Sparse connectivity is a hallmark of the brain and a desired property of artificial neural networks. It promotes energy efficiency, simplifies training, and enhances the robustness of network function. Thus, a detailed understanding of how to achieve sparsity without jeopardizing network performance is beneficial for neuroscience, deep learning, and neuromorphic computing applications. We used an exactly solvable model of associative learning to evaluate the effects of various sparsity-inducing constraints on connectivity and function. We determine the optimal level of sparsity achieved by the ${\ell }_0$ norm constraint and find that nearly the same efficiency can be obtained by eliminating weak connections. We show that this method of achieving sparsity can be implemented online, making it compatible with neuroscience and machine learning applications.

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• Learning
• Memory
• Machine learning
• Machine learning models
• Neuroscience, neural computation & artificial intelligence
• Replica methods