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Samuel Vaiter

@vaiter • 3,072 subscribers

@CNRS Researcher

Shorts

Gauss-Lucas theorem states that the roots of the derivative of a polynomial with complex coefficients always lie within the convex hull of the original polynomial's roots.

Gauss-Lucas theorem states that the roots of the derivative of a polynomial with complex coefficients always lie within the convex hull of the original polynomial's roots.

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Singular Value Decomposition is a matrix factorization that expresses a matrix M as UΣVᵀ, where U and V are orthogonal matrices, and Σ is diagonal. It can interpreted as the action of a rotation, a scaling and a rotation/reflection.

Singular Value Decomposition is a matrix factorization that expresses a matrix M as UΣVᵀ, where U and V are orthogonal matrices, and Σ is diagonal. It can interpreted as the action of a rotation, a scaling and a rotation/reflection.

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Morley's theorem (1899) states that the intersections of the adjacent angle trisectors of any triangle defines an equilateral triangle.

Morley's theorem (1899) states that the intersections of the adjacent angle trisectors of any triangle defines an equilateral triangle.

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When optimization problems have multiple minima, algorithms favor specific solutions due to their implicit bias. For ordinary least squares (OLS), gradient descent inherently converges to the minimal norm solution among all possible solutions.

When optimization problems have multiple minima, algorithms favor specific solutions due to their implicit bias. For ordinary least squares (OLS), gradient descent inherently converges to the minimal norm solution among all possible solutions.

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Barycenters in the Wasserstein space were studied by Agueh & Carlier in 2011. They define meaningful geometric mean for probability distribution, and are used in practice for instance for histogram transfer (Rabin et al. ’15)

Barycenters in the Wasserstein space were studied by Agueh & Carlier in 2011. They define meaningful geometric mean for probability distribution, and are used in practice for instance for histogram transfer (Rabin et al. ’15)

11,957 просмотров