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

Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…

All artificial Intelligence (AI) systems make errors. These errors are unexpected, and differ often from the typical human mistakes ("non-human" errors). The AI errors should be corrected without damage of existing skills and, hopefully,…

In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as…

Human-AI teams fail to outperform their best member in 70% of studies, yet no theory specifies when complementarity is achievable. We derive tight bounds for the broad class of confidence-based aggregation rules by integrating signal…

The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete,…

We show that the R\'enyi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite-size of the data despite being additive. It is demonstrated that this is so because it does not…

Conceptual abstraction and analogy-making are key abilities underlying humans' abilities to learn, reason, and robustly adapt their knowledge to new domains. Despite of a long history of research on constructing AI systems with these…

Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that…

Developments in the field of Artificial Intelligence (AI), and particularly large language models (LLMs), have created a 'perfect storm' for observing 'sparks' of Artificial General Intelligence (AGI) that are spurious. Like simpler models,…

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…

The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…

We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their…

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as…

Automated grading systems can efficiently score short-answer responses, yet they often fail to indicate when a grading decision is uncertain or potentially contentious. We introduce semantic entropy, a measure of variability across multiple…

We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined."…

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…

The general public often encounters complex texts but does not have the time or expertise to fully understand them, leading to the spread of misinformation. Automatic Text Simplification (ATS) helps make information more accessible, but its…

In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are…

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…