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We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, $a_i$ and $a_j$, diverge to $\\pm$infinity, and their input weight vectors, $\\mathbf{w_i}$ and $\\mathbf{w_j}$, become equal to each other. At convergence, the two neurons implement a gated linear unit: $a_i\\sigma(\\mathbf{w_i} \\cdot \\mathbf{x}) + a_j\\sigma(\\mathbf{w_j} \\cdot \\mathbf{x}) \\rightarrow \\sigma(\\mathbf{w} \\cdot \\mathbf{x}) + (\\mathbf{v} \\cdot \\mathbf{x}) \\sigma'(\\mathbf{w} \\cdot \\mathbf{x})$. Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high pro","title":"Flat Channels to Infinity in Neural Loss Landscapes","url":"https://arxiv.org/abs/2506.14951","vendor":"arxiv_cs_ai"},"summary":"arXiv:2506.14951v4 Announce Type: replace-cross \nAbstract: The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, $a_i$ and $a_j$, diverge to $\\pm$infinity, and their input weight vectors, $\\mathbf{w_i}$ and $\\mathbf{w_j}$, become equal to each other. At convergence, the two neurons implement a gated linear unit: $a_i\\sigma(\\mathbf{w_i} \\cdot \\mathbf{x}) + a_j\\sigma(\\mathbf{w_j} \\cdot \\mathbf{x}) \\rightarrow \\sigma(\\mathbf{w} \\cdot \\mathbf{x}) + (\\mathbf{v} \\cdot \\mathbf{x}) \\sigma'(\\mathbf{w} \\cdot \\mathbf{x})$. Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high pro","title":"Flat Channels to Infinity in Neural Loss Landscapes","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-11T04:43:50Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2506.14951"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0269a3b1e5b56919a06505677330f8606d2ce5d9a5cf69c1368fb0af1645fc90145beb9dce42ebd199dee5a4836203b532f296b70e3adc871a9a64854968e800","signer":"crovia.substrate","subject":{"observed_at":"2026-05-11T04:43:50Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2506.14951"},"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":"0468396a9ae10a5a8b894401c4adaf456f9fe08655156439c0b564b2990a621f","leaf_index":126627,"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":"372af04ba502780ef045ffd99a123c3fe6a60ee446f8bd2355c2a7e2a74c5532","side":"left"},{"sibling":"9a177a9a400e9bbdfe836c2d9bfe0483f4fb1ef4b93bd03ac639290a714d2a8f","side":"left"},{"sibling":"5f4c4d9c64a4f7116e1376c4796e989f6bf7b4c30a8bc7366eb267d89a41c885","side":"right"},{"sibling":"bf09ea8d73b6d2a5200c7fb3e6fda874d963a0b339f1a6fdae3885539264e1d7","side":"right"},{"sibling":"236008aff933094f074c42e3863d574b0f736b16220096f30610d161c8b54857","side":"right"},{"sibling":"4a0b2eccafd921383ef289a705a01f6439d294ee62bc6cb12a42e16eb9f381dd","side":"left"},{"sibling":"54aeb1b325b6ed32e0e93fc93a91c18b716eb6c01be8986d8e913f5ba02e2683","side":"right"},{"sibling":"8145236c073312ace1276c28162c95dcc0d2fd49b8c636293fac87efad823f12","side":"left"},{"sibling":"62d48549e4d4466089a57a96bd9bea15741d62a7cb314f0f9c37c4c22ac650fa","side":"right"},{"sibling":"a2c696699a233359c7b4b418ebd356db453d4b886f4bd076ef34b15ee86144a3","side":"left"},{"sibling":"1a581be91236d1f25e8d47fe5efa0e2b51b7f0f6d706ef76a9093067688e5d56","side":"left"},{"sibling":"878cc30108509c9fa1fc52705a216f519d73b647916fcbdfc30a389934d3364b","side":"left"},{"sibling":"ae7dfff36ba07d9f48c36c28a341482ef244ee13cd0efd49aee2bbef2fd65f87","side":"right"},{"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_691b69aa685848ba23358d8a78a153c1ba7e2b88b68e3d93653396e0dc16d3c0"}}