Towards holographic "brain" memory based on randomization and Walsh–Hadamard transformation. (May 2016) - Berend, Daniel; Dolev, Shlomi; Frenkel, Sergey; Hanemann, Ariel
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.