Related papers: Deep $\Pi^0_1$ Classes
We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by $ R\le S \iff \ex f \, \forall x, y \, [xRy…
Gravitational-wave searches for signals of intermediate-mass black hole binaries are hindered by detector glitches, as the increased masses from stellar-mass systems hinder current generation detectors from observing the inspiral phase of…
Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…
Let $f(x) \in \bbz[x]$ and consider the index divisibility set $D = \{n \in \bbn : n \mid f^n(0)\}$. We present a number of properties of $D$ in the case that $(f^n(0))_{n=1}^\infty$ is a rigid divisibility sequence, generalizing a number…
We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior…
We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…
The Universal Coding of Integers~(UCI) is suitable for discrete memoryless sources with unknown probability distributions and infinitely countable alphabet sizes. A UCI is a class of prefix codes for which the ratio of the average codeword…
Dropout poses a significant challenge to causal inference in longitudinal studies with time-varying treatments. However, existing research does not simultaneously address dropout and time-varying treatments. We examine selective…
The ratio between the probability that two distributions $R$ and $P$ give to points $x$ are known as importance weights or propensity scores and play a fundamental role in many different fields, most notably, statistics and machine…
Numerous machine learning classifiers have been proposed for binary classification of domain names as either benign or malicious, and even for multiclass classification to identify the domain generation algorithm (DGA) that generated a…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Let $n>1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$, are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, which are generated by an element of degree $1$ and an element…
Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\chi$ of $G$ such that $\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
In 2012, inspired by developments in group theory and complexity, Jockusch and Schupp introduced generic computability, capturing the idea that an algorithm might work correctly except for a vanishing fraction of cases. However, we observe…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries…
Deep learning (DL) techniques are on the rise in the software engineering research community. More and more approaches have been developed on top of DL models, also due to the unprecedented amount of software-related data that can be used…
Let 2<n\leq l<m< \omega. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments of first order logic with respect to clique guarded…