Do transformers "think ahead" during inference at a given position? It is known transformers prepare information in the hidden states of the forward pass at $t$ that is then used in future forward passes $t+\tau$. We posit two explanations for this phenomenon: pre-caching, in which off-diagonal gradient terms present in training result in the model computing features at $t$ irrelevant to the present inference task but useful for the future, and breadcrumbs, in which features most relevant to time step $t$ are already the same as those that would most benefit inference at time $t+\tau$. We test these hypotheses by training language models without propagating gradients to past timesteps, a scheme we formalize as myopic training. In a synthetic data setting, we find clear evidence for pre-caching. In the autoregressive language modeling setting, our experiments are more suggestive of the breadcrumbs hypothesis.

The staple of human intelligence is the capability of acquiring knowledge in a continuous fashion. In stark contrast, Deep Networks forget catastrophically and, for this reason, the sub-field of Class-Incremental Continual Learning fosters methods that learn a sequence of tasks incrementally, blending sequentially-gained knowledge into a comprehensive prediction. This work aims at assessing and overcoming the pitfalls of our previous proposal Dark Experience Replay (DER), a simple and effective approach that combines rehearsal and Knowledge Distillation. Inspired by the way our minds constantly rewrite past recollections and set expectations for the future, we endow our model with the abilities to i) revise its replay memory to welcome novel information regarding past data ii) pave the way for learning yet unseen classes. We show that the application of these strategies leads to remarkable improvements; indeed, the resulting method - termed eXtended-DER (X-DER) - outperforms the state of the art on both standard benchmarks (such as CIFAR-100 and miniImagenet) and a novel one here introduced. To gain a better understanding, we further provide extensive ablation studies that corroborate and extend the findings of our previous research (e.g. the value of Knowledge Distillation and flatter minima in continual learning setups).