Search Results for author: Siting Liu

Found 4 papers, 2 papers with code

Wasserstein proximal operators describe score-based generative models and resolve memorization

no code implementations9 Feb 2024 Benjamin J. Zhang, Siting Liu, Wuchen Li, Markos A. Katsoulakis, Stanley J. Osher

Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation.

Inductive Bias Memorization

Fine-Tune Language Models as Multi-Modal Differential Equation Solvers

1 code implementation9 Aug 2023 Liu Yang, Siting Liu, Stanley J. Osher

In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trained to learn operators and solve differential equations using prompted data, during the inference stage without weight updates.

Efficient Neural Network Language Modelling +1

In-Context Operator Learning with Data Prompts for Differential Equation Problems

2 code implementations17 Apr 2023 Liu Yang, Siting Liu, Tingwei Meng, Stanley J. Osher

This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update.

Operator learning

Fault-Tolerant Deep Learning: A Hierarchical Perspective

no code implementations5 Apr 2022 Cheng Liu, Zhen Gao, Siting Liu, Xuefei Ning, Huawei Li, Xiaowei Li

With the rapid advancements of deep learning in the past decade, it can be foreseen that deep learning will be continuously deployed in more and more safety-critical applications such as autonomous driving and robotics.

Autonomous Driving

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