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  • Publication . Article . Preprint . 1995
    Open Access English
    Authors: 
    Peres, Asher;

    Experimental tests of Bell inequalities ought to take into account all detection events. If the latter are postselected, and only some of these events are included in the statistical analysis, a Bell inequality may be violated, even by purely classical correlations. The paradoxical properties of Werner states, recently pointed out by Popescu, can be explained as the result of a postselection of the detection events, or, equivalently, as due to the preparation of a new state by means of a nonlocal process. 7 pages LaTeX

  • Publication . Preprint . Article . 2017
    Open Access English
    Authors: 
    Shalev-Shwartz, Shai; Shamir, Ohad; Shammah, Shaked;

    In recent years, Deep Learning has become the go-to solution for a broad range of applications, often outperforming state-of-the-art. However, it is important, for both theoreticians and practitioners, to gain a deeper understanding of the difficulties and limitations associated with common approaches and algorithms. We describe four types of simple problems, for which the gradient-based algorithms commonly used in deep learning either fail or suffer from significant difficulties. We illustrate the failures through practical experiments, and provide theoretical insights explaining their source, and how they might be remedied.

  • Publication . Article . Preprint . 2017
    Open Access English
    Authors: 
    Vladimir Gol'dshtein; Valerii Pchelintsev; Alexander Ukhlov;
    Country: Russian Federation

    In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of of the first nontrivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem (initially proposed by J.~J.~Sylvester in 1857). 12 pages

  • Publication . Conference object . Preprint . Article . 2020
    Open Access English
    Authors: 
    Jingfei Du; Edouard Grave; Beliz Gunel; Vishrav Chaudhary; Onur Celebi; Michael Auli; Veselin Stoyanov; Alexis Conneau;

    Unsupervised pre-training has led to much recent progress in natural language understanding. In this paper, we study self-training as another way to leverage unlabeled data through semi-supervised learning. To obtain additional data for a specific task, we introduce SentAugment, a data augmentation method which computes task-specific query embeddings from labeled data to retrieve sentences from a bank of billions of unlabeled sentences crawled from the web. Unlike previous semi-supervised methods, our approach does not require in-domain unlabeled data and is therefore more generally applicable. Experiments show that self-training is complementary to strong RoBERTa baselines on a variety of tasks. Our augmentation approach leads to scalable and effective self-training with improvements of up to 2.6% on standard text classification benchmarks. Finally, we also show strong gains on knowledge-distillation and few-shot learning. 8 pages

  • Open Access English
    Authors: 
    M. D. Petrović; Goran Gligorić; Aleksandra Maluckov; Lj. Hadžievski; Boris A. Malomed;
    Country: Serbia
    Project: MESTD | Photonics of micro and na... (45010)

    Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger equations linearly coupled at the single site. Symmetric, antisymmetric and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones. Comment: 9 figures

  • Publication . Article . Preprint . 2012
    Open Access English
    Authors: 
    Ehud Lehrer; Marco Scarsini;

    We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games. 25 pages

  • Open Access English
    Authors: 
    Sodin, Mikhail;

    We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class by the Schwartz and Cauchy integrals. These conditions extend a previous result of Aleksandrov. 10 pages, to appear in Mat. fizika, analiz, geometriya (Kharkov)

  • Publication . Article . Preprint . 2018
    Open Access English
    Authors: 
    Alexander I. Bufetov; Boris Solomyak;
    Publisher: HAL CCSD
    Country: France
    Project: EC | IChaos (647133), NSF | Fractals and Ergodic Theo... (1361424)

    We consider a direct product of a suspension flow over a substitution dynamical system and an arbitrary ergodic flow and give quantitative estimates for the speed of convergence for ergodic integrals of such systems. Our argument relies on new uniform estimates of the spectral measure for suspension flows over substitution dynamical systems. The paper answers a question by Jon Chaika. 14 pages, minor corrections, to appear in Bulletin de la SMF. arXiv admin note: text overlap with arXiv:1305.7373

  • Publication . Article . Preprint . 2017
    Open Access English
    Authors: 
    Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;

    We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare. Comment: 8 pages, 8 figures

  • Publication . Article . Preprint . 2013
    Open Access English
    Authors: 
    Uriya A. First;
    Project: EC | EXPANDERS (226135)

    We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers and bilinear pairings as special cases. We prove a Krull-Schmidt Theorem in this general context, which results in a Krull-Schmidt Theorem for the special cases just mentioned. We also show that cancellation holds under milder assumptions. Using similar ideas we prove a version of Fitting's Lemma for natural transformations between functors. 12 pages

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Include:
14,610 Research products, page 1 of 1,461
  • Publication . Article . Preprint . 1995
    Open Access English
    Authors: 
    Peres, Asher;

    Experimental tests of Bell inequalities ought to take into account all detection events. If the latter are postselected, and only some of these events are included in the statistical analysis, a Bell inequality may be violated, even by purely classical correlations. The paradoxical properties of Werner states, recently pointed out by Popescu, can be explained as the result of a postselection of the detection events, or, equivalently, as due to the preparation of a new state by means of a nonlocal process. 7 pages LaTeX

  • Publication . Preprint . Article . 2017
    Open Access English
    Authors: 
    Shalev-Shwartz, Shai; Shamir, Ohad; Shammah, Shaked;

    In recent years, Deep Learning has become the go-to solution for a broad range of applications, often outperforming state-of-the-art. However, it is important, for both theoreticians and practitioners, to gain a deeper understanding of the difficulties and limitations associated with common approaches and algorithms. We describe four types of simple problems, for which the gradient-based algorithms commonly used in deep learning either fail or suffer from significant difficulties. We illustrate the failures through practical experiments, and provide theoretical insights explaining their source, and how they might be remedied.

  • Publication . Article . Preprint . 2017
    Open Access English
    Authors: 
    Vladimir Gol'dshtein; Valerii Pchelintsev; Alexander Ukhlov;
    Country: Russian Federation

    In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of of the first nontrivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem (initially proposed by J.~J.~Sylvester in 1857). 12 pages

  • Publication . Conference object . Preprint . Article . 2020
    Open Access English
    Authors: 
    Jingfei Du; Edouard Grave; Beliz Gunel; Vishrav Chaudhary; Onur Celebi; Michael Auli; Veselin Stoyanov; Alexis Conneau;

    Unsupervised pre-training has led to much recent progress in natural language understanding. In this paper, we study self-training as another way to leverage unlabeled data through semi-supervised learning. To obtain additional data for a specific task, we introduce SentAugment, a data augmentation method which computes task-specific query embeddings from labeled data to retrieve sentences from a bank of billions of unlabeled sentences crawled from the web. Unlike previous semi-supervised methods, our approach does not require in-domain unlabeled data and is therefore more generally applicable. Experiments show that self-training is complementary to strong RoBERTa baselines on a variety of tasks. Our augmentation approach leads to scalable and effective self-training with improvements of up to 2.6% on standard text classification benchmarks. Finally, we also show strong gains on knowledge-distillation and few-shot learning. 8 pages

  • Open Access English
    Authors: 
    M. D. Petrović; Goran Gligorić; Aleksandra Maluckov; Lj. Hadžievski; Boris A. Malomed;
    Country: Serbia
    Project: MESTD | Photonics of micro and na... (45010)

    Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger equations linearly coupled at the single site. Symmetric, antisymmetric and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones. Comment: 9 figures

  • Publication . Article . Preprint . 2012
    Open Access English
    Authors: 
    Ehud Lehrer; Marco Scarsini;

    We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games. 25 pages

  • Open Access English
    Authors: 
    Sodin, Mikhail;

    We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class by the Schwartz and Cauchy integrals. These conditions extend a previous result of Aleksandrov. 10 pages, to appear in Mat. fizika, analiz, geometriya (Kharkov)

  • Publication . Article . Preprint . 2018
    Open Access English
    Authors: 
    Alexander I. Bufetov; Boris Solomyak;
    Publisher: HAL CCSD
    Country: France
    Project: EC | IChaos (647133), NSF | Fractals and Ergodic Theo... (1361424)

    We consider a direct product of a suspension flow over a substitution dynamical system and an arbitrary ergodic flow and give quantitative estimates for the speed of convergence for ergodic integrals of such systems. Our argument relies on new uniform estimates of the spectral measure for suspension flows over substitution dynamical systems. The paper answers a question by Jon Chaika. 14 pages, minor corrections, to appear in Bulletin de la SMF. arXiv admin note: text overlap with arXiv:1305.7373

  • Publication . Article . Preprint . 2017
    Open Access English
    Authors: 
    Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;

    We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare. Comment: 8 pages, 8 figures

  • Publication . Article . Preprint . 2013
    Open Access English
    Authors: 
    Uriya A. First;
    Project: EC | EXPANDERS (226135)

    We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers and bilinear pairings as special cases. We prove a Krull-Schmidt Theorem in this general context, which results in a Krull-Schmidt Theorem for the special cases just mentioned. We also show that cancellation holds under milder assumptions. Using similar ideas we prove a version of Fitting's Lemma for natural transformations between functors. 12 pages

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