Interpretability of the Bottom-k selection parameter in MeMix

Investigate the interpretability of the Bottom-k patch selection parameter used by MeMix to route state updates in the recurrent memory, including how this heuristic relates to the underlying geometry and its effect on long-horizon stability.

Background

MeMix performs sparse memory updates by selecting Bottom-k memory patches (based on dot-product similarity scores) for writing while preserving others. This routing aims to reduce interference and catastrophic forgetting without retraining.

The authors explicitly acknowledge that the Bottom-k choice is heuristic and that they have not analyzed its interpretability with respect to the state update, indicating a need for a principled understanding of this parameter.