Related papers: Monotone and Separable Set Functions: Characteriza…
Semantic composition functions have been playing a pivotal role in neural representation learning of text sequences. In spite of their success, most existing models suffer from the underfitting problem: they use the same shared…
A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving subset that can be written as an at most countably infinite…
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…
Consider a quantum cat map $M$ associated to a matrix $A\in\mathop{\mathrm{Sp}}(2n,\mathbb Z)$, which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of $M$ on any nonempty open set in the position-frequency…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
We establish a general condition on the cost function to obtain uniqueness and Monge solutions in the multi-marginal optimal transport problem, under the assumption that a given collection of the marginals are absolutely continuous with…
Over the last two decades, submodular function maximization has been the workhorse of many discrete optimization problems in machine learning applications. Traditionally, the study of submodular functions was based on binary function…
For the purpose of monitoring the behavior of complex infrastructures (e.g. aircrafts, transport or energy networks), high-rate sensors are deployed to capture multivariate data, generally unlabeled, in quasi continuous-time to detect…
Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper,…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
Submodular functions and variants, through their ability to characterize diversity and coverage, have emerged as a key tool for data selection and summarization. Many recent approaches to learn submodular functions suffer from limited…
While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of…
Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
Increasing attention is being focussed on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed,…
Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a…