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1

Gradient Regularization Improves Accuracy of Discriminative Models

Varga Dániel, Csiszárik Adrián, Zombori Zsolt

Schedae Informaticae

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2018

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Vol. 27

31--45

EN

Regularizing the gradient norm of the output of a neural network is a powerful technique, rediscovered several times. This paper presents evidence that gradient regularization can consistently improve classification accuracy on vision tasks, using modern deep neural networks, especially when the amount of training data is small. We introduce our regularizers as members of a broader class of Jacobian-based regularizers. We demonstrate empirically on real and synthetic data that the learning process leads to gradients controlled beyond the training points, and results in solutions that generalize well.

2

Circulant matrices: norm, powers, and positivity

Lindner M.

Opuscula Mathematica

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2018

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Vol. 38, no. 6

849--857

EN

In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix C equals the modulus of its row/column sum. We improve on their sufficient condition until we have a necessary one. Our results connect the above problem to positivity of sufficiently high powers of the matrix CTC. We then generalize the result to complex circulant matrices.

3

Stochastic version of the Erdos-Renyi limit theorem

Khorunzhy A.

Probability and Mathematical Statistics

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2002

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Vol. 22, Fasc. 2

221--230

EN

We generalize the Erdös-Rényi limit theorem on the maximum of partial sums of random variables to the case when the number of terms in these sums in randomly distributed. Relations between this limit theorem and the spectral theory of random graphs and random matrices are discussed.

4

Properties of the strict spectral approximation of a complex matrix

Ziętak K.

Opuscula Mathematica

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2002

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Vol. 22

41-46

EN

The aim of this paper is the approximation of complex matrices with respect to unitary invariant norms by means of matrices from linear subspaces. We summarize the properties and characterizations of the strict spectral approximation which is best in some sense among all spectral approximations of the given matrix. We notice the similarity of the properties of spectral approximants and of the properties of the strict Chebyshev solutions of overdetermined systems of linear real equations.

PL

Tematem pracy jest aproksymacja macierzy zespolonych, względem norm unitarnie niezmienniczych, za pomocą macierzy z podprzestrzeni liniowych. Podsumowujemy własności i charakteryzacje ścisłej aproksymacji spektralnej, która w przypadku, gdy najlepsza aproksymacja spektralna nie jest jednoznaczna, jest w pewnym sensie najlepsza spośród wszystkich aproksymacji spektralnych danej macierzy. Zwracamy uwagę na podobieństwo własności spektralnej aproksymacji macierzy do własności ścisłych rozwiązań w sensie Czebyszewa nadokreślonych układów równań liniowych rzeczywistych.