  Language models (LMs) are known to suffer from forgetting of previously
learned examples when fine-tuned, breaking stability of deployed LM systems.
Despite efforts on mitigating forgetting, few have investigated whether, and
how forgotten upstream examples are associated with newly learned tasks.
Insights on such associations enable efficient and targeted mitigation of
forgetting. In this paper, we empirically analyze forgetting that occurs in $N$
upstream examples while the model learns $M$ new tasks and visualize their
associations with a $M \times N$ matrix. We empirically demonstrate that the
degree of forgetting can often be approximated by simple multiplicative
contributions of the upstream examples and newly learned tasks. We also reveal
more complicated patterns where specific subsets of examples are forgotten with
statistics and visualization. Following our analysis, we predict forgetting
that happens on upstream examples when learning a new task with matrix
completion over the empirical associations, outperforming prior approaches that
rely on trainable LMs. Project website:
https://inklab.usc.edu/lm-forgetting-prediction/
