Related papers: Derived smooth induction with applications

Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…

We analyze actual methods that generate smooth frame fields both in 2D and in 3D. We formalize the 2D problem by representing frames as functions (as it was done in 3D), and show that the derived optimization problem is the one that…

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We…

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…

In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

This article studies optional and predictable projections of integrands and convex-valued stochastic processes. The existence and uniqueness are shown under general conditions that are analogous to those for conditional expectations of…

Since curved dg algebras, and modules over them, have differentials whose square is not zero, these objects have no cohomology, and there is no classical derived category. For different purposes, different notions of "derived" categories…

We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…

In the 2000s, Sadofsky constructed a spectral sequence which converges to the mod $p$ homology groups of a homotopy limit of a sequence of spectra. The input for this spectral sequence is the derived functors of sequential limit in the…

This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises…

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…

In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…

An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.

For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X \rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of…

Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown recently (LICS'13) that…

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…

We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…