Project Summary: To successfully guide behaviour, individual neurons have to integrate multiple sources of information across different modalities. For example, previous studies in perceptual decision making have implicated the integration of multiple cues (e.g visual and tactile) on the improvement of discrimination sensitivity, whilst behavioural experiments have shown that neurons in the prefrontal cortex exhibit non-linear mixed selectivity towards visual stimuli and abstract task-relevant rules. A simple canonical cortical circuit - consisting of a layer of feedforward random weights followed by a Hebbian readout - has been previously proposed by theoreticians as a solution to the integration problem, yet a complete characterisation of its storage and generalization (the ability to learn from unseen examples) properties are yet lacking.

In this project, we develop and exact theory for such an architecture, showing that such a circuit can store and extensive number of stimuli and context (i.e the number of stored stimuli-context pairs can grow with the system size), and further provide a novel link between signal reformatting in a deep feedforward circuit and the generalization ability of Hebbian readout weights. Besides being able to guide future behavioural experiments in this space, our study also provides insight into signal reformatting in deep feedforward neural networks (e.g those used in deep learning) at initialization, for simple assumptions on the input signal and non-linearity.