Related papers: Algebraic Dynamical Systems in Machine Learning

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…

Traditional model-based diagnosis relies on constructing explicit system models, a process that can be laborious and expertise-demanding. In this paper, we propose a novel framework that combines concepts of model-based diagnosis with deep…

Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…

Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…

While one of the first steps in many NLP systems is selecting what pre-trained word embeddings to use, we argue that such a step is better left for neural networks to figure out by themselves. To that end, we introduce dynamic…

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…

We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these…

Answer set programming is a leading declarative constraint programming paradigm with wide use for complex knowledge-intensive applications. Modern answer set programming languages support many equivalent ways to model constraints and…

Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…

In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These…

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…

A document spanner models a program for Information Extraction (IE) as a function that takes as input a text document (string over a finite alphabet) and produces a relation of spans (intervals in the document) over a predefined schema. A…

Widespread deployment of societal-scale machine learning systems necessitates a thorough understanding of the resulting long-term effects these systems have on their environment, including loss of trustworthiness, bias amplification, and…

Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive…