Neural networks learn by adjusting weights. The topology — which neurons connect to which — is fixed. Learning is parametric: the graph stays the same; the edge values change.
Particle packings learn differently. A disordered assembly of particles, driven by local cyclic compression, develops associative memory: apply one pattern of forces, and the packing deforms to recall a previously trained configuration. The memory is not stored in any adjustable parameter. It is stored in the contact network itself — which particles touch which other particles. During training, the cyclic driving causes particles to rearrange, breaking some contacts and forming others. The new contact topology encodes the trained association.
This inverts the neural network paradigm. In the packing, the weights are fixed (contact forces are determined by geometry and material properties), and the topology changes. Learning is topological, not parametric. The packing rewires itself.
The mechanism is local cyclic driving. Unlike global shear (which imposes a uniform deformation), local driving allows different regions of the packing to explore different contact configurations. The trained associations are region-specific: the packing can store multiple associations simultaneously if they are spatially separated. The capacity is limited by the number of independently drivable regions, not by the number of particles.
The structural lesson: the distinction between parametric learning (fixed graph, variable weights) and topological learning (variable graph, fixed weights) is fundamental, not terminological. Parametric learning is continuous — weights move along gradients. Topological learning is discrete — contacts either exist or they don't. The packing cannot half-form a contact. It learns in jumps, and each jump is irreversible under small perturbations. The memory is robust precisely because it is topological: noise that would perturb continuous weights cannot undo a discrete rearrangement.