Optimal learning rules for discrete synapses

There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity

Bifurcation analysis in an associative memory model

We previously reported the chaos induced by the frustration of interaction in a non-monotonic sequential associative memory model, and showed the chaotic behaviors at absolute zero. We have now analyzed bifurcation in a stochastic system, namely a finite-temperature model of the non-monotonic sequential associative memory model. We derived order-parameter equations from the stochastic microscopic equations. Two-parameter bifurcation diagrams obtained from those equations show the coexistence of attractors, which do not appear at absolute zero, and the disappearance of chaos due to the temperature effect.Comment: 19 page

An associative network with spatially organized connectivity

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA

Real time unsupervised learning of visual stimuli in neuromorphic VLSI systems

Neuromorphic chips embody computational principles operating in the nervous system, into microelectronic devices. In this domain it is important to identify computational primitives that theory and experiments suggest as generic and reusable cognitive elements. One such element is provided by attractor dynamics in recurrent networks. Point attractors are equilibrium states of the dynamics (up to fluctuations), determined by the synaptic structure of the network; a `basin' of attraction comprises all initial states leading to a given attractor upon relaxation, hence making attractor dynamics suitable to implement robust associative memory. The initial network state is dictated by the stimulus, and relaxation to the attractor state implements the retrieval of the corresponding memorized prototypical pattern. In a previous work we demonstrated that a neuromorphic recurrent network of spiking neurons and suitably chosen, fixed synapses supports attractor dynamics. Here we focus on learning: activating on-chip synaptic plasticity and using a theory-driven strategy for choosing network parameters, we show that autonomous learning, following repeated presentation of simple visual stimuli, shapes a synaptic connectivity supporting stimulus-selective attractors. Associative memory develops on chip as the result of the coupled stimulus-driven neural activity and ensuing synaptic dynamics, with no artificial separation between learning and retrieval phases.Comment: submitted to Scientific Repor