{"_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_41be3bfe4963aac3b6c87f37e7cb3942fe5c0466419bccf9459f7a24bc668eed","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_41be3bfe4963aac3b6c87f37e7cb3942fe5c0466419bccf9459f7a24bc668eed","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"5692682baeb05a4b270d85e95b55756d9ed4466ad010a9202a7033061c78c5a9","published":"Wed, 22 Jul 2026 00:00:00 -0400","receipt_hash":"5692682baeb05a4b270d85e95b55756d9ed4466ad010a9202a7033061c78c5a9","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":"5692682baeb05a4b270d85e95b55756d9ed4466ad010a9202a7033061c78c5a9","observed_at":"2026-07-22T04:43:18.261256Z","parent_run_hash":"4765c85b8b4b27ff9a690c1ae11c3b009baa2c60297295f395ad422f5afed68c","published":"Wed, 22 Jul 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:2607.19195v1 Announce Type: cross \nAbstract: Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also evaluate the disorder-averaged ground-state energy of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact full-retrieval threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.","title":"Free energy landscape of Dense Associative Memory","url":"https://arxiv.org/abs/2607.19195","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.19195v1 Announce Type: cross \nAbstract: Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also evaluate the disorder-averaged ground-state energy of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact full-retrieval threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.","title":"Free energy landscape of Dense Associative Memory","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-22T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.19195"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:ae0863fe84e34e0328db1f2013c719647c97d4ecd1d4bda43b5d894a9770114d08b65000c5a1959fd612318639692dfd741ab168086d525e57059fae94cf770c","signer":"crovia.substrate","subject":{"observed_at":"2026-07-22T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.19195"},"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":"277fe4cada41fc544eb23c71ef30e06f88ed497ccf43ca18a8ae46ee8806384b","leaf_index":340308,"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":"52d090363385e784cd7955027f94e99c3658eec1e87ce0da6d362d5d5ce70e4f","side":"right"},{"sibling":"f8b13ce97cd89f12d86a833ef2d07fc0550acdf9202dfff4538f1c398324a6f4","side":"right"},{"sibling":"6c3c13e298bc371554d495296efa852bd019a84add04b21826db7e724bf800f6","side":"left"},{"sibling":"799a468cb1b087944c1958e0474a84cfa82ac1786c16784db6f07ae8065878f6","side":"right"},{"sibling":"157a627527ca4d12abc26bc4abc9d251ab527f1a4792cad8004adf2fc4c59ec8","side":"left"},{"sibling":"0de8da1e8d6ef3da84ec6c8780b70947348e1224350d02d828d431c146f09d95","side":"right"},{"sibling":"8802f296fb33ebb1f95ce56604f2c35b5365467e892c99b8d3e26d404adfa3df","side":"left"},{"sibling":"617d94b8a1da646ac45b4d986747eccb1604c294cb2a78b6cf4c70df505a76f4","side":"right"},{"sibling":"99d4b7aea5e7c917c580af0f1a9556bbd4d44f3f36cf9391892e7ef0340a8258","side":"left"},{"sibling":"c7fc9d4187cdc36f4c03b4b13daf4b880ea65536b051f71a5cc2543839d02697","side":"right"},{"sibling":"1758ec6ac206ce40e8368cb702195322fe3737d0fb03d8bd9e3b30acc4fa7d81","side":"right"},{"sibling":"0c407f0d553cf3fab8f9bd79205b8180e090cbf29fa0490ebb55155041ad5c86","side":"right"},{"sibling":"2dd9cb2521044ee7c6b74f2315e0a0253b8df0d04a7b810bbbbe7da5a9788769","side":"left"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"787ee3744642ff909d610b0514cb100784f0ef1ba0ef4c70a0dc91f0ab2bb192","side":"right"},{"sibling":"9fc8a8ebbc1bff7e62b9f1e1c681c91e7196092ce9551573df6e23096df13e4d","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"ee6f33920899d9bdef2eb706dfff29e26eea61e29ea9824c6c8e6bcd48275d76","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":340557,"merkle_root":"7d45d94f20b5bf82263df45b87749e19e06161972f25141dd573cc138d566338","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260722T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-22T05:38:39Z","sig_algorithm":"ed25519","signature":"812cb61e90d3582ba508db8515c4168bbf8ee1c6762885609049d012f680f8068f15c98b9accf2042047dcfc6a6fc3885820ee34b0be350846386f64f2591309","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_41be3bfe4963aac3b6c87f37e7cb3942fe5c0466419bccf9459f7a24bc668eed"}}