Related papers: Building on the Diamonds between Theories: Theory …
We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application…
Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
Universal induction is a crucial issue in AGI. Its practical applicability can be achieved by the choice of the reference machine or representation of algorithms agreed with the environment. This machine should be updatable for solving…
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
In this paper we study possibilities of efficient reasoning in combinations of theories over possibly non-disjoint signatures. We first present a class of theory extensions (called local extensions) in which hierarchical reasoning is…
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
Weighted bipolar argumentation frameworks allow modeling decision problems and online discussions by defining arguments and their relationships. The strength of arguments can be computed based on an initial weight and the strength of…
Two major learning theories have dominated recent literature on optimizing knowledge acquisition: constructivism and cognitive load theory. Constructivism, on the one hand, gives preeminent value to the development of students'…
Large Language Models (LLMs) have garnered considerable interest due to their impressive natural language capabilities, which in conjunction with various emergent properties make them versatile tools in workflows ranging from complex code…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
We develop a framework for combining differentiable programming languages with neural networks. Using this framework we create end-to-end trainable systems that learn to write interpretable algorithms with perceptual components. We explore…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension…