WriteSAE: Sparse Autoencoders for Recurrent State

arXiv:2605.12770v1 Announce Type: cross Abstract: We introduce WriteSAE, the first sparse autoencoder that decomposes and edits the matrix cache write of state-space and hybrid recurrent language models, where residual SAEs cannot reach. Existing SAEs read residual streams, but Gated DeltaNet, Mamba-2, and RWKV-7 write to a $d_k \times d_v$ cache through rank-1 updates $k_t v_t^\top$ that no vector atom can replace. WriteSAE factors each decoder atom into the native write shape, exposes a closed