Neural Distributed Autoassociative Memories: A Survey

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension. The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons). Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections and networks with a bipartite graph structure for non-binary data with linear constraints. Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors.Comment: 31 page

Capacity for patterns and sequences in Kanerva's SDM as compared to other associative memory models

The information capacity of Kanerva's Sparse Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used, it is shown that the total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and Hopfield-type models independent of the particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences of spatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns

Multiple-Modality Associative Memory: a framework for Learning

Drawing from memory the face of a friend you have not seen in years is a difficult task. However, if you happen to cross paths, you would easily recognize each other. The biological memory is equipped with an impressive compression algorithm that can store the essential, and then infer the details to match perception. Willshaw's model of Associative memory is a likely candidate for a computational model of this brain function, but its application on real-world data is hindered by the so-called Sparse Coding Problem. Due to a recently proposed sparse encoding prescription [31], which maps visual patterns into binary feature maps, we were able to analyze the behavior of the Willshaw Network (WN) on real-world data and gain key insights into the strengths of the model. To further enhance the capabilities of the WN, we propose the Multiple-Modality architecture. In this new setting, the memory stores several modalities (e.g., visual, or textual) simultaneously. After training, the model can be used to infer missing modalities when just a subset is perceived, thus serving as a flexible framework for learning tasks. We evaluated the model on the MNIST dataset. By storing both the images and labels as modalities, we were able to successfully perform pattern completion, classification, and generation with a single model.Comment: 21 pages, 15 figure

Binary Willshaw learning yields high synaptic capacity for long-term familiarity memory

We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments with modified neural activity patterns in the prefrontal and perirhinal cortex regions. Our motivation for recovering this well-known learning prescription is two-fold: first, the switch-like nature of the induced synaptic bonds, as there is evidence that biological synaptic transitions might occur in a discrete stepwise fashion. Second, the possibility that in the mammalian brain, unused, silent synapses might be pruned in the long-term. Besides the usual pattern and network capacities, we calculate the synaptic capacity of the model, a recently proposed measure where only the functional subset of synapses is taken into account. We find that in terms of network capacity, Willshaw learning is strongly affected by the pattern coding rates, which have to be kept fixed and very low at any time to achieve a non-zero capacity in the large network limit. The information carried per functional synapse, however, diverges and is comparable to that of the pattern association case, even for more realistic moderately low activity levels that are a function of network size.Comment: 20 pages, 4 figure