Multimodal Knowledge Edit-Scoped Generalization for Online Recursive MLLM Editing

Abstract: Online multimodal knowledge editing requires injecting a continual stream of visual-textual corrections into multimodal LLMs (MLLMs) with bounded overhead and minimal disruption to unrelated behaviors. Existing editors mainly emphasize edit reliability and long-horizon stability, but rarely control the semantic boundary of each edit. Our pilot analyses of post-edit behaviors and internal neuronal activities reveal a scope gap behind reliable edits: instance-level success neither guarantees transfer to valid cross-modal variants nor prevents leakage to unrelated inputs, while edit-related cross-modal responses concentrate in deeper semantic layers. Therefore, we formulate Edit-Scoped Generalization, reframing online MLLM editing from merely correcting an instance to controlling the propagation boundary of each edit. To this end, we propose ScopeEdit, a scope-aware online editor that decomposes each update into a modality-local absorption branch and an evidence-gated shared generalization branch. The local branch supports stable edit absorption, whereas the shared branch enables cross-modal propagation only when visual and textual evidence are sufficiently aligned. Both branches perform scope-separated write geometries in orthogonal low-rank spaces and maintain branch-wise preconditioners via Sherman--Morrison recursions, yielding constant per-edit overhead. Extensive experiments across diverse benchmarks, long-horizon edit streams, MLLM backbones, real-world VLKEB scenarios, and complex vision-language architectures show that ScopeEdit consistently improves the trade-off between in-scope cross-modal transfer and out-of-scope locality, while preserving edit reliability, stability and online efficiency. Our code is available at https://github.com/lab-klc/ScopeEdit.