Learning Associations in Reconfigurable Particle Packings via Local Cyclic Driving
We investigate associative-memory behavior in a reconfigurable particle packing programmed by purely local cyclic driving. The system is a two-dimensional bidisperse Lennard--Jones particle assembly with periodic boundaries evolved under athermal quasistatic relaxation. During training, a fixed set of input particles is driven cyclically while output particles are selected on-the-fly by a region-driving rule and driven according to a prescribed flow pattern; during retrieval, only the inputs are driven. Associative-memory performance is quantified by the cosine similarity between realized and target output displacement directions. Unlike physical learning systems with fixed architecture, learning here arises through emergent weight updates: localized rearrangements modify the contact network and reshape the effective mechanical couplings between inputs and outputs. Across task difficulty we identify three regimes. In an easy setting, the intrinsic mechanical response already produces coherent motion in the right-hand region under input-only driving, yielding high performance without training. In a hard setting, the desired mapping conflicts with the dominant collective drift, resulting in low baseline performance and only modest training gains; introducing intermittent relaxation cycles reduces train--retrieval mismatch and improves performance. In an intermediate quadrupolar task, repositioning the input--output geometry stabilizes the desired response and converts initially stochastic trajectories into reproducible learned motions. Together these results identify minimal physical ingredients for association-based functionality in athermally driven particulate media and motivate an association learning phase diagram for reconfigurable matter.