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Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles 20 of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-P\'erot interferometers, but almost no quantum interference when transmitted via the propagating states of Mach-Zehnder interferometers. Here, using a novel interferometric 25 approach, we demonstrate that anyons do keep quantum coherence while propagating. Performing two-particle time-domain interference measurements sensitive to the two-particle Hanbury Brown Twiss phase, we find 53% and 60% visibilities for anyons with charges e/5 and e/3. Our results give a positive message for the challenge of performing controlled quantum coherent braiding of anyons., Comment: Main text and supplementary materials, 24 pages, 11 figures

This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model the principle of diminishing returns. A new formulation for learning a deep submodular set function that is consistent with the real-valued attribution maps obtained by existing attribution methods is proposed. The final attribution value of a feature is then defined as the marginal gain in the induced submodular score of the feature in the context of other highly attributed features, thus decreasing the attribution of redundant yet discriminatory features. Experiments on multiple datasets illustrate that the proposed attribution method achieves higher specificity along with good discriminative power. The implementation of our method is publicly available at https://github.com/Piyushi-0/SEA-NN.

We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on regularization based on $\phi$-divergence (e.g., KL divergence). Despite the popularity of MMD, its role as a regularizer in the context of UOT seems less understood. We begin by deriving a specific dual of MMD-regularized UOT (MMD-UOT), which helps us prove several useful properties. One interesting outcome of this duality result is that MMD-UOT induces novel metrics, which not only lift the ground metric like the Wasserstein but are also sample-wise efficient to estimate like the MMD. Further, for real-world applications involving non-discrete measures, we present an estimator for the transport plan that is supported only on the given ($m$) samples. Under certain conditions, we prove that the estimation error with this finitely-supported transport plan is also $\mathcal{O}(1/\sqrt{m})$. As far as we know, such error bounds that are free from the curse of dimensionality are not known for $\phi$-divergence regularized UOT. Finally, we discuss how the proposed estimator can be computed efficiently using accelerated gradient descent. Our experiments show that MMD-UOT consistently outperforms popular baselines, including KL-regularized UOT and MMD, in diverse machine learning applications.

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings. The proposed estimator controls overfitting by employing maximum mean discrepancy based regularization, which is complementary to $\phi$-divergence (entropy) based regularization popularly employed in existing estimators. A key result is that, under very mild conditions, $\epsilon$-optimal recovery of the transport plan as well as the Barycentric-projection based transport map is possible with a sample complexity that is completely dimension-free. Moreover, the implicit smoothing in the kernel mean embeddings enables out-of-sample estimation. An appropriate representer theorem is proved leading to a kernelized convex formulation for the estimator, which can then be potentially used to perform OT even in non-standard domains. Empirical results illustrate the efficacy of the proposed approach.

We demonstrate efficient current induced spin orbit torque switching in perpendicularly magnetized epitaxial MgO(001)//Pd/Co2FeAl/MgO heterostructures grown by magnetron sputtering. The advantage of such heterostructures for spin orbit torque MRAM devices is that they allow a unique combination of critical ingredients: i) low resistivity required for reduced electric energy consumption during writing, ii) high TMR ratio required for efficient reading and iii) strong perpendicular magnetic anisotropy for increased thermal stability., Comment: 14 pages, 6 figures

This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases., Comment: ICML2012