Fetching the paper…
Reading the bibliography…
We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above.
Die Brunn–Minkowskische ungleichung für beliebige messbare mengen
L. Lusternik · 1935
Earlier work this paper cites.
A logical calculus of the ideas immanent in nervous activity
W. S. McCulloch and W. Pitts · 1943
Earlier work this paper cites.
The organization of behavior
D. O. Hebb · 1949
Earlier work this paper cites.
Brunn-Minkowskischer Satz und Isoperimetrie
H. Hadwiger and D. Ohmann · 1956
Earlier work this paper cites.
A problem in geometric probability
J. G. Wendel · 1962
Earlier work this paper cites.
Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition
T. M. Cover · 1965
Earlier work this paper cites.
Logarithmic concave measures with application to stochastic programming
A. Prékopa · 1971
Earlier work this paper cites.
On a certain converse of Hölder’s inequality
L. Leindler · 1972
Earlier work this paper cites.
On logarithmic concave measures and functions
A. Prékopa · 1973
Earlier work this paper cites.
The existence of persistent states in the brain
W. A. Little · 1974
Earlier work this paper cites.
The Brunn-Minkowski inequality in Gauss space
C. Borell · 1975
Earlier work this paper cites.
Sums of independent random variables
V. V. Petrov · 1975
Earlier work this paper cites.
Solvable model of a spin-glass
D. Sherrington and S. Kirkpatrick · 1975
Earlier work this paper cites.
On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
H. J. Brascamp and E. H. Lieb · 1976
Earlier work this paper cites.
Norms of Gaussian sample functions
B. S. Tsirelson, I. A. Ibragimov, and V. N. Sudakov · 1976
Earlier work this paper cites.
Solution of ‘solvable model of a spin glass’
D. J. Thouless, P. W. Anderson, and R. G. Palmer · 1977
Earlier work this paper cites.
Stability of the Sherrington–Kirkpatrick solution of a spin glass model
J. R. de Almeida and D. J. Thouless · 1978
Earlier work this paper cites.
Neural networks and physical systems with emergent collective computational abilities
J. J. Hopfield · 1982
Earlier work this paper cites.
Convergence condition of the tap equation for the infinite-ranged ising spin glass model
T. Plefka · 1982
Earlier work this paper cites.
Some inequalities for Gaussian processes and applications
Y. Gordon · 1985
Earlier work this paper cites.
Probabilistic methods in the geometry of Banach spaces
G. Pisier · 1986
Earlier work this paper cites.
Maximum storage capacity in neural networks
E. Gardner · 1987
Earlier work this paper cites.
The space of interactions in neural network models
E. Gardner · 1988
Earlier work this paper cites.
Optimal storage properties of neural network models
E. Gardner and B. Derrida · 1988
Earlier work this paper cites.
On Milman’s inequality and random subspaces which escape through a mesh in 𝐑 n {\bf R}^{n}
Y. Gordon · 1988
Earlier work this paper cites.
Three unfinished works on the optimal storage capacity of networks
E. Gardner and B. Derrida · 1989
Cited alongside, same era.
Storage capacity of memory networks with binary couplings
W. Krauth and M. Mézard · 1989
Cited alongside, same era.
The space of interactions in neural networks: Gardner’s computation with the cavity method
M. Mézard · 1989
Cited alongside, same era.
Some deviation inequalities
B. Maurey · 1991
Cited alongside, same era.
Covering cubes by random half cubes, with applications to binary neural networks
J. H. Kim and J. R. Roche · 1995
Cited alongside, same era.
Intersecting random half cubes
M. Talagrand · 1997
Cited alongside, same era.
Generalization and refinement of the integro-local Stone theorem for sums of random vectors
A. Borovkov · 2017
Later among the works it cites.
Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems
S. Franz, G. Parisi, M. Sevelev, P. Urbani, and F. Zamponi · 2017
Later among the works it cites.
Mean-field message-passing equations in the Hopfield model and its generalizations
M. Mézard · 2017
Later among the works it cites.
The generalized TAP free energy
W.-K. Chen, D. Panchenko, and E. Subag · 2018
Later among the works it cites.
Capacity lower bound for the Ising perceptron
J. Ding and N. Sun · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Hopfield models as generalized random mean field models
A. Bovier and V. Gayrard · 1998
Cited alongside, same era.
Self-averaging and the space of interactions in neural networks
M. Talagrand · 1999
Cited alongside, same era.
From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
S. G. Bobkov and M. Ledoux · 2000
Cited alongside, same era.
Intersecting random half-spaces: toward the Gardner-Derrida formula
M. Talagrand · 2000
Cited alongside, same era.
Analysis
E. H. Lieb and M. Loss · 2001
Cited alongside, same era.
Adaptive and self-averaging Thouless–Anderson–Palmer mean-field theory for probabilistic modeling
M. Opper and O. Winther · 2001
Cited alongside, same era.
Finite sample analysis of approximate message passing algorithms
C. Rush and R. Venkataramanan · 2018
Later among the works it cites.
Storage capacity in symmetric binary perceptrons
B. Aubin, W. Perkins, and L. Zdeborová · 2019
Later among the works it cites.
Optimal errors and phase transitions in high-dimensional generalized linear models
J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová · 2019
Later among the works it cites.
A Morita type proof of the replica-symmetric formula for SK
E. Bolthausen · 2019
Later among the works it cites.
Biased landscapes for random constraint satisfaction problems
L. Budzynski, F. Ricci-Tersenghi, and G. Semerjian · 2019
Later among the works it cites.
Memory-free dynamics for the Thouless–Anderson–Palmer equations of Ising models with arbitrary rotation-invariant ensembles of random coupling matrices
B. Çakmak and M. Opper · 2019
Later among the works it cites.
Algorithmic pure states for the negative spherical perceptron
A. E. Alaoui and M. Sellke · 2020
Later among the works it cites.
State evolution for approximate message passing with non-separable functions
R. Berthier, A. Montanari, and P.-M. Nguyen · 2020
Later among the works it cites.
Approximate message passing algorithms for rotationally invariant matrices
Z. Fan · 2020
Later among the works it cites.
Dynamical approach to the TAP equations for the Sherrington-Kirkpatrick model
A. Adhikari, C. Brennecke, P. von Soosten, and H.-T. Yau · 2021
Closest in time.
Shattering versus metastability in spin glasses
G. B. Arous and A. Jagannath · 2021
Closest in time.
Proof of the contiguity conjecture and lognormal limit for the symmetric perceptron
E. Abbe, S. Li, and A. Sly · 2021
Closest in time.
A note on the replica symmetric formula for the SK model
C. Brennecke and H.-T. Yau · 2021
Closest in time.
The generalized TAP free energy II
W.-K. Chen, D. Panchenko, and E. Subag · 2021
Closest in time.
TAP free energy, spin glasses and variational inference
Z. Fan, S. Mei, and A. Montanari · 2021
Closest in time.
The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
Z. Fan and Y. Wu · 2021
Closest in time.
Tractability from overparametrization: the example of the negative perceptron
A. Montanari, Y. Zhong, and K. Zhou · 2021
Closest in time.
Frozen 1-RSB structure of the symmetric Ising perceptron
W. Perkins and C. Xu · 2021
Closest in time.
Sharp threshold for the Ising perceptron model
C. Xu · 2021
Closest in time.