Related papers: Replica Symmetry Breaking in Attractor Neural Netw…
Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…
During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick…
In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables)…
Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The…
For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered…
In this short note, we present supporting evidence for the replica symmetric approach to the random bond q-state Potts models. The evidence is statistically strong enough to reject the applicability of the Parisi replica symmetry breaking…
We study the critical properties of the weakly disordered $p$-component random Heisenberg ferromagnet. It is shown that if the specific heat critical exponent of the pure system is positive, the traditional renormalization group (RG) flows…
We study the replica symmetry breaking (RSB) in the Gaussian Unitary Ensemble (GUE) random matrix model. We find that the RSB occurs at the transition temperature $T_{\text{RSB}}\sim N^{-2/3}$ in the large $N$ limit. We argue that this…
In this work we present a rigorous and straightforward method to detect the onset of the instability of replica-symmetric theories in information processing systems, which does not require a full replica analysis as in the method originally…
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…
We perform the replica symmetry breaking (RSB) in the vicinity of the point of instability of the replica symmetric solution in the model of axial quadrupolar glass. It is shown that the solution with the first stage RSB is stable against…
We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model in $d>2$ and demonstrate the existence of a glass-like replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting…
Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines. Tackling this approach, at the fairly standard replica symmetric level of…
Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the…
We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…
We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…