Related papers: Assembly Theory Reduced to Shannon Entropy and Ren…
We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP,…
Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…
Assembly Theory (AT) was developed to help distinguish living from non-living systems. The theory is simple as it posits that the amount of selection or Assembly is a function of the number of complex objects where their complexity can be…
We demonstrate that the assembly pathway method underlying assembly theory (AT) is an encoding scheme widely used by popular statistical compression algorithms. We show that in all cases (synthetic or natural) AT performs similarly to other…
Assembly Theory (AT) is a theory that explains how to determine if a complex object is the product of evolution. Here we explain why attempts to compare AT to compression algorithms, ref 1, does not help identify if the object is the…
Assembly theory (AT) introduces causation as a material property and establishes a metrology for objects produced by evolution and selection. The physical scale of causation is quantified by the assembly index, defined as the minimum number…
Quantifying the evolution and complexity of materials is of importance in many areas of science and engineering, where a central open challenge is developing experimental complexity measurements to distinguish random structures from evolved…
We introduce an increasing-complexity, open-ended, and human-agnostic metric to evaluate foundational and frontier AI models in the context of Artificial General Intelligence (AGI) and Artificial Super Intelligence (ASI) claims. Unlike…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…
Deep-learning based classification algorithms have been shown to be susceptible to adversarial attacks: minor changes to the input of classifiers can dramatically change their outputs, while being imperceptible to humans. In this paper, we…
Evolution is often understood through genetic mutations driving changes in an organism's fitness, but there is potential to extend this understanding beyond the genetic code. We propose that natural products - complex molecules central to…
In this paper, we present a theoretical discussion on AI deep learning neural network uncertainty investigation based on the classical Rademacher complexity and Shannon entropy. First it is shown that the classical Rademacher complexity and…
This paper establishes a theoretical foundation for understanding the fundamental limits of AI explainability through algorithmic information theory. We formalize explainability as the approximation of complex models by simpler ones,…
Information-theoretic (IT) measures are ubiquitous in artificial intelligence: entropy drives decision-tree splits and uncertainty quantification, cross-entropy is the default classification loss, mutual information underpins representation…
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
We present assembly-theory, a Rust package for computing assembly indices of covalently bonded molecular structures. This is a key complexity measure of assembly theory, a recent theoretical framework quantifying selection across diverse…
Assembly Theory, as developed by Cronin and co-workers, assigns to an object an assembly index: the minimal number of binary join operations required to build at least one copy of the object from a specified set of basic building blocks,…
For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…