We explore task-free continual learning (CL), in which a model is trained to avoid catastrophic forgetting, but without being provided any explicit task boundaries or identities. However, since CL models are continually updated, the utility of stored seen examples may diminish over time. Here, we propose Gradient based Memory EDiting (GMED), a framework for editing stored examples in continuous input space via gradient updates, in order to create a wide range of more ``challenging examples for replay. GMED-edited examples remain similar to their unedited forms, but can yield increased loss in the upcoming model updates, thereby making the future replays more effective in overcoming catastrophic forgetting. By construction, GMED can be seamlessly applied in conjunction with other memory-based CL algorithms to bring further improvement. Experiments on six datasets validate that GMED is effective, and our single best method significantly outperforms existing approaches on three datasets. Code and data can be found at https://github.com/INK-USC/GMED.
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