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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 level structure of ancestors and descendents (examples) are embedded in the network and the categorization task consists in recognizing the ancestors when the network is trained exclusively with their descendents. Explicit results for the dependence of the equilibrium properties of a Q=3-state model and a $Q=infty$-state model are obtained in the form of phase diagrams and categorization curves. A strong improvement of the categorization ability is found when the network is trained with examples of low activity. The categorization ability is found to be robust to finite threshold and synaptic noise. The Almeida-Thouless lines that limit the validity of the replica-symmetric results, are also obtained.
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied at zero temperature for arbitrary using a probabilistic approach. A recursive scheme is found determining the complete time evolution of the order para
It is known that a trained Restricted Boltzmann Machine (RBM) on the binary Monte Carlo Ising spin configurations, generates a series of iterative reconstructed spin configurations which spontaneously flow and stabilize to the critical point of physi
The fully connected (FC) layer, one of the most fundamental modules in artificial neural networks (ANN), is often considered difficult and inefficient to train due to issues including the risk of overfitting caused by its large amount of parameters.
The effects of a variable amount of random dilution of the synaptic couplings in Q-Ising multi-state neural networks with Hebbian learning are examined. A fraction of the couplings is explicitly allowed to be anti-Hebbian. Random dilution represents
Starting from the mutual information we present a method in order to find a hamiltonian for a fully connected neural network model with an arbitrary, finite number of neuron states, Q. For small initial correlations between the neurons and the patter