6 papers
Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain Ridge Integral Spaces for ReLU Networks
Juncai He, Zitong Tian
We develop the space and approximation theory for shallow neural networks with activations. The central object is the Radon-domain space $\mathcal{R}L…
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
Shuang Chen, Juncai He, Xue-Cheng Tai
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition an…
Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
Juncai He, Xinliang Liu, Zitong Tian
This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron sp…
Second Language (Arabic) Acquisition of LLMs via Progressive Vocabulary Expansion
Jianqing Zhu, Huang Huang, Zhihang Lin +18
This paper addresses the critical need for democratizing large language models (LLM) in the Arab world, a region that has seen slower progress in developing models comparable to st…
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Juncai He, Xinliang Liu, Jinchao Xu
Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framew…
Alignment at Pre-training! Towards Native Alignment for Arabic LLMs
Juhao Liang, Zhenyang Cai, Jianqing Zhu +9
The alignment of large language models (LLMs) is critical for developing effective and safe language models. Traditional approaches focus on aligning models during the instruction…