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Whether the weight norm causes this delay is disputed: some studies report a critical norm at the transition, others observe grokking with no fixed norm at all. We settle this by intervening on the norm during training rather than only observing it. Under free training with weight decay, networks grok when the weight norm reaches a value Wc that varies little across seeds and learning rates (CV 1 to 2 percent) and grows with the modular base as a power law. When we instead clamp the norm to a fixed multiple rho of Wc and hold it there, the network still groks, but the delay follows T_grok proportional to exp(alpha rho). One exponent, alpha near 7.5, fits this delay across four moduli (R^2 = 0.996). Over the swept ranges the held norm moves the delay by about 19x and the learning rate by only about 2x, and holding the norm ","title":"The Weight Norm Sets the Grokking Timescale: A Causal Delay Law","url":"https://arxiv.org/abs/2606.13753","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.13753v1 Announce Type: cross \nAbstract: Grokking is the delayed onset of generalization in neural networks, arising long after they fit the training data. Whether the weight norm causes this delay is disputed: some studies report a critical norm at the transition, others observe grokking with no fixed norm at all. We settle this by intervening on the norm during training rather than only observing it. Under free training with weight decay, networks grok when the weight norm reaches a value Wc that varies little across seeds and learning rates (CV 1 to 2 percent) and grows with the modular base as a power law. When we instead clamp the norm to a fixed multiple rho of Wc and hold it there, the network still groks, but the delay follows T_grok proportional to exp(alpha rho). One exponent, alpha near 7.5, fits this delay across four moduli (R^2 = 0.996). Over the swept ranges the held norm moves the delay by about 19x and the learning rate by only about 2x, and holding the norm ","title":"The Weight Norm Sets the Grokking Timescale: A Causal Delay Law","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-15T04:43:09Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.13753"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:07fb5646e908d942d410107cac54c2c6c529c3746e85c1bc9828e215de46a737eff0155b029f97e2a8a089738d34f00494bf4b970f3c567df03f136eae819206","signer":"crovia.substrate","subject":{"observed_at":"2026-06-15T04:43:09Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.13753"},"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":"50192b511698aa0e92f2674b572703c852b95f82e05e50ba93f914de3ccbcc33","leaf_index":229981,"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":"39018bd8162e26b9e42382cc428eaa7c0e5d94de0bfaa866ffe63ba0578d25bc","side":"left"},{"sibling":"e84995f582df8c87104961107b6dedb1078f8b4683ead61bfd99ae7d5d3b243d","side":"right"},{"sibling":"8a42379c387367b92c47709ebe7eef9171349652ead2f483880cfd1b80a6d431","side":"left"},{"sibling":"f0eedacd9cf641accfd0aa827c26ce1ef6f2714a78201f1d1152841ed9627437","side":"left"},{"sibling":"79745845703aa924ba647345d1751e4bd3b7cb562e18080d7c93d8b2a99d2fa0","side":"left"},{"sibling":"861237052056050d2c3d73bb49e6445a4c553842a8208d157d0049c55f967800","side":"right"},{"sibling":"117727e77823a42d7a3da4dfbc182b574e2d826f75958c69340ae784488a0cfe","side":"left"},{"sibling":"bc1002bb7e3da047b8a7c8f3990db61fb56edf499868605dc0c31aa0dee387b7","side":"right"},{"sibling":"14c50c43949e1ad41f149ffea691627d3f715c5861766c693b9fbac9d03b0d90","side":"right"},{"sibling":"74897e850164dddc689c3c65b33f9bae0268ab0bf429867a4e193d9b9b685040","side":"left"},{"sibling":"bde25d7e94e64717e426a97f6fcb4907e92b5c61fc89d92d7e0947a2249c3f6b","side":"right"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_845060adf1098a41c395062c7b7d22ffd8c1847a46a47f1218e0cd0c567399d9"}}