Competitor Interactions and Recall Lifetimes in Spherical Log-Sum-Exp Associative Memory

How long does a retrieved memory persist under noisy updates? We study this question in spherical log-sum-exp associative memory, defining recall loss as the target losing to competitors for a fixed, uninterrupted interval. We test two ways to simplify the dynamics: representing a bank by its target–competitor similarities, and tracking only the overlaps with the target and leading rival. Both omit information relevant to recall. In a controlled three-key example, banks with identical target similarities, initial logits, margin and entropy have mean recall times differing by a factor of approximately 1.74. A numerical solution of the joint dynamics closely reproduces this ratio without fitting a time scale. A separate control shows that the effect persists with distinct keys. In two pairs of 128-key banks, changing the collective drift changes the lifetime ratio even though the exit boundaries remain fixed. Within a bank, replicated short-time tests find different future gaps from states with the same target and leading-rival overlaps and leader. Conditional equilibrium averaging improves the held-out aggregate lifetime ratio over isolated-pair addition, although individual mean times remain systematically biased. These finite-dimensional examples show how interactions among competitors and unresolved state coordinates affect predictions of noisy recall lifetimes.