Fetching the paper…
Reading the bibliography…
In matrix sensing, we first numerically identify the sensitivity to the initialization rank as a new limitation of the implicit bias of gradient flow.
Gradient methods for minimizing functionals
Boris Teodorovich Polyak · 1963
Earlier work this paper cites.
Sur les trajectoires du gradient d’une fonction analytique
Stanislaw Lojasiewicz · 1982
Earlier work this paper cites.
Some np-complete problems in quadratic and nonlinear programming
Katta G Murty and Santosh N Kabadi · 1985
Earlier work this paper cites.
Numerical computation of an analytic singular value decomposition of a matrix valued function
Angelika Bunse-Gerstner, Ralph Byers, Volker Mehrmann, and Nancy K Nichols · 1991
Earlier work this paper cites.
Matrix procrustes problems
Nick Higham and Pythagoras Papadimitriou · 1995
Earlier work this paper cites.
On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues
Gábor Pataki · 1998
Earlier work this paper cites.
Proof of the gradient conjecture of r. thom
Krzysztof Kurdyka, Tadeusz Mostowski, and Adam Parusinski · 2000
Earlier work this paper cites.
Gradient flow in recurrent nets: the difficulty of learning long-term dependencies, 2001
Sepp Hochreiter, Yoshua Bengio, Paolo Frasconi, Jürgen Schmidhuber, et al · 2001
Earlier work this paper cites.
Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
Earlier work this paper cites.
A survey of the s-lemma
Imre Pólik and Tamás Terlaky · 2007
Earlier work this paper cites.
Lectures on Analytic Differential Equations
S. Yakovenko and Y. Ilyashenko · 2008
Earlier work this paper cites.
Tensor decompositions and applications
Tamara G Kolda and Brett W Bader · 2009
Earlier work this paper cites.
Nonlinear optimization
Andrzej Ruszczynski · 2011
Earlier work this paper cites.
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized gauss–seidel methods
Hedy Attouch, Jérôme Bolte, and Benar Fux Svaiter · 2013
Earlier work this paper cites.
Matrix Computations
G.H. Golub and C.F. Van Loan · 2013
Earlier work this paper cites.
Smooth manifolds
John M Lee · 2013
Earlier work this paper cites.
Understanding machine learning: From theory to algorithms
Shai Shalev-Shwartz and Shai Ben-David · 2014
Cited alongside, same era.
An overview of low-rank matrix recovery from incomplete observations
Mark A Davenport and Justin Romberg · 2016
Cited alongside, same era.
Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
Cited alongside, same era.
The non-convex burer-monteiro approach works on smooth semidefinite programs
Nicolas Boumal, Vlad Voroninski, and Afonso Bandeira · 2016
Cited alongside, same era.
Linear convergence of gradient and proximal-gradient methods under the polyak-lojasiewicz condition
Hamed Karimi, Julie Nutini, and Mark Schmidt · 2016
Cited alongside, same era.
Nonconvex optimization meets low-rank matrix factorization: An overview
Yuejie Chi, Yue M Lu, and Yuxin Chen · 2019
Later among the works it cites.
Iterative hard thresholding for low-rank recovery from rank-one projections
Simon Foucart and Srinivas Subramanian · 2019
Later among the works it cites.
An inexact augmented lagrangian framework for nonconvex optimization with nonlinear constraints
Mehmet Fatih Sahin, Ahmet Alacaoglu, Fabian Latorre, Volkan Cevher, et al · 2019
Later among the works it cites.
Implicit regularization of discrete gradient dynamics in linear neural networks
Gauthier Gidel, Francis Bach, and Simon Lacoste-Julien · 2019
Later among the works it cites.
The non-convex geometry of low-rank matrix optimization
Qiuwei Li, Zhihui Zhu, and Gongguo Tang · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Ben Recht · 2016
Cited alongside, same era.
Implicit regularization in matrix factorization
Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2017
Cited alongside, same era.
A globally convergent algorithm for nonconvex optimization based on block coordinate update
Yangyang Xu and Wotao Yin · 2017
Cited alongside, same era.
Charles H Martin and Michael W Mahoney · 2018
Cited alongside, same era.
The implicit bias of gradient descent on separable data
Daniel Soudry, Elad Hoffer, Mor Shpigel Nacson, Suriya Gunasekar, and Nathan Srebro · 2018
Cited alongside, same era.
To understand deep learning we need to understand kernel learning
Mikhail Belkin, Siyuan Ma, and Soumik Mandal · 2018
Cited alongside, same era.
Algorithmic regularization in over-parameterized matrix sensing and neural networks with quadratic activations
Yuanzhi Li, Tengyu Ma, and Hongyang Zhang · 2018
Cited alongside, same era.
Training linear neural networks: Non-local convergence and complexity results
Armin Eftekhari · 2020
Closest in time.
Weighted optimization: better generalization by smoother interpolation
Yuege Xie, Rachel Ward, Holger Rauhut, and Hung-Hsu Chou · 2020
Closest in time.
Just interpolate: Kernel “ridgeless” regression can generalize
Tengyuan Liang, Alexander Rakhlin, et al · 2020
Closest in time.
Low-rank regularization and solution uniqueness in over-parameterized matrix sensing
Kelly Geyer, Anastasios Kyrillidis, and Amir Kalev · 2020
Closest in time.
Deterministic guarantees for burer-monteiro factorizations of smooth semidefinite programs
Nicolas Boumal, Vladislav Voroninski, and Afonso S Bandeira · 2020
Closest in time.
Kernel and rich regimes in overparametrized models
Blake Woodworth, Suriya Gunasekar, Jason D Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, and Nathan Srebro · 2020
Closest in time.
Implicit regularization in relu networks with the square loss
Gal Vardi and Ohad Shamir · 2020
Closest in time.
Can implicit bias explain generalization? stochastic convex optimization as a case study
Assaf Dauber, Meir Feder, Tomer Koren, and Roi Livni · 2020
Closest in time.
Implicit regularization in deep learning may not be explainable by norms
Noam Razin and Nadav Cohen · 2020
Closest in time.
https://www.mathworks.com/matlabcentral/fileexchange/63731-surface-reconstruction-from-scattered-points-cloud-open-surfaces
Surface reconstruction from scattered points cloud (open surfaces) · 2021
Closest in time.