Related papers: Kleisli semantics and hypergraph composition for G…
Kleisli simulation is a categorical notion introduced by Hasuo to verify finite trace inclusion. They allow us to give definitions of forward and backward simulation for various types of systems. A generic categorical theory behind Kleisli…
Despite enormous progress in Natural Language Processing (NLP), our field is still lacking a common deep semantic representation scheme. As a result, the problem of meaning and understanding is typically sidestepped through more simple,…
Approaches to Natural language processing (NLP) may be classified along a double dichotomy open/opaque - strict/adaptive. The former axis relates to the possibility of inspecting the underlying processing rules, the latter to the use of…
Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…
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…
The well-known conditions for a simplicial set to be the nerve of a small category generalize with respect to two parameters: the dimension n of the things which compose, and the position i of the thing which is the result of the…
Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli…
Convolutional neural networks (CNN) have made significant advances in hyperspectral image (HSI) classification. However, standard convolutional kernel neglects the intrinsic connections between data points, resulting in poor region…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
Attack trees (ATs) are popular graphical models for reasoning about the security of complex systems, allowing for the quantification of risk through so-called AT metrics. A large variety of different such AT metrics have been proposed, and…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…
Given a pool of observations selected from a sensor stream, input data can be robustly represented, via a multiscale process, in terms of invariant concepts, and themes. Applying this to episodic natural language data, one may obtain a…
We study the Sherali-Adams linear programming hierarchy in the context of promise constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy accepts an instance in terms of a homomorphism problem for an…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
A key requirement on any well-behaved process language is its compositionality: behavioural equivalence of processes should be respected by the constructors of the language. Turi and Plotkin's abstract GSOS provides an elegant bialgebraic…
Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample…
The impressive performance of neural networks on natural language processing tasks attributes to their ability to model complicated word and phrase compositions. To explain how the model handles semantic compositions, we study hierarchical…
Discourse Representation Theory (DRT) distinguishes itself from other semantic representation frameworks by its ability to model complex semantic and discourse phenomena through structural nesting and variable binding. While seq2seq models…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…