Storing sparse messages in networks of neural cliques

On Neural Associative Memory Structures: Storage and Retrieval of Sequences in a Chain of Tournaments

Associative memories enjoy many interesting properties in terms of error correction capabilities, robustness to noise, storage capacity, and retrieval performance, and their usage spans over a large set of applications. In this letter, we investigate and extend tournament-based neural networks, originally proposed by Jiang, Gripon, Berrou, and Rabbat (2016), a novel sequence storage associative memory architecture with high memory efficiency and accurate sequence retrieval. We propose a more general method for learning the sequences, which we call feedback tournament-based neural networks. The retrieval process is also extended to both directions: forward and backward-in other words, any large-enough segment of a sequence can produce the whole sequence. Furthermore, two retrieval algorithms, cache-winner and explore-winner, are introduced to increase the retrieval performance. Through simulation results, we shed light on the strengths and weaknesses of each algorithm.

Iterative Retrieval and Block Coding in Autoassociative and Heteroassociative Memory

Neural associative memories (NAM) are perceptron-like single-layer networks with fast synaptic learning typically storing discrete associations between pairs of neural activity patterns. Gripon and Berrou ( 2011 ) investigated NAM employing block coding, a particular sparse coding method, and reported a significant increase in storage capacity. Here we verify and extend their results for both heteroassociative and recurrent autoassociative networks. For this we provide a new analysis of iterative retrieval in finite autoassociative and heteroassociative networks that allows estimating storage capacity for random and block patterns. Furthermore, we have implemented various retrieval algorithms for block coding and compared them in simulations to our theoretical results and previous simulation data. In good agreement of theory and experiments, we find that finite networks employing block coding can store significantly more memory patterns. However, due to the reduced information per block pattern, it is not possible to significantly increase stored information per synapse. Asymptotically, the information retrieval capacity converges to the known limits [Formula: see text] and [Formula: see text] also for block coding. We have also implemented very large recurrent networks up to [Formula: see text] neurons, showing that maximal capacity [Formula: see text] bit per synapse occurs for finite networks having a size [Formula: see text] similar to cortical macrocolumns.

Nested-Clique Network Model of Neural Associative Memory

Clique-based neural associative memories introduced by Gripon and Berrou (GB), have been shown to have good performance, and in our previous work we improved the learning capacity and retrieval rate by local coding and precoding in the presence of partial erasures. We now take a step forward and consider nested-clique graph structures for the network. The GB model stores patterns as small cliques, and we here replace these by nested cliques. Simulation results show that the nested-clique structure enhances the clique-based model.

Storing Sequences in Binary Tournament-Based Neural Networks

An extension to a recently introduced architecture of clique-based neural networks is presented. This extension makes it possible to store sequences with high efficiency. To obtain this property, network connections are provided with orientation and with flexible redundancy carried by both spatial and temporal redundancies, a mechanism of anticipation being introduced in the model. In addition to the sequence storage with high efficiency, this new scheme also offers biological plausibility. In order to achieve accurate sequence retrieval, a double-layered structure combining heteroassociation and autoassociation is also proposed.

Twin Neurons for Efficient Real-World Data Distribution in Networks of Neural Cliques: Applications in Power Management in Electronic Circuits

Associative memories are data structures that allow retrieval of previously stored messages given part of their content. They, thus, behave similarly to the human brain's memory that is capable, for instance, of retrieving the end of a song, given its beginning. Among different families of associative memories, sparse ones are known to provide the best efficiency (ratio of the number of bits stored to that of the bits used). Recently, a new family of sparse associative memories achieving almost optimal efficiency has been proposed. Their structure, relying on binary connections and neurons, induces a direct mapping between input messages and stored patterns. Nevertheless, it is well known that nonuniformity of the stored messages can lead to a dramatic decrease in performance. In this paper, we show the impact of nonuniformity on the performance of this recent model, and we exploit the structure of the model to improve its performance in practical applications, where data are not necessarily uniform. In order to approach the performance of networks with uniformly distributed messages presented in theoretical studies, twin neurons are introduced. To assess the adapted model, twin neurons are used with the real-world data to optimize power consumption of electronic circuits in practical test cases.