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The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
This paper leverages insights from Alignment Theory (AT) research, which primarily focuses on the potential pitfalls of technical alignment in Artificial Intelligence, to critically examine the European Union's Artificial Intelligence Act…
Learning to disentangle and represent factors of variation in data is an important problem in AI. While many advances have been made to learn these representations, it is still unclear how to quantify disentanglement. While several metrics…
Artificial intelligence (AI) has been increasingly applied in scientific activities for decades; however, it is still far from an insightful and trustworthy collaborator in the scientific process. Most existing AI methods are either too…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
This paper is about conceptual modeling of aggregates in software engineering. An aggregate is a cluster of domain objects that can be treated as a single unit. In UML, an aggregation is a type of association in which objects are configured…
We introduce SMGI, a structural theory of general artificial intelligence, and recast the foundational problem of learning from the optimization of hypotheses within fixed environments to the controlled evolution of the learning interface…
Contemporary neural networks still fall short of human-level generalization, which extends far beyond our direct experiences. In this paper, we argue that the underlying cause for this shortcoming is their inability to dynamically and…
A leading proposal for aligning artificial superintelligence (ASI) is to use AI agents to automate an increasing fraction of alignment research as capabilities improve. We argue that, even when research agents are not scheming to…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
Interpolation is an essential tool in software verification, where first-order theories are used to constrain datatypes manipulated by programs. In this paper, we introduce the datatype theory of contiguous arrays with maxdiff, where arrays…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
As artificial intelligence (AI) capabilities advance rapidly, frontier models increasingly demonstrate systematic deception and scheming, complying with safety protocols during oversight but defecting when unsupervised. This paper examines…
This position paper argues that the theoretical inconsistency often observed among Responsible AI (RAI) metrics, such as differing fairness definitions or tradeoffs between accuracy and privacy, should be embraced as a valuable feature…
The AI revolution is data driven. AI "data wrangling" is the process by which unusable data is transformed to support AI algorithm development (training) and deployment (inference). Significant time is devoted to translating diverse data…