Related papers: Exercises on derived categories, resolutions, and …

We generalize the concept of ascending and descending runs from permutations to rooted labelled trees and mappings, i.e., functions from the set $\{1, \dots, n\}$ into itself. A combinatorial decomposition of the corresponding functional…

Deep learning embeddings have been successfully used for many natural language processing problems. Embeddings are mostly computed for word forms although a number of recent papers have extended this to other linguistic units like morphemes…

We study the derived categories of small categories over commutative noetherian rings. Our main result is a parametrization of the localizing subcategories in terms of the spectrum of the ring and the localizing subcategories over residue…

For a triangulated category with products we develop a method for constructing a nice set of cogenerators, allowing us to prove a formal criterion in order to satisfy Brown representability for covariant functors. We apply this criterion…

Given an adjunction connecting reasonable categories with weak equivalences, we define a new derived bar and cobar construction associated to the adjunction. This yields homotopical models of the completion and cocompletion associated to…

This is a sequel to our paper "Permute, Graph, Map, Derange", involving decomposable combinatorial labeled structures in the exp-log class of type a=1/2, 1, 3/2, 2. As before, our approach is to establish how well existing theory matches…

Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…

In this paper, we present series representations of the remainders in the expansions for certain trigonometric and hyperbolic functions. By using the obtained results, we establish some inequalities for trigonometric and hyperbolic…

For degenerate stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H>1/2$, the derivative formulas are established by using Malliavin calculus and coupling method, respectively. Furthermore, we find…

Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a…

We identify an issue in multi-task learnable compression, in which a representation learned for one task does not positively contribute to the rate-distortion performance of a different task as much as expected, given the estimated amount…

Most efforts in interpretability in deep learning have focused on (1) extracting explanations of a specific downstream task in relation to the input features and (2) imposing constraints on the model, often at the expense of predictive…

We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves…

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

This is the reproducibility report for the paper "Learning To Count Objects In Natural Images For Visual QuestionAnswering"

These are the notes from my courses on the arithmetic of quadratic forms.

Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…

Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…

This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the material on the derived 2-functors and the proof of the…

The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown that, for any ring, the pure global…