Daydreaming algorithm for Biased Patterns

TL;DR

The paper extends the Daydreaming algorithm to biased patterns in associative memory models, demonstrating improved basin sizes and distinct energy landscape shaping compared to pseudo-inverse methods.

Contribution

It reformulates Daydreaming for biased patterns using the pseudo-inverse framework, introducing centered dynamics and comparing their effects on retrieval stability.

Findings

Centered Daydreaming has a larger basin of attraction than the pseudo-inverse rule.

Both methods stabilize stored patterns but shape the energy landscape differently.

Results confirm the effectiveness of the reformulated algorithm for biased patterns.

Abstract

The \emph{Daydreaming} algorithm was proposed as a learning rule that simultaneously reinforces stored patterns and suppresses spurious attractors to improve the storage capacity of the Hopfield model. Its effectiveness has been reported for both uncorrelated and correlated data. However, the existing formulation has mainly assumed unbiased patterns, and the formulation for biased patterns has not yet been sufficiently established. Biased patterns are known to be much more problematic for models of associative memories. In this study, we reformulate Daydreaming for biased patterns by starting from the underlying rationale of the pseudo-inverse rule. Specifically, we introduce the retrieval dynamics and an energy function based on the centered representation, and we derive a corresponding update rule for centered Daydreaming. We compare the centered pseudo-inverse rule with centered Daydreaming for biased patterns and examine the retrieval maps and eigenvalue distributions of the coupling matrices. Our results confirm that centered Daydreaming yields a larger basin of attraction than the centered pseudo-inverse rule. Moreover, as in previous studies, although both approaches aim to stabilize the stored patterns as fixed points, our results suggest that they shape the energy landscape through different mechanisms.