If the label distribution across the clients is skewed and the class conditionals have the same support, then the class probabilities {pi(y |x) |i [m]} are non-identical, i.e., for all i 6= uand i,u [m], there exists x, y such that pi(y | x) 6= pu(y | x). We prove the result by contradiction.

Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra convolutional network (L-conv) can automatically discover symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant feedforward architecture. Both CNNs and Graph Convolutional Networks can be expressed as L-conv with appropriate groups. We discover direct connections between L-conv and physics: (1) group invariant loss generalizes field theory (2) Euler-Lagrange equation measures the robustness, and (3) equivariance leads to conservation laws and Noether current.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The Artemis II crew saw first-hand how water behaves a bit differently in zero-G. Breakthroughs, discoveries, and DIY tips sent six days a week. While space exploration is serious and sometimes dangerous scientific work, that does not mean that there is no room for fun. Something as mundane as a little ball of water can be supremely entertaining.

In: ECCV (2020)[34] Yang, Z., Wei, Y., Yang, Y.: Collaborative video object segmentation by multi-scale foreground-background integration.

This paper investigates how to realize better and more efficient embedding learning to tackle the semi-supervised video object segmentation under challenging multi-object scenarios. The state-of-the-art methods learn to decode features with a single positive object and thus have to match and segment each target separately under multi-object scenarios, consuming multiple times computing resources. To solve the problem, we propose an Associating Objects with Transformers (AOT) approach to match and decode multiple objects uniformly. In detail, AOT employs an identification mechanism to associate multiple targets into the same high-dimensional embedding space. Thus, we can simultaneously process multiple objects' matching and segmentation decoding as efficiently as processing a single object.

Most existing point cloud completion methods assume the input partial point cloud is clean, which is not the case in practice, and are generally based on supervised learning. In this paper, we present an unsupervised generative adversarial autoencoding network, named UGAAN, which completes the partial point cloud contaminated by surroundings from real scenes and cutouts the object simultaneously, only using artificial CAD models as assistance. The generator of UGAAN learns to predict the complete point clouds on real data from both the discriminator and the autoencoding process of artificial data. The latent codes from generator are also fed to discriminator which makes encoder only extract object features rather than noises. We also devise a refiner for generating better complete cloud with a segmentation module to separate the object from background. We train our UGAAN with one real scene dataset and evaluate it with the other two. Extensive experiments and visualization demonstrate our superiority, generalization and robustness. Comparisons against the previous method show that our method achieves the state-of-the-art performance on unsupervised point cloud completion and segmentation on real data.

A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions to improve competitive ratios, running times, or other performance measures, less effort has been devoted to the question of how to obtain the predictions themselves, especially in the critical online setting. We introduce a general design approach for algorithms that learn predictors: (1) identify a functional dependence of the performance measure on the prediction quality and (2) apply techniques from online learning to learn predictors, tune robustness-consistency trade-offs, and bound the sample complexity. We demonstrate the effectiveness of our approach by applying it to bipartite matching, ski-rental, page migration, and job scheduling. In several settings we improve upon multiple existing results while utilizing a much simpler analysis, while in the others we provide the first learning-theoretic guarantees.