Cooperative communication plays a central role in theories of human cognition, language, development, culture, and human-robot interaction. Prior models of cooperative communication are algorithmic in nature and do not shed light on why cooperation may yield effective belief transmission and what limitations may arise due to differences between beliefs of agents.

In recent years, breakthroughs in artificial intelligence (AI) technology have triggered global industrial transformations, with applications permeating various fields such as finance, healthcare, education, and manufacturing. However, this rapid iteration is accompanied by irrational development, where enterprises blindly invest due to technology hype, often overlooking systematic value assessments. This paper develops a multi-dimensional evaluation model that integrates information theory's entropy reduction principle, economics' bounded rationality framework, and psychology's irrational decision theories to quantify AI product value. Key factors include positive dimensions (e.g., uncertainty elimination, efficiency gains, cost savings, decision quality improvement) and negative risks (e.g., error probability, impact, and correction costs). A non-linear formula captures factor couplings, and validation through 10 commercial cases demonstrates the model's effectiveness in distinguishing successful and failed products, supporting hypotheses on synergistic positive effects, non-linear negative impacts, and interactive regulations. Results reveal value generation logic, offering enterprises tools to avoid blind investments and promote rational AI industry development. Future directions include adaptive weights, dynamic mechanisms, and extensions to emerging AI technologies like generative models.

Cooperative communication plays a central role in theories of human cognition, language, development, culture, and human-robot interaction. Prior models of cooperative communication are algorithmic in nature and do not shed light on why cooperation may yield effective belief transmission and what limitations may arise due to differences between beliefs of agents. We derive prior models as special cases, statistical interpretations of belief transfer plans, and proofs of robustness and instability. Computational simulations support and elaborate our theoretical results, and demonstrate fit to human behavior. The results show that cooperative communication provably enables effective, robust belief transmission which is required to explain feats of human learning and improve human-machine interaction.

Nobel laureate Philip Anderson and Elihu Abrahams once stated that, "even if machines did contribute to normal science, we see no mechanism by which they could create a Kuhnian revolution and thereby establish a new physical law." In this Perspective, we draw upon insights from the philosophies of science and artificial intelligence (AI) to propose necessary conditions of precisely such a mechanism for generating revolutionary mathematical theories. Recent advancements in AI suggest that satisfying the proposed necessary conditions by machines may be plausible; thus, our proposed necessary conditions also define a moonshot challenge. We also propose a heuristic definition of the intelligibility of mathematical theories to accelerate the development of machine theorists.

Prediction markets are useful for estimating probabilities of claims whose truth will be revealed at some fixed time -- this includes questions about the values of real-world events (i.e. statistical uncertainty), and questions about the values of primitive recursive functions (i.e. logical or algorithmic uncertainty). However, they cannot be directly applied to questions without a fixed resolution criterion, and real-world applications of prediction markets to such questions often amount to predicting not whether a sentence is true, but whether it will be proven. Such questions could be represented by countable unions or intersections of more basic events, or as First-Order-Logic sentences on the Arithmetical Hierarchy (or even beyond FOL, as hyperarithmetical sentences). In this paper, we propose an approach to betting on such events via options, or equivalently as bets on the outcome of a "verification-falsification game". Our work thus acts as an alternative to the existing framework of Garrabrant induction for logical uncertainty, and relates to the stance known as constructivism in the philosophy of mathematics; furthermore it has broader implications for philosophy and mathematical logic.

Analogical proportions are expressions of the form ``$a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning which itself is at the core of human and artificial intelligence. The author has recently introduced {\em from first principles} an abstract algebro-logical framework of analogical proportions within the general setting of universal algebra and first-order logic. In that framework, the source and target algebras have the {\em same} underlying language. The purpose of this paper is to generalize his unilingual framework to a bilingual one where the underlying languages may differ. This is achieved by using hedges in justifications of proportions. The outcome is a major generalization vastly extending the applicability of the underlying framework. In a broader sense, this paper is a further step towards a mathematical theory of analogical reasoning.

This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.

Is there a mathematical theory of intelligence? It all depends on how you define intelligence, as animal, human, machine or alien, or in the abstract terms, as a general mechanism transcending its specific operations and functions, as perception, cognitive processing, learning, reasoning, decision-making, and action. There are all sorts of models and approximations by means of mathematical logics, mathematical optimization, probability theory, statistic models, information theory, #computerscience. Accordingly, an intelligence could be realized in many forms and modalities, as an information entity, an animal/human being, an advanced algorithmic system, a learning software application, complex data-processing software/hardware, a sophisticated computing device, statistical machines, or a goal-directed agent, which "intelligence measures an agent's ability to achieve goals in a wide range of environments, situations, tasks and problems". The current situation is too divided, specific and fragmented.

Reproduced under a CC-BY-4.0 license from the AlphaFold Protein Structure Database. In this post, we summarise the first two invited talks from the International Conference on Machine Learning (ICML 2022). These presentations covered two very different topics: mathematical theories of machine learning, and machine learning models for healthcare and the life sciences. Towards a mathematical theory of machine learning – Weinan E In his talk, Weinan gave a review of the current status of the field of mathematical theory for neural network-based machine learning. The central theme of his work treats the understanding of high dimensional functions.

In the past decade, deep learning as a branch of machine learning has influenced scientific computing in a fundamental way. This computational breakthrough presents tremendous opportunities and needs for new perspectives on computational mathematics and related emerging fields, such as approximation theory, operator estimation, numerical PDEs, inverse problems, data-driven modeling of dynamical systems, unsupervised and semi-supervised learnings.