{"_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_7baee1a7a3111ee743ef9c814faeea744fb6445186e612e6b6fd767d9b94fb10","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_7baee1a7a3111ee743ef9c814faeea744fb6445186e612e6b6fd767d9b94fb10","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"d43fc5baca10779c24d852e7b76844d579e33fcacf2ad3023c54457433a39af5","published":"Fri, 08 May 2026 00:00:00 -0400","receipt_hash":"d43fc5baca10779c24d852e7b76844d579e33fcacf2ad3023c54457433a39af5","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":"d43fc5baca10779c24d852e7b76844d579e33fcacf2ad3023c54457433a39af5","observed_at":"2026-05-08T04:43:40.537619Z","parent_run_hash":"9837a17a0d4866b3bef2929e933ca29d96f4bd9656766df36f8260d720835b95","published":"Fri, 08 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:2605.05209v1 Announce Type: cross \nAbstract: Neural networks that land in flat regions of the loss landscape tend to generalise better than those in sharp regions. Sharpness-Aware Minimisation exploits this to improve generalisation. But function-preserving reparameterisation can inflate the Hessian of any minimum by two orders of magnitude without changing a single prediction. If the geometry of weight space can be manufactured from nothing, it cannot be the cause of anything. In other words, flat is simple and simplicity depends on encoding. Here I show that the actual driver is weakness, the volume of completions compatible with the learned function in the learner's embodied language. Weakness is reparameterisation-invariant because it is defined over what the network \\emph{does}, not how it is parameterised. I prove weakness is minimax-optimal under exchangeable demands, and that PAC-Bayes bounds work because they correlate with it. On MNIST, the large-batch generalisation ad","title":"Are Flat Minima an Illusion?","url":"https://arxiv.org/abs/2605.05209","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.05209v1 Announce Type: cross \nAbstract: Neural networks that land in flat regions of the loss landscape tend to generalise better than those in sharp regions. Sharpness-Aware Minimisation exploits this to improve generalisation. But function-preserving reparameterisation can inflate the Hessian of any minimum by two orders of magnitude without changing a single prediction. If the geometry of weight space can be manufactured from nothing, it cannot be the cause of anything. In other words, flat is simple and simplicity depends on encoding. Here I show that the actual driver is weakness, the volume of completions compatible with the learned function in the learner's embodied language. Weakness is reparameterisation-invariant because it is defined over what the network \\emph{does}, not how it is parameterised. I prove weakness is minimax-optimal under exchangeable demands, and that PAC-Bayes bounds work because they correlate with it. On MNIST, the large-batch generalisation ad","title":"Are Flat Minima an Illusion?","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-08T04:43:40Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.05209"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:68723358ffd62860269d662f472c5c50ed1d2a6f6fb6488bcf5aa9dac242de8c6d7b918ac75176f9221f23fca3a2ae747491039d8be773dc4512ffb6aefed00d","signer":"crovia.substrate","subject":{"observed_at":"2026-05-08T04:43:40Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.05209"},"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":"b9f85130f7d7ba68e230a0394b28e2ecb98f6de6c31f29bb478b40466bb22746","leaf_index":120144,"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":"47b7f2abfe988ffe14a0b1825ae231114ef1c536f1ce150b3a3b205a7804ba70","side":"right"},{"sibling":"7ffc853bec8f96c953f104159133e9b9b6461c0b1860c0b4546986d5eceb138b","side":"right"},{"sibling":"7e8c901b9a2e2c27d0256356eff75225dfcc039c1de3005d93cbd744005609d2","side":"right"},{"sibling":"06e2fc7934de0cbefb81373f07376fa684119b8f6ecc27ce218973c00fa7a4d8","side":"right"},{"sibling":"1f27017dbcf23f45626b4312401ddea08d92bf69f9d8c8df4a77405dd31e3ad1","side":"left"},{"sibling":"fe773cf8e22879373eb1acd8f4c6b5370e5c5117aa2b8e9356b5cb27d86da11b","side":"right"},{"sibling":"fbc97c8ffc4e0529c02cda4ab186b044b09b474182fb9fbd8e687b59c97e08b2","side":"left"},{"sibling":"b1a469ecc2c62da181fb78fb052d1f4d059aafbe92dbb6d04682090381d419fd","side":"right"},{"sibling":"34e93c6f591cc4fb93a4c29771210eb73573b454d2c5329963f437f1309fe46f","side":"left"},{"sibling":"b9834433f5bd1deeaab4ced2b3bcc0d91d19763a5d0981fb299d124b63459eb3","side":"right"},{"sibling":"143f33d3924b3840fd6dd8ba12566fc35bf86189e663ef0ad4884d676f295e3a","side":"left"},{"sibling":"b1ed99341c327c7c9ab2489f40af2547ab3b3b4b6a74fb684210164fb891a413","side":"right"},{"sibling":"6ee3be9bdfc9bee55d32f7dbb0075f02fe87d20887d563d3e300caf36b1b88c7","side":"left"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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_7baee1a7a3111ee743ef9c814faeea744fb6445186e612e6b6fd767d9b94fb10"}}