Many animals learn cognitive maps of their environment - a simultaneous representation of context, experience, and position.

Network pruning is a commonly used measure to alleviate the storage and computational burden of deep neural networks. However, the fundamental limit of network pruning is still lacking. To close the gap, in this work we'll take a first-principles approach, i.e. we'll directly impose the sparsity constraint on the loss function and leverage the framework of statistical dimension in convex geometry, thus enabling us to characterize the sharp phase transition point, which can be regarded as the fundamental limit of the pruning ratio. Through this limit, we're able to identify two key factors that determine the pruning ratio limit, namely, weight magnitude and network sharpness .

The Rashomon set is the set of models that are approximately as good as the best model in the class. That is, it is the set of all good models.

The John ellipsoid problem has far-reaching applications in numerous fields of computer science.

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