Memory annihilation of structured maps in bidirectional associative memories

Area of Science:

• Boolean algebra
• Associative memory models
• Information theory

Background:

• Structured sets are defined by Boolean vectors with consistent pair-wise Hamming distances (h).
• Centroids are external vectors equidistant from all vectors within a structured set.
• Structured maps represent one-to-one mappings between these structured sets.

Purpose of the Study:

• To investigate the memory behavior of structured maps encoded into bidirectional associative memories.
• To identify conditions under which memory annihilation occurs.
• To characterize the emergence of stable centroidal associations as alien attractors.

Main Methods:

• Encoding structured maps into bidirectional associative memories using outer-product correlation.
• Analyzing memory annihilation under specific mathematical conditions.
• Examining the special case of maps with h=2 and varying dimensions.

Main Results:

• Memory annihilation of structured map associations is demonstrated under mild conditions.
• Centroidal associations stabilize and emerge as alien attractors when annihilation occurs.
• Self-annihilation is shown to occur for maps with h=2 when dimensions exceed five, and for dimensions greater than eight with as few as three associations.
• Annihilation is observed even with bipolar decoding, known for error correction.

Conclusions:

• The encoding of structured maps in associative memory can lead to the loss of specific associations (annihilation).
• Alien attractors, representing stable centroidal associations, can emerge from this annihilation process.
• The phenomenon is sensitive to map dimensions and the number of associations, with implications for memory capacity and stability.