title: Towards holographic "brain" memory based on randomization and Walsh-Hadamard transformation.
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.
authors.affiliation: Computer Science Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Mathematics Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
authors.forename: Daniel
authors.initials: D
authors.lastname: Berend
authors.affiliation: Computer Science Department, Ben Gurion University of the Negev, Beer Sheva, Israel. Electronic address: dolev@cs.bgu.ac.il.
authors.forename: Shlomi
authors.initials: S
authors.lastname: Dolev
authors.affiliation: Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, Moscow, Russia.
authors.forename: Sergey
authors.initials: S
authors.lastname: Frenkel
authors.affiliation: Computer Science Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
authors.forename: Ariel
authors.initials: A
authors.lastname: Hanemann
mesh_terms: D006696:Holography / Q000379:methods*; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods; D016247:Information Storage and Retrieval / Q000379:methods*; D016571:Neural Networks, Computer
keywords: Holographic memory; Neural computation; Neural networks; Walsh–Hadamard