QCD corrections to tri-boson production

We present a computation of the next-to-leading order QCD corrections to the production of three Z bosons at the LHC. We calculate these corrections using a completely numerical method that combines sector decomposition to extract infrared singularities with contour deformation of the Feynman parameter integrals to avoid internal loop thresholds. The NLO QCD corrections to pp -> ZZZ are approximately 50%, and are badly underestimated by the leading order scale dependence. However, the kinematic dependence of the corrections is minimal in phase space regions accessible at leading order.Comment: 15 pages, 3 figures; typos fixed, references and event listing adde

End-to-End Cross-Modality Retrieval with CCA Projections and Pairwise Ranking Loss

Cross-modality retrieval encompasses retrieval tasks where the fetched items are of a different type than the search query, e.g., retrieving pictures relevant to a given text query. The state-of-the-art approach to cross-modality retrieval relies on learning a joint embedding space of the two modalities, where items from either modality are retrieved using nearest-neighbor search. In this work, we introduce a neural network layer based on Canonical Correlation Analysis (CCA) that learns better embedding spaces by analytically computing projections that maximize correlation. In contrast to previous approaches, the CCA Layer (CCAL) allows us to combine existing objectives for embedding space learning, such as pairwise ranking losses, with the optimal projections of CCA. We show the effectiveness of our approach for cross-modality retrieval on three different scenarios (text-to-image, audio-sheet-music and zero-shot retrieval), surpassing both Deep CCA and a multi-view network using freely learned projections optimized by a pairwise ranking loss, especially when little training data is available (the code for all three methods is released at: https://github.com/CPJKU/cca_layer).Comment: Preliminary version of a paper published in the International Journal of Multimedia Information Retrieva

Efficient Construction of Local Parametric Reduced Order Models Using Machine Learning Techniques

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve the design of parametric reduced order models. Specifically, machine learning is used to develop feasible regions in the parameter space where the admissible target accuracy is achieved with a predefined reduced order basis, to construct parametric maps, to chose the best two already existing bases for a new parameter configuration from accuracy point of view and to pre-select the optimal dimension of the reduced basis such as to meet the desired accuracy. By combining available information using bases concatenation and interpolation as well as high-fidelity solutions interpolation we are able to build accurate reduced order models associated with new parameter settings. Promising numerical results with a viscous Burgers model illustrate the potential of machine learning approaches to help design better reduced order models.Comment: 28 pages, 15 figures, 6 table

Efficient Batch Query Answering Under Differential Privacy

Differential privacy is a rigorous privacy condition achieved by randomizing query answers. This paper develops efficient algorithms for answering multiple queries under differential privacy with low error. We pursue this goal by advancing a recent approach called the matrix mechanism, which generalizes standard differentially private mechanisms. This new mechanism works by first answering a different set of queries (a strategy) and then inferring the answers to the desired workload of queries. Although a few strategies are known to work well on specific workloads, finding the strategy which minimizes error on an arbitrary workload is intractable. We prove a new lower bound on the optimal error of this mechanism, and we propose an efficient algorithm that approaches this bound for a wide range of workloads.Comment: 6 figues, 22 page

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed---either explicitly or implicitly---to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, speed, and robustness. These claims are supported by extensive numerical experiments and a detailed error analysis

Tensor Ensemble Learning for Multidimensional Data

In big data applications, classical ensemble learning is typically infeasible on the raw input data and dimensionality reduction techniques are necessary. To this end, novel framework that generalises classic flat-view ensemble learning to multidimensional tensor-valued data is introduced. This is achieved by virtue of tensor decompositions, whereby the proposed method, referred to as tensor ensemble learning (TEL), decomposes every input data sample into multiple factors which allows for a flexibility in the choice of multiple learning algorithms in order to improve test performance. The TEL framework is shown to naturally compress multidimensional data in order to take advantage of the inherent multi-way data structure and exploit the benefit of ensemble learning. The proposed framework is verified through the application of Higher Order Singular Value Decomposition (HOSVD) to the ETH-80 dataset and is shown to outperform the classical ensemble learning approach of bootstrap aggregating

ATOMO: Communication-efficient Learning via Atomic Sparsification

Distributed model training suffers from communication overheads due to frequent gradient updates transmitted between compute nodes. To mitigate these overheads, several studies propose the use of sparsified stochastic gradients. We argue that these are facets of a general sparsification method that can operate on any possible atomic decomposition. Notable examples include element-wise, singular value, and Fourier decompositions. We present ATOMO, a general framework for atomic sparsification of stochastic gradients. Given a gradient, an atomic decomposition, and a sparsity budget, ATOMO gives a random unbiased sparsification of the atoms minimizing variance. We show that recent methods such as QSGD and TernGrad are special cases of ATOMO and that sparsifiying the singular value decomposition of neural networks gradients, rather than their coordinates, can lead to significantly faster distributed training

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed—either explicitly or implicitly—to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, robustness, and/or speed. These claims are supported by extensive numerical experiments and a detailed error analysis. The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition of an m × n matrix. (i) For a dense input matrix, randomized algorithms require O(mn log(k)) floating-point operations (flops) in contrast to O(mnk) for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to O(k) passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data

Symmetry breaking by bi-fundamentals

We derive all possible symmetry breaking patterns for all possible Higgs fields that can occur in intersecting brane models: bi-fundamentals and rank-2 tensors. This is a field-theoretic problem that was already partially solved in 1973 by Ling-Fong Li. In that paper the solution was given for rank-2 tensors of orthogonal and unitary group, and U(N x U(M) and O(N) x O(M) bi-fundamentals. We extend this first of al to symplectic groups. When formulated correctly, this turns out to be straightforward generalization of the previous results from real and complex numbers to quaternions. The extension to mixed bi-fundamentals is more challenging and interesting. The scalar potential has up to six real parameters. Its minima or saddle points are described by block-diagonal matrices built out of K blocks of size p x q. Here p=q=1 for the solutions of Ling-Fong Li, and the number of possibilities for p x q is equal to the number of real parameters in the potential, minus 1. The maximum block size is p x q=2 x 4. Different blocks cannot be combined, and the true minimum occurs for one choice of basic block, and for either K=1 or K maximal, depending on the parameter values.Comment: 43 pages, 2 figures. Misprints corrected; two summary sections added for quick access to main result

Fractional ridge regression: a fast, interpretable reparameterization of ridge regression

Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of regularization. Cross-validation is typically used to select the best $\alpha$ from a set of candidates. However, efficient and appropriate selection of $\alpha$ can be challenging, particularly where large amounts of data are analyzed. Because the selected $\alpha$ depends on the scale of the data and predictors, it is not straightforwardly interpretable. Here, we propose to reparameterize RR in terms of the ratio $\gamma$ between the L2-norms of the regularized and unregularized coefficients. This approach, called fractional RR (FRR), has several benefits: the solutions obtained for different $\gamma$ are guaranteed to vary, guarding against wasted calculations, and automatically span the relevant range of regularization, avoiding the need for arduous manual exploration. We provide an algorithm to solve FRR, as well as open-source software implementations in Python and MATLAB (https://github.com/nrdg/fracridge). We show that the proposed method is fast and scalable for large-scale data problems, and delivers results that are straightforward to interpret and compare across models and datasets