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06/13/2023
Symmetry Critical Points for Symmetric Tensor Decomposition Problems
We consider the non-convex optimization problem associated with the deco...
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10/12/2022
Annihilation of Spurious Minima in Two-Layer ReLU Networks
We study the optimization problem associated with fitting two-layer ReLU...
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07/21/2021
Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks
We study the optimization problem associated with fitting two-layer ReLU...
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07/06/2021
Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of S_n
Motivated by questions originating from the study of a class of shallow ...
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03/10/2021
Symmetry Breaking in Symmetric Tensor Decomposition
In this note, we consider the optimization problem associated with compu...
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08/04/2020
Analytic Characterization of the Hessian in Shallow ReLU Models: A Tale of Symmetry
We consider the optimization problem associated with fitting two-layers ...
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06/24/2020
Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations
We design an algorithm which finds an ϵ-approximate stationary point (wi...
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06/11/2020
IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method
We introduce a framework for designing primal methods under the decentra...
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03/23/2020
Symmetry critical points for a model shallow neural network
A detailed analysis is given of a family of critical points determining ...
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02/09/2020
On the Complexity of Minimizing Convex Finite Sums Without Using the Indices of the Individual Functions
Recent advances in randomized incremental methods for minimizing L-smoot...
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12/26/2019
Spurious Local Minima of Shallow ReLU Networks Conform with the Symmetry of the Target Model
We consider the optimization problem associated with fitting two-layer R...
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12/05/2019
Lower Bounds for Non-Convex Stochastic Optimization
We lower bound the complexity of finding ϵ-stationary points (with gradi...
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06/26/2018
A Tight Convergence Analysis for Stochastic Gradient Descent with Delayed Updates
We provide tight finite-time convergence bounds for gradient descent and...
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06/06/2017
Limitations on Variance-Reduction and Acceleration Schemes for Finite Sum Optimization
We study the conditions under which one is able to efficiently apply var...
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11/15/2016
Oracle Complexity of Second-Order Methods for Finite-Sum Problems
Finite-sum optimization problems are ubiquitous in machine learning, and...
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06/05/2015