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A rank decomposition for the topological classification of neural representations
May 1, 2024, 4:42 a.m. | Kosio Beshkov, Gaute T. Einevoll
cs.LG updates on arXiv.org arxiv.org
Abstract: Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic mappings for optimal solutions, such as classification problems. In this work, we leverage the fact that neural networks are equivalent to continuous piecewise-affine maps, whose rank can be used to pinpoint regions in the input space that undergo …
abstract arxiv change classification cs.lg dataset math.at networks neural networks practical q-bio.nc significance solutions tasks the way thought topology transformation type
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