Sparse neural networks with large learning diversity

Coded recurrent neural networks with three levels of sparsity are introduced. The first level is related to the size of messages, much smaller than the number of available neurons. The second one is provided by a particular coding rule, acting as a local constraint in the neural activity. The third one is a characteristic of the low final connection density of the network after the learning phase. Though the proposed network is very simple since it is based on binary neurons and binary connections, it is able to learn a large number of messages and recall them, even in presence of strong erasures. The performance of the network is assessed as a classifier and as an associative memory

Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks

We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using an STDP-based learning process, we store in the connectivity several phase-coded spike patterns, and we find that, depending on the excitability of the network, different working regimes are possible, with transient or persistent replay activity induced by a brief signal. We introduce an order parameter to evaluate the similarity between stored and recalled phase-coded pattern, and measure the storage capacity. Modulation of spiking thresholds during replay changes the frequency of the collective oscillation or the number of spikes per cycle, keeping preserved the phases relationship. This allows a coding scheme in which phase, rate and frequency are dissociable. Robustness with respect to noise and heterogeneity of neurons parameters is studied, showing that, since dynamics is a retrieval process, neurons preserve stablecprecise phase relationship among units, keeping a unique frequency of oscillation, even in noisy conditions and with heterogeneity of internal parameters of the units

Neural Pre-coding Increases the Pattern Retrieval Capacity of Hopfield and Bidirectional Associative Memories

We consider the problem of neural association, which deals with the retrieval of a previously memorized pattern from its noisy version. The performance of various neural networks developed for this task may be judged in terms of their pattern retrieval capacities (the number of patterns that can be stored), and their error-correction (noise tolerance) capabilities. While significant progress has been made, most prior works in this area show poor performance with regard to pattern retrieval capacity and/or error correction. In this paper, we propose two new methods to significantly increase the pattern retrieval capacity of the Hopfield and Bidirectional Associative Memories (BAM). The main idea is to store patterns drawn from a family of low correlation sequences, similar to those used in Code Division Multiple Access (CDMA) communications, instead of storing purely random patterns as in prior works. These low correlation patterns can be obtained from random sequences by pre-coding the original sequences via simple operations that both real and artificial neurons are capable of accomplishing

Nonbinary Associative Memory With Exponential Pattern Retrieval Capacity and Iterative Learning

We consider the problem of neural association for a network of nonbinary 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, the same network should be able to recall the previously memorized patterns from their noisy versions. Prior work in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network. In our formulation of the problem, we concentrate on exploiting redundancy and internal structure of the patterns to improve the pattern retrieval capacity. Our first result shows that if the given patterns have a suitable linear-algebraic structure, i.e., comprise a subspace of the set of all possible patterns, then the pattern retrieval capacity is exponential in terms of the number of neurons. The second result extends the previous finding to cases where the patterns have weak minor components, i.e., the smallest eigenvalues of the correlation matrix tend toward zero. We will use these minor components (or the basis vectors of the pattern null space) to increase both the pattern retrieval capacity and error correction capabilities. An iterative algorithm is proposed for the learning phase, and two simple algorithms are presented for the recall phase. Using analytical methods and simulations, we show that the proposed methods can tolerate a fair amount of errors in the input while being able to memorize an exponentially large number of patterns

Exponential Pattern Retrieval Capacity with Non-Binary Associative Memory

We consider the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network