A simple normative network approximates local non-Hebbian learning in the cortex

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.