{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_3bd46984136b4111b72a9e778542060ff7b1a47aa2bb4ef70e02bf857cddef02","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_3bd46984136b4111b72a9e778542060ff7b1a47aa2bb4ef70e02bf857cddef02","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"be84f87d327952bc45835aeec5bc29449379f7d3850cba04add17b7b9759d367","published":"Tue, 02 Jun 2026 00:00:00 -0400","receipt_hash":"be84f87d327952bc45835aeec5bc29449379f7d3850cba04add17b7b9759d367","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"be84f87d327952bc45835aeec5bc29449379f7d3850cba04add17b7b9759d367","observed_at":"2026-06-02T04:43:38.825628Z","parent_run_hash":"c2a9665c814770d56765bb764e6a6c7e4fa7d4e9708e157ca0f7440c89927d54","published":"Tue, 02 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2606.02133v1 Announce Type: cross \nAbstract: Non-monotonic sequence generation methods, such as masked diffusion models, provide a flexible alternative to left-to-right autoregressive modeling by allowing tokens to be generated in non-fixed and prescribed orders. Despite their practical advantages, most existing non-monotonic models are order-agnostic and rely on a fixed-length grid, limiting their ability to support variable-length generation and adaptive insertion order. In this work, we introduce a probabilistic framework for learning insertion order in variable-length insertion models. We formalize a bijective correspondence between insertion trajectories and permutations, which enables an exact reparameterization of the data likelihood as a sum over permutations. Building on this result, we propose the Insertion Process (IP), a stochastic generative model that jointly learns where to insert, what to insert, and when to terminate, trained via permutation-based variational inf","title":"Variational Learning for Insertion-based Generation","url":"https://arxiv.org/abs/2606.02133","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.02133v1 Announce Type: cross \nAbstract: Non-monotonic sequence generation methods, such as masked diffusion models, provide a flexible alternative to left-to-right autoregressive modeling by allowing tokens to be generated in non-fixed and prescribed orders. Despite their practical advantages, most existing non-monotonic models are order-agnostic and rely on a fixed-length grid, limiting their ability to support variable-length generation and adaptive insertion order. In this work, we introduce a probabilistic framework for learning insertion order in variable-length insertion models. We formalize a bijective correspondence between insertion trajectories and permutations, which enables an exact reparameterization of the data likelihood as a sum over permutations. Building on this result, we propose the Insertion Process (IP), a stochastic generative model that jointly learns where to insert, what to insert, and when to terminate, trained via permutation-based variational inf","title":"Variational Learning for Insertion-based Generation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.02133"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:9f85bed4cfd01da09378bea405f5bb1821e30149a70c2772489e9cbf1c43b0a4d4a587b0ea002cc64f5d5b5e2a48d11fd31cfa7c2f7360289a4fa0ed07c7fa04","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.02133"},"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":"326d9dcadee940bbb1796fecbf9b89005348ff1aa1acaff7d0ab9a7629ab82ef","leaf_index":205695,"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":"73c280e0b40e3d2b232a656e5750fb2e883c357e26cb52529832ceb15613e892","side":"left"},{"sibling":"21eaec56c02291867eb5cb6d250a5e4e1f8ef3d7bea481173c140e9f8382daa9","side":"left"},{"sibling":"f3ceb8f5f516fcd7f09eeeba52bae4992959c5d43db73197809a310517a4be40","side":"left"},{"sibling":"90f801f6c6a649b5773e01905f2ac0b29fcfdce2d9b814f6afe3d6b8283b4044","side":"left"},{"sibling":"b927a78a6585f00d5901b9474270bd5ce554ebc5598f59878ae487978e7327d3","side":"left"},{"sibling":"73683d003ac3b85f21a62294f19bc8c1dd0411bb470fae1584462f7d5938a116","side":"left"},{"sibling":"ed8954602c8dc2208f9836b8ffc4c53db7b272b0fd703c7c7d1edc5f7b9ace8c","side":"left"},{"sibling":"41924649fb2045a8eb1c76bcccd1d2cd8c7e0ab0bba7b07a79bf25a0c1677263","side":"right"},{"sibling":"21332ee1c3955bf1803955bf945ab0966ce5e0aa48d8642320cdbc044a72b935","side":"left"},{"sibling":"6620a5008acf732cd3e57b0f2d1437293e88366c2e5b175ebeb7d796fc1e0c62","side":"left"},{"sibling":"a82575bfb494af7afcc13aaae718afa6f74030f09d71b02819ea25efd4186fc4","side":"right"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"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":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","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_3bd46984136b4111b72a9e778542060ff7b1a47aa2bb4ef70e02bf857cddef02"}}