Gating for Memory and Computation in Many-Body Systems

Memory––the retention of information about the past––organizes much of how many-body systems compute, adapt, and self-organize. This thesis studies it in two guises: as the storage and retrieval of information in neural networks, and as the persistence of temporal correlations in driven and active matter. A single object connects them, a timescale, either the effective time-constant of a gated network or the correlation time of a persistent fluctuation, that creates and controls memory.

The first half concerns recurrent neural networks controlled by gating––a multiplicative neuromodulatory control in which the collective neuronal activity sets each unit's effective time constant in a state-dependent self-adaptive way. We show that gating substantially enlarges what such a network can remember and do. In an associative memory, it extends reliable retrieval well beyond the classical capacity limit and turns the stored memories into a continuous family of "generalized" stable states. When the network must produce, via learning, sustained, temporally structured activity rather than settle to rest, gating supplies the dynamical richness needed for flexible temporal computation that the recurrent connectivity alone could not support.

The second half concerns systems driven by persistent fluctuations, where memory enters through the persistence of the driving itself. In generative diffusion models, replacing the usual memoryless noise with active noise, which carries an auxiliary coordinate that relaxes on its own timescale, changes the information geometry of the forward corruption, leaving a temporal memory trace that reshapes how and when structure re-emerges during generation. We then show that in phase-separating biomolecular liquids, whose interactions fluctuate in time, the persistence and the symmetry of those fluctuations govern the collective state: fluctuations can drive a mixture apart or hold it together, and can be used to dissolve and regrow structure on demand.

Across these many-body systems, an effective timescale, set by a gate or carried by a persistent fluctuation, is the knob that controls memory, setting how much of the past stays coupled to the present. The thesis develops this idea across neural computation, generative diffusion, and multi-component active matter, showing how the temporal structure of the dynamics gives rise to rich collective behavior.