Phase Transitions

"Phase Transitions. Finally, small external changes to the system – such as the introduction of new agents or a distributional shift – can cause phase transitions, where the system undergoes an abrupt qualitative shift in overall behaviour (Barfuss et al., 2024). Formally, this corresponds to bifurcations in the system’s parameter space, which lead to the creation or destruction of dynamical attractors, resulting in complex and unpredictable dynamics (Crawford, 1991; Zeeman, 1976). For example, Leonardos & Piliouras (2022) show that changes to the exploration hyperparameter of RL agents can lead to phase transitions that drastically change the number and stability of the equilibria in a game, which in turn can have potentially unbounded negative effects on agents’ performance. Relatedly, there have been many observations of phase transitions in ML (Carroll, 2021; Olsson et al., 2022; Ziyin & Ueda, 2022), such as ‘grokking’, in which the test set error decreases rapidly long after the training error has plateaued (Power et al., 2022). These phenomena are still poorly understood, even in the case of a single system."(p. 32)