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This undermines knowledge distillation pipelines that transfer chain-of-thought reasoning to smaller students. We introduce Invariant Gradient Alignment (IGA), a training framework that aligns gradient updates across semantically diverse but logically isomorphic examples via three innovations: (i) Logical Isomer Sets, groups of problems sharing identical logical structure across distinct semantic domains (mathematics, medicine, law, science); (ii) a differentiable \\emph{Continuous Gradient Conflict Mask}, that suppresses parameter dimensions with high cross-domain gradient variance while preserving invariant directions; and (iii) a truncated SVD projection of the masked gradient back onto the LoRA low-rank manifold, maint","title":"Invariant Gradient Alignment for Robust Reasoning Distillation","url":"https://arxiv.org/abs/2606.05025","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.05025v1 Announce Type: cross \nAbstract: Large language models (LLMs) suffer from shortcut learning: they systematically fail on out-of-distribution (OOD) inputs whose semantic surface differs from training data, even when the logical structure is identical. This undermines knowledge distillation pipelines that transfer chain-of-thought reasoning to smaller students. We introduce Invariant Gradient Alignment (IGA), a training framework that aligns gradient updates across semantically diverse but logically isomorphic examples via three innovations: (i) Logical Isomer Sets, groups of problems sharing identical logical structure across distinct semantic domains (mathematics, medicine, law, science); (ii) a differentiable \\emph{Continuous Gradient Conflict Mask}, that suppresses parameter dimensions with high cross-domain gradient variance while preserving invariant directions; and (iii) a truncated SVD projection of the masked gradient back onto the LoRA low-rank manifold, maint","title":"Invariant Gradient Alignment for Robust Reasoning Distillation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-04T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.05025"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:968ad98def7a9c6836e2d02447af988f5832637346147cf5b8ba194dc2d6f2170e0cfa50f92306eb577ff9d8d2f43a7188cd2196893eae8bc5033387bf60570c","signer":"crovia.substrate","subject":{"observed_at":"2026-06-04T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.05025"},"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":"eea3c114ec6aa63cff2cd719a8d490d834e83e0a8c211f8d91960381a82c050d","leaf_index":212746,"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":"54983ec0b4817d5f05c181713e4c925369bd6bb53f5465da8b9e781be2290aa6","side":"right"},{"sibling":"ff8d166e8064d5f7178cd0ba60eb2c85d89ebff49baa761b9d8fdee218c73681","side":"left"},{"sibling":"a732a51395294900f9d6f3528717580aca7e14a90b6782d9a203d19068436cb2","side":"right"},{"sibling":"c039c55bf48ec15958f46993a9ee94fcc54b0a44d65985a30d502238a49486f2","side":"left"},{"sibling":"57150dd47c5cdd0c1234afae53b69990c7808e5067a1229370e1070d4f30b71b","side":"right"},{"sibling":"b23e05f5a3c9defe23316ce264fed0315481fd5b7e3632665405d3a829b5ff76","side":"right"},{"sibling":"9abe7beed823fcb4fca86168a937bdf567afb433b776352858b68322288bbf2a","side":"right"},{"sibling":"5d10c089cc50333cc6f5ec8f5c37b251f9cdd4252a9604bb46ec83ac720abdd9","side":"right"},{"sibling":"b4e8a5af3a9fdc4bb815270cd541ee4baf09fb1d9e2cccd75c7346558e1f1e4c","side":"left"},{"sibling":"cfb460164a914d1f96a36aa17124b45bb5417829d2adbe5ca48375dbd842ec44","side":"left"},{"sibling":"a84ebc8e894a9893ee34d1afc942d15f28243b926f1e5f9d7f10a3de1e795262","side":"left"},{"sibling":"f8f6bd9da448fa097e2115b71146f61691d9f8807aca291c87c633192a7224e9","side":"left"},{"sibling":"2dca509b3eb767a47cf215d4315f230ce9103a76264412008ae23a349b519ef1","side":"left"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"422bcf7e281ca3a607f3726a5e6b8fabdb85e8b32199b4a86356998e260a0b34","side":"right"},{"sibling":"54a99163a4a62374c3ca6fb46294222f1d4b1a9d0b636e27256b0e093e98239a","side":"right"},{"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":213053,"merkle_root":"19d104b92c4d7299881c447fb8422611fc9cb8615d37a538959e34a2da7ef55f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260604T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-04T05:37:49Z","sig_algorithm":"ed25519","signature":"630748e88645187aa3b4d4cb8c872cc146180d0301e4c6656f15f99081d7776432715cea2a997b32b7b3a5216f215d19c1b536c0b093100ec843fa0bd65f2101","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_69ed91c605061e83a41ee5b883bc4fc947939e766dc3380f54fc97940c940684"}}