and CVD graphene quality. By demonstrating the reproducibility of the results across hundreds of devices, this work resolves the bottleneck of graphene wafer-scale integration. Furthermore, CMOS-compatible processing enables co-integration of graphene-based devices with other photonics and electronics building blocks on the same chip, and for high-volume low-cost manufacturing.

physics.app-ph↗