{"paper":{"title":"WriteSAE: Sparse Autoencoders for Recurrent State","license":"http://creativecommons.org/licenses/by/4.0/","headline":"WriteSAE factors decoder atoms to match rank-1 cache writes so they can be swapped directly into recurrent state models.","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Jack Young","submitted_at":"2026-05-12T21:32:45Z","abstract_excerpt":"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-n"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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 R²=0.98, and Mamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3× lift midrank target-in-continuation from 33.3% to 100% under greedy decoding.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That atoms trained under matched Frobenius norm can be substituted into the live cache without unintended side effects on the model's recurrent dynamics, and that the closed-form logit shift remains accurate when atoms are installed in real forward passes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"WriteSAE decomposes recurrent model cache writes into substitutable atoms with a closed-form logit shift, achieving high substitution success and targeted behavioral installs on models like Qwen3.5 and Mamba-2.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"WriteSAE factors decoder atoms to match rank-1 cache writes so they can be swapped directly into recurrent state models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e0fb960556d804e6b7c1c481418ed07c1f92eaf0218840f5c97256e8b7646697"},"source":{"id":"2605.12770","kind":"arxiv","version":2},"verdict":{"id":"3b4408d2-f91e-48b0-a4fe-ab97f385de31","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T04:55:35.992971Z","strongest_claim":"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 R²=0.98, and Mamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3× lift midrank target-in-continuation from 33.3% to 100% under greedy decoding.","one_line_summary":"WriteSAE decomposes recurrent model cache writes into substitutable atoms with a closed-form logit shift, achieving high substitution success and targeted behavioral installs on models like Qwen3.5 and Mamba-2.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That atoms trained under matched Frobenius norm can be substituted into the live cache without unintended side effects on the model's recurrent dynamics, and that the closed-form logit shift remains accurate when atoms are installed in real forward passes.","pith_extraction_headline":"WriteSAE factors decoder atoms to match rank-1 cache writes so they can be swapped directly into recurrent state models."},"references":{"count":106,"sample":[{"doi":"","year":null,"title":"Transformer Circuits Thread , year=","work_id":"991c2136-e27f-4704-8007-af667a9780c4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Sparse Autoencoders Find Highly Interpretable Features in Language Models","work_id":"51960d72-c69f-4db8-8efd-e90e8b4d9524","ref_index":2,"cited_arxiv_id":"2309.08600","is_internal_anchor":true},{"doi":"","year":null,"title":"Scaling and evaluating sparse autoencoders","work_id":"f3faddeb-36ed-42bc-a7c9-9e764dc9b368","ref_index":3,"cited_arxiv_id":"2406.04093","is_internal_anchor":true},{"doi":"","year":2024,"title":"and McDougall, Callum and MacDiarmid, Monte and Freeman, C","work_id":"20374c13-eaee-46d1-92b2-ed3cfe1f4ac9","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Improving Dictionary Learning with Gated Sparse Autoencoders","work_id":"3f6ee9ca-2e43-4536-a753-1e8c881c9229","ref_index":5,"cited_arxiv_id":"2404.16014","is_internal_anchor":true}],"resolved_work":106,"snapshot_sha256":"84e8888ffd16bf204b07b247925573f8a81dd75b22c0bea9303050d85ede6bee","internal_anchors":19},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9d970397d5c6a4a18287ed3a6f4319a9cdc45478cd1f53a46f8e1c4f0865e2e0"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}