Expressive and trainable computation in physical systems with dense mediated interactions

Models of learning and high dimensional computation usually start from neural networks of linear threshold elements, and even "physical" implementations often mimic these architectures element by element. Here we explore an alternative paradigm in which inevitable collective processes in physical systems themselves serve as the computing substrate. I will focus on networks of many distinct molecular species interacting through a dense network of mediated interactions, some where each species can be seen as mediating effective interactions between others. I will show, using theory and experiments, collective phase behavior in such systems already realizes rich, high dimensional mappings from inputs to outputs without requiring that any component be engineered to behave like a neuron. Further, these mappings can be trained in situ by changing the levels of mediator `hidden' species according to simple local rules that correspond to a molecular Hebbian principle of "get together, grow to like each other." This adaptation positions phase boundaries to solve tasks such as Pavlovian conditioning, classification, and learning probabilistic generative behavior. This framework is largely insensitive to microscopic details, suggesting a general route to expressive and trainable computation in complex physical and molecular systems.