Limits of coupled learning for multifunctional allosteric responses in physical flow networks

Traditional methods of designing functional materials often involve extensive trial and error or a deep understanding of material properties. Physical coupled learning offers a promising alternative as a local method for training networks to accomplish tasks and perform computations in response to external stimuli. Utilizing the framework of coupled learning, this work expands on how the scaling of networks can affect the training of successful linear allosteric responses. Through simulations of 2D flow networks we show how the error of responses decreases with the size of the network and increases with the number of tasks to be trained. We also analyze how geometry and connectivity of sources (inputs) and targets (outputs) can impair learning, making a task achievable or not. Comparison with global gradient descent reveals similar results, indicating that network properties — rather than the learning method — may dictate limitations of multifunctionality in physical systems.