Related papers: Categorization by a three-state attractor neural n…

The categorization ability of fully connected neural network models, with either discrete or continuous Q-state units, is studied in this work in replica symmetric mean-field theory. Hierarchically correlated multi-state patterns in a two…

The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training…

The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…

The information conveyed by a hierarchical attractor neural network is examined. The network learns sets of correlated patterns (the examples) in the lowest level of the hierarchical tree and can categorize them at the upper levels. A way…

We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for…

How can we discover and succinctly summarize the concepts that a neural network has learned? Such a task is of great importance in applications of networks in areas of inference that involve classification, like medical diagnosis based on…

We introduce a framework for reasoning about what meaning is captured by the neurons in a trained neural network. We provide a strategy for discovering meaning by training a second model (referred to as an observer model) to classify the…

The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…

The time evolution of an exactly solvable layered feedforward neural network with three-state neurons and optimizing the mutual information is studied for arbitrary synaptic noise (temperature). Detailed stationary temperature-capacity and…

We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…

Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…

Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design…

The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…

The mutual information, I, of the three-state neural network can be obtained exactly for the mean-field architecture, as a function of three macroscopic parameters: the overlap, the neural activity and the {\em activity-overlap}, i.e. the…

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well…

The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…

In this lecture I will present some models of neural networks that have been developed in the recent years. The aim is to construct neural networks which work as associative memories. Different attractors of the network will be identified…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

Attractor neural network models of cortical decision-making circuits represent them as dynamical systems in the state space of neural firing rates with the attractors of the network encoding possible decisions. While the attractors of these…