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This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient $\\kappa_R$. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from $1/4$ to $1/2$ as loop count grows at fixed physical depth. The resulting method, \\textbf{DeepLoop}, keeps the Post-LN DeepNorm architecture and sets $\\alpha=(2N)^{1/2}$ and $\\be","title":"DeepLoop: Depth Scaling for Looped Transformers","url":"https://arxiv.org/abs/2607.13491","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.13491v1 Announce Type: cross \nAbstract: Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters. This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient $\\kappa_R$. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from $1/4$ to $1/2$ as loop count grows at fixed physical depth. The resulting method, \\textbf{DeepLoop}, keeps the Post-LN DeepNorm architecture and sets $\\alpha=(2N)^{1/2}$ and $\\be","title":"DeepLoop: Depth Scaling for Looped Transformers","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-16T04:44:04Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.13491"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:6106cd3f450245605c73f6ba755076ee8c0579f0ef4817c7afaa8f56ddb1e4854f98765de55ef4b870cce5d973d9020104fa198d291254998c7db6a988b77209","signer":"crovia.substrate","subject":{"observed_at":"2026-07-16T04:44:04Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.13491"},"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":"1de697e39505d26c3519d992879bb4fc1df5c3ea8082e826a12ee5331330f8e7","leaf_index":319837,"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":"e9e737f449866fd8bbf12681939cce14521eff9835bcb3c825205c4d68101f3c","side":"left"},{"sibling":"cc6a6d52f7e4c600495dcfeb0df568c4aeb5a28faa1e9f9c6cc36134c76d342c","side":"right"},{"sibling":"ec7011ef44693aba0274ed60e481676556f34beda4ab52b884a6a986834a2931","side":"left"},{"sibling":"6f5d0031f2240673e3a127853e4e9c530b1412f000d6ed01f3a4293715224f26","side":"left"},{"sibling":"0a0b942f846b9605e61fa96d154bb8f3a77c10e55695a5b38993290f481f4684","side":"left"},{"sibling":"d4883068a918de3912db61033720014f921694c62ea82aab5e7e249915b74ffd","side":"right"},{"sibling":"2c7004d4be02967141b4e5609671d597ca4f0e246e61da911ae67ca20ab6e7e7","side":"left"},{"sibling":"ec3fec9bb698cfe3c65d9f75111532c318eaa7e7c5b933ded046cea471e330ab","side":"right"},{"sibling":"929619d7bb5abd9d4c015f749565f8d43a371ed382bafe122457d67edb9b8323","side":"left"},{"sibling":"1290775fa2a1fe2079ed83a9c60b8cb479714b6312967daa62f6a91dbbe1cac9","side":"right"},{"sibling":"95977bf2fb44d423026e874e6c275f78b1cf48666d2c472c5e4603d16f4faf7f","side":"right"},{"sibling":"6b83879fdb76b5b7270071f1edfe4d1a059fa9b92653e70fc8c8893214b8f237","side":"right"},{"sibling":"ff49c1d8749b258f58cc33cfaf20d723098ed6860fb62a6779db960d6250915b","side":"right"},{"sibling":"34d85f6ad6cc7dfa79d90e2b9ff99a561bcdc75b0301bbbd3e83861f54535c1e","side":"left"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"3ee6ab8db1878db0b324dd807ca233edd472899b8e90d2c5e018848ea5d12d99","side":"right"},{"sibling":"73a8d1605c15a74de720f0c54b5b4567e3eb8b5999bd8812dc66eedc461540fa","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":320080,"merkle_root":"1e159bceacfdb1f3c930dae410f8759ddc4c762abcfa4a257b150d6f44ab16e0","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260716T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-16T05:38:31Z","sig_algorithm":"ed25519","signature":"c1cd1fc5704d4fec4dee47b29a0e9877f8cfb41eb61dcfd783d82344a15f6e44d80d6cd5128849547b62fe9d9724fc71433319ab6030445b4ac1c9e6bf8a3709","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_cd840d6b1bbf4fd9a2bd9edbf62f169a41be1498663323c8acc408eb53292a37"}}