Towards holographic "brain" memory based on randomization and Walsh–Hadamard transformation. (May 2016)

• Record Type: Journal Article
• Authors: Berend, Daniel; Dolev, Shlomi; Frenkel, Sergey; Hanemann, Ariel
• Is Part Of: Neural networks. Volume 77(2016)
• Page Start: 87
• Page End: 94
• Publication Date: 2016-05
• Subjects: Holographic memory -- Walsh–Hadamard -- Neural networks -- Neural computation; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2016.02.001
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: The holographic conceptual approach to cognitive processes in the human brain suggests that, in some parts of the brain, each part of the memory (a neuron or a group of neurons) contains some information regarding the entire data. In Dolev and Frenkel (2010, 2012) we demonstrated how to encode data in a holographic manner using the Walsh–Hadamard transform. The encoding is performed on randomized information, that is then represented by a set of Walsh–Hadamard coefficients. These coefficients turn out to have holographic properties. Namely, any portion of the set of coefficients defines a "blurry image" of the original data. In this work, we describe a built-in error correction technique—enlarging the width of the matrix used in the Walsh–Hadamard transform to produce a rectangular Hadamard matrix. By adding this redundancy, the data can bear more errors, resulting in a system that is not affected by missing coefficients up to a certain threshold. Above this threshold, the loss of data is reflected by getting a "blurry image" rather than a concentrated damage. We provide a heuristic analysis of the ability of the technique to correct errors, as well as an example of an image saved using the system. Finally, we give an example of a simple implementation of our approach using neural networks as a proof of concept.