Related papers: Adelic descent for continuous localizing invariant…
We find new bi-Lipschitz invariants for functions of two complex variables.
We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
We study a continuous-time approximation of the stochastic gradient descent process for minimizing the population expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending…
We prove a local version of the Mazur-Ulam theorem.
We present a new proof of descent for stably dominated types in any theory, dropping the hypothesis of the existence of global invariant extensions. Additionally, we give a much simpler proof of descent for stably dominated types in…
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…
We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.
For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough.…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.
We consider generalized inversions and descents in finite Weyl groups. We establish Coxeter-theoretic properties of indicator random variables of positive roots such as the covariance of two such indicator random variables. We then compute…
We derive a symplectic analogue of A-directed immersion theorem.
We consider coordinate descent methods on convex quadratic problems, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
We present some extensions to the limited memory steepest descent method based on spectral properties and cyclic iterations. Our aim is to show that it is possible to combine sweep and delayed strategies for improving the performance of…
We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and…
In these notes we give an Alperin's Fusion Theorem for localities.