Supervised Deep Similarity Matching

We propose a novel biologically-plausible solution to the credit assignment problem, being motivated by observations in the ventral visual pathway and trained deep neural networks. In both, representations of objects in the same category become progressively more similar, while objects belonging to different categories becomes less similar. We use this observation to motivate a layer-specific learning goal in a deep network: each layer aims to learn a representational similarity matrix that interpolates between previous and later layers. We formulate this idea using a supervised deep similarity matching cost function and derive from it deep neural networks with feedforward, lateral and feedback connections, and neurons that exhibit biologically-plausible Hebbian and anti-Hebbian plasticity. Supervised deep similarity matching can be interpreted as an energy-based learning algorithm, but with significant differences from others in how a contrastive function is constructed.