Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
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[1] Dmitry Yarotsky,et al. Optimal approximation of continuous functions by very deep ReLU networks , 2018, COLT.
[2] John A. Nelder,et al. A Simplex Method for Function Minimization , 1965, Comput. J..
[3] Ruosong Wang,et al. Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks , 2019, ICML.
[4] Kurt Hornik,et al. Multilayer feedforward networks are universal approximators , 1989, Neural Networks.
[5] Amos Ron,et al. Approximation using scattered shifts of a multivariate function , 2008, 0802.2517.
[6] E Weinan,et al. Representation formulas and pointwise properties for Barron functions , 2020, ArXiv.
[7] Philipp Petersen,et al. Optimal approximation of piecewise smooth functions using deep ReLU neural networks , 2017, Neural Networks.
[8] E. Weinan,et al. A Priori Estimates of the Population Risk for Residual Networks , 2019, ArXiv.
[9] F. Cao,et al. The rate of approximation of Gaussian radial basis neural networks in continuous function space , 2013 .
[10] Yuanzhi Li,et al. Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers , 2018, NeurIPS.
[11] Namig J. Guliyev,et al. Approximation capability of two hidden layer feedforward neural networks with fixed weights , 2018, Neurocomputing.
[12] Zuowei Shen,et al. Deep Network Approximation for Smooth Functions , 2020, ArXiv.
[13] Charles K. Chui,et al. Construction of Neural Networks for Realization of Localized Deep Learning , 2018, Front. Appl. Math. Stat..
[14] R. Srikant,et al. Why Deep Neural Networks? , 2016, ArXiv.
[15] Masaaki Imaizumi,et al. Adaptive Approximation and Estimation of Deep Neural Network to Intrinsic Dimensionality , 2019, ArXiv.
[16] Shijun Zhang,et al. Nonlinear Approximation via Compositions , 2019, Neural Networks.
[17] E Weinan,et al. Exponential convergence of the deep neural network approximation for analytic functions , 2018, Science China Mathematics.
[18] Yoram Singer,et al. Adaptive Subgradient Methods for Online Learning and Stochastic Optimization , 2011, J. Mach. Learn. Res..
[19] Amos Ron,et al. Nonlinear approximation using Gaussian kernels , 2010 .
[20] Matus Telgarsky,et al. Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks , 2020, ICLR.
[21] Zuowei Shen,et al. Deep Learning via Dynamical Systems: An Approximation Perspective , 2019, Journal of the European Mathematical Society.
[22] Haizhao Yang,et al. Deep ReLU networks overcome the curse of dimensionality for bandlimited functions , 2019, 1903.00735.
[23] Lingfeng Niu,et al. Optimization Strategies in Quantized Neural Networks: A Review , 2019, 2019 International Conference on Data Mining Workshops (ICDMW).
[24] Lei Wu,et al. Approximation Analysis of Convolutional Neural Networks , 2023, East Asian Journal on Applied Mathematics.
[25] Allan Pinkus,et al. Lower bounds for approximation by MLP neural networks , 1999, Neurocomputing.
[26] R. Pinnau,et al. A consensus-based model for global optimization and its mean-field limit , 2016, 1604.05648.
[27] Kunihiko Fukushima,et al. Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position , 1980, Biological Cybernetics.
[28] Arnulf Jentzen,et al. Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations , 2018, SIAM J. Math. Data Sci..
[29] Riccardo Poli,et al. Particle swarm optimization , 1995, Swarm Intelligence.
[30] Taiji Suzuki,et al. Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality , 2018, ICLR.
[31] C. D. Gelatt,et al. Optimization by Simulated Annealing , 1983, Science.
[32] Tong Zhang,et al. Accelerating Stochastic Gradient Descent using Predictive Variance Reduction , 2013, NIPS.
[33] Wu Lei. A PRIORI ESTIMATES OF THE POPULATION RISK FOR TWO-LAYER NEURAL NETWORKS , 2020 .
[34] Michael Griebel,et al. On a Constructive Proof of Kolmogorov’s Superposition Theorem , 2009 .
[35] Jack Xin,et al. Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets , 2019, ICLR.
[36] Haizhao Yang,et al. Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem , 2019, Neural Networks.
[37] Dmitry Yarotsky,et al. The phase diagram of approximation rates for deep neural networks , 2019, NeurIPS.
[38] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..
[39] Andrew R. Barron,et al. Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.
[40] Peter L. Bartlett,et al. Almost Linear VC-Dimension Bounds for Piecewise Polynomial Networks , 1998, Neural Computation.
[41] Gitta Kutyniok,et al. Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms , 2019, Analysis and Applications.
[42] Goldberg,et al. Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.
[43] Rémi Gribonval,et al. Approximation Spaces of Deep Neural Networks , 2019, Constructive Approximation.
[44] Ran El-Yaniv,et al. Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations , 2016, J. Mach. Learn. Res..
[45] Dmitry Yarotsky,et al. Error bounds for approximations with deep ReLU networks , 2016, Neural Networks.
[46] Sungho Shin,et al. Quantized Neural Networks: Characterization and Holistic Optimization , 2020, 2020 IEEE Workshop on Signal Processing Systems (SiPS).
[47] Yoshua Bengio,et al. Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation , 2013, ArXiv.
[48] Qiang Du,et al. New error bounds for deep networks using sparse grids. , 2017, 1712.08688.
[49] Yuan Cao,et al. Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks , 2019, NeurIPS.
[50] Boris Igelnik,et al. Kolmogorov's spline network , 2003, IEEE Trans. Neural Networks.
[51] V. Tikhomirov. On the Representation of Continuous Functions of Several Variables as Superpositions of Continuous Functions of a Smaller Number of Variables , 1991 .
[52] Qiang Du,et al. New Error Bounds for Deep ReLU Networks Using Sparse Grids , 2017, SIAM J. Math. Data Sci..
[53] V. Tikhomirov. On the Representation of Continuous Functions of Several Variables as Superpositions of Continuous Functions of one Variable and Addition , 1991 .
[54] Dan Boneh,et al. On genetic algorithms , 1995, COLT '95.
[55] Vera Kurková,et al. Kolmogorov's theorem and multilayer neural networks , 1992, Neural Networks.
[56] Tuo Zhao,et al. Efficient Approximation of Deep ReLU Networks for Functions on Low Dimensional Manifolds , 2019, NeurIPS.
[57] Lei Wu,et al. A Priori Estimates of the Generalization Error for Two-layer Neural Networks , 2018, Communications in Mathematical Sciences.
[58] R. DeVore,et al. Optimal nonlinear approximation , 1989 .
[59] Tao Luo,et al. Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory , 2020, ArXiv.
[60] Ding-Xuan Zhou,et al. Universality of Deep Convolutional Neural Networks , 2018, Applied and Computational Harmonic Analysis.
[61] Yuan Cao,et al. How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks? , 2019, ICLR.
[62] Yang Liu,et al. Two-Step Quantization for Low-bit Neural Networks , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.
[63] Lorenzo Rosasco,et al. Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review , 2016, International Journal of Automation and Computing.
[64] Shi Jin,et al. A consensus-based global optimization method for high dimensional machine learning problems , 2019 .
[65] P. Werbos,et al. Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .
[66] Helmut Bölcskei,et al. Optimal Approximation with Sparsely Connected Deep Neural Networks , 2017, SIAM J. Math. Data Sci..
[67] Liang Chen,et al. A note on the expressive power of deep rectified linear unit networks in high‐dimensional spaces , 2019, Mathematical Methods in the Applied Sciences.
[68] Yang Wang,et al. Approximation in shift-invariant spaces with deep ReLU neural networks , 2020, ArXiv.
[69] Sven Behnke,et al. Evaluation of Pooling Operations in Convolutional Architectures for Object Recognition , 2010, ICANN.
[70] Zuowei Shen,et al. Deep Network Approximation Characterized by Number of Neurons , 2019, Communications in Computational Physics.
[71] Arthur Jacot,et al. Neural tangent kernel: convergence and generalization in neural networks (invited paper) , 2018, NeurIPS.
[72] Abbas Mehrabian,et al. Nearly-tight VC-dimension bounds for piecewise linear neural networks , 2017, COLT.