🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001063s)
Graph Filtration Learning (2020)Christoph Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, Roland Kwitt
AbstractWe propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.
Topologically Densified Distributions (2020)Christoph Hofer, Florian Graf, Marc Niethammer, Roland Kwitt
AbstractWe 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.