Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such embeddings cannot capture local structure arising in complex networks.

We propose a novel Frank-Wolfe (FW) procedure for the optimization of infinite-dimensional functionals of probability measures - a task which arises naturally in a wide range of areas including statistical learning (e.g.

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects.

In this supplementary document, we present the implementation details, model analyses, and additional results of our method. We also provide a short video to explain our framework with illustrations and visual results. We then collect and cluster the features of salient image patches by thresholding the saliency scores. As shown in Figure 3, the primitive MLP and part MLPs adopt a similar architecture as NeRS, i.e., three fully-connected layers with instance normalization and Leaky ReLU activation for middle layers. We show the architecture diagrams for primitive MLP and part MLPs.

Moreover, each input image ensemble can contain animal instances with varying poses, backgrounds, illuminations, and textures. Our key insight is that 3D parts have much simpler shape compared to the overall animal and that they are robust w.r.t.

The increasing impact of black box models, and particularly of unsupervised ones, comes with an increasing interest in tools to understand and interpret them.

Devoid of some assumption, aPU learning is impossible [6].