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The prior remains the standard Gaussian. Before VAE training, we select a fixed teacher posterior from a GMM-based view of the data and attach a fixed latent-only simplex witness to the encoder mean. This construction yields two linked objects. The first is a certificate: if the witness prediction improves on the best constant predictor of the teacher, the encoder mean cannot be input-independent constant. The second is a local escape direction: on the collapsed manifold, the teacher residual gives a sample-dependent descent direction for the alignment loss. For any full-support teacher posterior, the same geometry also gives a closed-form latent code with zero teacher-witness alignment error. Its scaled versions trace a margin-energy path from the constant predictor to the exact teacher code, which qua","title":"A Simplex Witness Certificate for Constant Collapse in Variational Autoencoders","url":"https://arxiv.org/abs/2605.18224","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.18224v3 Announce Type: replace-cross \nAbstract: We study exact constant collapse in variational autoencoders: the deterministic encoder mean becomes independent of the input. The prior remains the standard Gaussian. Before VAE training, we select a fixed teacher posterior from a GMM-based view of the data and attach a fixed latent-only simplex witness to the encoder mean. This construction yields two linked objects. The first is a certificate: if the witness prediction improves on the best constant predictor of the teacher, the encoder mean cannot be input-independent constant. The second is a local escape direction: on the collapsed manifold, the teacher residual gives a sample-dependent descent direction for the alignment loss. For any full-support teacher posterior, the same geometry also gives a closed-form latent code with zero teacher-witness alignment error. Its scaled versions trace a margin-energy path from the constant predictor to the exact teacher code, which qua","title":"A Simplex Witness Certificate for Constant Collapse in Variational Autoencoders","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-26T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.18224"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f51c104fdca47083fff241e8278bee81cb62897552250a0fbcfc209a9fc927dec50fd3f398c3fece3287ada9bd4916eac1a1a29abd38cb1f7d34e9491cd0b90b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-26T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.18224"},"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":"37ba13bf3da53505b91aa39069e4ad73594e9180a1826cf1f921eab8a1f2d298","leaf_index":152030,"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":"f53bbeb493378a21aba7d271a35a9c092c011449961358bca33f3eefada98ed3","side":"right"},{"sibling":"d3137cafe08fde05b7835389e554c67753df6f95d74e0395145c0aea4c394ff6","side":"left"},{"sibling":"66b82f8a0be1d2cdc496b48d96955224376d59924c37179f20c6f4d9acdfc46c","side":"left"},{"sibling":"20e152e728135b286bfedb517b9e871a67e1bee20780b79a1c1deaed5d3e892b","side":"left"},{"sibling":"34f4963280a8fb3f52fb5a72935d77b90596ed14bf79a97fd511f321588c5b2b","side":"left"},{"sibling":"b4801bbab92366d891a505f694549044c3364b60d3bacc44f081beb8d3430695","side":"right"},{"sibling":"54ecd916cdbd2e94176c7d608334aecfb97db5681b6acb08e8daa14ac57fec78","side":"left"},{"sibling":"8b0755e3ba26ea95e61e8d0e6362ce6cbe9991903d18e148b0cba214724147ec","side":"left"},{"sibling":"6c8b632bc887ad8683d2d08a66a66babfd1e8e43de4b1b760ed3f3d35d5b02e1","side":"left"},{"sibling":"879666fab72e779ab55d0564eaabd64b00534fd6bba7f18412c7f31f61ffd09f","side":"right"},{"sibling":"f40ccedd90c323817e961adc0a2e2db82b8aabe192b6c9d5a373ff988987b207","side":"right"},{"sibling":"b85ea61ae405eed84392a7b6b1eee5536f5a38d6b04070638e23ec7b71e3443a","side":"right"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"e5893793e3591ed7f5e58ca94ffcfba46bb30f69fb1c25d5ba8ef49eb99f9126","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e3eecaf996dbe7229a7bb1d234c97aea97a252c5f7c89f8547b6d091db0f0e40","side":"right"},{"sibling":"55bcbd4da3e20d93931f7e58673f10232e81a5b1514d7396cb4b71e8f95788d0","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":152106,"merkle_root":"ac5182c6f3dd09931f2a689df5f4be36df7b55e55bcf106e195671f5ed55fd8f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260526T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-26T05:37:34Z","sig_algorithm":"ed25519","signature":"a401243fbd2c077d29a623c6ef616c78fbd5c8ce1930afa7af7165b2386e5a8cf15d5094983a1c962e71b27b911a3f3ce09c8cfab9393be2ce5ce8ee6513da06","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_71e2786446f1a9f99ccdc34762af138add3d17d694b5184a1e489a2b4a5bf574"}}