As large language models (LLMs) are increasingly deployed as multilingual services, keeping their factual knowledge accurate across languages has become both essential and challenging. However, most of the existing knowledge editing (KE) methods are static, in that they update parameters offline for given accumulated edits of knowledge, and are struggling to effectively propagate edits in one language to others, while avoiding side effects. To mitigate this issue, we propose **CLICKER**, a KE method with stepwise reasoning that dynamically retrieves only knowledge relevant to a given query and then edit, while maintaining cross-lingual consistency through: (1) relevance-aware knowledge retrieval, (2) on-demand in-context KE, and (3) language alignment of the outputs. To rigorously evaluate the locality of edits in cross-lingual KE, we develop **Multi-CounterFact** dataset that contain many semantically-similar but irrelevant prompts for the edit. Experiments on Multi-CounterFact and MzsRE with both open- and closed-source LLMs confirmed that CLICKER effectively localizes edits and resolves cross-lingual inconsistencies, outperforming dynamic KE baselines.

While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs.This leaves the broader role of neuron activations unclear, limiting progress in areas like knowledge editing.We uncover a global linear relationship between neuron activations and outputs using neuron interventions on a knowledge probing dataset.The gradient of this linear relationship, which we call the **neuron empirical gradient (NEG)**, captures how changes in activations affect predictions.To compute NEG efficiently, we propose **NeurGrad**, enabling large-scale analysis of neuron behavior in PLMs.We also show that NEG effectively captures language skills across diverse prompts through skill neuron probing. Experiments on **MCEval8k**, a multi-genre multiple-choice knowledge benchmark, support NEG’s ability to represent model knowledge. Further analysis highlights the key properties of NEG-based skill representation: efficiency, robustness, flexibility, and interdependency.Code and data are released.