Related papers: Equivariant Frames and the Impossibility of Contin…
Appropriate weight initialization has been of key importance to successfully train neural networks. Recently, batch normalization has diminished the role of weight initialization by simply normalizing each layer based on batch statistics.…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications,…
There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
The role of quantization within implicit/coordinate neural networks is still not fully understood. We note that using a canonical fixed quantization scheme during training produces poor performance at low-rates due to the network weight…
Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…
Compositional generalization-a key open challenge in modern machine learning-requires models to predict unknown combinations of known concepts. However, assessing compositional generalization remains a fundamental challenge due to the lack…
It is well known that --differing from ordinary gauge systems-- canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…