Learning from gradient discontinuities : Emergence of multiple memories in athermal disordered packing

In recent years, the topic of learning has emerged as a profoundly interdisciplinary field that encompasses diverse disciplines. Adaptation, optimization and learning are processes fundamental to both biological and artificial systems, and they learn to adapt to changing environments through optimization of their intrinsic properties. Despite ongoing efforts, it remains unclear how such systems acquire memory and how environmental variation influences adaptation. A broad theory for learning is essential that provides a unified framework across these disparate fields. In this context a recent study showed that athermal disordered systems, subject to cyclic inverse design, acquire return-point memory, governed by gradient discontinuities in the trained quantities. This proposed novel learning mechanism allows us to investigate how a system encodes multiple memories in response to environmental cues. We aim to answer this in the context of allosteric responses in disordered systems. Subjecting these systems to suitable cyclic training pertaining to optimize the responses at multiple targets for a perturbation at a single distant source, we study how gradient discontinuities lead to the formation of return-point memories in mechanical responses of disordered systems.