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cs.LG2024★ 1 cited
Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
Hao Liu, Zecheng Zhang, Wenjing Liao +1
Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for un…
stat.ML2024
Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation
Hao Liu, Jiahui Cheng, Wenjing Liao
Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Neverthe…
cs.LG2024
Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
Hao Liu, Biraj Dahal, Rongjie Lai +1
Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this co…