(no subject)
On replica method
& message passing:
M.Advani, S.Lahiri,
S.Ganguli (2013)
"Statistical mechanics
of complex neural systems
and high dimensional data."
On replica method, see:
M. Mezard, G. Parisi,
M. Virasoro (1987)
"Spin Glass Theory and
Beyond" Singapore:
World Scientific.
E. Kanzieper (2011)
"Replica approach in
Random Matrix Theory."
Ch. in: The Oxford Handbook
on Random Matrix Theory.
Parisi, G. (1997) "On the replica
approach to spin glasses." PS.
T. Castellani, A. Cavagna (2005)
"Spin-glass theory for pedestrians."
Arxiv.
Edwards S.F., Anderson P.W. (1975)
"Theory of spin glasses" J. Phys. F:
Met. Phys. 5, pp.:965-974.
Marco Di Gennaro (2010) "Replica trick
in a finite size spin glass" M.Sc. Th.
J.L. van Hemmen, R.G. Palmer (1979)
"The replica method and solvable spin
glass model" J. Phys. A: Math. Gen. 12, p.563.
E. Kanzieper (2001) "Random matrices and
the replica method" Nucl. Phys.B 596, 548.
E. Kanzieper (2002) "Replica field theories,
Painlevé transcendents and exact correlation
functions" Phys. Rev. Lett. 89, 250201. Arxiv.
H.Nishimori (2001) "Statistical physics
of spin glasses and information processing.
An introduction."
M. Kac, Trondheim Theoretical Physics Seminar,
Nordita Publ. No. 286, 1968 (unpublished)
T.-F. Lin (1970) "Problem of the Disordered
Chain." J. Math. Phys. 11, 1584.
S.F.Edwards, P.W.Anderson (1975)
"Theory of spin glasses." J. Phys.
F: Met. Phys. 5, 965.
additional, related:
N.Sourlas (1989) "Spin-glass
models as error-correcting
codes." Nature 339, 693.
N.Sourlas (1990) "Statistical
Mechanics of error-correcting
codes" In Statistical Mechanics
of Neural Networks, Lecture
Notes in Physics 368, ed. L.
Garrido, Springer Verlag.
N.Sourlas (1994) "Statistical Mechanics
and error-correcting codes" in From
Statistical Physics to Statistical
Inference and Back, ed. P.Grassberger,
J.-P.Nadal, Kluwer Academic, p.195.
N.Sourlas (1998) "Statistical Mechanics
and error-correcting codes." Arxiv.
N.Sourlas (2001) "Statistical mechanics
and capacity-approaching error-correcting
codes" Physica A 302, 14-21. Arxiv.
N. Sourlas (2005) "Statistical Mechanics
Approach to Error-Correcting Codes."
N.Sourlas (2000) "Statistical Mechanics of
turbo codes." KURENAI, 73(5): 811-819.
A.Montanari, N.Sourlas (1999) "The statistical
mechanics of turbo codes."
A. Montanari, N. Sourlas (2000) "The statistical
mechanics of turbo codes." Eur.Phys.J., B 18, 107-119.
A. Montanari (2000) "Turbo codes: the phase
transition." Eur. Phys. J. B, 18, 121-136.
Y.Kabashima (2003) "Propagating Beliefs in
Spin-Glass Models" J.Phys.Soc.Jpn.72, pp.1645-1649.
B.Derrida (1981) "Random-energy model:
An exactly solvable model of disordered
systems." Phys.Rev. B 24 2613-2626.
Gardner, E. (1986) "Structure of metastable
states in the Hopfield model" J. Phys. A 19, L1047.
Gardner, E. (1987) "Maximum Storage Capacity
in NNs" Europhys. Lett. 4, 481. (replica method)
Gardner, E. (1988) "The space of interactions
in NN models" J. Phys. A 21, 257. (replica method)
Gardner, E., Derrida, B. (1988) "Optimal storage
properties of NN models" J. Phys. A 21, 271.
Gardner, E., Derrida, B. (1989) "Three unfinished
works on the optimal storage capacity of networks"
J. Phys. A 22, 1983. (links)
B. Derrida, J.P. Nadal (1987) "Learning and
forgetting on asymmetric diluted neural networks"
J. Stat. Phys. 49, 993-1009.
Gardner, E., Gutfreund, H., Yekutieli, I. (1989)
"The phase space of interactions in neural networks
with definite symmetry" J. Phys. A 22, 1995.
Amit D.J., Gutfreund H., Sompolinsky H. (1985)
"Storing infinite numbers of patterns in a spin-glass
model of neural networks" Phys.Rev.Lett. 55, 1530-1533.
Amit D.J., Gutfreund H., Sompolinsky H. (1985)
"Spin-glass models of neural networks."
Phys Rev A. 32(2):1007-1018.
Gutfreund, H., Toulouse, G. (1992) "The physics
of neural networks" in "Spin Glasses and Biology",
ed. by D.L.Stein (World Scientific, Singapore).
Györgyi G. (1990) "Inference of a Rule by a NN
with Thermal Noise" Phys.Rev.Lett. 64, 2957-2960.
Györgyi, G. (1990) "First-order transition to
perfect generalization in a neural network with
binary synapses" Phys. Rev. A 41, 7097-7100.
Györgyi, G., Tishby, N. (1990) "Statistical
Theory of Learning a Rule" in "Neural Networks
and Spin Glasses" ed. by W.K.Theumann, R.Köberle
(World Scientific, Singapore), p.3.
T.L.H.Watkin, A.Rau, M.Biehl (1993)
"The statistical mechanics of learning
a rule," Rev.Mod.Phys., 65(2), 499-556.
A. Engel, C.V. den Broeck (2001)
"Statistical Mechanics of Learning.
Cambridge Univ. Press." Content.
Cf.: refs about Reggeons.
& message passing:
M.Advani, S.Lahiri,
S.Ganguli (2013)
"Statistical mechanics
of complex neural systems
and high dimensional data."
On replica method, see:
M. Mezard, G. Parisi,
M. Virasoro (1987)
"Spin Glass Theory and
Beyond" Singapore:
World Scientific.
E. Kanzieper (2011)
"Replica approach in
Random Matrix Theory."
Ch. in: The Oxford Handbook
on Random Matrix Theory.
Parisi, G. (1997) "On the replica
approach to spin glasses." PS.
T. Castellani, A. Cavagna (2005)
"Spin-glass theory for pedestrians."
Arxiv.
Edwards S.F., Anderson P.W. (1975)
"Theory of spin glasses" J. Phys. F:
Met. Phys. 5, pp.:965-974.
Marco Di Gennaro (2010) "Replica trick
in a finite size spin glass" M.Sc. Th.
J.L. van Hemmen, R.G. Palmer (1979)
"The replica method and solvable spin
glass model" J. Phys. A: Math. Gen. 12, p.563.
E. Kanzieper (2001) "Random matrices and
the replica method" Nucl. Phys.B 596, 548.
E. Kanzieper (2002) "Replica field theories,
Painlevé transcendents and exact correlation
functions" Phys. Rev. Lett. 89, 250201. Arxiv.
H.Nishimori (2001) "Statistical physics
of spin glasses and information processing.
An introduction."
M. Kac, Trondheim Theoretical Physics Seminar,
Nordita Publ. No. 286, 1968 (unpublished)
T.-F. Lin (1970) "Problem of the Disordered
Chain." J. Math. Phys. 11, 1584.
S.F.Edwards, P.W.Anderson (1975)
"Theory of spin glasses." J. Phys.
F: Met. Phys. 5, 965.
additional, related:
N.Sourlas (1989) "Spin-glass
models as error-correcting
codes." Nature 339, 693.
N.Sourlas (1990) "Statistical
Mechanics of error-correcting
codes" In Statistical Mechanics
of Neural Networks, Lecture
Notes in Physics 368, ed. L.
Garrido, Springer Verlag.
N.Sourlas (1994) "Statistical Mechanics
and error-correcting codes" in From
Statistical Physics to Statistical
Inference and Back, ed. P.Grassberger,
J.-P.Nadal, Kluwer Academic, p.195.
N.Sourlas (1998) "Statistical Mechanics
and error-correcting codes." Arxiv.
N.Sourlas (2001) "Statistical mechanics
and capacity-approaching error-correcting
codes" Physica A 302, 14-21. Arxiv.
N. Sourlas (2005) "Statistical Mechanics
Approach to Error-Correcting Codes."
N.Sourlas (2000) "Statistical Mechanics of
turbo codes." KURENAI, 73(5): 811-819.
A.Montanari, N.Sourlas (1999) "The statistical
mechanics of turbo codes."
A. Montanari, N. Sourlas (2000) "The statistical
mechanics of turbo codes." Eur.Phys.J., B 18, 107-119.
A. Montanari (2000) "Turbo codes: the phase
transition." Eur. Phys. J. B, 18, 121-136.
Y.Kabashima (2003) "Propagating Beliefs in
Spin-Glass Models" J.Phys.Soc.Jpn.72, pp.1645-1649.
B.Derrida (1981) "Random-energy model:
An exactly solvable model of disordered
systems." Phys.Rev. B 24 2613-2626.
Gardner, E. (1986) "Structure of metastable
states in the Hopfield model" J. Phys. A 19, L1047.
Gardner, E. (1987) "Maximum Storage Capacity
in NNs" Europhys. Lett. 4, 481. (replica method)
Gardner, E. (1988) "The space of interactions
in NN models" J. Phys. A 21, 257. (replica method)
Gardner, E., Derrida, B. (1988) "Optimal storage
properties of NN models" J. Phys. A 21, 271.
Gardner, E., Derrida, B. (1989) "Three unfinished
works on the optimal storage capacity of networks"
J. Phys. A 22, 1983. (links)
B. Derrida, J.P. Nadal (1987) "Learning and
forgetting on asymmetric diluted neural networks"
J. Stat. Phys. 49, 993-1009.
Gardner, E., Gutfreund, H., Yekutieli, I. (1989)
"The phase space of interactions in neural networks
with definite symmetry" J. Phys. A 22, 1995.
Amit D.J., Gutfreund H., Sompolinsky H. (1985)
"Storing infinite numbers of patterns in a spin-glass
model of neural networks" Phys.Rev.Lett. 55, 1530-1533.
Amit D.J., Gutfreund H., Sompolinsky H. (1985)
"Spin-glass models of neural networks."
Phys Rev A. 32(2):1007-1018.
Gutfreund, H., Toulouse, G. (1992) "The physics
of neural networks" in "Spin Glasses and Biology",
ed. by D.L.Stein (World Scientific, Singapore).
Györgyi G. (1990) "Inference of a Rule by a NN
with Thermal Noise" Phys.Rev.Lett. 64, 2957-2960.
Györgyi, G. (1990) "First-order transition to
perfect generalization in a neural network with
binary synapses" Phys. Rev. A 41, 7097-7100.
Györgyi, G., Tishby, N. (1990) "Statistical
Theory of Learning a Rule" in "Neural Networks
and Spin Glasses" ed. by W.K.Theumann, R.Köberle
(World Scientific, Singapore), p.3.
T.L.H.Watkin, A.Rau, M.Biehl (1993)
"The statistical mechanics of learning
a rule," Rev.Mod.Phys., 65(2), 499-556.
A. Engel, C.V. den Broeck (2001)
"Statistical Mechanics of Learning.
Cambridge Univ. Press." Content.
Cf.: refs about Reggeons.