Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature regarding the development of surrogate models for diffusion processes on graphs. In this work, we fill this gap by proposing sparse polynomial-based surrogate models for parametric diffusion equations on graphs with community structure. In tandem, we provide convergence guarantees for both least squares and compressed sensing-based approximations by showing the holomorphic regularity of parametric solutions to these diffusion equations. Our theoretical findings are accompanied by a series of numerical experiments conducted on both synthetic and real-world graphs that demonstrate the applicability of our methodology.

This paper considers the kinds of AI systems we want involved in art and art practice. We explore this relationship from three perspectives: as artists interested in expanding and developing our own creative practice; as AI researchers interested in building new AI systems that contribute to the understanding and development of art and art practice; and as audience members interested in experiencing art. We examine the nature of both art practice and experiencing art to ask how AI can contribute. To do so, we review the history of work in intelligent agents which broadly speaking sits in two camps: autonomous agents (systems that can exhibit intelligent behaviour independently) in one, and multi-agent systems (systems which interact with other systems in communities of agents) in the other. In this context we consider the nature of the relationship between AI and Art and introduce two opposing concepts: that of "Heroic AI", to describe the situation where the software takes on the role of the lone creative hero and "Collaborative AI" where the system supports, challenges and provokes the creative activity of humans. We then set out what we believe are the main challenges for AI research in understanding its potential relationship to art and art practice.

It's a Wednesday night in North East London and upstairs at the Vortex Jazz Club the machines are calling the shots. The human spectators are jiggling happily in their seats, and the musicians are undeniably flesh-and-blood, sweating and straining at their instruments. But the music itself is the product of electronic brains -- trained to soak up the music of great artists and strain out new melodies. This is "the first concert consisting almost entirely of music composed by artificial intelligence" says professor Geraint Wiggins of Queen Mary's University at the beginning of the evening. In about a few minutes we'll be listening to Medieval chants, Baroque chorales, and jazz and pop -- all made by artificial intelligence with the help of computer scientists who programmed the evening's "composers."

This paper considers the kinds of AI systems we want involved in art and art practice. We explore this relationship from three perspectives: as artists interested in expanding and developing our own creative practice; as AI researchers interested in building new AI systems that contribute to the understanding and development of art and art practice; and as audience members interested in experiencing art. We examine the nature of both art practice and experiencing art to ask how AI can contribute. To do so, we review the history of work in intelligent agents which broadly speaking sits in two camps: autonomous agents (systems that can exhibit intelligent behaviour independently) in one, and multi-agent systems (systems which interact with other systems in communities of agents) in the other. In this context we consider the nature of the relationship between AI and Art and introduce two opposing concepts: that of “Heroic AI”, to describe the situation where the software takes on the role of the lone creative hero and “Collaborative AI” where the system supports, challenges and provokes the creative activity of humans. We then set out what we believe are the main challenges for AI research in understanding its potential relationship to art and art practice.