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We give a function-space account in the NTK regime: new-task training induces old-task prediction drift through the cross-task kernel, yielding a closed-form predictor for the forgetting vector before any new-task gradient step. In frozen-backbone linear-head PEFT-CL, where the model is linear in the trainable parameters, the predictor is exact up to numerical precision; for nonlinear adapters/full fine-tuning, it is a local NTK approximation. The same expression reveals that forgetting concentrates in a small number of old-task NTK eigenmodes and under frozen linear heads gives a Kronecker scaling rule for the vulnerable rank. These results clarify the relation to prior NTK-overlap theory, explain why parameter-space regularizers can miss outp","title":"Catastrophic Forgetting is Low-Rank: A Function-Space Theory for Continual Adaptation","url":"https://arxiv.org/abs/2606.18024","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.18024v1 Announce Type: cross \nAbstract: Catastrophic forgetting in continual adaptation is usually studied through parameter drift, replay, or distillation, but these views do not identify which output-space directions are vulnerable. We give a function-space account in the NTK regime: new-task training induces old-task prediction drift through the cross-task kernel, yielding a closed-form predictor for the forgetting vector before any new-task gradient step. In frozen-backbone linear-head PEFT-CL, where the model is linear in the trainable parameters, the predictor is exact up to numerical precision; for nonlinear adapters/full fine-tuning, it is a local NTK approximation. The same expression reveals that forgetting concentrates in a small number of old-task NTK eigenmodes and under frozen linear heads gives a Kronecker scaling rule for the vulnerable rank. These results clarify the relation to prior NTK-overlap theory, explain why parameter-space regularizers can miss outp","title":"Catastrophic Forgetting is Low-Rank: A Function-Space Theory for Continual Adaptation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-17T04:43:17Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.18024"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:51982580a3e3da95f8444ebb362d975d677aa658ea1e57d04add3e9cfce511296dd5079ee2457153303afb304e75be1f7829f9016b771543f2a8b9cc0825b10c","signer":"crovia.substrate","subject":{"observed_at":"2026-06-17T04:43:17Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.18024"},"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":"528b01b91601bccdd8de21f6e811846a262ab5a41878478a9827e95d75836028","leaf_index":231034,"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":"bdadb8b9a4db82c36ddcef9213d88ad7aa23bdce924bcc717200d6c49cf5e4b6","side":"right"},{"sibling":"663c34e3dc526c9f447817ea61d1a2fe0f58bf14c55489eed526565aba54eead","side":"left"},{"sibling":"c211ef79d30b390b860a5fb212b80a4a032018dc6f3681e76f0c611b4f53023d","side":"right"},{"sibling":"a67de0e1b6566af9b8ccff240a10e3c4026e8eaa372d513aa827d617dff9ee47","side":"left"},{"sibling":"5cd58ba0db9f2ad939967d211fa05489e30610c4b4994d9e73c91574d24f3a41","side":"left"},{"sibling":"5224392f43dd4a302bb61fc34434b5f9c72f8899d53418e9684bcc3cf814e3a4","side":"left"},{"sibling":"8daceae0255c786ffdef12a608da0c1a09b9a2ceedfcc067120bfd86b4ab9952","side":"left"},{"sibling":"ce828166a6a4fc2ff2681c985a56053a1f8b683cc245e0b232fa5939310b3ad9","side":"right"},{"sibling":"ebbec9ce4bf43a3f5f71e2c07df4c91301abefa2da727a4d748099a74e980bc3","side":"right"},{"sibling":"1d74941c32baeab8cad08f8700cb49427d8256f231534f2a225b2bb3e84e4ff8","side":"left"},{"sibling":"d5b9f8b1a2c9f6a46e17982dfbe6ce1f3b5fa4e730220397f2253d114dcc8486","side":"left"},{"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_bf7099582df7be973d2e63a00a5506a37033d12cc1624f508fa6844b91253d9d"}}