Dependence of the inferred dreaming parameter λ on pattern loading α

Determine the functional dependence of the inferred Hebbian unlearning parameter λ on the pattern-loading ratio α in the discrete Hopfield model when configurations are generated by the proposed non-Markovian active spin-flip dynamics and fitted using the deep hybrid Restricted Boltzmann Machine representation of the Hebbian-unlearned Hamiltonian. Clarify how λ varies with α across loading regimes to characterize the relationship λ(α).

Background

The paper introduces an active, non-Markovian spin-flip dynamics for the discrete Hopfield model to mimic persistent noise, and uses a deep hybrid Restricted Boltzmann Machine (RBM) to infer an effective Hebbian-unlearned Hamiltonian characterized by the parameter λ, which quantifies the extent of "dreaming" or unlearning.

Across experiments varying temperature T, activity parameter a, and loading α, the authors report clear trends for λ with a (increasing) and weak sensitivity to T, but they explicitly state that the dependence of λ on α remains unclear, identifying it as a direction for future work.