Related papers: Replica Symmetry Breaking in Attractor Neural Netw…
In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…
Fully connected Blume-Emery-Griffiths neural networks performing pattern recognition and associative memory have been heuristically studied in the past (mainly via the replica trick and under the replica symmetric assumption) as…
Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…
We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there…
We analyze the full replica symmetry breaking (full--RSB) free energy functional for the Ising spin glass on a random regular graph proposed by the author in \cite{MyPaper}. We prove that the full--RSB formulation provides an improvement…
To test the stability of the Parisi solution near T=0, we study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field…
A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of…
It is shown that the Self-Consistent RPA (SCRPA) approach allows in a very natural way to restore symmetries, spontaneously broken on the mean field level. This is achieved via the introduction of a second Lagrange multiplier which…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
We integrate the recently proposed spatial transformer network (SPN) [Jaderberg et. al 2015] into a recurrent neural network (RNN) to form an RNN-SPN model. We use the RNN-SPN to classify digits in cluttered MNIST sequences. The proposed…
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…
Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…
In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field…
We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the…
We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…
A symmetry breaking (SB) involves an abrupt change in the set of microstates that a system can explore. This change has unavoidable thermodynamic implications. According to Boltzmann's microscopic interpretation of entropy, a shrinkage of…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…
The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schr\"odinger equation is…
The attention mechanism in its standard implementation contains extraneous rotational degrees of freedom that are carried through computation but do not affect model activations or outputs. We introduce a simple symmetry-breaking protocol…