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We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $\\beta_n^\\ast \\asymp n^{2/(d-1)}$ for uniform keys on $\\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across all regimes of $\\beta_n$: a subcritical regime in which the output reduces to a local average around $q$ with explicit deterministic bias and Gaussian fluctuations; a critical regime in which a finite collection of nearest keys retains macroscop","title":"Scaling Limits of Long-Context Transformers","url":"https://arxiv.org/abs/2605.08505","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.08505v1 Announce Type: cross \nAbstract: We study the long-context limit of softmax self-attention with a fixed query and a random context of $n$ i.i.d. keys on the sphere, viewing the inverse temperature $\\beta_n$ as the scaling parameter that decides whether attention degenerates into uniform averaging or collapses onto the single closest key. We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $\\beta_n^\\ast \\asymp n^{2/(d-1)}$ for uniform keys on $\\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across all regimes of $\\beta_n$: a subcritical regime in which the output reduces to a local average around $q$ with explicit deterministic bias and Gaussian fluctuations; a critical regime in which a finite collection of nearest keys retains macroscop","title":"Scaling Limits of Long-Context Transformers","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.08505"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:43fce19188668dd7c20eca492aacb6247b364177db1396536cc453a350c1418c6bef51d25790c7f17e91c0ae67ad7439c44cbdec13a611ac74c11f72bc088a07","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.08505"},"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":"07dcf705e48aa30646a43c0341891d89f7a1a81d7182cef6bc8bc0d864f9d74d","leaf_index":128584,"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":"be05f4fdc9a3e70e154ff95ed2ce2aee6710d5e699768c7507ee64a9c424ff84","side":"right"},{"sibling":"dc68e3971c3b7fd8f6e8fd9514994bb07f35d17c2e3f0ed7bdfd0507b6db6c6d","side":"right"},{"sibling":"43aaea701642b34494c16d7a7ec0e8474a8b8c09dcac50753aa8810018522279","side":"right"},{"sibling":"9764675bbfc8f627ff8a90a50b08c7055edae9b4d8339e90d92b434a906645b0","side":"left"},{"sibling":"16789e966e0cf4544982b59006793a26843ccba25fa4aa6ed5b3e341ce969671","side":"right"},{"sibling":"dfd38390185abfa793e2aa7dcb95cb915b04addc87e066e6ca0990d3618463e4","side":"right"},{"sibling":"ba60cf3cfbedfa4be8e552df69fe9f00d4748fabd7f2f1d5098bfd63cd558f19","side":"left"},{"sibling":"2be4781bec47f25a197c8a3d5b3f30a3d2f2d1517add8590753a933d122c2b40","side":"right"},{"sibling":"831b04b4dcc29bcff4577c406291bc4f644057b650a55f064d46d1cab5185326","side":"right"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_4d2bc9504ca0cc903f9d8563e60c1ea4aa5c2dce9b08677d07ed4ccab1345f17"}}