Related papers: Wheeler Bisimulations
Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the n-th level of the hierarchy is over an…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
An automatic word classification system has been designed which processes word unigram and bigram frequency statistics extracted from a corpus of natural language utterances. The system implements a binary top-down form of word clustering…
We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…
Heuristic search has traditionally relied on hand-crafted or programmatically derived heuristics. Neural networks (NNs) are newer powerful tools which can be used to learn complex mappings from states to cost-to-go heuristics. However,…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
The problem of inclusion of the language accepted by timed automaton $A$ (e.g., the implementation) in the language accepted by $B$ (e.g., the specification) is, in general, undecidable in the class of non-deterministic timed automata. In…
Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and…
We introduce a data-driven approach to computing finite bisimulations for state transition systems with very large, possibly infinite state space. Our novel technique computes stutter-insensitive bisimulations of deterministic systems,…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks…
This paper studies the algorithms for the minimisation of weighted automata. It starts with the definition of morphisms-which generalises and unifies the notion of bisimulation to the whole class of weighted automata-and the unicity of a…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
Neural Machine Translation (NMT) models generally perform translation using a fixed-size lexical vocabulary, which is an important bottleneck on their generalization capability and overall translation quality. The standard approach to…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Understanding recurrent networks through rule extraction has a long history. This has taken on new interests due to the need for interpreting or verifying neural networks. One basic form for representing stateful rules is deterministic…
Neural language modeling (LM) has led to significant improvements in several applications, including Automatic Speech Recognition. However, they typically require large amounts of training data, which is not available for many domains and…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship…