For holographic data storage, holographic associative memory (HAM) is an information storage and retrieval system based on the principles of

holography Holography is a technique that allows a wavefront to be recorded and later reconstructed. It is best known as a method of generating three-dimensional images, and has a wide range of other uses, including data storage, microscopy, and interfe ...

. Holograms are made by using two beams of light, called a "reference beam" and an "object beam". They produce a pattern on the

film A film, also known as a movie or motion picture, is a work of visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, emotions, or atmosphere through the use of moving images that are generally, sinc ...

that contains them both. Afterwards, by reproducing the reference beam, the hologram recreates a visual image of the original object. In theory, one could use the object beam to do the same thing: reproduce the original reference beam. In HAM, the pieces of information act like the two beams. Each can be used to retrieve the other from the pattern. It can be thought of as an

artificial neural network In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected ...

which mimics the way the brain uses information. The information is presented in abstract form by a complex vector which may be expressed directly by a

waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any dis ...

possessing frequency and magnitude. This waveform is analogous to electrochemical impulses believed to transmit information between biological

neuron A neuron (American English), neurone (British English), or nerve cell, is an membrane potential#Cell excitability, excitable cell (biology), cell that fires electric signals called action potentials across a neural network (biology), neural net ...

cells.

Definition

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. It can be considered as a

complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...

valued

. The holographic associative memory exhibits some remarkable characteristics. Holographs have been shown to be effective for

associative In mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for express ...

memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembe ...

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. It 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 a

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

. 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 In machine learning, backpropagation is a gradient computation method commonly used for training a neural network to compute its parameter updates. It is an efficient application of the chain rule to neural networks. Backpropagation computes th ...

, unlike

connectionist Connectionism is an approach to the study of human mental processes and cognition that utilizes mathematical models known as connectionist networks or artificial neural networks. Connectionism has had many "waves" since its beginnings. The first ...

neural networks. The principal requirement is for stimulus patterns to be made symmetric or

orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...

in the complex domain. HAM typically employs

sigmoid Sigmoid means resembling the lower-case Greek letter sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς) or the Latin letter S. Specific uses include: * Sigmoid function, a mathematical function * Sigmoid colon, part of the l ...

pre-processing where raw inputs are orthogonalized and converted to

Gaussian distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is f(x ...

Principles of operation

# Stimulus-response associations are both learned and expressed in one non-iterative transformation. No

of error terms or iterative processing required. # The method forms a non-

model in which the ability to superimpose a very large set of analog stimulus-response patterns or complex associations exists within the individual

cell. # The generated phase angle communicates response information, and magnitude communicates a measure of recognition (or confidence in the result). # The process permits a capability with neural system to establish dominance profile of stored information, thus exhibiting a memory profile of any range - from short-term to

long-term memory Long-term memory (LTM) is the stage of the Atkinson–Shiffrin memory model in which informative knowledge is held indefinitely. It is defined in contrast to sensory memory, the initial stage, and short-term or working memory, the second stage ...

. # The process follows the non-disturbance rule, that is prior stimulus-response associations are minimally influenced by subsequent learning. # The information is presented in abstract form by a complex vector which may be expressed directly by a

possessing frequency and magnitude. This waveform is analogous to electrochemical impulses believed to transmit information between biological

cells.

Definition

Principles of operation

See also

References

Further reading