Month: February 2022

Advancing mathematics by guiding human intuition with AI

Alex Davies, Petar Veličković, Lars Buesing, Sam Blackwell, Daniel Zheng, Nenad Tomašev, Richard Tanburn, Peter Battaglia, Charles Blundell, András Juhász, Marc Lackenby, Geordie Williamson, Demis Hassabis & Pushmeet Kohli 
Nature volume 600, pages70–74 (2021)

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures, most famously in the Birch and Swinnerton-Dyer conjecture, a Millennium Prize Problem. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

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Researcher position at the intersection between Social Complexity and Cooperative AI – FBK

FBK-CHuB is seeking a Researcher in the field of the analysis and modelling of complex social systems.
In particular, the candidate will be involved in a research project focused on the modelling of the interaction between human and artificial agents in complex social scenarios. The work will include the exploration of the interaction of different typologies of actors, artificial or natural, acting following different goals and strategies in paradigmatical complex social scenarios such as ant colonies, flocks of birds or interaction models on networks, as well as in more realistic scenarios such as online communication (bots) or traffic (self-driving cars).

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The Paradigm of Social Complexity

Volume I: An Alternative Way of Understanding Societies and their Economies
Volume II: Computational Models, Validation, and Applications

Gonzalo Castañeda

With the recent developments in computing technologies and the thriving research scene in Complexity Science, economists and other social scientists have become aware of a more flexible and promising alternative for modelling socioeconomic systems; one that, in contrast with neoclassical economics, advocates for the realism of the assumptions, the importance of context and culture, the heterogeneity of agents (individuals or organisations), and the bounded rationality of individuals who behave and learn in multifaceted ways in uncertain environments. The book synthesises an extensive body of work in the field of social complexity and constructs a unifying framework that allows developing concrete applications to important socioeconomic problems. This one-of-a-kind textbook provides a comprehensive panorama for advanced undergraduates and graduate students who want to become familiar with a wide range of issues related to social complexity. It is also a pioneering text that can support professors who wish to learn techniques and produce research in this novel field.

After reviewing the main concepts, premises and implications of complexity theory, the book frames this vision within the history of economic thought. Then, it articulates a meta-theory in which interdependent agents are embedded in a social context and whose collective and decentralised behaviour generates socio-economic phenomena. Such a framework builds on theories from evolutionary, institutional and behavioural economics, as well as analytical sociology. The book then reviews different computational tools for modelling complex adaptive systems, such as cellular automata, networks, and agent-based models. It elaborates on their analytical advantages in comparison to equation-based models, and how they can be calibrated/estimated and validated with empirical data. Finally, the book advocates for the practical use of these computational tools and makes a case for policy applications and the study of causal mechanisms.

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Reintroducing Pierre Teilhard de Chardin to Modern Evolutionary Science

David Sloan Wilson

Pierre Teilhard Chardin (1881-1955) developed an evolutionary worldview that was both spiritual and consistent with the scientific knowledge of his day. He has been largely forgotten by modern evolutionary scientists but remains widely read by those who are inspired by his vision of conscious evolution leading to a planetary superorganism. This working paper examines the major tenets of Teilhard’s vision from a modern evolutionary perspective in an effort to integrate “hard” evolutionary science with conscious efforts to manage cultural change.

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