The multiscale structure of non-differentiable image manifolds

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Geometric Deep Learning: Going beyond Euclidean data (2016, background): “[24], [25] represented as a time-dependent signal on the vertices of the social graph.”
Manitest: Are classifiers really invariant? (2015, methodology): “14, 38 Following the works of [ ] that considered similar manifolds in different contexts, we call M ( I ) an Image Appearance Manifold (IAM), and we follow here their approach. that Assuming γ : [ 0 , 1 ] (cid:55)→ T is a C 1 curve in T , and that I γ ( t ) is differentiable with respect to t , we…”
Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance (2017, background): “A common phenomenon in practice is for a measure to exhibit different dimensional structure at different scales; this so-called multi-scale behavior arises in a range of applications [32, 50, 56].”
Random Projections of Smooth Manifolds (2009, methodology): “• parameters governing the output of some articulated physical system [23,26, 45 ].”
Geometric Robustness of Deep Networks: Analysis and Improvement (2017, unknown): “This set forms a differentiable manifold called the image appearance manifold (IAM) following the works of [27, 13] and it inherits a Riemannian metric from its ambient space, L 2 .”