Related papers: Bidirectional Nested Weighted Automata
Recurrent Neural Networks (RNN) are a type of statistical model designed to handle sequential data. The model reads a sequence one symbol at a time. Each symbol is processed based on information collected from the previous symbols. With…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA*…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
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…
The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature. Lifting this result to a weighted setting has been widely studied.…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…
The transformer architecture by Vaswani et al. (2017) is now ubiquitous across application domains, from natural language processing to speech processing and image understanding. We propose DenseFormer, a simple modification to the standard…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
Text normalization (TN) systems in production are largely rule-based using weighted finite-state transducers (WFST). However, WFST-based systems struggle with ambiguous input when the normalized form is context-dependent. On the other hand,…
The inverse probability weighting (IPW) is broadly utilized to address missing data problems including causal inference but may suffer from large variances and biases due to propensity score model misspecification. To solve these problems,…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…
In this paper, we define a new kind of weighted tree automata where the weights are only supported by final states. We show that these automata are sequentializable and we study their closures under classical regular and algebraic…