相关论文: Assembly Theory Reduced to Shannon Entropy and Ren…

In this study, we explored the progression trajectories of artificial intelligence (AI) systems through the lens of complexity theory. We challenged the conventional linear and exponential projections of AI advancement toward Artificial…

One of the challenges artificial intelligence (AI) faces is how a collection of agents coordinate their behaviour to achieve goals that are not reachable by any single agent. In a recent article by Ozmen et al this was framed as one of six…

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…

The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…

Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…

Based on Alan Turing's proposition on AI and computing machinery, which shaped Computing as we know it today, the new AI computing machinery should comprise a universal computer and a universal learning machine. The later should understand…

Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…

In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a-priori quantifiable guarantees - or more specifically remove classification errors -…

Foundation models excel in stable environments, yet often fail where reliability matters most: medicine, finance, and policy. This Fidelity Paradox is not just a data problem; it is structural. In domains where rules change over time, extra…

Artificial intelligence (AI) has made significant strides in recent years, yet it continues to struggle with a fundamental aspect of cognition present in all animals: common sense. Current AI systems, including those designed for complex…

To study arithmetic structures of natural numbers, we introduce a notion of entropy of arithmetic functions, called anqie entropy. This entropy possesses some crucial properties common to both Shannon's and Kolmogorov's entropies. We show…

A recent paper (van Rooij et al. 2024) claims to have proved that achieving human-like intelligence using learning from data is intractable in a complexity-theoretic sense. We point out that the proof relies on an unjustified assumption…

Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…

It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow…

We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d copies…

In direct response to requests for a logico-mathematical test of the conjecture, we formally disprove a recently conjectured artificial intelligence trade-off between epistemic certainty and scope in its published universal hyperbolic…

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…

Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…