Related papers: Algebraic Dynamical Systems in Machine Learning
The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…
We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
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…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
This paper proposes a modal typing system that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
We describe an approach to learn, in a term-rewriting setting, function definitions from input/output equations. By confining ourselves to structurally recursive definitions we obtain a fairly fast learning algorithm that often yields…
In this paper, we develop a set of genetic programming operators and an initialization population process based on concepts of functional programming rewriting for boosting inductive genetic programming. Such genetic operators are used…
Flexible neural sequence models outperform grammar- and automaton-based counterparts on a variety of tasks. However, neural models perform poorly in settings requiring compositional generalization beyond the training data -- particularly to…
Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable…
Along with the proliferation of digital data collected using sensor technologies and a boost of computing power, Deep Learning (DL) based approaches have drawn enormous attention in the past decade due to their impressive performance in…
In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…