2021/10/13 by Nico Courts, Courts, Nico, Henry Kvinge +1 · 2 citations
Computer Science · #Neural Networks and Applications #Computational Physics and Python Applications #Data Visualization and Analytics
paper · pdf · doi:10.48550/arxiv.2110.06983
Many-to-one maps are ubiquitous in machine learning, from the image\nrecognition model that assigns a multitude of distinct images to the concept of\n"cat" to the time series forecasting model which assigns a range of distinct\ntime-series to a single scalar regression value. While the primary use of such\nmodels is naturally to associate correct output to each input, in many problems\nit is also useful to be able to explore, understand, and sample from a model's\nfibers, which are the set of input values x such that f(x) = y, for fixed\ny in the output space. In this paper we show that popular generative\narchitectures are ill-suited to such tasks. Motivated by this we introduce a\nnovel generative architecture, a Bundle Network, based on the concept of a\nfiber bundle from (differential) topology. BundleNets exploit the idea of a\nlocal trivialization wherein a space can be locally decomposed into a product\nspace that cleanly encodes the many-to-one nature of the map. By enforcing this\ndecomposition in BundleNets and by utilizing state-of-the-art invertible\ncomponents, investigating a network's fibers becomes natural.\n