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We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing.
Quasi-monte carlo sampling for machine-learning partial differential equations
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How much over-parameterization is sufficient to learn deep relu networks?
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Reconstructing continuous distributions of 3d protein structure from cryo-em images
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Solving parametric pde problems with artificial neural networks
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Error bounds for approximations with deep relu networks
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Towards theoretical understanding of large batch training in stochastic gradient descent
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Gradient descent provably optimizes over-parameterized neural networks
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Exponential convergence of the deep neural network approximation for analytic functions
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The deep ritz method: a deep learning-based numerical algorithm for solving variational problems
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Solving high-dimensional partial differential equations using deep learning
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Neural tangent kernel: Convergence and generalization in neural networks
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Optimal approximation of continuous functions by very deep relu networks
Yarotsky, D · 2018
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Arora, S., Du, S. S., Hu, W., Li, Z., and Wang, R · 2019
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A phase shift deep neural network for high frequency approximation and wave problems
Cai, W., Li, X., and Liu, L · 2019
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Towards understanding the spectral bias of deep learning
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Local deep implicit functions for 3d shape
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Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion monte carlo like approach
Han, J., Lu, J., and Zhou, M · 2020
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Int-deep: A deep learning initialized iterative method for nonlinear problems
Huang, J., Wang, H., and Yang, H · 2020
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Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
Jagtap, A. D., Kawaguchi, K., and Em Karniadakis, G · 2020
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Learning implicit fields for generative shape modeling
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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
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Deep nitsche method: Deep ritz method with essential boundary conditions
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Theory of the frequency principle for general deep neural networks
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Implicit surface representations as layers in neural networks
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Deep relu networks overcome the curse of dimensionality for bandlimited functions
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Wide neural networks of any depth evolve as linear models under gradient descent
Lee, J., Xiao, L., Schoenholz, S. S., Bahri, Y., Novak, R., Sohl-Dickstein, J., and Pennington, J · 2020
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Dist: Rendering deep implicit signed distance function with differentiable sphere tracing
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Multi-scale deep neural network (mscalednn) for solving poisson-boltzmann equation in complex domains
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Deep Network Approximation for Smooth Functions
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Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
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Enforcing exact boundary and initial conditions in the deep mixed residual method
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Nerf: Representing scenes as neural radiance fields for view synthesis
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Error bounds for deep relu networks using the kolmogorov–arnold superposition theorem
Montanelli, H. and Yang, H · 2020
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Neural network approximation: Three hidden layers are enough
Shen, Z., Yang, H., and Zhang, S · 2020
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Implicit neural representations with periodic activation functions
Sitzmann, V., Martel, J., Bergman, A., Lindell, D., and Wetzstein, G · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., and Ng, R · 2020
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Multi-scale deep neural network (mscalednn) methods for oscillatory stokes flows in complex domains
Wang, B · 2020
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When and why pinns fail to train: A neural tangent kernel perspective
Wang, S., Yu, X., and Perdikaris, P · 2020
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Frequency principle: Fourier analysis sheds light on deep neural networks
Xu, Z.-Q. J., Zhang, Y., Luo, T., Xiao, Y., and Ma, Z · 2020
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Deep network with approximation error being reciprocal of width to power of square root of depth
Shen, Z., Yang, H., and Zhang, S · 2021
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