Training Stress Patterns in 3D Reconfigurable Cellular Networks

Physical learning in reconfigurable matter requires understanding how function emerges when both system parameters and network architecture evolve. In nonliving disordered particle packings, recent work has shown that local cyclic driving can train associations between inputs and outputs through contact rearrangements that rewire the network. These associations emerge only within an intermediate window of plasticity where rearrangements are frequent enough to discover new response pathways yet sufficiently reproducible for training and testing to revisit the same configurations. Too little motion leads to a frozen, unlearnable solid, while too much produces yielding without memory. Living matter introduces an additional mode of adaptation: constituents can intrinsically modify properties while simultaneously reconfiguring. Here we investigate training in three-dimensional cellular networks. Using a contrastive learning method, we determine whether prescribed multicellular stress patterns can be encoded and recalled. We identify an upper bound on the number of trainable cells relative to the number of hidden cells in the network. We also find that, as in particle packings, successful training is governed by the compatibility between the desired pattern and the system's intrinsic mechanics. Moreover, parameter adaptation in cellular networks enlarges the learnable regime relative to particle packings. This indicates that cellular networks can exploit coupled parameter–topology adaptation to achieve robust, trainable mechanics and provide a framework for designing protocols to write, erase, and retrain collective stress memories with far-reaching implications for disease and development.