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(2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) -- nullspace projection and counterfactual flipping -- on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP intervent","title":"Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP","url":"https://arxiv.org/abs/2606.13720","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.13720v1 Announce Type: new \nAbstract: Arditi et al. (2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) -- nullspace projection and counterfactual flipping -- on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP intervent","title":"Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-15T04:43:09Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.13720"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d5b281997aced6c9b7b8c0f8b824c0b3cf6f33a22dac14e32881ae9cc0be09bd5c1f32b9dbf04be2285a221595ada5437f03fdb78f0660eaa513cc435fd28905","signer":"crovia.substrate","subject":{"observed_at":"2026-06-15T04:43:09Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.13720"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"689a4a59dab94015bae5b8c64ee9bb3bdf8bede6ec29684278a6b77591f3d2bb","leaf_index":229929,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"2fb542912fc2db75a90656fa2e662e545c8acd18372c30493120f16d029ae9e2","side":"left"},{"sibling":"527e7877032b70e1749a69c4dab93f15d435dd51a3088f2ba191e4a53f5e2c1f","side":"right"},{"sibling":"0a3df4564c55952b634aaf1ae955051f197ce00319c09491807a05e616f209e4","side":"right"},{"sibling":"bcda13e23e00c78c972972aa8572f684af00d29f02e78c19add245dcb2c711ad","side":"left"},{"sibling":"16620991a0f27b14ffedb603c0eb162b262a73e0a05bd91fbefd99113f584539","side":"right"},{"sibling":"e6cdecdfc7ac8cd05b0d8e3c44fb53f93f9a4b64780bdd1cc70e657d50712a06","side":"left"},{"sibling":"6bde248411f8ec3173e97ec3895054895c25f208bf85a22fd09c8fdf4911671b","side":"right"},{"sibling":"bc1002bb7e3da047b8a7c8f3990db61fb56edf499868605dc0c31aa0dee387b7","side":"right"},{"sibling":"14c50c43949e1ad41f149ffea691627d3f715c5861766c693b9fbac9d03b0d90","side":"right"},{"sibling":"74897e850164dddc689c3c65b33f9bae0268ab0bf429867a4e193d9b9b685040","side":"left"},{"sibling":"bde25d7e94e64717e426a97f6fcb4907e92b5c61fc89d92d7e0947a2249c3f6b","side":"right"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_483c87c2701770f6c67014ce10314823f08c017c0f579f3dbb8a646f4137076e"}}