Related papers: A replica approach to the state-dependent synapses…
Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
In the context of disordered systems with quenched Hamiltonians I address the problem of characterizing rare samples where the thermal average of a specific observable has a value different from the typical one. These rare samples can be…
We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the…
The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method…
We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical…
We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…
In these lectures I will review the approach to glasses based on the replica formalism. Many of the physical ideas are very similar to those of older approaches. The replica approach has the advantage of describing in an unified setting…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
While the no-cloning theorem forbids the perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take…
Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies…
In this paper we review the predictions of the replica approach on the probability distribution of the overlaps among replicas and on the sample to sample fluctuations of this probability. We stress the role of replica equivalence in…
We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises…
We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential -- a theory with a…
Application of the minimal state-space realization to hysteresis systems is studied. The method allows to construct the space of states and establish the state transition rules using the input equivalence, which can be obtained for…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
Differential replication through copying refers to the process of replicating the decision behavior of a machine learning model using another model that possesses enhanced features and attributes. This process is relevant when external…
We have used a mean-field Monte Carlo method to study the zero-temperature synchronous dynamics of a one-pattern model of associative memory with random asymmetric couplings. In the case of symmetric couplings, we find evidence for a…