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Although PTQ is efficient and often accurate at moderate bitwidths, it can fail sharply at aggressive bitwidths; QAT is more expensive but can often recover the lost accuracy. We propose a unified geometric framework that explains both PTQ failure and QAT recovery. We model full-precision training as following a low-loss \\emph{river} inside a wider \\emph{valley}: a normal neighborhood of the river forms a nearly flat \\emph{basin}, while leaving this basin incurs a sharp loss increase. When the quantization grid is comparable to the basin width, local PTQ objectives, including rounding and Hessian-based second-order reconstruction, can select a high-loss deployed quantized point outside the basin even when nearby low-loss qua","title":"Understanding Quantization-Aware Training: Gradients at Quantized Weights Bias to the Low-Loss Basin","url":"https://arxiv.org/abs/2606.09012","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.09012v1 Announce Type: cross \nAbstract: Post-training quantization (PTQ) converts a trained full-precision model into low-bit weights without task-level retraining, while quantization-aware training (QAT) incorporates quantization into the training loop. Although PTQ is efficient and often accurate at moderate bitwidths, it can fail sharply at aggressive bitwidths; QAT is more expensive but can often recover the lost accuracy. We propose a unified geometric framework that explains both PTQ failure and QAT recovery. We model full-precision training as following a low-loss \\emph{river} inside a wider \\emph{valley}: a normal neighborhood of the river forms a nearly flat \\emph{basin}, while leaving this basin incurs a sharp loss increase. When the quantization grid is comparable to the basin width, local PTQ objectives, including rounding and Hessian-based second-order reconstruction, can select a high-loss deployed quantized point outside the basin even when nearby low-loss qua","title":"Understanding Quantization-Aware Training: Gradients at Quantized Weights Bias to the Low-Loss Basin","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-09T04:43:45Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.09012"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:8ff233bbc2c16f6cfa8728242e13276bde524143b3ed8bb4c8cfd56abd5580010832bb2c87b2d4d8d5adfa7f5a44768dc10595d50fc29f6da8dc931402da8e0d","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.09012"},"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":"d7a15267206dba153b369a2198c5f1a99b56637042f13a16155ef24e501f73a3","leaf_index":224349,"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":"ad62d549513ad88fd5e86657f1b4e074c2086adeaa284c48d22da4a903632d39","side":"left"},{"sibling":"ac74433ed8e634b648f8e2716bbfadd60a375e3d72ab4c22b6825549e34ad3a1","side":"right"},{"sibling":"91c13b56a631414853369e97b1ba691af89d9846452b7a2e082f5af66c706941","side":"left"},{"sibling":"5615163b6288eaf3fcdcd26f2c07aa46af986319a662129f67ca217c11061ab7","side":"left"},{"sibling":"162c91f02f666728a41a78e6de0c530025602476120e1da8f2e989dcd892b0fc","side":"left"},{"sibling":"cac653fa1469e2ebd5ae32b3679c243421d80a3b155a89b34ff132a34528a8dc","side":"right"},{"sibling":"f0a492f36de5d4a50581f2f490a2e1704c68ff29d4b921f427506dbbc19159fc","side":"left"},{"sibling":"6aee4d57225362b2670992e69503217771be95795abcdc0a9d9022571196aa2b","side":"right"},{"sibling":"f6fb234a4e2f067b22329eec05b093a8b38f0411de9434d5a8eb55c2f70f1a2f","side":"right"},{"sibling":"b2df6a4bb3e928f0b447931cc688ae01d2415773a2b07cfed0b1cba689078aed","side":"right"},{"sibling":"b1c9ec856caa0fd46bb47b46f18c59ebcd295d774ca17adb3b46f05d394a6a5d","side":"left"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","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":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","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_3425c5838b7ed2814d97b9b80f7dd764f6064764cefc14231ca10b2bed347f6d"}}