Related papers: Differential Tree Automata
Differentiable forest is an ensemble of decision trees with full differentiability. Its simple tree structure is easy to use and explain. With full differentiability, it would be trained in the end-to-end learning framework with…
Data augmentation is an effective way to diversify corpora in machine translation, but previous methods may introduce semantic inconsistency between original and augmented data because of irreversible operations and random subword sampling…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
We consider the computational complexity of tree transducers, depending on their separable sets of input variables.
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
This paper presents differential algebra-based differential dynamic programming (DADDy), a publicly available C++ framework for constrained, fuel-optimal low-thrust trajectory optimisation. The method uses differential algebra (DA) for two…
Turing machine and decision tree have developed independently for a long time. With the recent development of differentiable models, there is an intersection between them. Neural turing machine(NTM) opens door for the memory network. It use…
Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown…
Recurrent Neural Networks (RNNs) have achieved tremendous success in processing sequential data, yet understanding and analyzing their behaviours remains a significant challenge. To this end, many efforts have been made to extract finite…
Using the theoretical basis developed by Yao and Zeilberger, we consider certain graph families whose structure results in a rational generating function for sequences related to spanning tree enumeration. Said families are Powers of Cycles…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*,…
Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a…