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Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural nets.
1912
Earlier work this paper cites.
B Malgrange. Ideals of differentiable functions (OUP, London, 1966)
1966
Earlier work this paper cites.
J Milnor. Singular points of complex hypersurfaces (Annals of Math. Studies 61, Princeton University Press, 1968)
1968
Earlier work this paper cites.
F Rellich. Perturbation Theory of Eigenvalue Problems (1953 New York University Lect. Notes reprinted by Gordon and Breach, 1968)
1968
Earlier work this paper cites.
J N Mather. ‘Stratifications and mappings’, Proceedings of the dynamical systems conference, Salvador, Brazil (ed M Peixoto) (Academic Press, New York, 1973), 195–223
1973
Earlier work this paper cites.
T Kato. Perturbation theory for linear operators (Grundlehren 132
1976
Earlier work this paper cites.
E Bierstone. ‘Generic equivariant maps’, Real and Complex Singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976, Sijthoff and Noordhoff, Alphen aan den Rijn, 1977), 127–161
1977
Earlier work this paper cites.
J N Mather. ‘Differentiable invariants’, Topology 16
1977
Earlier work this paper cites.
G D James. The Representation Theory of the Symmetric Groups (Spring Lecture Notes 682
1978
Earlier work this paper cites.
R J Walker. Algebraic Curves , Springer, 1978
1978
Earlier work this paper cites.
A Vanderbauwhede, ‘”Local bifurcation and symmetry’, Research Notes in Mathematics 75
1982
Earlier work this paper cites.
E Ihrig and M Golubitsky. ‘Pattern selection with O ( 3 ) O(3) symmetry’, Physica D 12
1984
Earlier work this paper cites.
W Pawłlucki. ‘Quasi-regular Boundary and Stokes formula for a sub-analytic leaf’, (in Seminar on Deformations, Łodz-Warsaw 1981–83 , Springer Lect. Notes in Math. 1165
1985
Earlier work this paper cites.
M Golubitsky and D G Schaeffer. Singularities and Groups in Bifurcation Theory, Vol. I (Appl. Math. Sci. Ser. 51, Springer-Verlag, New York, 1988.)
1988
Earlier work this paper cites.
M Golubitsky, I N Stewart, & D G Schaeffer. Singularities and Groups in Bifurcation Theory, Vol. II (Appl. Math. Sci. Ser. 69, Springer-Verlag, New York, 1988.)
1988
Cited alongside, same era.
M J Field. ‘Equivariant Bifurcation Theory and Symmetry Breaking’, J. Dynamics and Diff. Eqns. 1
1989
Cited alongside, same era.
M J Field and R W Richardson. ‘Symmetry breaking and the Maximal Isotropy Subgroup Conjecture for Reflection Groups’, Arch. Rational Mech. Anal 105
1989
Cited alongside, same era.
P Chossat, R Lauterbach & I Melbourne. ‘Steady-State Bifurcation with O ( 3 ) {\text{\rm O}({3})} Symmetry’, Arch. Rational Mech. Anal 113
1990
Cited alongside, same era.
M J Field and R W Richardson. ‘Symmetry breaking in equivariant bifurcation problems’, Bull. Am. Math. Soc. 22
1990
Cited alongside, same era.
J Milnor. Topology from the differentiable viewpoint (Princeton University Press, 1997)
1997
Later among the works it cites.
P Chossat and R Lauterbach, Mathods in Equivariant Bifurcations and Dynamical Systems (World Scientific, Advanced series in nonlinear dynamicsi 15
2000
Later among the works it cites.
M Golubitsky and I Stewart. The symmetry perspective: from equilibrium to chaos in phase space and physical space (Birkhäuser Verlag 200
2002
Later among the works it cites.
2003
Later among the works it cites.
M J Field. Dynamics and Symmetry (Imperial College Press Advanced Texts in Mathematics — Vol. 3, 2007.)
2007
Later among the works it cites.
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D G Aronson, M G Golubitsky & M Krupa. ‘Coupled arrays of Josephson junctions and bifurcation of maps S n S_{n} symmetry’, Nonlinearity 4
1991
Cited alongside, same era.
W Fulton and J Harris. Representation Theory (Graduate Texts in Mathematics 129, Springer-Verlag, 1991)
1991
Cited alongside, same era.
M J Field and R W Richardson. ‘Symmetry breaking and Branching Patterns in Equivariant Bifurcation Theory I’, Arch. Rational Mech. Anal 118
1992
Cited alongside, same era.
M J Field and R W Richardson. ‘Symmetry breaking and Branching Patterns in Equivariant Bifurcation Theory II’, Arch. Rational Mech. Anal 120
1992
Cited alongside, same era.
I Melbourne. ‘Maximal isotropy subgroups for absolutely irreducible representations of compact Lie groups’, Nonlinearity 7
1994
Cited alongside, same era.
S Lojasiewicz. ‘On semi-analytic and subanalytic geometry’, Banach Center Publications 34
1995
Cited alongside, same era.
M J Field. Symmetry breaking for compact Lie groups (Mem. Amer. Math. Soc., 574
1996
Cited alongside, same era.
2008
Later among the works it cites.
R. Lauterbach, ‘Equivariant Bifurcation and Absolute Irreducibility in ℝ 8 {\mathbb{R}}^{8} : A Contribution to Ize Conjecture and Related Bifurcations’, J. Dynam. and Diff. Eqns 27
2015
Later among the works it cites.
T C Kuo. ‘An old man’s mathematical Stories’ Proc. JARCS 2017, Australian-Japanese Real and Complex Singularities Workshop
2017
Later among the works it cites.
A Parusiński and L Păunescu. ‘Arc-wise analytic stratification, Whitney fibring conjecture and Zariski equisingularity’, Adv. in Math. 309
2017
Later among the works it cites.
I Safran and O Shamir. ‘Spurious Local Minima are Common in Two-Layer ReLU Neural Networks’, Proc. of the 35th Int. Conf. on Machine Learning 80
2018
Later among the works it cites.
D Trotman. Stratification theory (Cisneros-Milina José Luis, Dũng Tráng Lê, Seade José (Eds.). Handbook of Geometry and Topology of Singularities I, 2020. hal-03186972)
2020
Later among the works it cites.
2021
Closest in time.
Y Arjevani and M Field. ‘An analytic study of families of spurious minima in two-layer ReLU neural networks’, preprint 2021
2021
Closest in time.