Optimal storage of invariant sets of patterns in neural network memories

The authors investigate optimal conditions for the storage of invariant sets of patterns in neural network memories. The sets of patterns that they consider are highly correlated, non-random and invariant with respect to some symmetry transformations. They generalize Gardner's method to study the fractional volume in the space of neural interactions that allow for storage of invariant patterns. They demonstrate that optimal storage conditions correspond to non-trivial relations between the number of stored patterns, their stability, and other, symmetry-specific characteristics of patterns.