Existing models of learning in the brain explain how given circuits learn, but not how biology could assemble those circuits in the first place. To address this gap, we formulate Self-Assembling Learning (SAL)---the study of how learning systems can emerge from lower-level interactions---and introduce one example mechanism, the Self-Assembling Motif (SAM). SAM is self-assembling at two scales: the motif emerges from initially random connectivity under heterosynaptic plasticity rules, and networks of SAMs, composed hierarchically, self-organize into dynamics that provably approximate a generalized form of stochastic gradient descent---matching backpropagation-level performance. This suggests that biological learning need not be prescribed but can emerge from local rules---and to a far greater extent than previously thought.

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