Multi-dimensional driving reveals sequence-dependent memory

When trained by repeated deformation, glassy systems like jammed solids can learn features of their driving. The memory capacity of these systems and the types of features that can be remembered have been the subject of numerous studies — yet the focus has been almost exclusively on deformation along a single axis. Here, we experimentally explore training in a two-dimensional phase space by applying two independent types of shear strain to small, low-friction granular packings. In addition to amplitude memory, we show that memory is specific to the type of strain applied, allowing for the formation of multiple orthogonal memories. We also find that the memory is sensitive to the order in which strains are applied: the system learns the entire path through phase space rather than simply a list of amplitudes. Such sensitivity to perturbation order is not typically considered in condensed matter settings but becomes highly relevant in systems capable of encoding memory.