Replica Symmetry Breaking in Dense Hebbian Neural Networks

Replica Symmetry Breaking in Bipartite Spin Glasses and Neural Networks

Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study the mathematically tractable bipartite Sherrington-Kirkpatrick (SK) spin glass model, which is formally similar to a Restricted Boltzmann Machine (RBM) neura...

Replica Symmetry Breaking, Scaling Theory, and Sensor Networks

Device and sensor networks are shaping many activities in our society. These networks are being deployed in a growing number of applications as diverse as agricultural management, industrial controls, crime watch, and military applications. Indeed, sensor networks can be considered as a promising technology with a wide range of potential future markets [1]. Still, for all the promise, it is oft...

Replica symmetry breaking in the minority game

We extend and complete recent work concerning the analytic solution of the minority game. Nash equilibria (NE) of the game have been found to be related to the ground states of a disordered hamiltonian with replica symmetry breaking (RSB), signalling the presence of a large number of them. Here we study the number of NE both analytically and numerically. We then analyze the stability of the rec...

Spontaneous Symmetry Breaking in Neural Networks

We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks generalize better if such symmetries are broken to reduce the redundancies of the weights. Using a two parameter field theory, we find that the network can b...

Diluted neural networks with binary couplings: a replica symmetry breaking calculation of the storage capacity