A Local Associative Memory that Knows Where It Holds

An exemplar memory must both retrieve corrupted versions of stored items and reject cues absent from the store. We cast these as two outcomes of one local deci- sion: whether a cue lies in a region where a stored memory has grounds to answer. The escape and retrieval field (ERF) assigns each memory such a region using the spherical support of a truncated Gaussian well, together with a shared outward radial drift. Its static rule accepts cues inside the union of the supports and re- jects cues outside. Its dynamics provide conditional geometric guarantees for any chosen radii: every isolated support is forward invariant, while a cue whose ray from the reference point meets no support escapes geometrically. We construct the regions in two ways. Geometric radii, obtained from the store’s angular spacing, yield a closed-form tolerance to missing coordinates filled with the reference point and capacity bounds for random memory directions. Fitted radii instead adapt a metric and one region per memory using only stored items and their corrupted views. Across two frozen encoders, three stores and six corruption families, the fitted metric identifies the source memory with 87 % accuracy, compared with 64 % for modern Hopfield retrieval in the encoder’s original space. Because both methods select the same identity in the fitted metric, this gain comes from metric adaptation; the fitted radii determine whether to answer. Rejection performance depends on the store’s separation: above an exploratory threshold, ERF has the highest balanced accuracy in 83 % of conditions and on average in every corrup- tion family; below it, ERF trails the strongest comparator on average. With the threshold fixed, a subsequent test predicts the sign of ERF’s mean advantage in all 10 new store–encoder settings, but only a fraction 0.68 of individual conditions. ERF therefore unifies retrieval and rejection through the local regions in which its memories hold.