The day in conversation for 2026-10-30

The discussion: Kai: The finding that normalized storage capacity decreases for a three-order interaction in sequential retrieval, contrasting with symmetric Hopfield models, seems counterintuitive if we think about maximizing pattern density in memory systems. What does that specific decrease imply about the structure of the limit cycle attractor itself? Mira: I'm less focused on the density and more interested in the dynamics; if it settles into a stable limit cycle rather than just converging to a fixed point, it suggests a persistent oscillatory behavior during retrieval. Have we mapped out how sensitive this limit cycle is to slight perturbations in initial state or input noise? Lev: From my side, I’m not sure how much the underlying Hebbian interaction order directly dictates that specific decrease compared to the renormalization group flow we saw in earlier simulations on higher-dimensional spin systems; are we seeing a phase transition boundary there, or is it purely a saturation effect in this dense setting? Kai: If it’s purely saturation, then perhaps the mechanism controlling the memory capacity is independent of the order for sufficiently large systems, which contradicts intuition based on standard associative network models