  Memory encoding by cyclic shear is a reliable process to store information in
jammed solids, yet its underlying mechanism and its connection to the amorphous
structure are not fully understood. When a jammed sphere packing is repeatedly
sheared with cycles of the same strain amplitude, it optimizes its mechanical
response to the cyclic driving and stores a memory of it. We study memory by
cyclic shear training as a function of the underlying stability of the
amorphous structure in marginally stable and highly stable packings, the latter
produced by minimizing the potential energy using both positional and radial
degrees of freedom. We find that jammed solids need to be marginally stable in
order to store a memory by cyclic shear. In particular, highly stable packings
store memories only after overcoming brittle yielding and the cyclic shear
training takes place in the shear band, a region which we show to be marginally
stable.
