Related papers: Differential Tree Automata
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
In abstract visual reasoning, monolithic deep learning models suffer from limited interpretability and generalization, while existing neuro-symbolic approaches fall short in capturing the diversity and systematicity of attributes and…
Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…
Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
Behavior Trees constitute a widespread AI tool which has been successfully spun out in robotics. Their advantages include simplicity, modularity, and reusability of code. However, Behavior Trees remain a high-level decision making engine;…
Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of this technique, depends on applying the ARA-transform and using Taylor's…
To satisfy the high-resolution requirements of direction-of-arrival (DOA) estimation, conventional deep neural network (DNN)-based methods using grid idea need to significantly increase the number of output classifications and also produce…
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…
Semantic representations in the form of directed acyclic graphs (DAGs) have been introduced in recent years, and to model them, we need probabilistic models of DAGs. One model that has attracted some attention is the DAG automaton, but it…
Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian…
Table serialization remains a critical bottleneck for Large Language Models (LLMs) in complex table question answering, hindered by challenges such as structural neglect, representation gaps, and reasoning opacity. Existing serialization…
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module…
Understanding how a learned black box works is of crucial interest for the future of Machine Learning. In this paper, we pioneer the question of the global interpretability of learned black box models that assign numerical values to…
Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance…