相关论文: Associative networks with diluted patterns: dynami…
Using the Hopfield model as a benchmark case, the present work focuses on the investigation of partially annealed associative neural networks, wherein neural dynamics is coupled to slowly evolving patterns within the…
The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…
We consider the dynamics of diluted neural networks with clipped and adapting synapses. Unlike previous studies, the learning rate is kept constant as the connectivity tends to infinity: the synapses evolve on a time scale intermediate…
In the context of attractor neural networks, we study how the equilibrium analog neural activities, reached by the network dynamics during memory retrieval, may improve storage performance by reducing the interferences between the recalled…
We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…
We study the role played by the dilution in the average behavior of a perceptron model with continuous coupling with the replica method. We analyze the stability of the replica symmetric solution as a function of the dilution field for the…
Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily…
We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics…
Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
Associative network models featuring multi-tasking properties have been introduced recently and studied in the low load regime, where the number $P$ of simultaneously retrievable patterns scales with the number $N$ of nodes as $P\sim \log…
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…
For distributions over discrete product spaces $\prod_{i=1}^n \Omega_i'$, Glauber dynamics is a Markov chain that at each step, resamples a random coordinate conditioned on the other coordinates. We show that $k$-Glauber dynamics, which…
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…
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the…