Journal of Physics A: Mathematical and Theoretical
In this paper we investigate the equilibrium properties of bidirectional associative memories (BA... more In this paper we investigate the equilibrium properties of bidirectional associative memories (BAMs). 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. We characterize the computational capabilities of a stochastic extension of this model in the thermodynamic limit, by applying rigorous techniques from statistical physics. A detailed picture of the phase diagram at the replica symmetric level is provided, both at finite temperature and in the noiseless regimes. Also for the latter, the critical load is further investigated up to one step of replica symmetry breaking. An analytical and numerical inspection of the transition cur...
In this paper we continue our investigation on the high storage regime of the neural network with... more In this paper we continue our investigation on the high storage regime of the neural network with Gaussian patterns. Trough an exact mapping among its partition function and one of a bipartite spin glass (whose parties are made of by Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observable and their fluctuations as well as overlap fluctuations are achieved and discussed. Then, we move further, protracting such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two spin glass quenched free energies even in the replica symmetric framework.
Journal of Physics A: Mathematical and Theoretical
In this paper we investigate the equilibrium properties of bidirectional associative memories (BA... more In this paper we investigate the equilibrium properties of bidirectional associative memories (BAMs). 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. We characterize the computational capabilities of a stochastic extension of this model in the thermodynamic limit, by applying rigorous techniques from statistical physics. A detailed picture of the phase diagram at the replica symmetric level is provided, both at finite temperature and in the noiseless regimes. Also for the latter, the critical load is further investigated up to one step of replica symmetry breaking. An analytical and numerical inspection of the transition cur...
In this paper we continue our investigation on the high storage regime of the neural network with... more In this paper we continue our investigation on the high storage regime of the neural network with Gaussian patterns. Trough an exact mapping among its partition function and one of a bipartite spin glass (whose parties are made of by Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observable and their fluctuations as well as overlap fluctuations are achieved and discussed. Then, we move further, protracting such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two spin glass quenched free energies even in the replica symmetric framework.
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Papers by Adriano Barra