Towards holographic “brain” memory based on randomization and Walsh–Hadamard transformation

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.