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A normative approach called Similarity Matching was recently introduced forderiving and understanding the algorithmic basis of neural computation focusedon unsupervised problems. It involves deriving algorithms from computationalobjectives and evaluating their compatibility with anatomical and physiologicalobservations. In particular, it introduces neural architectures by consideringdual alternatives instead of primal formulations of popular models such as PCA.However, its connection to the Representer theorem remains unexplored. In thiswork, we propose to use teachings from this approach to explore supervisedlearning algorithms and clarify the notion of Hebbian learning. We examineregularized supervised learning and elucidate the emergence of neuralarchitecture and additive versus multiplicative update rules. In this work, wefocus not on developing new algorithms but on showing that the Representertheorem offers the perfect lens to study biologically plausible learningalgorithms. We argue that many past and current advancements in the field relyon some form of dual formulation to introduce biological plausibility. Inshort, as long as a dual formulation exists, it is possible to derivebiologically plausible algorithms. Our work sheds light on the pivotal role ofthe Representer theorem in advancing our comprehension of neural computation.

Duality Principle and Biologically Plausible Learning: Connecting the Representer Theorem and Hebbian Learning