Mixture-of-Experts (MoE) language models scale model capacity efficiently by activating a small subset of parameters per token. However, in long-context inference, memory remains a major bottleneck because the KV cache grows linearly with sequence length. Existing KV cache compression methods reduce this cost for dense transformers, but overlook a problem specific to MoE: KV eviction can change which experts are selected during answer generation, degrading the generation quality. We propose MoEZip, a routing-aware KV cache compression for sparse MoE language models. To estimate the sensitivity of expert routing to perturbation, we propose a novel metric based on the Fisher information matrix of routing distributions. MoEZip combines this metric with attention weights for routing-aware scoring of contexts. Finally, we compose a complementary scoring system that combines eviction methods for dense and sparse-MoE architectures. Experiments show that MoEZip achieves robust performance under aggressive cache compression on various benchmarks. At a KV retention ratio of 10\%, MoEZip improves over the SoTA baseline by +24 and +20 points on average on LongBench and RULER, corresponding to 2.3$\times$ and 4.9$\times$ higher scores, respectively.

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