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An established normative approach for understanding the algorithmic basis ofneural computation is to derive online algorithms from principled computationalobjectives and evaluate their compatibility with anatomical and physiologicalobservations. Similarity matching objectives have served as successful startingpoints for deriving online algorithms that map onto neural networks (NNs) withpoint neurons and Hebbian/anti-Hebbian plasticity. These NN models account formany anatomical and physiological observations; however, the objectives havelimited computational power and the derived NNs do not explainmulti-compartmental neuronal structures and non-Hebbian forms of plasticitythat are prevalent throughout the brain. In this article, we unify andgeneralize recent extensions of the similarity matching approach to addressmore complex objectives, including a large class of unsupervised andself-supervised learning tasks that can be formulated as symmetric generalizedeigenvalue problems or nonnegative matrix factorization problems.Interestingly, the online algorithms derived from these objectives naturallymap onto NNs with multi-compartmental neurons and local, non-Hebbian learningrules. Therefore, this unified extension of the similarity matching approachprovides a normative framework that facilitates understandingmulti-compartmental neuronal structures and non-Hebbian plasticity foundthroughout the brain.

Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity