{"list":"other","total":55,"rows":[{"id":"1912.01703","title":"PyTorch: An Imperative Style, High-Performance Deep Learning Library","created":"2019-12-03","cited_by_count":20305},{"id":"1806.07572","title":"Neural Tangent Kernel: Convergence and Generalization in Neural Networks","created":"2018-06-20","cited_by_count":2621},{"id":"1811.03962","title":"A Convergence Theory for Deep Learning via Over-Parameterization","created":"2018-11-09","cited_by_count":787},{"id":"1902.06720","title":"Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent","created":"2019-02-18","cited_by_count":738},{"id":"1812.07956","title":"On Lazy Training in Differentiable Programming","created":"2018-12-19","cited_by_count":675},{"id":"1810.02054","title":"Gradient Descent Provably Optimizes Over-parameterized Neural Networks","created":"2018-10-04","cited_by_count":659},{"id":"1610.01145","title":"Error bounds for approximations with deep ReLU networks","created":"2016-10-03","cited_by_count":574},{"id":"1811.03804","title":"Gradient Descent Finds Global Minima of Deep Neural Networks","created":"2018-11-09","cited_by_count":574},{"id":"1904.11955","title":"On Exact Computation with an Infinitely Wide Neural Net","created":"2019-04-26","cited_by_count":573},{"id":"1901.08584","title":"Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks","created":"2019-01-24","cited_by_count":566},{"id":"1501.01571","title":"An Introduction to Matrix Concentration Inequalities","created":"2015-01-07","cited_by_count":397},{"id":"1412.8690","title":"Breaking the Curse of Dimensionality with Convex Neural Networks","created":"2014-12-30","cited_by_count":331},{"id":"1808.01204","title":"Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data","created":"2018-08-03","cited_by_count":261},{"id":"2010.15110","title":"Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel","created":"2020-10-28","cited_by_count":187},{"id":"1709.05289","title":"Optimal approximation of piecewise smooth functions using deep ReLU neural networks","created":"2017-09-15","cited_by_count":179},{"id":"1905.12173","title":"On the Inductive Bias of Neural Tangent Kernels","created":"2019-05-29","cited_by_count":177},{"id":"1902.04674","title":"Towards moderate overparameterization: global convergence guarantees for training shallow neural networks","created":"2019-02-12","cited_by_count":176},{"id":"1802.03620","title":"Optimal approximation of continuous functions by very deep ReLU networks","created":"2018-02-10","cited_by_count":166},{"id":"2001.03040","title":"Deep Network Approximation for Smooth Functions","created":"2020-01-09","cited_by_count":164},{"id":"1810.08033","title":"Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality","created":"2018-10-18","cited_by_count":162},{"id":"2007.15801","title":"Finite Versus Infinite Neural Networks: an Empirical Study","created":"2020-07-31","cited_by_count":157},{"id":"1611.00740","title":"Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review","created":"2016-11-02","cited_by_count":155},{"id":"1906.04688","title":"An Improved Analysis of Training Over-parameterized Deep Neural Networks","created":"2019-06-11","cited_by_count":121},{"id":"1909.12292","title":"Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks","created":"2019-09-26","cited_by_count":121},{"id":"1909.05989","title":"Finite Depth and Width Corrections to the Neural Tangent Kernel","created":"2019-09-13","cited_by_count":115},{"id":"1902.07896","title":"Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms","created":"2019-02-21","cited_by_count":95},{"id":"2009.10713","title":"Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't","created":"2020-09-22","cited_by_count":95},{"id":"1901.02220","title":"Deep Neural Network Approximation Theory","created":"2019-01-08","cited_by_count":93},{"id":"1906.09477","title":"The phase diagram of approximation rates for deep neural networks","created":"2019-06-22","cited_by_count":88},{"id":"1607.07819","title":"Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $ \\ell^1 $ and $ \\ell^0 $ Controls","created":"2016-07-26","cited_by_count":84},{"id":"1911.12360","title":"How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?","created":"2019-11-27","cited_by_count":84},{"id":"1901.01608","title":"Scaling description of generalization with number of parameters in deep learning","created":"2019-01-06","cited_by_count":83},{"id":"1910.01619","title":"Beyond Linearization: On Quadratic and Higher-Order Approximation of Wide Neural Networks","created":"2019-10-03","cited_by_count":79},{"id":"2007.01580","title":"On the Similarity between the Laplace and Neural Tangent Kernels","created":"2020-07-03","cited_by_count":76},{"id":"1904.00377","title":"A Theoretical Analysis of Deep Neural Networks and Parametric PDEs","created":"2019-03-31","cited_by_count":74},{"id":"2009.10683","title":"Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS","created":"2020-09-22","cited_by_count":74},{"id":"2002.07867","title":"Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topology","created":"2020-02-18","cited_by_count":66},{"id":"2105.04026","title":"The Modern Mathematics of Deep Learning","created":"2021-05-09","cited_by_count":63},{"id":"1509.07385","title":"Provable approximation properties for deep neural networks","created":"2015-09-24","cited_by_count":60},{"id":"1906.03593","title":"Quadratic Suffices for Over-parametrization via Matrix Chernoff Bound","created":"2019-06-09","cited_by_count":59},{"id":"2001.07523","title":"The gap between theory and practice in function approximation with deep neural networks","created":"2020-01-16","cited_by_count":54},{"id":"1905.01208","title":"Approximation spaces of deep neural networks","created":"2019-05-03","cited_by_count":51},{"id":"1902.10170","title":"Nonlinear Approximation via Compositions","created":"2019-02-26","cited_by_count":38},{"id":"1910.06956","title":"Neural tangent kernels, transportation mappings, and universal approximation","created":"2019-10-15","cited_by_count":30},{"id":"2104.02746","title":"Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces","created":"2021-04-06","cited_by_count":30},{"id":"2202.00553","title":"Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization","created":"2022-02-01","cited_by_count":30},{"id":"1908.02419","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","created":"2019-08-05","cited_by_count":29},{"id":"1905.10826","title":"On Learning Over-parameterized Neural Networks: A Functional Approximation Perspective","created":"2019-05-26","cited_by_count":28},{"id":"2111.01875","title":"Subquadratic Overparameterization for Shallow Neural Networks","created":"2021-11-02","cited_by_count":26},{"id":"2010.12217","title":"Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities","created":"2020-10-23","cited_by_count":20},{"id":"2009.06132","title":"Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms","created":"2020-09-14","cited_by_count":19},{"id":"2006.04048","title":"Sharp Representation Theorems for ReLU Networks with Precise Dependence on Depth","created":"2020-06-07","cited_by_count":13},{"id":"2202.02981","title":"Neural Tangent Kernel Analysis of Deep Narrow Neural Networks","created":"2022-02-07","cited_by_count":11},{"id":"2202.00992","title":"Tight Convergence Rate Bounds for Optimization Under Power Law Spectral Conditions","created":"2022-02-02","cited_by_count":9},{"id":"2105.00507","title":"Universal scaling laws in the gradient descent training of neural networks","created":"2021-05-02","cited_by_count":4}],"next_cursor":null}