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We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, developmental grokking, and collapse. A near-transition logistic fit localizes the memorization-to-developmental boundary at $\\lambda_c=0.0158$ (95% CI [0.0109, 0.0200], N=210); a power-law fit gives an empirical exponent $\\nu=0.757$ (CI [0.725, 0.799]). Reference exponents $\\nu=1/2$ and 3D Ising $\\nu \\approx 0.63$ lie outside this empirical CI under o","title":"Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics","url":"https://arxiv.org/abs/2605.20441","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.20441v1 Announce Type: cross \nAbstract: Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, developmental grokking, and collapse. A near-transition logistic fit localizes the memorization-to-developmental boundary at $\\lambda_c=0.0158$ (95% CI [0.0109, 0.0200], N=210); a power-law fit gives an empirical exponent $\\nu=0.757$ (CI [0.725, 0.799]). Reference exponents $\\nu=1/2$ and 3D Ising $\\nu \\approx 0.63$ lie outside this empirical CI under o","title":"Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics","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/2605.20441"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:24988e2d4d7ca9faae2909f9d1167f67aa5a80fa29fdea2cbf0ed25de616b3ba54fbf750ed877f71ba8787d0c84f82efa0131eec457a676c6976180a9055960e","signer":"crovia.substrate","subject":{"observed_at":"2026-05-22T04:43:12Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.20441"},"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":"cbafe6a9fe86b06af752341286113956b1b4386ae3a4c4bd9d92fcb29cdb357f","leaf_index":148226,"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":"2f8a9f6c19c6488932e673db3e8a5c526f55e99fc297ebe8e9a9e68957a1703d","side":"right"},{"sibling":"86d05f8510b29f462300711b2af2ff0e33b47098b8ff277b34be7e783f22806a","side":"left"},{"sibling":"79c7b1d262fc0490e56c81573d4ea23a324671c069e68a9f660def56087f87a5","side":"right"},{"sibling":"0af8501851a7ffee74657e8b9dcbf1cdf54ef84af8ca15de20634bf6ce588d85","side":"right"},{"sibling":"4719d72db3535b04c69a3b1a92eaf8b76e4ae41300132f462730e0f36d72e2bf","side":"right"},{"sibling":"0cdd6f74518a78e2d51c6d1c6d14d0688bc4da61583f7df49842f7924f36305e","side":"right"},{"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_4be6e6a2502dece9c02fa498d7eeb85573bcbd2fe1ec904488044f0a07a486df"}}