  An established normative approach for understanding the algorithmic basis of
neural computation is to derive online algorithms from principled computational
objectives and evaluate their compatibility with anatomical and physiological
observations. Similarity matching objectives have served as successful starting
points for deriving online algorithms that map onto neural networks (NNs) with
point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for
many anatomical and physiological observations; however, the objectives have
limited computational power and the derived NNs do not explain
multi-compartmental neuronal structures and non-Hebbian forms of plasticity
that are prevalent throughout the brain. In this article, we unify and
generalize recent extensions of the similarity matching approach to address
more complex objectives, including a large class of unsupervised and
self-supervised learning tasks that can be formulated as symmetric generalized
eigenvalue problems or nonnegative matrix factorization problems.
Interestingly, the online algorithms derived from these objectives naturally
map onto NNs with multi-compartmental neurons and local, non-Hebbian learning
rules. Therefore, this unified extension of the similarity matching approach
provides a normative framework that facilitates understanding
multi-compartmental neuronal structures and non-Hebbian plasticity found
throughout the brain.
