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In this paper, we show that this nonlinearity can also be achieved by input-conditioned threshold gating through branches as a universal primitive. We demonstrate that standard activations -- whether piecewise-linear (ReLU, PReLU, Hardtanh) or smooth (SiLU, Sigmoid, Tanh, GELU) -- are in fact instances of a single Threshold Gating (TG) primitive. For softmax, we show that it admits an exact TG conversion via its equivalent per-element Sigmoid form. We then validate these equivalences by converting pretrained networks across CNNs, transformer-based models, and recurrent architectures, preserving model performance without requiring retraining. Threshold Gating also enables training from scratch that goes beyond replacing existing activations, enabling gains in model compression, perfor","title":"Rethinking Neural Nonlinearity as Gating","url":"https://arxiv.org/abs/2607.03148","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.03148v1 Announce Type: cross \nAbstract: Activation functions are considered an essential primitive for neural nonlinearity, i.e., they enable neural networks to serve as universal approximators. In this paper, we show that this nonlinearity can also be achieved by input-conditioned threshold gating through branches as a universal primitive. We demonstrate that standard activations -- whether piecewise-linear (ReLU, PReLU, Hardtanh) or smooth (SiLU, Sigmoid, Tanh, GELU) -- are in fact instances of a single Threshold Gating (TG) primitive. For softmax, we show that it admits an exact TG conversion via its equivalent per-element Sigmoid form. We then validate these equivalences by converting pretrained networks across CNNs, transformer-based models, and recurrent architectures, preserving model performance without requiring retraining. Threshold Gating also enables training from scratch that goes beyond replacing existing activations, enabling gains in model compression, perfor","title":"Rethinking Neural Nonlinearity as Gating","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-07T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.03148"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0e425ebaf7f9b89e79d5ee9face37a99d66d9e84b014b3c97545c51db9d1ba39ee7dd92f15a3e52da3558254ea2ff48b0780f305bd0ab920f2b1d2186fc98d06","signer":"crovia.substrate","subject":{"observed_at":"2026-07-07T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.03148"},"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":"baeb5a4f186abae98df36ccd6e870b63e8817bf885c5442a4e60da899c0576b2","leaf_index":288897,"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":"143b5569921510047be90229df097be596b164a82802947f8228bb7e80941d02","side":"left"},{"sibling":"b7abc016bde3750a9a16c665299b6f2d9b4f8b7f967b6625ea82518b8b597bc1","side":"right"},{"sibling":"c5ca31eee13fba34e9b680740c3c3dee8d88dcb4fd05e5eb3a4e687ca4214687","side":"right"},{"sibling":"9d26e6e7be124436bd4ec9e65cb12872b92859a02465f8e61adc3ffcf580b280","side":"right"},{"sibling":"2e58089caf7f1db1aa460c4b6c14253f3d1a529584541dfdf03beb7165621963","side":"right"},{"sibling":"8cbf75eeadb066c37f24fe8ba9fb81dfedfc0de4f722cb8e2a8b6db86c087934","side":"right"},{"sibling":"b234297839b708da55a19049dd232521d12e8204fc98edded13d91a03a53d90f","side":"right"},{"sibling":"e2f3465fc74f48bb335c248143b3811c6e2bffa1b6671301e8a48cb5569a68db","side":"left"},{"sibling":"1fe4f74c7ddb4bf1f3105cee6c2413b68972083840bc89ce8e21eddb44153505","side":"right"},{"sibling":"841129c21a7583176cdc7de281cadfe0e00d04673461e199760cd5128d8cc2d5","side":"right"},{"sibling":"19d6dfd29bc47f35fa02e8fe765277ba9cc3e6da5072309f24ebaac5b5f295e3","side":"right"},{"sibling":"8e0ad7889eb2d4b40e5b6c3d8e2eb19d4e202374983f468aa76321823de07a9f","side":"left"},{"sibling":"aae716235efcb893a1f219dbcd5095070d08a497769fc6d50c14976aa26d5750","side":"right"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"1b72ad8d12164fdf329e7871711be99d8569d140b21f94056e6962da21da9ce1","side":"right"},{"sibling":"5f5109c2bfdcc7a7e70554bba25862e2d7ce86b6b0cd48a72eb66d2eb735f321","side":"right"},{"sibling":"05fd8a05dddb2e7f72bbb5b290ca55c378f1aed709f132277908d9a5f30eb605","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":289613,"merkle_root":"dc428b9d9ba248d4f93f63147bf7c700bf5be7f500cec6c3507b9df6e9401601","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260707T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-07T05:38:15Z","sig_algorithm":"ed25519","signature":"c468b0e183383ab71992be40bda451093e6cd8cd8efb0d26f68e135a804b287c209d12a0f4fdd95c69c835c04b78df8cb1903dee1f53d4730b36f5332a29fe05","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_39c296467df8e5dc3464fb028dbb756b9fb39f2eb6e6247647eaba172ee1d51e"}}