Related papers: Biform Theories: Project Description
This paper describes some biologically-inspired processes that could be used to build the sort of networks that we associate with the human brain. New to this paper, a 'refined' neuron will be proposed. This is a group of neurons that by…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
The concept of intelligent software is flawed. The behaviour of software is determined by the hardware that "interprets" it. This undermines claims regarding the behaviour of theorised, software superintelligence. Here we characterise this…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
Transparent machine learning is introduced as an alternative form of machine learning, where both the model and the learning system are represented in source code form. The goal of this project is to enable direct human understanding of…
A visual type theory is a cognitive tool that has much in common with language, and may be regarded as an exceptional form of spatial text adjunct. A mathematical visual type theory, called NPM, has been under development that can be viewed…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition…
Mechanistic Interpretability aims to understand neural networks through causal explanations. We argue for the Explanatory View Hypothesis: that Mechanistic Interpretability research is a principled approach to understanding models because…
This study explores the integration of generative artificial intelligence (AI), specifically large language models, with multi-modal analogical reasoning as an innovative approach to enhance science, technology, engineering, and mathematics…
This paper motivates the study of decision theory as necessary for aligning smarter-than-human artificial systems with human interests. We discuss the shortcomings of two standard formulations of decision theory, and demonstrate that they…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
Neurosymbolic AI focuses on integrating learning and reasoning, in particular, on unifying logical and neural representations. Despite the existence of an alphabet soup of neurosymbolic AI systems, the field is lacking a generally accepted…
Ontologies have been used for the purpose of bringing system and consistency to subject and knowledge areas. We present a criticism of the present mathematical structure of ontologies and indicate that they are not sufficient in their…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…