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We formulate attention recall as a spherical-packing problem and introduce Kernelized Linear Attention Activations (KATA), a framework whose feature maps are derived from first principles by certifying nonnegative attention weights through a self-dual homogeneous cone. Building on this observation, we show that rank-one positive semi-definite (PSD) features offer a favorable capacity--interference tradeoff. KATA recovers a parameter-free convex output gate and characterizes associative capacity through the Welch interference floor. For tolerances above this floor, KATA enlarges the state without adding parameters and admits spherical codes with exponentially many keys in the projection dimension. We implement KATA as fused Triton kernels at two operating points: a flash-attention-style forward up to ${\\sim}1.6\\times$ FlashAttention-2","title":"Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones","url":"https://arxiv.org/abs/2607.17419","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.17419v1 Announce Type: cross \nAbstract: Linear attention promises constant-time recurrent inference but degrades sharply on associative recall. We formulate attention recall as a spherical-packing problem and introduce Kernelized Linear Attention Activations (KATA), a framework whose feature maps are derived from first principles by certifying nonnegative attention weights through a self-dual homogeneous cone. Building on this observation, we show that rank-one positive semi-definite (PSD) features offer a favorable capacity--interference tradeoff. KATA recovers a parameter-free convex output gate and characterizes associative capacity through the Welch interference floor. For tolerances above this floor, KATA enlarges the state without adding parameters and admits spherical codes with exponentially many keys in the projection dimension. We implement KATA as fused Triton kernels at two operating points: a flash-attention-style forward up to ${\\sim}1.6\\times$ FlashAttention-2","title":"Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-21T04:43:35Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.17419"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:11033ed50ab717110759ba73edbc3d75560ca354bb29209027ec79451b649ef244652f25201638b825df384fe4d6dc44974c031156e423585cec8c6fbf975e08","signer":"crovia.substrate","subject":{"observed_at":"2026-07-21T04:43:35Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.17419"},"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":"04a463e1e96f34eb01b8e0d4913e693e2014232d6fe9addbb9ae587c44633ef8","leaf_index":336770,"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":"85b0ab4ae31becd4ced6d124b5423a7054076ed2ec58c9fb9a8085c06c9d1801","side":"right"},{"sibling":"9716d20d18de19e9fb0ee53ced582eed5ee25099a6dc66177c434b307a288e6f","side":"left"},{"sibling":"5f8902607f9cca8dc41e24347e73ae350fa9562e370884a0f402151f3e055c81","side":"right"},{"sibling":"8dcacf31bff7cffcfb6f97a83fcd6029cc694a37b1118e9e16462f3e646081b8","side":"right"},{"sibling":"e069ed1d9623dd116b05c3e191d49f40c1b3becf0d6dd593f3018ab458af4ff8","side":"right"},{"sibling":"52787d46cc76e7e83ec3a0eaa22f4ae41bb67c7960f5881f177b72a4199b9f85","side":"right"},{"sibling":"dae3e3795f6d531f6a2706d4e4f5a3367055dc5b4c40cea216b79f6a61941ab2","side":"right"},{"sibling":"90ee1b815719c44a83e23429473a176437135319947bc07c6e3752315a40068d","side":"left"},{"sibling":"bd233cee8c0876447824d86de33608c36e3a8e17dca0737155291ed768cf56d1","side":"left"},{"sibling":"7b927551b5db06b6571913b4e6792ffcce5291a3eca5a0df4a3b6e296271105f","side":"left"},{"sibling":"b77a0b5ae4607c8fe6ba73449d46b35076e3dedc0c82a2c65a05780d42a7bc2e","side":"right"},{"sibling":"9eb5077edfb3dc553857d4794b925bfce117e0f8a1d049af5d0dd9026b470eef","side":"right"},{"sibling":"414b1a70fd1dcb25489a194714b97492b066684b15d0b7a48a176c4b9b5bc713","side":"right"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"613f015699131eb89bd755dee67133be95af25cf5f16c1c8ce4b99d963b8dd86","side":"right"},{"sibling":"a729b574b1135956436ded5eef1fe8f08014ff6a0729749d307ab1bca93fcdc9","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"4bf21052e085e8ac81f1dec1d2b310bd12bf948992de6177d12e9d2fda8d39f0","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":337144,"merkle_root":"5e969cc01afa67e4dbe5d37b712cdb10f4aa1fd74404e02eab724cf487c8d6d9","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260721T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-21T05:38:38Z","sig_algorithm":"ed25519","signature":"5c0c1a8dd2793d787ccd5e49e8b4d70eed136352555518589f05c74be357fc171702e42a76c3a556d90e3d51ff36cb3d292aaac83c66566de7b943f318bda50c","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_e0439c75beb3a6996aa0b7e45133ae763b2b3d65943c3e39963c5c785388f8a6"}}