Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings Zu, Mengjie Goodrich, Carl Peter ; https://orcid.org/0000-0002-1307-5074 ddc:570 Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how environmental variation shapes adaptation, what is learned, and when memory of past conditions is retained. Here we show how cyclic environmental change can produce robust memory. Using a model athermal disordered solid trained by inverse design to attain target elastic properties over a prescribed range, we find that the system evolves toward a marginally absorbing manifold (MAM), meaning that training is reversible within the training range but not beyond it, which encodes a memory of that range. We further propose a general mechanism for MAM formation and memory encoding based on discontinuities in the gradient of the trained quantity. These results provide a simple, broadly applicable physical framework for how adaptive systems learn under changing environments and retain memory of past conditions. American Physical Society 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22248 https://research-explorer.ista.ac.at/download/22248/22251 Zu M, Goodrich CP. Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings. <i>PRX Life</i>. 2026;4(2). doi:<a href="https://doi.org/10.1103/48k2-cw3b">10.1103/48k2-cw3b</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1103/48k2-cw3b info:eu-repo/semantics/altIdentifier/e-issn/2835-8279 info:eu-repo/semantics/openAccess