{"_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_89265602e71c79d91a1e2358889e374b330ccd7104083da4642583ca4731c582","bitcoin_anchor":{"bitcoin_attestations":["bitcoin_block_949451"],"calendar_attestations":["https://finney.calendar.eternitywall.com","https://btc.calendar.catallaxy.com","https://alice.btc.calendar.opentimestamps.org","https://bob.btc.calendar.opentimestamps.org"],"ots_url":"/registry/data/substrate/anchors/77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3.ots","stamped_at":"2026-05-15T03:00:03Z","status":"bitcoin"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_89265602e71c79d91a1e2358889e374b330ccd7104083da4642583ca4731c582","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"bffc66e0124669e7a2bc404b9832a001dafe7779d2b604ace7aa9fd24d2ce2ee","published":"Thu, 14 May 2026 00:00:00 -0400","receipt_hash":"bffc66e0124669e7a2bc404b9832a001dafe7779d2b604ace7aa9fd24d2ce2ee","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":"bffc66e0124669e7a2bc404b9832a001dafe7779d2b604ace7aa9fd24d2ce2ee","observed_at":"2026-05-14T04:43:36.462865Z","parent_run_hash":"eb105e641aec4518c665fb1a0f748c2a8c8189675990bd4092425661eb7af1d8","published":"Thu, 14 May 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:2605.12940v1 Announce Type: cross \nAbstract: Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous depen","title":"The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models","url":"https://arxiv.org/abs/2605.12940","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.12940v1 Announce Type: cross \nAbstract: Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous depen","title":"The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-14T04:43:36Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.12940"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:3278e99fc6c00d3619bb88fe26ba7b5be92b8222a486ec12c5c161966fcb2f9c6ddb560dc31c0a13f66c8e4ef29e98acdf7151d438d9c4ab64b22a35b0f83604","signer":"crovia.substrate","subject":{"observed_at":"2026-05-14T04:43:36Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.12940"},"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":"0656cd338bd7c92a6b042e74edaa9f2f1c1918968cb43c62d409752bc82c07ff","leaf_index":132566,"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":"9c623ebbffaf2f80de47da93a686d03b35e7ec4c8a84dc68754aa70760970344","side":"right"},{"sibling":"818dfbbf0e72b1c160a0b201dcb5e5134bf25d18c1b669d9ab00d499ed9d1eb1","side":"left"},{"sibling":"ff51b4fb15284ce926be0ed13b641c5fcf0ae56eae1f34b4e9f84d64b124a562","side":"left"},{"sibling":"4937e036e3a177e543d0201cdc7ee6ed05b543db6e498359ed1c8e88ad46133b","side":"right"},{"sibling":"f068c3b6dfe550506abbaa8154bd3d13018b6afddd191747c40432e5e870c543","side":"left"},{"sibling":"b73ae76f14bffb2d8b88fbea95caf35a45c2c7a4bdab30329c97fbcdcbd21dd6","side":"right"},{"sibling":"5c93e75b7ee6b7c15dd4ccfeb2ad5773606f9e202ac37c66e6cfe32ca75f287f","side":"left"},{"sibling":"5481966fbd92dc66ec8b3fff9fc4dcddbff0f35b3e0cafc74158f753d7858d6b","side":"left"},{"sibling":"ed110cac74740161e005dcd47c35637ac99ecf93121b3961837570c3af56caa0","side":"left"},{"sibling":"2270188e7d95b52d2bade0ab7da2d0816592f30757dcf71636f21b8f46eb1317","side":"right"},{"sibling":"c03f0a468f574a08ffe8b17e1a17bd88216e1359f0e33a54447e160cd8675da0","side":"left"},{"sibling":"038ff12da6f55509125ef0d96e1e57dda29a2fe63bf03fba2af4cf7cbcd88b36","side":"right"},{"sibling":"b0419206fe62ef216df3900ca93cffd44df267435a4643dda354c1310079cf91","side":"right"},{"sibling":"0d4a9c03674f9d0ce64df15c15e9f656a54b41f93c428aac8e615fda26291956","side":"right"},{"sibling":"7856d920f3f1f1d2194c1ed7351bf0d674440df3cb423a6911f89cb3e9578c0b","side":"right"},{"sibling":"6ac6396bdd2e9df315427a46155531476e7f9012b4bd962e0d2d6d1209b11723","side":"right"},{"sibling":"7c8dc85cbfe43e19ac759ad176cfa11dba2467ae17927c471d5c55663c4f490d","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":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_89265602e71c79d91a1e2358889e374b330ccd7104083da4642583ca4731c582"}}