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Hebbian Learning from First Principles
Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for both the supervised and unsupervised protocols.
Unsupervised and Supervised learning by Dense Associative Memory under replica symmetry breaking
Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines.
Parallel Learning by Multitasking Neural Networks
A modern challenge of Artificial Intelligence is learning multiple patterns at once (i. e. parallel learning).
Statistical Mechanics of Learning via Reverberation in Bidirectional Associative Memories
We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this setting, learning is heteroassociative -- involving couples of patterns -- and it is achieved by reverberating the information depicted from the examples through the layers of the network.
Dense Hebbian neural networks: a replica symmetric picture of supervised learning
We consider dense, associative neural-networks trained by a teacher (i. e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations.
Dense Hebbian neural networks: a replica symmetric picture of unsupervised learning
We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations.
Thermodynamics of bidirectional associative memories
Introduced by Kosko in 1988 as a generalization of the Hopfield model to a bipartite structure, the simplest architecture is defined by two layers of neurons, with synaptic connections only between units of different layers: even without internal connections within each layer, information storage and retrieval are still possible through the reverberation of neural activities passing from one layer to another.
Pavlov Learning Machines
As well known, Hebb's learning traces its origin in Pavlov's Classical Conditioning, however, while the former has been extensively modelled in the past decades (e. g., by Hopfield model and countless variations on theme), as for the latter modelling has remained largely unaddressed so far; further, a bridge between these two pillars is totally lacking.
Recurrent neural networks that generalize from examples and optimize by dreaming
The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning.
Supervised Hebbian Learning
In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i. e., definite patterns that are experienced just once to form the synaptic matrix).
The emergence of a concept in shallow neural networks
We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable ``archetypes'' and we show that there exists a critical sample size beyond which the RBM can learn archetypes, namely the machine can successfully play as a generative model or as a classifier, according to the operational routine.
A statistical-inference approach to reconstruct inter-cellular interactions in cell-migration experiments
In the first experiment, cell migrate in a wound-healing model: when applied to this experiment, the inference method predicts the existence of cell-cell interactions, correctly mirroring the strong intercellular contacts which are present in the experiment.
Neural networks with redundant representation: detecting the undetectable
We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4.
Dreaming neural networks: rigorous results
Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it consolidates pure patterns and removes spurious ones: this forces the synaptic matrix to collapse to the projector one (ultimately approaching the Kanter-Sompolinksy model).
Dreaming neural networks: forgetting spurious memories and reinforcing pure ones
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0. 14$, far from the theoretical bound for symmetric networks, i. e. $\alpha =1$.
A relativistic extension of Hopfield neural networks via the mechanical analogy
We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both with deep learning and network pruning.
Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priors
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network.
Phase transitions in Restricted Boltzmann Machines with generic priors
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables.
