When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks | Paper Citation Record

Observation 57185953-a4df-4a34-9bd0-a1b5c1925799 · outbound

This paper cites Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks

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This paper cites High-dimensional asymptotics of feature learning: How one gradient step improves the representation.Advances in Neural Information Processing Systems, 35:37932–37946, 2022.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks High-dimensional asymptotics of feature learning: How one gradient step improves the representation.Advances in Neural Information Processing Systems, 35:37932–37946, 2022

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This paper cites Neural networks and principal component analysis: Learning from examples without local minima.Neural Networks, 2(1):53–58, 1989.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Neural networks and principal component analysis: Learning from examples without local minima.Neural Networks, 2(1):53–58, 1989

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This paper cites Simplicity bias and optimization threshold in two-layer relu networks, 2025.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Simplicity bias and optimization threshold in two-layer relu networks, 2025

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This paper cites A Bennett concentration inequality and its application to suprema of empirical processes.C.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks A Bennett concentration inequality and its application to suprema of empirical processes.C

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This paper cites Globally optimal gradient descent for a convnet with gaussian inputs, 2017.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Globally optimal gradient descent for a convnet with gaussian inputs, 2017

Reference 6

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This paper cites Candès, Xiaodong Li, and Mahdi Soltanolkotabi.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Candès, Xiaodong Li, and Mahdi Soltanolkotabi

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This paper cites Nonconvex rectangular matrix completion via gradient descent without ℓ2,∞regularization.IEEE Trans.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Nonconvex rectangular matrix completion via gradient descent without ℓ2,∞regularization.IEEE Trans

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Unresolved cited work

Reference 9

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This paper cites Learning a neuron by a shallow relu network: Dynamics and implicit bias for correlated inputs, 2023.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Learning a neuron by a shallow relu network: Dynamics and implicit bias for correlated inputs, 2023

Reference 10

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This paper cites On lazy training in differentiable programming.Advances in Neural Information Processing Systems, 32:2937–2947, 2019.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks On lazy training in differentiable programming.Advances in Neural Information Processing Systems, 32:2937–2947, 2019

Reference 11

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This paper cites Neural networks can learn representations with gradient descent.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Neural networks can learn representations with gradient descent

Reference 12

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This paper cites Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity.Advances in neural information processing systems, 29, 2016.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity.Advances in neural information processing systems, 29, 2016

Reference 13

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This paper cites Gradient descent finds global minima of deep neural networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Gradient descent finds global minima of deep neural networks

Reference 14

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This paper cites Gradient Descent Provably Optimizes Over-parameterized Neural Networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Gradient Descent Provably Optimizes Over-parameterized Neural Networks

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This paper cites Humus-net: Hybrid unrolled multi-scale network architecture for accelerated mri reconstruction.Advances in Neural Information Processing Systems, 35:25306–25319, 2022.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Humus-net: Hybrid unrolled multi-scale network architecture for accelerated mri reconstruction.Advances in Neural Information Processing Systems, 35:25306–25319, 2022

Reference 16

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Unresolved cited work

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This paper cites Matrix completion has no spurious local minimum.Advances in Neural Information Processing Systems, 29:2973–2981, 2016.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Matrix completion has no spurious local minimum.Advances in Neural Information Processing Systems, 29:2973–2981, 2016

Reference 18

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This paper cites When Do Neural Networks Outperform Kernel Methods?.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks When Do Neural Networks Outperform Kernel Methods?

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This paper cites Phase retrieval under a generative prior.Advances in Neural Information Processing Systems, 31, 2018.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Phase retrieval under a generative prior.Advances in Neural Information Processing Systems, 31, 2018

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This paper cites Neural tangent kernel: Convergence and generalization in neural networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Neural tangent kernel: Convergence and generalization in neural networks

Reference 21

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This paper cites Gradient descent aligns the layers of deep linear networks, 2019.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Gradient descent aligns the layers of deep linear networks, 2019

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This paper cites Kakade, and Michael I.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Kakade, and Michael I

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This paper cites Deep convolutional neural network for inverse problems in imaging.IEEE transactions on image processing, 26(9):4509–4522, 2017.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Deep convolutional neural network for inverse problems in imaging.IEEE transactions on image processing, 26(9):4509–4522, 2017

Reference 24

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Photo-realistic single image super-resolution using a generative adversarial network

Reference 25

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This paper cites Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit

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This paper cites Feature Averaging: An Implicit Bias of Gradient Descent Leading to Non-Robustness in Neural Networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Feature Averaging: An Implicit Bias of Gradient Descent Leading to Non-Robustness in Neural Networks

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This paper cites Rapid, robust, and reliable blind deconvolution via nonconvex optimization.Appl.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Rapid, robust, and reliable blind deconvolution via nonconvex optimization.Appl

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This paper cites Regularized gradient descent: a non-convex recipe for fast joint blind deconvolution and demixing.Inf.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Regularized gradient descent: a non-convex recipe for fast joint blind deconvolution and demixing.Inf

Reference 29

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Implicit regularization in nonconvex statistical estimation: gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution.Found

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Unresolved cited work

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This paper cites A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case

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This paper cites Overparameterized nonlinear learning: Gradient descent takes the shortest path? InInternational Conference on Machine Learning, pages 4951–4960.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Overparameterized nonlinear learning: Gradient descent takes the shortest path? InInternational Conference on Machine Learning, pages 4951–4960

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This paper cites Towards moderate overparameterization: global convergence guarantees for training shallow neural networks.IEEE Journal on Selected Areas in Information Theory, 2020.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Towards moderate overparameterization: global convergence guarantees for training shallow neural networks.IEEE Journal on Selected Areas in Information Theory, 2020

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This paper cites Grokking: Generalization beyond overfitting on small algorithmic datasets, 2022.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Grokking: Generalization beyond overfitting on small algorithmic datasets, 2022

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This paper cites Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis

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This paper cites Learning relus via gradient descent.Advances in neural information processing systems, 30, 2017.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Learning relus via gradient descent.Advances in neural information processing systems, 30, 2017

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This paper cites Theoretical insights into the optimization landscape of over-parameterized shallow neural networks.IEEE Transactions on Information Theory, 65(2):742–769, 2018.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Theoretical insights into the optimization landscape of over-parameterized shallow neural networks.IEEE Transactions on Information Theory, 65(2):742–769, 2018

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Implicit balancing and regularization: Generalization and convergence guarantees for overparameterized asymmetric matrix sensing

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This paper cites End-to-end variational networks for accelerated mri reconstruction.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks End-to-end variational networks for accelerated mri reconstruction

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction

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This paper cites When Are Nonconvex Problems Not Scary?.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks When Are Nonconvex Problems Not Scary?

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This paper cites A geometric analysis of phase retrieval.Found.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks A geometric analysis of phase retrieval.Found

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Low-rank solutions of linear matrix equations via procrustes flow

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Van der Vaart and Jon A

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Learning a single neuron with bias using gradient descent, 2022

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When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Wainwright.High-dimensional statistics

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This paper cites Image inpainting via generative multi-column convolutional neural networks.Advances in neural information processing systems, 31, 2018.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Image inpainting via generative multi-column convolutional neural networks.Advances in neural information processing systems, 31, 2018

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This paper cites Large learning rate tames homogeneity: Convergence and balancing effect, 2022.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Large learning rate tames homogeneity: Convergence and balancing effect, 2022

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This paper cites Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult, 2023.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult, 2023

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This paper cites Learning a single neuron with gradient methods, 2022.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Learning a single neuron with gradient methods, 2022

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This paper cites Zhang, Somayeh Sojoudi, and Javad Lavaei.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Zhang, Somayeh Sojoudi, and Javad Lavaei

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Observation 2a55c107-15df-49cf-b214-9510fd40dc36 · outbound

This paper cites Learning one-hidden-layer relu networks via gradient descent, 2018.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Learning one-hidden-layer relu networks via gradient descent, 2018

Reference 57

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This paper cites A hitting time analysis of stochastic gradient langevin dynamics.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks A hitting time analysis of stochastic gradient langevin dynamics

Reference 58

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This paper cites Bartlett, and Inderjit S.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Bartlett, and Inderjit S

Reference 59

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Observation a4868aed-ff9f-4e2b-aa3d-003293fc4c6d · outbound

This paper cites How gradient descent balances features: A dynamical analysis for two-layer neural networks.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks How gradient descent balances features: A dynamical analysis for two-layer neural networks

Reference 60

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Observation f8acf33b-3d50-4302-b93e-ea5f66a40076 · outbound

This paper cites Here we use the fact that µv2 1 ≤c 0c2 2 ≤ 1.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks Here we use the fact that µv2 1 ≤c 0c2 2 ≤ 1

Reference 61

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This paper cites As a result, the sum v1 +∥w 1∥ will increase by a factor 1 + 1 8 µ∥a∥ as long as v1 ∥w1∥< 1 4 ∥a∥.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks As a result, the sum v1 +∥w 1∥ will increase by a factor 1 + 1 8 µ∥a∥ as long as v1 ∥w1∥< 1 4 ∥a∥

Reference 62

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This paper cites v(τ) 1 v(τ) 2 #! W (τ) −W 2 F . 45 By further upper bounding the right-hand side using the fact that the ReLU activation is 1-Lipschitz, we have L θ(T) ≤ diag.

When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks v(τ) 1 v(τ) 2 #! W (τ) −W 2 F . 45 By further upper bounding the right-hand side using the fact that the ReLU activation is 1-Lipschitz, we have L θ(T) ≤ diag

Reference 63

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