Chaos

"Chaos. Unlike the systems that tend towards fixed points or cycles described above, chaotic systems are inherently unpredictable and highly sensitive to initial conditions. While it might seem easy to dismiss such notions as mathematical exoticisms, recent work has shown that, in fact, chaotic dynamics are not only possible in a wide range of multi-agent learning setups (Andrade et al., 2021; Galla & Farmer, 2013; Palaiopanos et al., 2017; Sato et al., 2002; Vlatakis-Gkaragkounis et al., 2023), but can become the norm as the number of agents increases (Bielawski et al., 2021; Cheung & Piliouras, 2020; Sanders et al., 2018). To the best of our knowledge, such dynamics have not been seen in today’s frontier AI systems, but the proliferation of such systems increases the importance of reliably predicting their behaviour."