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A significant issue in training deep neural networks to solve supervised learning tasks is the need for large numbers of labelled datapoints. The goal of semi-supervised learning is to leverage ubiquitous unlabelled data, together with small quantities of labelled data, to achieve high task performance. Though substantial recent progress has been made in developing semi-supervised algorithms that are effective for comparatively small datasets, many of these techniques do not scale readily to the large (unlaballed) datasets characteristic of real-world applications. In this paper we introduce a novel approach to scalable semi-supervised learning, called Local Label Propagation (LLP). Extending ideas from recent work on unsupervised embedding learning, LLP first embeds datapoints, labelled and otherwise, in a common latent space using a deep neural network. It then propagates pseudolabels from known to unknown datapoints in a manner that depends on the local geometry of the embedding, taking into account both inter-point distance and local data density as a weighting on propagation likelihood. The parameters of the deep embedding are then trained to simultaneously maximize pseudolabel categorization performance as well as a metric of the clustering of datapoints within each psuedo-label group, iteratively alternating stages of network training and label propagation. We illustrate the utility of the LLP method on the ImageNet dataset, achieving results that outperform previous state-of-the-art scalable semi-supervised learning algorithms by large margins, consistently across a wide variety of training regimes. We also show that the feature representation learned with LLP transfers well to scene recognition in the Places 205 dataset.

We derive the general supertrace formula for a system with $N$ chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral superfield breaking supersymmetry spontaneously. As we show, however, the modified formula is not simply related to the scalar-decoupling limit of the supertrace in linearly-realized supersymmetry. We also show that the supertrace formula reduces to that of a linearly realized supersymmetric theory with a decoupled sGoldstino if the Goldstino is the fermion in the nilpotent multiplet., Comment: 14 pages

The characteristics of tree level scattering amplitudes in theories with nonlinear (super)symmetries were recently proposed by Kallosh to be encoded in a simple way directly from the action, based on a background field method. We check this conjecture to lowest non-trivial order in the Volkov-Akulov theory, where the local 6-point diagram cancels and the results up to 6 points indeed are in agreement with S-matrix computations., Comment: 13 pages. v2: refs. added. v3: refs added, intro and discussion improved

We list all potential candidates for U(1) anomalous non-local 1-loop 4-point amplitudes and higher loop UV divergences in $\mathcal{N}\geq 5$ supergravities. The relevant chiral superinvariants are constructed from linearized chiral superfields and define the corresponding superamplitudes. The anomalous amplitudes, of the kind present in $\mathcal{N}=4$, are shown to be absent in $\mathcal{N} \geq 5$. In $\mathcal{N}=6$ supergravity the result is deduced from the double-copy $\mathcal{N}=4_{YM} \times (\mathcal{N}=2)_{YM}$ model, whereas in $\mathcal{N}=5,8$ the result on absence of anomalous amplitudes is derived in supergravities as well as in the $(\mathcal{N}=4)_{YM} \times (\mathcal{N}-4)_{YM}$ double-copy models., Comment: 32 pages, v2:typo corrected, reference added, v3:typos corrected

We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries., Comment: 10 p

We derive supersymmetry/supergravity models with constrained orthogonal nilpotent superfields from the linear models in the formal limit where the masses of the sgoldstino, inflatino and sinflaton tend to infinity. The case where the sinflaton mass remains finite leads to a model with a `relaxed' constraint, where the sinflaton remains an independent field. Our procedure is equivalent to a requirement that some of the components of the curvature of the moduli space tend to infinity., Comment: 18 pages, minor textual changes, small corrections, no conceptual changes. Added appendix C and extended appendix B

We derive a complete pure de Sitter supergravity action with non-linearly realized supersymmetry and its rigid limit, the Volkov-Akulov action, from the corresponding models with linear supersymmetry, by computing the path integral in the limit of infinite sgoldstino mass. In this, we use a non-Gaussian functional integration formula that was recently discovered in a derivation of de Sitter supergravity from the superconformal theory. We also present explicit examples of pure dS supergravity and the case with one matter multiplet. These two simple examples serve as a test and a demo of the universal action formula valid for de Sitter supergravities with general matter coupling., Comment: 15 pages