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Neural networks can generate rectifiable measures

Researchers have demonstrated that ReLU neural networks can approximate m-rectifiable measures with arbitrary precision. The study shows that these networks can generate measures that are push-forwards of the one-dimensional Lebesgue measure on [0,1]. The number of networks required for a given approximation error scales with the rectifiability parameter 'm', offering an improvement over previous findings. AI

IMPACT Demonstrates theoretical capabilities of neural networks for generating complex measures, potentially impacting fields requiring precise data representation.

RANK_REASON This is a research paper published on arXiv detailing theoretical results about neural network capabilities. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Erwin Riegler, Alex B\"uhler, Yang Pan, Helmut B\"olcskei ·

    Generating Rectifiable Measures through Neural Networks

    arXiv:2412.05109v2 Announce Type: replace-cross Abstract: We derive universal approximation results for the class of (countably) $m$-rectifiable measures. Specifically, we prove that $m$-rectifiable measures can be approximated as push-forwards of the one-dimensional Lebesgue mea…