Related papers: Ordered {AND, OR}-Decomposition and Binary-Decisio…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
Given a set of finite words, the Overlap Graph (OG) is a complete weighted digraph where each word is a node and where the weight of an arc equals the length of the longest overlap of one word onto the other (Overlap is an asymmetric…
Based on a newly proposed spatial data model - spatial chromatic model (SCM), we developed a spatial coding scheme, called full-coded ordinary arranged chromatic diagram (full-OACD). Full-OACD is a type of spatial tessellation, where space…
Previous deforestation and supercompilation algorithms may introduce accidental termination when applied to call-by-value programs. This hides looping bugs from the programmer, and changes the behavior of a program depending on whether it…
In computational pathology, cancer grading has been mainly studied as a categorical classification problem, which does not utilize the ordering nature of cancer grades such as the higher the grade is, the worse the cancer is. To incorporate…
Algorithmic decision making has proliferated and now impacts our daily lives in both mundane and consequential ways. Machine learning practitioners make use of a myriad of algorithms for predictive models in applications as diverse as movie…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…
There is inherent information captured in the order in which we write words in a list. The orderings of binomials --- lists of two words separated by `and' or `or' --- has been studied for more than a century. These binomials are common…
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…
Outcomes with a natural order commonly occur in prediction tasks and often the available input data are a mixture of complex data like images and tabular predictors. Deep Learning (DL) models are state-of-the-art for image classification…
We present the first optimal randomized algorithm for constructing the order-$k$ Voronoi diagram of $n$ points in two dimensions. The expected running time is $O(n\log n + nk)$, which improves the previous, two-decades-old result of Ramos…
Machine learning methods must be trusted to make appropriate decisions in real-world environments, even when faced with out-of-distribution (OOD) samples. Many current approaches simply aim to detect OOD examples and alert the user when an…
Out-of-distribution (OOD) detection is crucial for ensuring the reliability of deep learning models. Existing methods mostly focus on regular entangled representations to discriminate in-distribution (ID) and OOD data, neglecting the rich…
The ability to reason with multiple hierarchical structures is an attractive and desirable property of sequential inductive biases for natural language processing. Do the state-of-the-art Transformers and LSTM architectures implicitly…
This research concerns Learned Data Structures, a recent area that has emerged at the crossroad of Machine Learning and Classic Data Structures. It is methodologically important and with a high practical impact. We focus on Learned Indexes,…
Out-of-distribution (OOD) generalization has emerged as a significant challenge in graph recommender systems. Traditional graph neural network algorithms often fail because they learn spurious environmental correlations instead of stable…
Benders decomposition (BD) is a widely used solution approach for solving two-stage stochastic programs arising in real-world decision-making under uncertainty. However, it often suffers from slow convergence as the master problem grows…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…