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The method replicates a model \\(M\\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \\(Q\\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \\(Q\\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to di","title":"Improving Generalization by Permutation Routing Across Model Copies","url":"https://arxiv.org/abs/2605.09256","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.09256v1 Announce Type: cross \nAbstract: We introduce a use of the \\(M\\)-cover (or \\(M\\)-layer) transform for machine learning. The method replicates a model \\(M\\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \\(Q\\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \\(Q\\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to di","title":"Improving Generalization by Permutation Routing Across Model Copies","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.09256"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:19d0e04e2c525be472c49481481e86122d1afcbcb4fd81950ed17940ee8ef1f2869fd56c2c41edf4cfc9fa7773e9f1378f714b27c0203603e848c32738da630b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.09256"},"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":"a7f2878ac25405a9e898e3ff30dfb98930b279a442407d22257a3aed3ec3ad9a","leaf_index":128692,"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":"53a89831e8a1cdf427576f5e843c5aef899821f1aa2af9eafa49bac171f09cd1","side":"right"},{"sibling":"58df93a3bfb0b5c07cd361bcb6288fa417d84afeaa3b0a5aac3aa2cce4fdcdc2","side":"right"},{"sibling":"969f6fb8eeefc54b729ed64ee23993ab034d4ed12db9c73569286cbe27031f71","side":"left"},{"sibling":"8e665a442a5a3b69ff8f18d194796db83443a5eaf5e26ba98acef319c8067f82","side":"right"},{"sibling":"225be4a70e05b18467a0cd76fc5c13aa4802b903c76193321314e0231c94690e","side":"left"},{"sibling":"980b39944898260d0f29f7098638441343b64897e9789398edaf81c70860f939","side":"left"},{"sibling":"0b6591633a3212977257746858166dde4a12c0138f81b09c09f3ff243f23f3ca","side":"right"},{"sibling":"66ed9d27919b2830cd6c07ec62488d62635d76aad26e26435c6ebbcd12730198","side":"left"},{"sibling":"831b04b4dcc29bcff4577c406291bc4f644057b650a55f064d46d1cab5185326","side":"right"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"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_a55a65d8c2534098a579419bc3098624e6d1372fb6a8a49b2179636d1ea0581f"}}