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09/12/2023
Interpolation, Approximation and Controllability of Deep Neural Networks
We investigate the expressive power of deep residual neural networks ide...
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11/25/2022
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks
We study the approximation of shift-invariant or equivariant functions b...
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08/18/2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems
We study the approximation of functions which are invariant with respect...
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05/19/2022
Neural Network Architecture Beyond Width and Depth
This paper proposes a new neural network architecture by introducing an ...
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03/10/2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
Discretization invariant learning aims at learning in the infinite-dimen...
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11/15/2021
ReLU Network Approximation in Terms of Intrinsic Parameters
This paper studies the approximation error of ReLU networks in terms of ...
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07/06/2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons
This paper develops simple feed-forward neural networks that achieve the...
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02/28/2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth
This paper concentrates on the approximation power of deep feed-forward ...
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10/25/2020
Neural Network Approximation: Three Hidden Layers Are Enough
A three-hidden-layer neural network with super approximation power is in...
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06/22/2020
Deep Network Approximation with Discrepancy Being Reciprocal of Width to Power of Depth
A new network with super approximation power is introduced. This network...
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04/18/2020
Optimization in Machine Learning: A Distribution Space Approach
We present the viewpoint that optimization problems encountered in machi...
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01/09/2020
Deep Network Approximation for Smooth Functions
This paper establishes optimal approximation error characterization of d...
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12/22/2019
Deep Learning via Dynamical Systems: An Approximation Perspective
We build on the dynamical systems approach to deep learning, where deep ...
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06/13/2019
Deep Network Approximation Characterized by Number of Neurons
This paper quantitatively characterizes the approximation power of deep ...
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02/26/2019
Nonlinear Approximation via Compositions
We study the approximation efficiency of function compositions in nonlin...
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09/29/2018
On the Convergence and Robustness of Batch Normalization
Despite its empirical success, the theoretical underpinnings of the stab...
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02/17/2016
Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis
Image restoration is one of the most important areas in imaging science....
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12/25/2011