WebWe show that global injectivity with iid Gaussian matrices, a commonly used tractable model, requires larger expansivity between 3.4 and 10.5. We also characterize the … WebWe show that global injectivity with iid Gaussian matrices, a commonly used tractable model, requires larger expansivity between 3.4 and 10.5. We also characterize the stability of inverting an injective network via worst-case Lipschitz constants of the inverse.

ReLU Deep Neural Networks from the Hierarchical Basis Perspective

WebGlobally Injective ReLU Networks We study injective ReLU neural networks. Injectivity plays an important ... 0 Michael Puthawala, et al. ∙. share ... Webglobally injective architectures are not well understood. In this work, we address approximation-theoretic proper-ties of injective flows. We prove that under mild condi-tions these networks universally approximate probability measures supported on low-dimensional manifolds and de-scribe how their design enables applications to inference indulge restaurant clonakilty

(PDF) Globally Injective ReLU Networks - Academia.edu

WebJun 15, 2024 · Injectivity plays an important role in generative models where it facilitates inference; in inverse problems with generative priors it is a precursor to well posedness. We establish sharp... WebGlobally injective relu networks. arXiv preprint arXiv:2006.08464, 2024. Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. arXiv preprint arXiv:1505.05770, 2015. Murray Rosenblatt. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, pp. 832–837, 1956. WebMay 10, 2024 · We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation schemes of ReLU DNNs for x^2 and xy are composition versions of the hierarchical basis approximation for these two functions. log cabin creek