When associative memory fails, are the synapses degraded? I measured them directly — they aren't. [R]

Capacity in associative memory is usually treated as a storage problem — patterns superpose in a shared weight matrix until interference makes them unrecoverable. I built a sparse binary assembly network where the weights can be read exactly at any point (4-bit counters whose functional state is a single bit, assemblies as explicit neuron sets, 131k neurons / 1.07B synapses on one consumer GPU), and asked whether that's what actually happens when recall degrades.

It isn't, over the range where the behavioural transition occurs.

Over 24→60 stored patterns (5 seeds/load), sustained recall falls 3.7x while within-assembly functional synaptic density stays flat at 80.7–82.2%. That holds separately for neurons exclusive to one assembly (82.7→81.2%) and for neurons shared across several (69.3→82.1%, rising) while the shared fraction of each assembly goes 4.8%→64.4% — so it isn't a mean concealing a degrading sub-population.

Retrieval initiation is also load-invariant on two independent measures (overlap lost at cue release, 0.694–0.728, SD ≤0.022; recurrent drive at the first free step, 116–120). At intermediate load, loop gain holds at 0.977–1.016 across the entire free run while overlap with the stored assembly still decays 0.720→0.520. Whatever is failing, it isn't amplitude.

The failure mode is identity drift into a structured neighbourhood. Neurons visited during free running but outside the target assembly receive within-assembly recurrent input at 6.9x the population baseline at low load (untrained control: 1.00x), falling to 1.8x at high load — and their assembly-multiplicity inverts over the same range, from below the population mean to nearly twice it. Load doesn't just widen the explored population, it changes its composition from unallocated neurons to neurons owned by competing assemblies.

Because recall depends on how long retrieval is allowed to run, capacity is reported as a pair: sustained ~36 patterns, transient ~200.

What this is not: the framing isn't novel. Tamamori (arXiv 2605.00366) argues the practical limit is loss of dynamical stability rather than geometric separability, and Clark (Phys Rev E 113, 054301) separates transient from persistent recall capacity. Both are theoretical. What I add is reading the substrate while behaviour fails, plus eight alternative mechanisms tested and excluded: hub capture, LTD erosion at the boundary, allocation interference, input-space collisions, pool size, averaging artifact, drive magnitude, and readout-side rescue.

Scope: one architecture, one machine (M1 Pro), one task family (cued recall of random column patterns). Generality untested.

One methodological note I'll volunteer because it changed the paper. At n=1 per load the sustained-ratio curve looked like a sharp bifurcation, and I had a parameter-free model (gain^14.5, exponent derived from the measurement window) that predicted it within 1 SD at four loads. Five seeds killed both. The transition is a smooth monotone decline, and an exponent of 14.5 turns a 1% error in gain into a 14.5% error in the prediction, so the n=1 agreement was near-random by construction. Neither claim survived into the paper.

Two things I'd genuinely like pushback on:

1. Is m²/U the right null for allocation overlap under forced reuse? I use the realised union rather than pool size, because at high load storing many 1536-neuron assemblies requires sharing. Measured overlap comes out at 0.79–1.04x that null at 4.45x mean multiplicity. If there's a standard baseline for this I've missed, I'd like to know.

2. Does the Fusi & Abbott comparison survive the protocol difference? They analyse sequential palimpsest storage where each new memory perturbs the old; I train interleaved to equilibrium over 40 epochs. I argue the shared-member result answers the obvious objection — if interleaving trivially avoided overwriting, the multiply-assigned neurons are exactly where it would show, and they're the group whose density rises. I'd like that attacked.

Links:

Preprint (Zenodo): https://doi.org/10.5281/zenodo.21881612

Code + measurement logs: https://github.com/rakib-nyc/axon

Disclosure: my own work, independent, no affiliation. Free and open-source (CC BY / Apache 2.0), nothing paid.