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Sparse codes in neuroscience have been suggested to offer certaincomputational advantages over other neural representations of sensory data. Toexplore this viewpoint, a sparse code is used to represent natural images in anoptimal control task solved with neuro-dynamic programming, and itscomputational properties are investigated. The central finding is that whenfeature inputs to a linear network are correlated, an over-complete sparse codeincreases the memory capacity of the network in an efficient manner beyond thatpossible for any complete code with the same-sized input, and also increasesthe speed of learning the network weights. A complete sparse code is found tomaximise the memory capacity of a linear network by decorrelating its featureinputs to transform the design matrix of the least-squares problem to one offull rank. It also conditions the Hessian matrix of the least-squares problem,thereby increasing the rate of convergence to the optimal network weights.Other types of decorrelating codes would also achieve this. However, anover-complete sparse code is found to be approximately decorrelated, extractinga larger number of approximately decorrelated features from the same-sizedinput, allowing it to efficiently increase memory capacity beyond that possiblefor any complete code: a 2.25 times over-complete sparse code is shown to atleast double memory capacity compared with a complete sparse code using thesame input. This is used in sequential learning to store a potentially largenumber of optimal control tasks in the network, while catastrophic forgettingis avoided using a partitioned representation, yielding a cost-to-go functionapproximator that generalizes over the states in each partition. Sparse codeadvantages over dense codes and local codes are also discussed.

A sparse code increases the speed and efficiency of neuro-dynamic programming for optimal control tasks with correlated inputs