Related papers: General Interpolation and Strong Amalgamation for …
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
The traditional approach to the quantitative study of segregation is to employ indices that are selected by ``desirable properties''. Here, we detail how information theory underpins entropy-based indices and demonstrate how desirable…
As machine learning systems are increasingly used to make real world legal and financial decisions, it is of paramount importance that we develop algorithms to verify that these systems do not discriminate against minorities. We design a…
The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…
In this paper, we propose two new interpolation algorithms for sparse multivariate polynomials represented by a straight-line program(SLP). Both of our algorithms work over any finite fields $F_q$ with large characteristic. The first one is…
Deployment of machine learning algorithms into real-world practice is still a difficult task. One of the challenges lies in the unpredictable variability of input data, which may differ significantly among individual users, institutions,…
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible…
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation.…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
Absence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok \cite{barvinok2017combinatorics} for designing deterministic approximation algorithms for various graph counting and computing partition…
Mixup - a neural network regularization technique based on linear interpolation of labeled sample pairs - has stood out by its capacity to improve model's robustness and generalizability through a surprisingly simple formalism. However, its…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched in the corresponding category of coalgebras of the same…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to…
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…
Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that…
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represented by star-algebras and star-ideals. This paper is written…
Hierarchical vector field interpolation introduces a structured probabilistic framework for lexical representation, ensuring that word embeddings transition smoothly across a continuous manifold rather than being constrained to discrete…