no. 3
Artificial neural networks. A review from physical and mathematical points of view
Annales de l'I.H.P. Physique théorique, Tome 64 (1996) no. 3, pp. 289-307. 
@article{AIHPA_1996__64_3_289_0,
     author = {Picco, Pierre},
     title = {Artificial neural networks. {A} review from physical and mathematical points of view},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {289--307},
     publisher = {Gauthier-Villars},
     volume = {64},
     number = {3},
     year = {1996},
     mrnumber = {1400293},
     zbl = {0848.68085},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1996__64_3_289_0/}
}
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Picco, Pierre. Artificial neural networks. A review from physical and mathematical points of view. Annales de l'I.H.P. Physique théorique, Tome 64 (1996) no. 3, pp. 289-307. http://www.numdam.org/item/AIHPA_1996__64_3_289_0/

[ALR] M. Aizenman, J. Lebowitz and D. Ruelle, Some rigorous results on the Sherrington-Kirkpatrick model, Com. Math. Phys. Vol. 112, 1987, pp. 3-20. | MR

[A] D.J. Amit, Modeling Brain Function, Cambridge Univ. Press. Cambridge, 1988. | MR | Zbl

[AGS1] D.J. Amit, H. Gutfreund and H. Sompolinsky, Spin-glass models of neural networks, Phys. Rev., Vol. A32, 1985, pp. 1007-1018. | MR

[AGS] D.J. Amit, H. Gutfreund and H. Sompolinsky, Statistical Mechanics of Neural Networks near Saturation, Ann. of Phys., Vol. 173, 1987, pp. 30-67.

[BG1] A. Bovier and V. Gayrard, Rigorous bounds on the storage capacity of the dilute Hopfield model, J. Stat. Phys., Vol. 69, 1992, pp. 597-627. | MR | Zbl

[BG2] A. Bovier and V. Gayrard, Rigorous results on the thermodynamics of the dilute Hopfield model, J. Stat. Phys., Vol. 69, 1993, pp. 597-627. | MR

[BGP1] A. Bovier, V. Gayrard and P. Picco, Gibbs states of the Hopfield model in the regime of perfect memory, to appear in Prob. Theor. Rel. Fields, 1995. | MR

[BGP2] A. Bovier, V. Gayrard and P. Picco, Large deviation principles for the Hopfield and the Kac-Hopfield model, to appear in Probability Theory and relatedfields, 1995. | Zbl

[BGP3] A. Bovier, V. Gayrard and P. Picco, Gibbs states for the Hopfield model with extensively many patterns, to appear in J.S.P., 1995. | MR | Zbl

[CT] B. Cheng and D.M. Titterington, Neural Networks: A Review from a Statistical Perspective, Statistical Science, Vol. 9, 1994, pp. 2-54. | MR | Zbl

[Co] F. Comets, Large deviation estimates for a conditional probability distribution. Applications to random Gibbs measures, Prob. Theor. Rel. Fields, Vol. 80, 1989, pp. 407-432. | MR | Zbl

[COP] M. Cassandro, E. Orlandi and E. Presutti, Interfaces and typical Gibbs configurations for one-dimensional Kac potentials, Prob. Theor. Rel. Fields, Vol. 96, 1993, pp. 57-96. | MR | Zbl

[E] R.S. Ellis, Entropy, large deviations, and statistical mechanics, Springer-Verlag, Berlin, 1985. | MR | Zbl

[FMP] P. Ferrari, S. Martinez and P. Picco, A lower bound for the memory capacity in the Hopfield-Potts model, J. Stat. Phys., Vol. 66, 1991, pp. 1643-1651. | MR | Zbl

[FP1] L.A. Pastur and A.L. Figotin, Exactly soluble model of a spin glass, Sov. J. Low Temp. Phys., Vol. 3(6), 1977, pp. 378-383.

[FP2] L.A. Pastur and A.L. Figotin, On the theory of disordered spin systems, Theor. Math. Phys., Vol. 35, 1978, pp. 403-414. | MR

[FP3] L.A. Pastur and A.L. Figotin, Infinite range limit for a class of disordered spin systems, Theor. Math. Phys., Vol. 51, 1982, pp. 564-569. | MR

[Gay] V. Gayrard, The thermodynamics limit of the q-state Potts-Hopfield model with infinitely many patterns, J. Stat. Phys., Vol. 68, 1992, pp. 977-1011. | MR | Zbl

[Gar] E. Gardner, The space of interactions in neural network models, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 257-270. | MR | Zbl

[GD] E. Gardner and B. Derrida, Optimal storage properties of neural network models, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 271-284. | MR

[GFP] E. Goles, F. Fogelman-Soulie and D. Pellegrin, Decreasing energy functons as a tool for studying threshold networks, Discrete App. Math., Vol. 12, 1985, pp. 261-277. | MR | Zbl

[GM] E. Goles and S. Martinez, Neural and automata networks. Dynamical behavior and applications, Kluwer Ac. Pub. Dordrecht, Boston, London, 1990. | MR | Zbl

[GK] D. Grensing and K. Kühn, On classical spin-glass models, J. Phys. Paris, Vol. 48, 1987, pp. 713-721. | MR

[GTA] M. Griniasty, M. Tsodyks and D.J. Amit, Neural Comp., Vol. 5, 1993, pp. 1-17.

[He] D.O. Hebb, The organisation of behavior, J. Willey & Son, New York, 1949.

[Ho] J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA, Vol. 79, 1982, pp. 2554- 2558. | MR

[KS] I. Kanter and H. Sompolinsky, Associative recall of memory without errors, Phys. Rev. A, Vol. 35, 1987, pp. 380-392.

[Ko] H. Koch, A free energy bound for the Hopfield model, J. Phys. A: Math Gen., Vol. 26, 1993, pp. L353-L355. | MR | Zbl

[Koh] T. Kohonen, Self-organisation and associative memory, Springer Verlag, Berlin, 1984. | MR | Zbl

[KP] H. Koch and J. Piasko, Some rigorous results on the Hopfield neural network model, J. Stat. Phys., Vol. 55, 1989, pp. 903-928. | MR | Zbl

[KUH] M. Kac, G. Uhlenbec and P.C. Hemmer, On the van der Waals theory of vapour-liquid equilibrium. I. Discussion of a one-dimensional model, J. Math. Phys., Vol. 4, 1963, pp. 216-228; II. Discussion of the distribution functions, J. Math. Phys., Vol. 4, 1963, pp. 229-247; III. Discussion of the critical region, J. Math. Phys., Vol. 5, 1964, pp. 60-74. | MR | Zbl

[KPa] J. Komlos and R. Paturi, Convergence results in an associative memory model, Neural Network., Vol. 1, 1988, pp. 239-250.

[LP] J. Lebowitz and O. Penrose, Rigorous treatment of the Van der Waals Maxwell theory of the liquid-vapour transition, J. Math. Phys., Vol. 7, 1966, pp. 98-113. | MR | Zbl

[LeC1] Y. Le Cun, B. Boser, J.S. Denker, D. Henderson, R.E. Howard, W. Hubbard and L.D. Jackel, Backpropagation applied to handwritten Zip code recognition, Neural Computation, Vol. 1, 1989, pp. 541-551.

[LeC2] Y. Le Cun, B. Boser, J.S. Denker, D. Henderson, R.E. Howard, W. Hubbard and L.D. Jackel, Handwritten digit recognition with a backpropagation network, Advances in Neural Information Processing Systems II (D. S. Touretzky, eds.), Morgan Kaufmann, San Mateo, CA, 1990, pp. 396-404.

[L] Y.C. Lee, G. Doolen, H.H. Chen, G.Z. Sun, T. Maxwell, H.Y. Lee and C.L. Giles, Machine learning using a higher order correlaton network, Physica D, Vol. 22, 1987, pp. 276-867. | MR

[Lo] D. Loukianova, Capacité de mémoire dans le modèle de Hopfield, C. R. Acad. Sc. Paris, Serie 1, Vol. 31, 1994, pp. 157-160. | MR | Zbl

[McE] R.J. Mceliece, E.C. Posner, E.R. Rodemich and S.S. Venkatesh, The capacity of the Hopfield associative memory, IEEE Trans. Inform. Theory, Vol. 33, 1987, pp. 461-482. | MR | Zbl

[McCP] W.S. Mcculloch and W.A. Pitts, A logical calculus of the ideas immanent in nervous activity, Bul. Math. Biophysics, Vol. 5, 1943, pp. 115-133. | MR | Zbl

[M] S. Martinez, Temuco summer school. To appear, 1992.

[MP] M. Minsky and S. Papert, Perceptrons, MIT Press, Cambridge MA, 1969. | Zbl

[MNT] M. Mézard, J.P. Nadal and G. Toulouse, Solvable models of working memories, J. Phys. Paris, Vol. 47, 1986, pp. 1457-1462. | MR

[MPV] M. Mézard, G. Parisi and M. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore, 1987. | MR | Zbl

[Mi] Y. Miyashita, Neuronal correlate of visual associative long-term memory in primate temporal cortex, Nature, Vol. 335, 1988, p. 817.

[Mo1] R. Monasson, Properties of neural networks storing spatially correlated patterns, J. Phys. A: Math. Gen., Vol. 25, 1992, pp. 3701-3720. | MR | Zbl

[Mo2] R. Monasson, Storage of spatially correlated patterns in auto-associative memories, J. Phys. Paris, Vol. 3, 1993, pp. 1141-1152.

[N] C.M. Newman, Memory capacity in neural network models: rigorous lower bounds, Neural Networks, Vol. 1, 1988, pp. 223-238.

[PST] L. Pastur, M. Shcherbina and B. Tirozzi, The replica symmetric solution without the replica trick for the Hopfield model, J. Stat. Phys., Vol. 74, 1994, pp. 1161-1183. | MR | Zbl

[PGD] L. Personnaz, I. Guyon and G. Dreyfus, Information storage and retrivial in Spin-glass like neural networks, J. Phys. Lett., Vol. 49, 1985, pp. 359-365.

[ST] E. Scacciatelli and B. Tirozzi, Fluctuation of the free energy in the Hopfield model, J. Stat. Phys., Vol. 67, 1992, pp. 981-1008. | MR | Zbl

[ShT] M. Shcherbina and B. Tirozzi, The free energy for a class of Hopfield models, J. Stat. Phys., Vol. 72, 1992, pp. 113-125. | MR | Zbl

[TL] W. Tarkowski and M. Lewenstein, Storage of sets of correlated data in neural network memories, J. Phys A: Math. Gen., Vol. 26, 1993, pp. 2453-2469. | MR | Zbl