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In this paper, we investigate the geometric structure of activation spaces offully connected layers in neural networks and then show applications of thisstudy. We propose an efficient approximation algorithm to characterize theconvex hull of massive points in high dimensional space. Based on this newalgorithm, four common geometric properties shared by the activation spaces areconcluded, which gives a rather clear description of the activation spaces. Wethen propose an alternative classification method grounding on the geometricstructure description, which works better than neural networks alone.Surprisingly, this data classification method can be an indicator ofoverfitting in neural networks. We believe our work reveals several criticalintrinsic properties of modern neural networks and further gives a new metricfor evaluating them.

On Geometric Structure of Activation Spaces in Neural Networks