Mathematical analysis of the gradients in deep learning | Paper Citation Record

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This paper cites TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems.

Mathematical analysis of the gradients in deep learning TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

Reference 1

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This paper cites Learning Theory from First Principles.

Mathematical analysis of the gradients in deep learning Learning Theory from First Principles

Reference 2

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This paper cites J., and Zhang, Y.

Mathematical analysis of the gradients in deep learning J., and Zhang, Y

Reference 3

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This paper cites On the complexity of nonsmooth automatic differentiation.

Mathematical analysis of the gradients in deep learning On the complexity of nonsmooth automatic differentiation

Reference 4

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This paper cites The /suppress lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems.

Mathematical analysis of the gradients in deep learning The /suppress lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems

Reference 5

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This paper cites A mathematical model for automatic differentiation in machine learning.

Mathematical analysis of the gradients in deep learning A mathematical model for automatic differentiation in machine learning

Reference 6

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This paper cites Conservative set valued ﬁelds, automatic diﬀerentiation, stochastic gradient methods and deep learning.

Mathematical analysis of the gradients in deep learning Conservative set valued ﬁelds, automatic diﬀerentiation, stochastic gradient methods and deep learning

Reference 7

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This paper cites Diﬀerentiating nonsmooth solutions to parametric monotone inclusion problems.

Mathematical analysis of the gradients in deep learning Diﬀerentiating nonsmooth solutions to parametric monotone inclusion problems

Reference 8

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This paper cites Automatic differentiation of nonsmooth iterative algorithms.

Mathematical analysis of the gradients in deep learning Automatic differentiation of nonsmooth iterative algorithms

Reference 9

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This paper cites A proof of conver- gence for gradient descent in the training of artiﬁcial neur al networks for constant target functions.

Mathematical analysis of the gradients in deep learning A proof of conver- gence for gradient descent in the training of artiﬁcial neur al networks for constant target functions

Reference 10

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This paper cites Non-convergence of stochastic gradient descent in the training of deep neural networks.

Mathematical analysis of the gradients in deep learning Non-convergence of stochastic gradient descent in the training of deep neural networks

Reference 11

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

Mathematical analysis of the gradients in deep learning Landscape analysis for shallow neural networks: complete classiﬁcation of critical point s for aﬃne target functions

Reference 12

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This paper cites On the mathematical foundations of learning.

Mathematical analysis of the gradients in deep learning On the mathematical foundations of learning

Reference 13

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This paper cites Conservative and semismooth derivatives are equiv- alent for semialgebraic maps.

Mathematical analysis of the gradients in deep learning Conservative and semismooth derivatives are equiv- alent for semialgebraic maps

Reference 14

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Mathematical analysis of the gradients in deep learning Unresolved cited work

Reference 15

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This paper cites Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates.

Mathematical analysis of the gradients in deep learning Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates

Reference 16

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This paper cites Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes.

Mathematical analysis of the gradients in deep learning Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes

Reference 17

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This paper cites Adam-family Methods with Decoupled Weight Decay in Deep Learning.

Mathematical analysis of the gradients in deep learning Adam-family Methods with Decoupled Weight Decay in Deep Learning

Reference 18

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This paper cites Sub-Optimal Local Minima Exist for Neural Networks with Almost All Non-Linear Activations.

Mathematical analysis of the gradients in deep learning Sub-Optimal Local Minima Exist for Neural Networks with Almost All Non-Linear Activations

Reference 19

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This paper cites Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't.

Mathematical analysis of the gradients in deep learning Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

Reference 20

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Reference 21

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Observation d3d9e9cc-cec9-4211-a353-d84650cddd89 · outbound

This paper cites Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks.

Mathematical analysis of the gradients in deep learning Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks

Reference 22

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This paper cites Handbook of Convergence Theorems for (Stochastic) Gradient Methods.

Mathematical analysis of the gradients in deep learning Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Reference 23

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Observation 34356b5b-423a-401e-be69-5d66b7e03ae3 · outbound

This paper cites Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$.

Mathematical analysis of the gradients in deep learning Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$

Reference 24

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This paper cites 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.

Mathematical analysis of the gradients in deep learning 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

Reference 25

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This paper cites Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions.

Mathematical analysis of the gradients in deep learning Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

Reference 26

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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.

Mathematical analysis of the gradients in deep learning 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

Reference 27

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Observation 23c3f78c-f589-4871-bc95-8213a9807e5f · outbound

This paper cites Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory.

Mathematical analysis of the gradients in deep learning Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Reference 28

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This paper cites On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.

Mathematical analysis of the gradients in deep learning On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks

Reference 29

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This paper cites On the existence of global minima and convergence analyses for gradient descent methods in the training of dee p neural networks.

Mathematical analysis of the gradients in deep learning On the existence of global minima and convergence analyses for gradient descent methods in the training of dee p neural networks

Reference 30

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This paper cites A proof of convergence for stochastic gradient descent in the training of artiﬁcial neural networks with ReLU activation for constant target functions.

Mathematical analysis of the gradients in deep learning A proof of convergence for stochastic gradient descent in the training of artiﬁcial neural networks with ReLU activation for constant target functions

Reference 31

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This paper cites Convergence analysis for gradient ﬂows in the training of artiﬁcial neural networks with ReLU activation.

Mathematical analysis of the gradients in deep learning Convergence analysis for gradient ﬂows in the training of artiﬁcial neural networks with ReLU activation

Reference 32

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This paper cites Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks.

Mathematical analysis of the gradients in deep learning Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks

Reference 33

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This paper cites M., and Lee, J.

Mathematical analysis of the gradients in deep learning M., and Lee, J

Reference 34

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This paper cites Does a sparse ReLU network training problem always admit an optimum?.

Mathematical analysis of the gradients in deep learning Does a sparse ReLU network training problem always admit an optimum?

Reference 35

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This paper cites On correctness of automatic diﬀerentiation for non-diﬀerentiable functions.

Mathematical analysis of the gradients in deep learning On correctness of automatic diﬀerentiation for non-diﬀerentiable functions

Reference 36

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This paper cites S., and Tian, T.

Mathematical analysis of the gradients in deep learning S., and Tian, T

Reference 37

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Reference 38

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This paper cites Introductory lectures on convex optimization , vol.

Mathematical analysis of the gradients in deep learning Introductory lectures on convex optimization , vol

Reference 39

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This paper cites Automatic diﬀerentiation in PyTorch.

Mathematical analysis of the gradients in deep learning Automatic diﬀerentiation in PyTorch

Reference 40

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This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Mathematical analysis of the gradients in deep learning PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 41

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This paper cites Conservative parametric optimality and the ridge method for tame min-max problems.

Mathematical analysis of the gradients in deep learning Conservative parametric optimality and the ridge method for tame min-max problems

Reference 42

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Observation c5e849ba-d9cf-4a7e-81b3-1e073f726c5d · outbound

This paper cites Topological properties of the set of functions generated by neural networks of ﬁxed size.

Mathematical analysis of the gradients in deep learning Topological properties of the set of functions generated by neural networks of ﬁxed size

Reference 43

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Observation d8bd2e87-a613-4e51-8aa5-9ae1eee4fbcc · outbound

This paper cites Mathematical theory of deep learning.

Mathematical analysis of the gradients in deep learning Mathematical theory of deep learning

Reference 44

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This paper cites On the Convergence of Adam and Beyond.

Mathematical analysis of the gradients in deep learning On the Convergence of Adam and Beyond

Reference 45

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This paper cites T., and Wets, R.

Mathematical analysis of the gradients in deep learning T., and Wets, R

Reference 46

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Observation 587b5c32-04c1-459a-b2e3-85e6a28f2179 · outbound

This paper cites An overview of gradient descent optimization algorithms.

Mathematical analysis of the gradients in deep learning An overview of gradient descent optimization algorithms

Reference 47

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This paper cites Spurious Local Minima are Common in Two-Layer ReLU Neural Networks.

Mathematical analysis of the gradients in deep learning Spurious Local Minima are Common in Two-Layer ReLU Neural Networks

Reference 48

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This paper cites The gradient’s limit of a deﬁnable family of functions is a co nservative set-valued ﬁeld.

Mathematical analysis of the gradients in deep learning The gradient’s limit of a deﬁnable family of functions is a co nservative set-valued ﬁeld

Reference 49

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Mathematical analysis of the gradients in deep learning Unresolved cited work

Reference 50

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This paper cites Optimization for deep learning: theory and algorithms.

Mathematical analysis of the gradients in deep learning Optimization for deep learning: theory and algorithms

Reference 51

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This paper cites Local minima in training of neural networks.

Mathematical analysis of the gradients in deep learning Local minima in training of neural networks

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-10T14:10:55.470243Z

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This paper cites S., and Bruna, J.

Mathematical analysis of the gradients in deep learning S., and Bruna, J

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:10:55.944838Z

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Observation c50e8cdc-96f1-4cd6-b8f4-348c3b7ac367 · outbound

This paper cites Approximation and Gradient Descent Training with Neural Networks.

Mathematical analysis of the gradients in deep learning Approximation and Gradient Descent Training with Neural Networks

Reference 54

Resolution: verified exact; local_arxiv, observed 2026-08-10T14:10:55.453704Z

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This paper cites Approximation results for gradient ﬂow trained neural netw orks.

Mathematical analysis of the gradients in deep learning Approximation results for gradient ﬂow trained neural netw orks

Reference 55

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Observation 18d67b15-0b65-4b23-84f4-71b7548b57a3 · outbound

This paper cites Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees.

Mathematical analysis of the gradients in deep learning Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees

Reference 56

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Observation 409d5b73-5735-41b6-b555-24d8cf6ce3d2 · outbound

This paper cites Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization.

Mathematical analysis of the gradients in deep learning Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization

Reference 57

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Observation 02b81597-8b7b-4ff3-98c1-b4846b707d05 · outbound

This paper cites an unresolved cited work.

Mathematical analysis of the gradients in deep learning Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:10:55.922227Z

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