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Samuel Vaiter

@vaiter • 3,101 subscribers

@CNRS Researcher in maths & computer science. My (current) focus is machine learning and optimization.

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.

51,937 Aufrufe

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.

31,385 Aufrufe

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.

21,929 Aufrufe

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.

20,433 Aufrufe

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 Aufrufe

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Zeros of random polynomials with i.i.d. coefficients exhibit interesting convergence properties. In particular, normal coefficient leads to weak convergence of the empirical measure to the unit circle.

Zeros of random polynomials with i.i.d. coefficients exhibit interesting convergence properties. In particular, normal coefficient leads to weak convergence of the empirical measure to the unit circle.

13,923 Aufrufe • vor 1 Jahr

Brownian motion is the fundamental martingale that arises in almost all areas of mathematics with a stochastic aspect, used in biology, passing by statistical mechanics and diffusion model.

Brownian motion is the fundamental martingale that arises in almost all areas of mathematics with a stochastic aspect, used in biology, passing by statistical mechanics and diffusion model.

12,300 Aufrufe • vor 1 Jahr

The Lorenz system is a model that describes chaotic behavior in atmospheric convection. Its study reveals how small changes in initial conditions can lead to different outcomes.

The Lorenz system is a model that describes chaotic behavior in atmospheric convection. Its study reveals how small changes in initial conditions can lead to different outcomes.

11,386 Aufrufe • vor 1 Jahr

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