Research graph
References from A Non-Local Convergence Analysis of Gradient Flow for Deep Linear Networks. Local targets link to admitted publications; unresolved targets remain external evidence.
Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
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Identity matters in deep learning
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A convergence analysis of gradient descent for deep linear neural networks
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On the optimization of deep networks: Implicit acceleration by overparameterization
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Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks
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Exponential convergence time of gradient descent for one-dimensional deep linear neural networks
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Width provably matters in optimization for deep linear neural networks
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Provable benefit of orthogonal initialization in optimizing deep linear networks
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On the global convergence of training deep linear ResNets
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Training linear neural networks: Non-local convergence and complexity results
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10.1093/imaiai/iaaa039
10.1093/imaiai/iaaa039 · External reference
On lazy training in differentiable programming
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Neural tangent kernel: Convergence and generalization in neural networks
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Global convergence of gradient descent for deep linear residual networks
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10.1109/cvpr.2016.90
10.1109/cvpr.2016.90 · External reference
Implicit bias of gradient descent on linear convolutional networks
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Convergence of gradient descent on separable data
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Gradient descent maximizes the margin of homogeneous neural networks
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Gradient descent aligns the layers of deep linear networks
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Directional convergence and alignment in deep learning
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Faster directional convergence of linear neural networks under spherically symmetric data
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10.1016/0893-6080(89)90014-2
10.1016/0893-6080(89)90014-2 · External reference
Deep learning without poor local minima
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Depth creates no bad local minima
2017 · External reference
Spurious local minima are common in two-layer ReLU neural networks
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Deep linear networks with arbitrary loss: All local minima are global
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10.5555/3305890.3305950
10.5555/3305890.3305950 · External reference
On the loss landscape of a class of deep neural networks with no bad local valleys
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On connected sublevel sets in deep learning
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Adding one neuron can eliminate all bad local minima
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Understanding the loss surface of neural networks for binary classification
2018 · External reference
10.1137/19m1299074
10.1137/19m1299074 · External reference
Spurious valleys in one-hidden-layer neural network optimization landscapes
2019 · External reference
10.1287/ijoo.2021.0062
10.1287/ijoo.2021.0062 · External reference
10.1137/21m1394205
10.1137/21m1394205 · External reference
Global minimizers, strict and non-strict saddle points, and implicit regularization for deep linear neural networks
2021 · External reference
10.1287/moor.2021.1228
10.1287/moor.2021.1228 · External reference
On the landscape of one-hidden-layer sparse networks and beyond
2022 · External reference
10.1007/s40305-020-00309-6
10.1007/s40305-020-00309-6 · External reference
10.1109/msp.2020.3004124
10.1109/msp.2020.3004124 · External reference
On non-local convergence analysis of deep linear networks
2022 · External reference
10.1109/tpami.2019.2919597
10.1109/tpami.2019.2919597 · External reference
10.1214/aos/1009210544
10.1214/aos/1009210544 · External reference
10.1007/s10959-010-0338-z
10.1007/s10959-010-0338-z · External reference
10.1214/13-aos1127
10.1214/13-aos1127 · External reference
10.1109/isit.2014.6875223
10.1109/isit.2014.6875223 · External reference
Implicit regularization in deep matrix factorization
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10.1016/0024-3795(87)90114-5
10.1016/0024-3795(87)90114-5 · External reference
Continuous vs. discrete optimization of deep neural networks
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Kernel and rich regimes in overparametrized models
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A unifying view on implicit bias in training linear neural networks
2020 · External reference
