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In this work, we study GLU by analyzing two-layer networks in the neural tangent kernel (NTK) regime. Our analysis reveals that the GLU structure reshapes the NTK spectrum, leading to a smaller condition number and a more compact eigenvalue distribution. Building on this finding, we further analyze the resulting training dynamics and show how the reshaped spectrum leads to faster convergence of GLU models, including a characteristic loss-crossing phenomenon observed between GLU and non-GLU models. Finally, we empirically observe that GLU has limited impact in reducing the generalization gap on various models, including ViT and GPT-2, suggesting that its primary benefit lies in accelerating optimizati","title":"The Devil is in the Condition Numbers: Why is GLU Better than non-GLU Structure?","url":"https://arxiv.org/abs/2605.20749","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.20749v1 Announce Type: cross \nAbstract: Gated Linear Units (GLU) and their variants are widely adopted in modern open-source large language model architectures and consistently outperform their non-gated counterparts, yet the underlying reasons for this advantage remain unclear. In this work, we study GLU by analyzing two-layer networks in the neural tangent kernel (NTK) regime. Our analysis reveals that the GLU structure reshapes the NTK spectrum, leading to a smaller condition number and a more compact eigenvalue distribution. Building on this finding, we further analyze the resulting training dynamics and show how the reshaped spectrum leads to faster convergence of GLU models, including a characteristic loss-crossing phenomenon observed between GLU and non-GLU models. Finally, we empirically observe that GLU has limited impact in reducing the generalization gap on various models, including ViT and GPT-2, suggesting that its primary benefit lies in accelerating optimizati","title":"The Devil is in the Condition Numbers: Why is GLU Better than non-GLU Structure?","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/2605.20749"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f1c96303e95f775cafe37cefcb326de0f1c5efc57740d1a256a3a8fc86b132cf25016f09cce1b7f614a1b5d087ae00230eb96b4b090920c874cf6c4b47cc2303","signer":"crovia.substrate","subject":{"observed_at":"2026-05-22T04:43:12Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.20749"},"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":"8bff4852cbf15c558d7efb8be97fc0df95c145d04a87ab140aca8c6bae3d78fd","leaf_index":148274,"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":"4574a19e69f92e763606852a77374a91268fba827d8afdbe461131f90edb3c43","side":"right"},{"sibling":"36cbcd513c2f7f62b2d9ba59b51a782f5129030cc96bde9b619b1b5d575af9de","side":"left"},{"sibling":"dbd477dd71420c4956a9aa3d7ddd66427895641ce9ebda7a25adcba3d12dc1cd","side":"right"},{"sibling":"cdd13c7d0540d5cf55aea6b4c9eabd871b89164aec54bafbafbed691b1551e55","side":"right"},{"sibling":"72cb6ab85fdc3521f06566960af6c2b322cde3e155bd16642c5df8f0b46a050a","side":"left"},{"sibling":"0e7e1f05ee2c16785b52fffc9d8a81fa99a3ecbade13700862d5e65f6d4b80a2","side":"left"},{"sibling":"2f67ce1ca4d405b588b0534baed360bc76fbba6b3678854914e0889a47207afb","side":"right"},{"sibling":"0fa191199f785899b5cc0f48838a3ffb2aa741ddcd9510fe1664869d36a8d31a","side":"right"},{"sibling":"e6aaada16cbe58b790855c6723700fd07821cc6df59048dc470d404b1ba60842","side":"left"},{"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_b0b4e715c4559eabadd40ee0dbe01b0b2965ba12791d1f47d1e986481d373500"}}