  Extensive previous research has focused on post-training knowledge editing
(KE) for language models (LMs) to ensure that knowledge remains accurate and
up-to-date. One desired property and open question in KE is to let edited LMs
correctly handle ripple effects, where LM is expected to answer its logically
related knowledge accurately. In this paper, we answer the question of why most
KE methods still create messy ripple effects. We conduct extensive analysis and
identify a salient indicator, GradSim, that effectively reveals when and why
updated knowledge ripples in LMs. GradSim is computed by the cosine similarity
between gradients of the original fact and its related knowledge. We observe a
strong positive correlation between ripple effect performance and GradSim
across different LMs, KE methods, and evaluation metrics. Further
investigations into three counter-intuitive failure cases (Negation,
Over-Ripple, Multi-Lingual) of ripple effects demonstrate that these failures
are often associated with very low GradSim. This finding validates that GradSim
is an effective indicator of when knowledge ripples in LMs.
