WriteSAE: Sparse Autoencoders for Recurrent State

Hugging Face Daily Papers Papers

Summary

WriteSAE introduces the first sparse autoencoder that decomposes matrix cache writes in state-space and hybrid recurrent language models, enabling superior token-level interventions compared to existing methods.

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 form for the per-token logit shift, and trains under matched Frobenius norm so atoms swap one cache slot at a time. Atom substitution beats matched-norm ablation on 92.4% of n=4{,}851 firings at Qwen3.5-0.8B L9 H4, the 87-atom population test holds at 89.8%, the closed form predicts measured effects at R^2=0.98, and Mamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3times lift midrank target-in-continuation from 33.3% to 100% under greedy decoding, the first behavioral install at the matrix-recurrent write site.
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Source: https://huggingface.co/papers/2605.12770

Abstract

WriteSAE enables sparse autoencoder decomposition and editing of matrix cache writes in state-space and hybrid recurrent language models, achieving superior performance in token-level interventions compared to existing methods.

We introduce WriteSAE, the firstsparse autoencoderthat decomposes and edits thematrix cache writeof state-space andhybrid recurrent language models, whereresidual SAEscannot reach. Existing SAEs read residual streams, butGated DeltaNet,Mamba-2, andRWKV-7write to a d_k times d_v cache throughrank-1 updatesk_t v_t^top that no vector atom can replace. WriteSAE factors each decoder atom into the native write shape, exposes a closed form for the per-token logit shift, and trains under matchedFrobenius normso atoms swap one cache slot at a time.Atom substitutionbeats matched-norm ablation on 92.4% of n=4{,}851 firings at Qwen3.5-0.8B L9 H4, the 87-atom population test holds at 89.8%, the closed form predicts measured effects at R^2=0.98, andMamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3times lift midrank target-in-continuation from 33.3% to 100% undergreedy decoding, the first behavioral install at the matrix-recurrent write site.

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