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This is possible because attention depends on $X$ only through the products $XW_Q, XW_K, XW_V$, allowing basis transformations to be absorbed by adjacent layers and propagated through the network. We replace $W_Q \\in \\R^{d \\times d}$ with a nonlinear residual of the form $Q(X) = X + f_\\theta(X)$, where $f_\\theta$ is a bottleneck MLP with $d^2 + O(d)$ parameters. The identity term anchors the nonlinearity to a known-good prior. Experiments on GPT-3 small style models show consistent improvement over the baseline ($2.40\\%$ lower validation log-loss, $6.81\\%$ lower perplexity), comfortably outperforming a model with 12.5\\% more non-embedding parameters. These results motivate investigation at larger scales and across modalities.","title":"Beyond Linearity in Attention Projections: The Case for Nonlinear Queries","url":"https://arxiv.org/abs/2603.13381","vendor":"arxiv_cs_ai"},"summary":"arXiv:2603.13381v3 Announce Type: replace-cross \nAbstract: Recent algebraic analysis shows that in decoder-only and encoder-only transformers, the Query projection $W_Q$ may be set to identity without noticeable performance deterioration. This is possible because attention depends on $X$ only through the products $XW_Q, XW_K, XW_V$, allowing basis transformations to be absorbed by adjacent layers and propagated through the network. We replace $W_Q \\in \\R^{d \\times d}$ with a nonlinear residual of the form $Q(X) = X + f_\\theta(X)$, where $f_\\theta$ is a bottleneck MLP with $d^2 + O(d)$ parameters. The identity term anchors the nonlinearity to a known-good prior. Experiments on GPT-3 small style models show consistent improvement over the baseline ($2.40\\%$ lower validation log-loss, $6.81\\%$ lower perplexity), comfortably outperforming a model with 12.5\\% more non-embedding parameters. These results motivate investigation at larger scales and across modalities.","title":"Beyond Linearity in Attention Projections: The Case for Nonlinear Queries","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-27T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2603.13381"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:fb18b499618adfb841e3b6c8815069cf87d18a6e1382720b99fe38ba78b47775c91fbb265600f8fa7bdb19109b872108a04ac2f738c8954b8b12fecdec78ba07","signer":"crovia.substrate","subject":{"observed_at":"2026-05-27T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2603.13381"},"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":"86d3c193183296948539bd8e0bd54b8883809bed741744ca3086be54de1f1f03","leaf_index":153951,"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":"b7d886601654b50e99706c063a7a5a9fbfdd7319ffc9078b3697e41d756f3395","side":"left"},{"sibling":"64d14c4ef9772a059504ea7450dd6390d14d0709fb9cacc8d7c06355913660e3","side":"left"},{"sibling":"ddce5014258b8bd8067b68c922e79980e12734ae7245c123120dff3af79053c6","side":"left"},{"sibling":"a3dff76b8a1eb944e16384e3feb20b118a787fe86a89847a5502e20311ebee7d","side":"left"},{"sibling":"0cfa6720105604b2f0e8d0ae49819565f5d186b28dc7515bab2652690a2fc764","side":"left"},{"sibling":"377536273325dc128b57510786f76e46ea56a372fbd6530419421c956176a81f","side":"right"},{"sibling":"bc35d95b20384bcefab067b00429ecc07965f080c071ee591082cba7c0f219a2","side":"left"},{"sibling":"16c794666e8ffc4b9e71a0bacc0e4f9bbc68a8544c340b385c6d1abff1d748e5","side":"right"},{"sibling":"c14a4eb4b07d22a6a83f548cf6c304559dc63f0e53071e550ecc566dbba50b14","side":"left"},{"sibling":"3165125427a29042fc9d02858a59a68858dbdcb2e19d1afa5f6dd6a95cfbce6a","side":"right"},{"sibling":"04b9a68b8ec6fa37251564383c685c23ce69e5e031df4eae69f79a3a334b68bf","side":"right"},{"sibling":"816f233274bb10f5a122aac086a0c8c697b78fec67a4af55190bb596b7506fab","side":"left"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"374c02d15fb12bd356c179c94766043a982052c6132af8bfc15361b431ffa9f7","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"990705096edf483cc877217308f731dc42d6f6d99f82880167bbdbbfef32560a","side":"right"},{"sibling":"dd265753d95fa2e2fb4f5768e37fab6f691ccff09ad60d0910ff7dc23bac9226","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":154065,"merkle_root":"4993cfdc172e7880b60667f16789dc2e831ff000f81bb1ecba248e73f1510eca","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260527T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-27T05:37:36Z","sig_algorithm":"ed25519","signature":"76ecf118011540405e96506e6219752df04a2850632f2903dc6f10e08b98bc5a42c8d9e1cb5b7c5bf714479806a403df5f34399afa40c23fbb71493a1f77bd0c","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_fdd60230cf2a295d3c99cef5aff79118322626d219423f866914f884cccdc08a"}}