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Topologically Densified Distributions
Christoph Hofer · Florian Graf · Marc Niethammer · Roland Kwitt

Thu Jul 16 12:00 PM -- 12:45 PM & Thu Jul 16 11:00 PM -- 11:45 PM (PDT) @ None #None

We study regularization in the context of small sample-size learning with over-parametrized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal representations before a linear classifier. Specifically, we impose a topological constraint on samples drawn from the probability measure induced in that space. This provably leads to mass concentration effects around the representations of training instances, i.e., a property beneficial for generalization. By leveraging previous work to impose topological constrains in a neural network setting, we provide empirical evidence (across various vision benchmarks) to support our claim for better generalization.

Author Information

Christoph Hofer (University of Salzburg)
Florian Graf (University of Salzburg)
Marc Niethammer (UNC)
Roland Kwitt ("University of Salzburg, Austria")

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