Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions | Paper Citation Record

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This paper cites Geometry and optimization of shallow polynomial networks.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Geometry and optimization of shallow polynomial networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Neural networks and principal component analysis: Learning from examples without local minima

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This paper cites Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Gradient descent provably escapes saddle points in the training of shallow R e LU networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions The Loss Surfaces of Multilayer Networks

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This paper cites Open problem: The landscape of the loss surfaces of multilayer networks.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Open problem: The landscape of the loss surfaces of multilayer networks

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This paper cites On the omnipresence of spurious local minima in certain neural network training problems.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the omnipresence of spurious local minima in certain neural network training problems

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Approximation by superpositions of a sigmoidal function

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This paper cites Identifying and attacking the saddle point problem in high-dimensional non-convex optimization.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Identifying and attacking the saddle point problem in high-dimensional non-convex optimization

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This paper cites On the existence of minimizers in shallow residual R e LU neural network optimization landscapes.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the existence of minimizers in shallow residual R e LU neural network optimization landscapes

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation

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This paper cites On the Power of Over-parametrization in Neural Networks with Quadratic Activation.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the Power of Over-parametrization in Neural Networks with Quadratic Activation

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This paper cites I., Wu, C., and Yahl, T.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions I., Wu, C., and Yahl, T

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Local minima and plateaus in hierarchical structures of multilayer perceptrons

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions C., and Zadik, I

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Approximation capabilities of multilayer feedforward networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Multilayer feedforward networks are universal approximators

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the existence of infinitely many realization functions of non-global local minima in the training of artificial neural networks with ReLU activation

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This paper cites Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability.

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Strong error analysis for stochastic gradient descent optimization algorithms

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Best approximation by Heaviside perceptron networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Deep Learning without Poor Local Minima

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the Expressive Power of Deep Polynomial Neural Networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Geometry of polynomial neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Some useful LaTeX commands

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions D., Panageas, I., Piliouras, G., Simchowitz, M., Jordan, M

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Gradient Descent Converges to Minimizers

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Y., Pinkus, A., and Schocken, S

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Visualizing the Loss Landscape of Neural Nets

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions On the Computational Efficiency of Training Neural Networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Universal gradient methods for convex optimization problems

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Lectures on convex optimization , second ed., vol

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions First-order methods almost always avoid saddle points: the case of vanishing step-sizes

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Topological properties of the set of functions generated by neural networks of fixed size

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Spurious Local Minima are Common in Two-Layer ReLU Neural Networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Unresolved cited work

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions No bad local minima: Data independent training error guarantees for multilayer neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Exponentially vanishing sub-optimal local minima in multilayer neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Local minima in training of neural networks

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions S., and Bruna, J

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Unresolved cited work

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Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions Mathematica, Version 14.3, Champaign, IL (2025)

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