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We study this phenomenon, known as catastrophic forgetting, and propose a post-hoc repair solution that uses only the pretrained checkpoint $W_{\\mathrm{base}}$ and its fine-tuned descendant $W_{\\mathrm{ft}}$. The goal is not merely to revert the model toward the base checkpoint, but to recover capabilities damaged by fine-tuning while preserving both the target-task gains and any beneficial held-out improvements. We introduce DG-Hard, a checkpoint-only spectral repair method for the fine-tuning update $\\Delta = W_{\\mathrm{ft}} - W_{\\mathrm{base}}$. DG-Hard treats $\\Delta$ as a low-rank task-aligned signal embedded in an IID-like noise residual that gradient descent has no incentive to remove, and applies the Donoho-Gavish hard singular-value threshold to each weight-delta matrix, keeping the structured high-ener","title":"Spectral Unforgetting: Post-Hoc Recovery of Damaged Capabilities Without Retraining","url":"https://arxiv.org/abs/2605.20296","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.20296v1 Announce Type: cross \nAbstract: Fine-tuning a language model for a target task routinely degrades capabilities the training data never explicitly threatened. We study this phenomenon, known as catastrophic forgetting, and propose a post-hoc repair solution that uses only the pretrained checkpoint $W_{\\mathrm{base}}$ and its fine-tuned descendant $W_{\\mathrm{ft}}$. The goal is not merely to revert the model toward the base checkpoint, but to recover capabilities damaged by fine-tuning while preserving both the target-task gains and any beneficial held-out improvements. We introduce DG-Hard, a checkpoint-only spectral repair method for the fine-tuning update $\\Delta = W_{\\mathrm{ft}} - W_{\\mathrm{base}}$. DG-Hard treats $\\Delta$ as a low-rank task-aligned signal embedded in an IID-like noise residual that gradient descent has no incentive to remove, and applies the Donoho-Gavish hard singular-value threshold to each weight-delta matrix, keeping the structured high-ener","title":"Spectral Unforgetting: Post-Hoc Recovery of Damaged Capabilities Without Retraining","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-22T04:43:12Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.20296"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:caefd8ccdab81c563e7cbefdb3d5be16c7a665024867880bf31060b822453986e32dec2e40105eecfe3a3063fb6310676d77180395bd7622d9accc8c0fd14d0f","signer":"crovia.substrate","subject":{"observed_at":"2026-05-22T04:43:12Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.20296"},"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":"e694603752b14b451aa4570d5bef7ff782ae0c149eae1a6c40cc5ed444e9b58a","leaf_index":148201,"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":"10947b5f983fb1d5d576436f5f3ad50f504ca1ff08b8ef3a7773b0daff90ba02","side":"left"},{"sibling":"6ac79a78fc47214f5731bcd3a687044ea76fe3ef41b359ffe3e43e44d71cf48b","side":"right"},{"sibling":"5f1f08e5794ca15c2060fb2ada3fd3314172892b2e2649204d5a5075bbe57cec","side":"right"},{"sibling":"6757acf93ea8e3c11adb6c2851b5d997086a28b262af01df568d744319df07dc","side":"left"},{"sibling":"1c7ab905eb4d289a16032228eaa2d4fc70c9c85fe0822b11312c184dad3a95f0","side":"right"},{"sibling":"9c8ee5d5ee587378292cc512af6677d5e68736fc250e3e729ba4a22e4dd9c55f","side":"left"},{"sibling":"9041a5a271687216ad8ad42ade0fd8c711a35ed68eb350b81aed4384188eec3c","side":"left"},{"sibling":"ce8423e7b33fd98ad2188ec515d860afebe3ce0e74717c41376c90ea6acfb384","side":"left"},{"sibling":"c5d582bc1cdd6d6494fd9e29c8b4aadd02d777f7ef92fc6d4afad7ee42785e79","side":"right"},{"sibling":"d337a9fdcfc121e9691d8db9173af6a3fe0c33d4a6d5f0c8a7a01af04f9fb856","side":"left"},{"sibling":"8b39e07457f5cc5d687d2ae42284dbe705bb87084e7db4b626aff81e51dacd19","side":"right"},{"sibling":"79a713e1e345ccb99c5fe994a11708c8e9bcfa2e91f940d70421cb7d8d77ecc6","side":"right"},{"sibling":"249870fb494bef050c409081e5de45f9042938d7b2823524ee496f296aa63667","side":"right"},{"sibling":"96c48ee8328f1b7925a4cc4421df5cb0bd81c92a5d8354c93126fa5f0166d225","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"4e13b4a3e69bb83d13913477a782913ce03937edd65046853c1964d3cbb6564b","side":"right"},{"sibling":"0f7b2df1c4580bf7bb7c24b9158ba20593a06af18a5f18d0973e5eff20c35cd8","side":"right"},{"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":148601,"merkle_root":"44900cffd986f40535c83f46a250e86fbf1019d41f27080a00fbf9b8d77ec33a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260524T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-24T13:37:32Z","sig_algorithm":"ed25519","signature":"059e428c3c5241de303721ad6ac7b748758372180f3f0a717810312aecd6fab073abb3ea264157666de581a2b361c4c6e2aa8ca081b08ce9be090721f0e3400e","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_a26c9bb3da53dbd384df7396fb4b645b4e9f2c16553061fd4748c95de707f19e"}}