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[1] Corrado Segre. Sulle corrispondenze quadrilineari tra forme di 1a specie e su alcune loro rappresentazioni spaziali , 1921 .
[2] Donald F. Specht,et al. Generation of Polynomial Discriminant Functions for Pattern Recognition , 1967, IEEE Trans. Electron. Comput..
[3] A. G. Ivakhnenko,et al. Polynomial Theory of Complex Systems , 1971, IEEE Trans. Syst. Man Cybern..
[4] Richard O. Duda,et al. Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.
[5] Grazia Lotti,et al. O(n2.7799) Complexity for n*n Approximate Matrix Multiplication , 1979, Inf. Process. Lett..
[6] Victor G. Kac,et al. Some remarks on nilpotent orbits , 1980 .
[7] Geoffrey E. Hinton,et al. Learning internal representations by error propagation , 1986 .
[8] G. Palm. Warren McCulloch and Walter Pitts: A Logical Calculus of the Ideas Immanent in Nervous Activity , 1986 .
[9] R. Lippmann,et al. An introduction to computing with neural nets , 1987, IEEE ASSP Magazine.
[10] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..
[11] W. Pitts,et al. A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.
[12] G. J. Gibson,et al. On the decision regions of multilayer perceptrons , 1990, Proc. IEEE.
[13] Bernard Widrow,et al. 30 years of adaptive neural networks: perceptron, Madaline, and backpropagation , 1990, Proc. IEEE.
[14] Tarun Khanna,et al. Foundations of neural networks , 1990 .
[15] Kurt Hornik,et al. Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.
[16] Joydeep Ghosh,et al. Approximation of multivariate functions using ridge polynomial networks , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.
[17] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..
[18] Sun-Yuan Kung,et al. Generalized perceptron networks with nonlinear discriminant functions , 1992 .
[19] V. Rao Vemuri,et al. Artificial neural networks: Concepts and control applications , 1992 .
[20] I. M. Gelʹfand,et al. Discriminants, Resultants, and Multidimensional Determinants , 1994 .
[21] Joydeep Ghosh,et al. Ridge polynomial networks , 1995, IEEE Trans. Neural Networks.
[22] Christopher M. Bishop,et al. Neural networks for pattern recognition , 1995 .
[23] M.H. Hassoun,et al. Fundamentals of Artificial Neural Networks , 1996, Proceedings of the IEEE.
[24] P. Wilson,et al. DISCRIMINANTS, RESULTANTS AND MULTIDIMENSIONAL DETERMINANTS (Mathematics: Theory and Applications) , 1996 .
[25] Jerzy Weyman,et al. Singularities of hyperdeterminants , 1996 .
[26] Simon Haykin,et al. Neural Networks: A Comprehensive Foundation , 1998 .
[27] Ian H. Witten,et al. Data mining: practical machine learning tools and techniques, 3rd Edition , 1999 .
[28] Peter L. Bartlett,et al. Neural Network Learning - Theoretical Foundations , 1999 .
[29] J. Cirac,et al. Three qubits can be entangled in two inequivalent ways , 2000, quant-ph/0005115.
[30] Jean-Luc Brylinski. Algebraic measures of entanglement , 2000 .
[31] G. Dreyfus,et al. Réseaux de neurones - Méthodologie et applications , 2002 .
[32] B. Moor,et al. Four qubits can be entangled in nine different ways , 2001, quant-ph/0109033.
[33] Akimasa Miyake,et al. Multipartite entanglement and hyperdeterminants , 2002, Quantum Inf. Comput..
[34] Karl Rihaczek,et al. 1. WHAT IS DATA MINING? , 2019, Data Mining for the Social Sciences.
[35] Hong-Xing Li,et al. INTERPOLATION FUNCTIONS OF FEEDFORWARD NEURAL NETWORKS , 2003 .
[36] A. Miyake. Classification of multipartite entangled states by multidimensional determinants , 2002, quant-ph/0206111.
[37] Sung-Kwun Oh,et al. Polynomial neural networks architecture: analysis and design , 2003, Comput. Electr. Eng..
[38] Victoria Hernández-Mederos,et al. Sampling points on regular parametric curves with control of their distribution , 2003, Comput. Aided Geom. Des..
[39] J. Luque,et al. Polynomial invariants of four qubits , 2002, quant-ph/0212069.
[40] Akimasa Miyake,et al. Multipartite entanglement in 2 x 2 x n quantum systems , 2003, quant-ph/0307067.
[41] F. Verstraete,et al. Multipartite entanglement in 2x2xn quantum systems (9 pages) , 2004 .
[42] J. Luque,et al. Algebraic invariants of five qubits , 2005, quant-ph/0506058.
[43] A. Osterloh,et al. ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS , 2005, quant-ph/0506073.
[44] Ong Hong Choon,et al. Non Linear Approximations using Multi-layered Perceptions and Polynomial Regressions , 2006 .
[45] F. J. Sainz,et al. Constructive approximate interpolation by neural networks , 2006 .
[46] Oleg Chterental,et al. Normal Forms and Tensor Ranks of Pure States of Four Qubits , 2006 .
[47] Chris Peterson,et al. Induction for secant varieties of Segre varieties , 2006, math/0607191.
[48] Willem A. de Graaf,et al. Secant Dimensions of Minimal Orbits: Computations and Conjectures , 2007, Exp. Math..
[49] G. Ottaviani,et al. On the Alexander–Hirschowitz theorem , 2007, math/0701409.
[50] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[51] Bernd Sturmfels,et al. The hyperdeterminant and triangulations of the 4-cube , 2006, Math. Comput..
[52] N. K. Langford,et al. Experimentally generating and tuning robust entanglement between photonic qubits , 2008, 0802.3161.
[53] Wenhu Xu,et al. Efficient generation of multi-photon W states by joint-measurement , 2008 .
[54] N. Wallach,et al. All maximally entangled four-qubit states , 2010, 1006.0036.
[55] Isaac L. Chuang,et al. Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .
[56] Giansalvo Cirrincione,et al. Neural-Based Orthogonal Data Fitting: The EXIN Neural Networks , 2010 .
[57] J. Landsberg. Tensors: Geometry and Applications , 2011 .
[58] Elizabeth C. Behrman,et al. Dynamic learning of pairwise and three-way entanglement , 2011, 2011 Third World Congress on Nature and Biologically Inspired Computing.
[59] Jean-Gabriel Luque,et al. Geometric descriptions of entangled states by auxiliary varieties , 2012, 1204.6375.
[60] Seth Lloyd,et al. Quantum algorithm for data fitting. , 2012, Physical review letters.
[61] Lin Chen,et al. Proof of the Gour-Wallach conjecture , 2013, 1308.1306.
[62] Geoffrey E. Hinton,et al. On the importance of initialization and momentum in deep learning , 2013, ICML.
[63] Jean-Gabriel Luque,et al. Singularity of type D4 arising from four-qubit systems , 2013, 1312.0639.
[64] Seth Lloyd,et al. Quantum algorithm for data fitting. , 2012, Physical review letters.
[65] Giorgio Ottaviani,et al. An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors , 2014, SIAM J. Matrix Anal. Appl..
[66] Maria Schuld,et al. The quest for a Quantum Neural Network , 2014, Quantum Information Processing.
[67] F. Petruccione,et al. An introduction to quantum machine learning , 2014, Contemporary Physics.
[68] F. Holweck,et al. Entanglement of four qubit systems: A geometric atlas with polynomial compass I (the finite world) , 2013, 1306.6816.
[69] Masoud Mohseni,et al. Quantum support vector machine for big feature and big data classification , 2013, Physical review letters.
[70] L. Oeding,et al. Four Lectures on Secant Varieties , 2013, 1309.4145.
[71] S. Lloyd,et al. Quantum principal component analysis , 2013, Nature Physics.
[72] Anmer Daskin. Quantum Principal Component Analysis , 2015 .
[73] Marek Sawerwain,et al. Detecting Entanglement in Quantum Systems with Artificial Neural Network , 2015, ACIIDS.
[74] Ian H. Witten,et al. Data Mining, Fourth Edition: Practical Machine Learning Tools and Techniques , 2016 .
[75] F. Holweck,et al. Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world) , 2016, 1606.05569.
[76] Guigang Zhang,et al. Deep Learning , 2016, Int. J. Semantic Comput..
[77] Hamza Jaffali,et al. Grover’s algorithm and the secant varieties , 2016, Quantum Inf. Process..
[78] Hamza Jaffali,et al. Three-qutrit entanglement and simple singularities , 2016, 1606.05537.
[79] Ashish Kapoor,et al. Quantum deep learning , 2014, Quantum Inf. Comput..
[80] Timothy Dozat,et al. Incorporating Nesterov Momentum into Adam , 2016 .
[81] J. M. Landsberg,et al. Geometry and Complexity Theory , 2017 .
[82] Liwei Wang,et al. The Expressive Power of Neural Networks: A View from the Width , 2017, NIPS.
[83] Bingjie Wang. Learning to Detect Entanglement , 2017 .
[84] Lishen. Govender,et al. Determination of quantum entanglement concurrence using multilayer perceptron neural networks. , 2017 .
[85] Jacob biamonte,et al. Quantum machine learning , 2016, Nature.
[86] Man-Hong Yung,et al. Transforming Bell’s inequalities into state classifiers with machine learning , 2017, npj Quantum Information.
[87] Yu-Bo Sheng,et al. Distributed secure quantum machine learning. , 2017, Science bulletin.
[88] F. Holweck,et al. Hyperdeterminants from the $E_8$ Discriminant , 2018, 1810.05857.
[89] Rohit Raturi. Large Data Analysis via Interpolation of Functions: Interpolating Polynomials vs Artificial Neural Networks , 2018 .
[90] Man-Hong Yung,et al. Transforming Bell’s inequalities into state classifiers with machine learning , 2018 .
[91] Yimin Wei,et al. Geometric measures of entanglement in multipartite pure states via complex-valued neural networks , 2018, Neurocomputing.
[92] Richard Berkovits,et al. Extracting many-particle entanglement entropy from observables using supervised machine learning , 2018, Physical Review B.
[93] Bernd Sturmfels,et al. Learning algebraic varieties from samples , 2018, Revista Matemática Complutense.
[94] Stanislav Fort,et al. Adaptive quantum state tomography with neural networks , 2018, npj Quantum Information.
[95] Paul J. Scott,et al. Curvature based sampling of curves and surfaces , 2018, Comput. Aided Geom. Des..
[96] S. Bose,et al. Machine-Learning-Assisted Many-Body Entanglement Measurement. , 2017, Physical review letters.
[97] Mikhail Belkin,et al. Reconciling modern machine learning and the bias-variance trade-off , 2018, ArXiv.
[98] Jun Li,et al. Separability-entanglement classifier via machine learning , 2017, Physical Review A.
[99] Xi Cheng,et al. Polynomial Regression As an Alternative to Neural Nets , 2018, ArXiv.
[100] Mikhail Belkin,et al. Reconciling modern machine-learning practice and the classical bias–variance trade-off , 2018, Proceedings of the National Academy of Sciences.
[101] Hamza Jaffali,et al. Quantum entanglement involved in Grover’s and Shor’s algorithms: the four-qubit case , 2018, Quantum Information Processing.
[102] Nicolai Friis,et al. Optimizing Quantum Error Correction Codes with Reinforcement Learning , 2018, Quantum.
[103] Joan Bruna,et al. On the Expressive Power of Deep Polynomial Neural Networks , 2019, NeurIPS.
[104] Simone Severini,et al. Quantum machine learning: Challenges and Opportunities , 2019 .
[105] Iordanis Kerenidis,et al. q-means: A quantum algorithm for unsupervised machine learning , 2018, NeurIPS.
[106] Emilie Dufresne,et al. Sampling Real Algebraic Varieties for Topological Data Analysis , 2018, 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA).
[107] Guang-Can Guo,et al. Experimental Simultaneous Learning of Multiple Nonclassical Correlations. , 2018, Physical review letters.
[108] Boris Hanin,et al. Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations , 2017, Mathematics.
[109] Mikhail Belkin,et al. Reconciling modern machine-learning practice and the classical bias–variance trade-off , 2018, Proceedings of the National Academy of Sciences.
[110] Roger G. Melko,et al. QuCumber: wavefunction reconstruction with neural networks , 2018, SciPost Physics.
[111] J. Voight. Discriminants , 2021, Graduate Texts in Mathematics.