Related papers: Fast Computations on Ordered Nominal Sets
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and…
Ordinal Classification (OC) is a widely encountered challenge in Natural Language Processing (NLP), with applications in various domains such as sentiment analysis, rating prediction, and more. Previous approaches to tackle OC have…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
We introduce MOS, a software application designed to facilitate the deployment, integration, management, and analysis of mathematical optimization models. MOS approaches mathematical optimization at a higher level of abstraction than…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint $k$ whose approximation ratio is arbitrarily close to $1-1/e$, is…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We give a simple, low resource method to produce order embeddings from ontologies. Such embeddings map words to vectors so that order relations on the words, such as hypernymy/hyponymy, are represented in a direct way. Our method uses…
Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using $\Oh{1}$ bits per node can break this bound on clustered point sets,…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
Neural architecture search (NAS) automates the design process of high-performing architectures, but remains bottlenecked by expensive performance evaluation. Most existing studies that achieve faster evaluation are mostly tied to cell-based…