Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors
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[1] Martin Anthony,et al. Classification by Polynomial Surfaces , 1995, Discret. Appl. Math..
[2] M. Rudelson,et al. Hanson-Wright inequality and sub-gaussian concentration , 2013 .
[3] Alexander A. Sherstov. SeparatingAC0 from Depth-2 Majority Circuits , 2009, SIAM J. Comput..
[4] G. Halász. Estimates for the concentration function of combinatorial number theory and probability , 1977 .
[5] M. Rudelson,et al. The least singular value of a random square matrix is O(n−1/2) , 2008, 0805.3407.
[6] Terence Tao,et al. A sharp inverse Littlewood-Offord theorem , 2010 .
[7] R. Stanley. An Introduction to Hyperplane Arrangements , 2007 .
[8] Pavel Pudlák,et al. Computing Boolean functions by polynomials and threshold circuits , 1998, computational complexity.
[9] Rocco A. Servedio,et al. Hardness results for agnostically learning low-degree polynomial threshold functions , 2011, SODA '11.
[10] Rocco A. Servedio,et al. Learning intersections and thresholds of halfspaces , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..
[11] Yaniv Plan,et al. Dimension Reduction by Random Hyperplane Tessellations , 2014, Discret. Comput. Geom..
[12] Alexander E. Litvak,et al. Adjacency matrices of random digraphs: singularity and anti-concentration , 2015, 1511.00113.
[13] Mark Rudelson,et al. No-gaps delocalization for general random matrices , 2015, Geometric and Functional Analysis.
[14] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[15] M. Rudelson,et al. The Littlewood-Offord problem and invertibility of random matrices , 2007, math/0703503.
[16] Konstantin E. Tikhomirov. The smallest singular value of random rectangular matrices with no moment assumptions on entries , 2014, 1409.7975.
[17] Ryan O'Donnell,et al. Analysis of Boolean Functions , 2014, ArXiv.
[18] Anwar Adkhamovich Irmatov,et al. On the number of threshold functions , 1993 .
[19] Gene H. Golub,et al. Rank-One Approximation to High Order Tensors , 2001, SIAM J. Matrix Anal. Appl..
[20] Jean Bourgain,et al. On the singularity probability of discrete random matrices , 2009, 0905.0461.
[21] G. Rota. On the Foundations of Combinatorial Theory , 2009 .
[22] Richard Beigel,et al. The polynomial method in circuit complexity , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.
[23] Rocco A. Servedio,et al. A Regularity Lemma and Low-Weight Approximators for Low-Degree Polynomial Threshold Functions , 2014, Theory Comput..
[24] Piyush C. Ojha,et al. Enumeration of linear threshold functions from the lattice of hyperplane intersections , 2000, IEEE Trans. Neural Networks Learn. Syst..
[25] Hoi H. Nguyen,et al. On the Singularity of Random Combinatorial Matrices , 2011, SIAM J. Discret. Math..
[26] Baldi. Symmetries and learning in neural network models. , 1987, Physical review letters.
[27] R. Buck. Partition of Space , 1943 .
[28] Pierre Baldi,et al. Deep Learning in Biomedical Data Science , 2018, Annual Review of Biomedical Data Science.
[29] P. Baldi,et al. Boolean polynomial threshold functions and random tensors , 2018, 1803.10868.
[30] Kevin P. Costello,et al. Random symmetric matrices are almost surely nonsingular , 2005, math/0505156.
[31] Zoltán Füredi,et al. Solution of the Littlewood-Offord problem in high dimensions , 1988 .
[32] James Aspnes,et al. The expressive power of voting polynomials , 1994, Comb..
[33] Gene H. Golub,et al. Symmetric Tensors and Symmetric Tensor Rank , 2008, SIAM J. Matrix Anal. Appl..
[34] Jehoshua Bruck,et al. Harmonic Analysis of Polynomial Threshold Functions , 1990, SIAM J. Discret. Math..
[35] Chi Wang,et al. The threshold order of a Boolean function , 1991, Discret. Appl. Math..
[36] Rocco A. Servedio,et al. Learning DNF in time 2Õ(n1/3) , 2004, J. Comput. Syst. Sci..
[37] Ryan O'Donnell,et al. New degree bounds for polynomial threshold functions , 2010, Comb..
[38] Van Vu,et al. Optimal Inverse Littlewood-Offord theorems , 2010, 1004.3967.
[39] Konstantin Tikhomirov. Sample covariance matrices of heavy-tailed distributions , 2016 .
[40] M. Anthony. Discrete Mathematics of Neural Networks: Selected Topics , 1987 .
[41] T. Tao,et al. Random Matrices: the Distribution of the Smallest Singular Values , 2009, 0903.0614.
[42] Mark Rudelson,et al. Invertibility of Sparse non-Hermitian matrices , 2015, 1507.03525.
[43] W. Pitts,et al. A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.
[44] Alexander E. Litvak,et al. Smallest singular value of random matrices with independent columns , 2008 .
[45] Konstantin Tikhomirov,et al. The limit of the smallest singular value of random matrices with i.i.d. entries , 2014, 1410.6263.
[46] J. Littlewood,et al. On the Number of Real Roots of a Random Algebraic Equation , 1938 .
[47] B. Bollobás. Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability , 1986 .
[48] Nicholas A. Cook. On the singularity of adjacency matrices for random regular digraphs , 2014, 1411.0243.
[49] Hoi H. Nguyen,et al. On the least singular value of random symmetric matrices , 2011, 1102.1476.
[50] Noga Alon,et al. Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs , 1997, J. Comb. Theory, Ser. A.
[51] Johan Håstad,et al. On the Size of Weights for Threshold Gates , 1994, SIAM J. Discret. Math..
[52] Pierre Baldi,et al. Group Actions and Learning for a Family of Automata , 1988, J. Comput. Syst. Sci..
[53] Pierre Baldi,et al. The capacity of feedforward neural networks , 2019, Neural Networks.
[54] T. Zaslavsky. Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes , 1975 .
[55] L. Schläfli. Gesammelte mathematische Abhandlungen , 1950 .
[56] Daniel A. Spielman,et al. PP is closed under intersection , 1991, STOC '91.
[57] E. Szemerédi,et al. On the probability that a random ±1-matrix is singular , 1995 .
[58] Jiri Matousek,et al. Lectures on discrete geometry , 2002, Graduate texts in mathematics.
[59] P. Erdös. On a lemma of Littlewood and Offord , 1945 .
[60] Friedrich Götze,et al. Asymptotic expansions for bivariate von Mises functionals , 1979 .
[61] T. Tao,et al. Inverse Littlewood-Offord theorems and the condition number of random discrete matrices , 2005, math/0511215.
[62] R. Winder. Partitions of N-Space by Hyperplanes , 1966 .
[63] Anwar Adkhamovich Irmatov,et al. Arrangements of Hyperplanes and the Number of Threshold Functions , 2001 .
[64] Marvin Minsky,et al. Perceptrons: An Introduction to Computational Geometry, Expanded Edition , 1987 .
[65] Timothy M. Chan,et al. Polynomial Representations of Threshold Functions and Algorithmic Applications , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).
[66] Saburo Muroga,et al. Lower Bounds of the Number of Threshold Functions and a Maximum Weight , 1962, IEEE Trans. Electron. Comput..
[67] Günter M. Ziegler,et al. Singular 0/1-Matrices, and the Hyperplanes Spanned by Random 0/1-Vectors , 2006, Comb. Probab. Comput..
[68] T. Tao,et al. On the singularity probability of random Bernoulli matrices , 2005, math/0501313.
[69] E. Giné,et al. Decoupling: From Dependence to Independence , 1998 .
[70] Roman Vershynin,et al. High-Dimensional Probability , 2018 .
[71] M. Talagrand. A new look at independence , 1996 .
[72] J. G. Wendel. A Problem in Geometric Probability. , 1962 .
[73] T. Tao,et al. On random ±1 matrices: Singularity and determinant , 2006 .
[74] Pierre Baldi,et al. On neuronal capacity , 2019, NeurIPS.
[75] M. Rudelson. Invertibility of random matrices: norm of the inverse , 2005, math/0507024.
[76] Thomas M. Cover,et al. Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition , 1965, IEEE Trans. Electron. Comput..
[77] Nigel J. Kalton,et al. Rademacher series and decoupling , 2005 .
[78] Roman Vershynin,et al. Invertibility of symmetric random matrices , 2011, Random Struct. Algorithms.
[79] M. Rudelson,et al. Non-asymptotic theory of random matrices: extreme singular values , 2010, 1003.2990.
[80] Jovisa D. Zunic. On encoding and enumerating threshold functions , 2004, IEEE Transactions on Neural Networks.
[81] Mark Rudelson,et al. Invertibility of random matrices: Unitary and orthogonal perturbations , 2012, 1206.5180.
[82] M. Ledoux. The concentration of measure phenomenon , 2001 .
[83] Andrew M. Odlyzko,et al. On subspaces spanned by random selections of plus/minus 1 vectors , 1988, Journal of combinatorial theory. Series A.
[84] I. Bárány. LECTURES ON DISCRETE GEOMETRY (Graduate Texts in Mathematics 212) , 2003 .
[85] T. Tao,et al. From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices , 2008, 0810.2994.
[86] P. McCullagh. Tensor Methods in Statistics , 1987 .
[87] Raghu Meka,et al. Anti-concentration for Polynomials of Independent Random Variables , 2016, Theory Comput..
[88] Hoi H. Nguyen,et al. Inverse Littlewood-Offord problems and The Singularity of Random Symmetric Matrices , 2011, 1101.3074.
[89] Ryan O'Donnell,et al. Extremal properties of polynomial threshold functions , 2008, J. Comput. Syst. Sci..
[90] M. Saks. Slicing the hypercube , 1993 .
[91] Alexey Naumov,et al. On minimal singular values of random matrices with correlated entries , 2013, 1309.5711.
[92] Jürgen Schmidhuber,et al. Deep learning in neural networks: An overview , 2014, Neural Networks.
[93] M. Rudelson,et al. The smallest singular value of a random rectangular matrix , 2008, 0802.3956.
[94] Pierre Baldi,et al. Neural networks, orientations of the hypercube, and algebraic threshold functions , 1988, IEEE Trans. Inf. Theory.
[95] D. Kane. A structure theorem for poorly anticoncentrated polynomials of Gaussians and applications to the study of polynomial threshold functions , 2017 .