Working memory via combinatorial persistent states atop chaos in a random multivariate network

Working memory (WM) lets us retain information over seconds, but its neural basis is poorly understood. While random networks yield chaotic dynamics reflecting observed irregular brain activity, it's unclear how this could support WM. Here we help reconcile chaos and WM via a network of N units with Q-dimensional activations, where each unit's activation is a weighted sum of all units' previous activations normalized by softmax; weights are i.i.d. Gaussian with variance GQ/N. For large (G, N) network activity is chaotic yet for large Q stably clings to only K of the Q "local" dimensions, enabling it to persist in one of Q-choose-K macrostates atop distributed chaotic microstate dynamics. We show analytically how this symmetry breaking emerges and find that K < 11 in the large G, Q, N limit, bounding the number of macrostates at Q-choose-10. Adding a mean weight, however, lets us increase the number of macrostates to Q-choose-Q/2, letting us employ the network as a distributed WM system similar to a Bloom filter, into whose dynamics we can write several "items" and later query them. This work thus reveals a chaotic network that can nonetheless retain any of a combinatorially large number of memories, shedding new light on how distributed dynamics could support WM.