arXiv:2407.07668v3 Announce Type: replace-cross Abstract: Many real-world applications require machine-learning models to be able to deal with non-stationary data distributions and thus learn autonomously over an extended period of time, often in an online setting. One of the main challenges in this scenario is the so-called catastrophic forgetting (CF) for which the learning model tends to focus on the most recent tasks while experiencing predictive degradation on older ones. In the online setting, the most effective solutions employ a fixed-size memory buffer to store old samples used for replay when training on new tasks. Many approaches have been presented to tackle this problem. However, it is not clear how predictive uncertainty information for memory management can be leveraged in the most effective manner and conflicting strategies are proposed to populate the memory. Are the easiest-to-forget or the easiest-to-remember samples more effective in combating CF? Starting from the intuition that predictive uncertainty provides an idea of the samples' location in the decision space, this work presents an in-depth analysis of different uncertainty estimates and strategies for populating the memory. The investigation provides a better understanding of the characteristics data points should have for alleviating CF. Then, we propose an alternative method for estimating predictive uncertainty via the generalised variance induced by the negative log-likelihood. Finally, we demonstrate that the use of predictive uncertainty measures helps in reducing CF in different settings.