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1710.11205
Cited By
Critical Points of Neural Networks: Analytical Forms and Landscape Properties
30 October 2017
Yi Zhou
Yingbin Liang
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Papers citing
"Critical Points of Neural Networks: Analytical Forms and Landscape Properties"
36 / 36 papers shown
Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders
Jonghyun Ham
Maximilian Fleissner
Debarghya Ghoshdastidar
AI4CE
187
0
0
30 May 2025
When Expressivity Meets Trainability: Fewer than
n
n
n
Neurons Can Work
Neural Information Processing Systems (NeurIPS), 2022
Jiawei Zhang
Yushun Zhang
Mingyi Hong
Tian Ding
Jianfeng Yao
323
10
0
21 Oct 2022
Understanding Deep Learning via Decision Boundary
IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2022
Shiye Lei
Fengxiang He
Yancheng Yuan
Dacheng Tao
203
23
0
03 Jun 2022
Spurious Local Minima Are Common for Deep Neural Networks with Piecewise Linear Activations
IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2021
Bo Liu
132
10
0
25 Feb 2021
The Landscape of Multi-Layer Linear Neural Network From the Perspective of Algebraic Geometry
Xiuyi Yang
81
2
0
30 Jan 2021
Mathematical Models of Overparameterized Neural Networks
Proceedings of the IEEE (Proc. IEEE), 2020
Cong Fang
Hanze Dong
Tong Zhang
281
25
0
27 Dec 2020
Recent advances in deep learning theory
Fengxiang He
Dacheng Tao
AI4CE
332
57
0
20 Dec 2020
Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
CSIAM Transactions on Applied Mathematics (CSIAM Trans. Appl. Math.), 2020
Yuqing Li
Yaoyu Zhang
N. Yip
221
5
0
07 Jul 2020
The Global Landscape of Neural Networks: An Overview
Tian Ding
Dawei Li
Shiyu Liang
Tian Ding
R. Srikant
222
93
0
02 Jul 2020
A Generalised Linear Model Framework for
β
β
β
-Variational Autoencoders based on Exponential Dispersion Families
Journal of machine learning research (JMLR), 2020
Robert Sicks
R. Korn
Stefanie Schwaar
258
13
0
11 Jun 2020
Piecewise linear activations substantially shape the loss surfaces of neural networks
International Conference on Learning Representations (ICLR), 2020
Fengxiang He
Bohan Wang
Dacheng Tao
ODL
188
33
0
27 Mar 2020
Some Geometrical and Topological Properties of DNNs' Decision Boundaries
Bo Liu
Mengya Shen
AAML
225
3
0
07 Mar 2020
Understanding Global Loss Landscape of One-hidden-layer ReLU Networks, Part 1: Theory
Bo Liu
FAtt
MLT
242
1
0
12 Feb 2020
Optimization for deep learning: theory and algorithms
Tian Ding
ODL
340
178
0
19 Dec 2019
Stationary Points of Shallow Neural Networks with Quadratic Activation Function
D. Gamarnik
Eren C. Kizildag
Ilias Zadik
204
15
0
03 Dec 2019
How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?
International Conference on Learning Representations (ICLR), 2019
Zixiang Chen
Yuan Cao
Difan Zou
Quanquan Gu
321
129
0
27 Nov 2019
Sub-Optimal Local Minima Exist for Neural Networks with Almost All Non-Linear Activations
Tian Ding
Dawei Li
Tian Ding
335
14
0
04 Nov 2019
Over Parameterized Two-level Neural Networks Can Learn Near Optimal Feature Representations
Cong Fang
Hanze Dong
Tong Zhang
123
18
0
25 Oct 2019
The Local Elasticity of Neural Networks
International Conference on Learning Representations (ICLR), 2019
Hangfeng He
Weijie J. Su
316
51
0
15 Oct 2019
Pure and Spurious Critical Points: a Geometric Study of Linear Networks
International Conference on Learning Representations (ICLR), 2019
Matthew Trager
Kathlén Kohn
Joan Bruna
185
36
0
03 Oct 2019
Are deep ResNets provably better than linear predictors?
Neural Information Processing Systems (NeurIPS), 2019
Chulhee Yun
S. Sra
Ali Jadbabaie
285
14
0
09 Jul 2019
Generalization Error Bounds of Gradient Descent for Learning Over-parameterized Deep ReLU Networks
Yuan Cao
Quanquan Gu
ODL
MLT
AI4CE
583
166
0
04 Feb 2019
Numerically Recovering the Critical Points of a Deep Linear Autoencoder
Charles G. Frye
Neha S. Wadia
M. DeWeese
K. Bouchard
272
6
0
29 Jan 2019
Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
Sanjeev Arora
S. Du
Wei Hu
Zhiyuan Li
Ruosong Wang
MLT
642
1,028
0
24 Jan 2019
On Connected Sublevel Sets in Deep Learning
Quynh N. Nguyen
276
106
0
22 Jan 2019
Non-attracting Regions of Local Minima in Deep and Wide Neural Networks
Henning Petzka
C. Sminchisescu
239
12
0
16 Dec 2018
Gradient Descent Finds Global Minima of Deep Neural Networks
International Conference on Machine Learning (ICML), 2018
S. Du
Jason D. Lee
Haochuan Li
Liwei Wang
Masayoshi Tomizuka
ODL
1.2K
1,190
0
09 Nov 2018
On the Convergence Rate of Training Recurrent Neural Networks
Zeyuan Allen-Zhu
Yuanzhi Li
Zhao Song
574
200
0
29 Oct 2018
Subgradient Descent Learns Orthogonal Dictionaries
Yu Bai
Qijia Jiang
Ju Sun
330
56
0
25 Oct 2018
Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity
Chulhee Yun
S. Sra
Ali Jadbabaie
363
124
0
17 Oct 2018
The loss surface of deep linear networks viewed through the algebraic geometry lens
D. Mehta
Tianran Chen
Tingting Tang
J. Hauenstein
ODL
232
35
0
17 Oct 2018
Gradient Descent Provably Optimizes Over-parameterized Neural Networks
S. Du
Xiyu Zhai
Barnabás Póczós
Aarti Singh
MLT
ODL
691
1,338
0
04 Oct 2018
Efficiently testing local optimality and escaping saddles for ReLU networks
International Conference on Learning Representations (ICLR), 2018
Chulhee Yun
S. Sra
Ali Jadbabaie
200
10
0
28 Sep 2018
Collapse of Deep and Narrow Neural Nets
Lu Lu
Yanhui Su
George Karniadakis
ODL
237
164
0
15 Aug 2018
Spurious Valleys in Two-layer Neural Network Optimization Landscapes
Luca Venturi
Afonso S. Bandeira
Joan Bruna
321
75
0
18 Feb 2018
Small nonlinearities in activation functions create bad local minima in neural networks
Chulhee Yun
S. Sra
Ali Jadbabaie
ODL
362
97
0
10 Feb 2018
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