Michael Field

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All published works

Action	Title	Year	Authors
+ PDF Chat	Symmetry & critical points for a model shallow neural network	2021	Yossi Arjevani Michael Field
+	Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks.	2021	Yossi Arjevani Michael Field
+	Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks: A Tale of Symmetry II	2021	Yossi Arjevani Michael Field
+	Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of S n .	2021	Yossi Arjevani Michael Field
+	Symmetry Breaking in Symmetric Tensor Decomposition	2021	Yossi Arjevani Joan Bruna Michael Field Joe Kileel Matthew Trager Francis Williams
+	Symmetry & critical points for a model shallow neural network	2020	Yossi Arjevani Michael Field
+	Heteroclinic cycles in equivariant bifurcations	2020	Michael Field
+	The invariant sphere theorem	2020	Michael Field
+	Analytic Characterization of the Hessian in Shallow ReLU Models: A Tale of Symmetry	2020	Yossi Arjevani Michael Field
+	Spurious Local Minima of Shallow ReLU Networks Conform with the Symmetry of the Target Model.	2019	Yossi Arjevani Michael Field
+	On the Principle of Least Symmetry Breaking in Shallow ReLU Models	2019	Yossi Arjevani Michael Field
+ PDF Chat	Asynchronous networks and event driven dynamics	2017	Christian Bick Michael Field
+ PDF Chat	Asynchronous networks: modularization of dynamics theorem	2017	Christian Bick Michael Field
+	Fractals and Iterated Function Systems	2017	Michael Field
+	Differential Calculus on ℝ m $$\mathbb{R}^{m}$$	2017	Michael Field
+	Sets, Functions and the Real Numbers	2017	Michael Field
+	Topics from Classical Analysis: The Gamma-Function and the Euler–Maclaurin Formula	2017	Michael Field
+	Basic Properties of Real Numbers, Sequences and Continuous Functions	2017	Michael Field
+	Metric Spaces	2017	Michael Field
+	Infinite Series	2017	Michael Field
+	Uniform Convergence	2017	Michael Field
+	Functions	2017	Michael Field
+	A gallery of Chua attractors	2010	Michael Field
+ PDF Chat	Stability of mixing and rapid mixing for hyperbolic flows	2007	Michael Field Ian Melbourne Andrei Török
+	Singularity and stratification theory applied to dynamical systems	2007	Michael Field
+ PDF Chat	A theory of fluctuations in stock prices	2005	Ángel L. Alejandro-Quiñones Kevin E. Bassler Michael Field Joseph L. McCauley Matthew Nicol Ilya Timofeyev Andrew Török Gemunu H. Gunaratne
+ PDF Chat	Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets	2005	Michael Field Ian Melbourne Andrei Török
+	Statistical properties of compact group extensions of hyperbolic flows and their time one maps	2005	Michael Field Ian Melbourne Matthew Nicol Andrei Török
+ PDF Chat	Product dynamics for homoclinic attractors	2004	Peter Ashwin Michael Field
+	A Theory of Fluctuations in Stock Prices	2004	Ángel L. Alejandro-Quiñones Kevin E. Bassler Michael Field Joseph L. McCauley Matthew Nicol I. Timofeyef Andrei Török Gemunu H. Gunaratne
+	Combinatorial dynamics	2004	Michael Field
+	Ergodic theory of equivariant diffeomorphisms: Markov partitions and stable ergodicity	2004	Michael Field Matthew Nicol
+	A Theory of Fluctuations in Stock Prices	2004	Ángel L. Alejandro-Quiñones Kevin E. Bassler Michael Field Joseph L. McCauley Matthew Nicol I. Timofeyef Andrei Török Gemunu H. Gunaratne
+ PDF Chat	Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions	2003	Michael Field Ian Melbourne Andrew Török
+	Persistent Ergodicity and Stably Ergodic SRB Attractors in Equivariant Dynamics	2003	Michael Field
+	Stable topological transitivity of skew and principal extensions	2001	Michael Field Viorel Niţică
+	Ergodicity and robustness of symmetric attractors	2000	Michael Field
+	Heteroclinic Networks in Coupled Cell Systems	1999	Peter Ashwin Michael Field
+	Generating sets for compact semisimple Lie groups	1999	Michael Field
+	Heteroclinic Cycles in Symmetrically Coupled Systems	1999	Michael Field
+	STABLE ERGODICITY OF SKEW EXTENSIONS BY COMPACT LIE GROUPS	1999	Michael Field William Parry
+	Symmetric Attractors for Diffeomorphisms and Flows	1996	Michael Field Ian Melbourne Matthew Nicol
+	Symmetry breaking for compact Lie groups	1996	Michael Field
+	Symmetry breaking for compact Lie groups	1996	Michael Field
+	Hopf bifurcation and the Hopf fibration	1994	Michael Field James W. Swift
+	Bifurcations on hemispheres	1991	Michael Field Martin Golubitsky Ian Stewart

Common Coauthors

Coauthor	Papers Together
Yossi Arjevani	9
Matthew Nicol	6
Andrei Török	5
Ian Melbourne	5
Ángel L. Alejandro-Quiñones	3
Kevin E. Bassler	3
Gemunu H. Gunaratne	3
Joseph L. McCauley	3
Peter Ashwin	2
I. Timofeyef	2
Christian Bick	2
Andrew Török	2
Francis Williams	1
Matthew Trager	1
Joe Kileel	1
Martin Golubitsky	1
James W. Swift	1
Ian Stewart	1
Ilya Timofeyev	1
Joan Bruna	1
William Parry	1
Viorel Niţică	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Probability	1996	John Lamperti	9
+	Topology from the Differentiable Viewpoint.	1967	Edgar H. Brown John Milnor	9
+ PDF Chat	Stratifications of equivariant varieties	1977	Mike Field	9
+	A Primer of Real Analytic Functions	1992	Steven G. Krantz Harold R. Parks	9
+	The Fractal Geometry of Nature	1982	Benoît B. Mandelbrot Paul Longley	8
+ PDF Chat	On uniform distribution of sequences	1987	Péter Kiss Robert F. Tichy	7
+ PDF Chat	A Primer of Real Analytic Functions	2002	Steven G. Krantz Harold R. Parks	7
+	Symmetry-breaking and branching patterns in equivariant bifurcation theory, I	1992	Mike Field R. W. Richardson	7
+	Equivariant bifurcation theory and symmetry breaking	1989	Mike Field	6
+	STABLE ERGODICITY OF SKEW EXTENSIONS BY COMPACT LIE GROUPS	1999	Michael Field William Parry	6
+	Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups	1989	Mike Field R. W. Richardson	6
+	Singularities and Groups in Bifurcation Theory	1988	Martin Golubitsky Ian Stewart David G. Schaeffer	6
+ PDF Chat	Ten Misconceptions from the History of Analysis and Their Debunking	2012	Piotr Błaszczyk Mikhail G. Katz David Sherry	5
+	Probability (2nd ed.)	1995	Albert N. Shiryaev R. P. Boas	5
+	Introduction to the modern theory of dynamical systems	1996	Anatole Katok Boris Hasselblatt	5
+	Uniform distribution of sequences	1974	L. Kuipers Harald Niederreiter	5
+	Topological transitivity of one class of dynamic systems and flows of frames on manifolds of negative curvature	1975	Michael Brin	5
+	Introduction to Compact Transformation Groups	1972	Glen E. Bredon	5
+	Principles of mathematical analysis	1964	Walter Rudin	5
+	NONCOMMUTATIVE JORDAN RIESZ ALGEBRAS	1988	Antonio Fernández López	5
+	Zeta functions and the periodic orbit structure of hyperbolic dynamics	1990	William Parry Mark Pollicott	5
+	Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima	2017	Simon S. Du Jason D. Lee Yuandong Tian Barnabás Póczos Aarti Singh	5
+	The Curious History of Faà di Bruno's Formula	2002	Warren P. Johnson	5
+	An Analytical Formula of Population Gradient for two-layered ReLU network and its Applications in Convergence and Critical Point Analysis	2017	Yuandong Tian	5
+	<i>The Fractal Geometry of Nature</i>	1983	Benoît B. Mandelbrot John Wheeler	5
+	Learning One-hidden-layer Neural Networks with Landscape Design	2017	Rong Ge Jason D. Lee Tengyu Ma	4
+	Porcupine Neural Networks: (Almost) All Local Optima are Global.	2017	Soheil Feizi Hamid Javadi Jesse M. Zhang David Tse	4
+ PDF Chat	Symmetry breaking in equivariant bifurcation problems	1990	M. J. Field R. W. Richardson	4
+	The Ergodic Theory of Axiom A Flows	1975	Rufus Bowen David Ruelle	4
+	On the Principle of Least Symmetry Breaking in Shallow ReLU Models	2019	Yossi Arjevani Michael Field	4
+ PDF Chat	Stably ergodic skew products	1996	Roy L. Adler Bruce Kitchens Michael Shub	4
+	Three Factors Influencing Minima in SGD	2017	Stanisław Jastrzȩbski Zachary Kenton Devansh Arpit Nicolas Ballas Asja Fischer Yoshua Bengio Amos Storkey	3
+	Diverse Neural Network Learns True Target Functions	2016	Bo Xie Yingyu Liang Le Song	3
+	Electron-Proton Dynamics in Deep Learning.	2017	Qiuyi Zhang Rina Panigrahy‎ Sushant Sachdeva	3
+	Recovery Guarantees for One-hidden-layer Neural Networks	2017	Kai Zhong Zhao Song Prateek Jain Peter L. Bartlett Inderjit S. Dhillon	3
+	Distribution-specific hardness of learning neural networks	2018	Ohad Shamir	3
+	Geodesic flows on closed Riemann manifolds with negative curvature	1969	D. V. Anosov	3
+	Maximal subgroups of finite groups	1985	Michael Aschbacher Leonard L. Scott	3
+ PDF Chat	Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms	1975	Rufus Bowen	3
+ PDF Chat	Asynchronous networks and event driven dynamics	2017	Christian Bick Michael Field	3
+	Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks	2018	Mahdi Soltanolkotabi Adel Javanmard Jason D. Lee	3
+	A classification of the maximal subgroups of the finite alternating and symmetric groups	1987	Martin W. Liebeck Cheryl E. Praeger Jan Saxl	3
+	Stable topological transitivity of skew and principal extensions	2001	Michael Field Viorel Niţică	3
+	Stationary bifurcation to limit cycles and heteroclinic cycles	1991	Martha S. Field James W. Swift	3
+	COHOMOLOGY OF DYNAMICAL SYSTEMS	1972	A N Livšic	3
+	Structurally stable heteroclinic cycles	1988	John Guckenheimer Philip Holmes	3
+ PDF Chat	Equivariant dynamical systems	1980	M. J. Field	3
+	Coupled cells with internal symmetry: II. Direct products	1996	B. Dionne Martin Golubitsky Ian Stewart	3
+ PDF Chat	Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection	1998	Peter Ashwin A. M. Rucklidge	3
+	The central limit theorem for geodesic flows onn-dimensional manifolds of negative curvature	1973	Marina Ratner	3