Related papers: Characterizing Van Kampen Squares via Descent Data
In this work, we explore the intersection of sparse coding theory and deep learning to enhance our understanding of feature extraction capabilities in advanced neural network architectures. We begin by introducing a novel class of Deep…
We study the behavior of fracture in disordered systems close to the breakdown point. We simulate numerically both scalar (resistor network) and vectorial (spring network) models with threshold disorder, driven at constant current and…
This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of…
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP…
This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian $J\textrm{-}2$ scheme is preserved by the derived pushforward of a proper morphism. Consequently, we can produce upper…
In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situations where this is simply not the case. Therefore, we do not…
We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various…
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional…
3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…
Human keypoint detection from a single image is very challenging due to occlusion, blur, illumination and scale variance of person instances. In this paper, we find that context information plays an important role in addressing these…
An important problem in machine learning and statistics is to identify features that causally affect the outcome. This is often impossible to do from purely observational data, and a natural relaxation is to identify features that are…
We determine the exact strong converse exponent for entanglement-assisted classical communication of a quantum channel. Our main contribution is the derivation of an upper bound for the strong converse exponent which is characterized by the…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
In this paper (as in [Ken15]), we consider an effective version of the characterization of separable metric spaces as zero-dimensional iff every nonempty closed subset is a retract of the space (actually, it is a relative result for closed…
In our analysis, we show that what Cottenden et al. accomplish is the derivation of the ordinary capstan equation, and a solution to a dynamic membrane with both a zero-Poisson's ratio and a zero-mass density on a rigid right-circular cone.…
Previous cycle-consistency correspondence learning methods usually leverage image patches for training. In this paper, we present a fully convolutional method, which is simpler and more coherent to the inference process. While directly…
Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…