Holographic associative memory

Holographic Associative Memory(HAM) is part of the family of analog, correlation-based, associative, stimulus-response memories, where information is mapped onto the phase orientation of complex numbers operating. It can be considered as a complex valued artificial neural network. The holographic associative memory exhibits some remarkable characteristics. Holographs have been shown to be effective for associative memory tasks, generalization, and pattern recognition with changeable attention. Ability of dynamic search localization is central to natural memory. For example, in visual perception, humans always tend to focus on some specific objects in a pattern. Humans can effortlessly change the focus from object to object without requiring relearning. HAM provides a computational model which can mimic this ability by creating representation for focus. At the heart of this new memory lies a novel bi-modal representation of pattern and a hologram-like complex spherical weight state-space. Besides the usual advantages of associative computing, this technique also has excellent potential for fast optical realization because the underlying hyper-spherical computations can be naturally implemented on optical computations.

Holographic Associative Memory (HAM) is based on principle of information storage in the form of stimulus-response patterns where information is presented by phase angle orientations of complex numbers on Riemann surface. A very large number of stimulus-response patterns may be superimposed or "enfolded" on a single neural element. Stimulus-response associations may be both encoded and decoded in one non-iterative transformation. The mathematical basis requires no optimization of parameters or error backpropagation, unlike connectionist neural networks. The principal requirement is for stimulus patterns to be made symmetric or orthogonal in the complex domain. HAM typically employs sigmoid pre-processing where raw inputs are orthogonalized and converted to Gaussian distributions.

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