{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CFSILDWJ3WZIKT72A6JMHQN2KH","short_pith_number":"pith:CFSILDWJ","canonical_record":{"source":{"id":"1902.00744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-02T16:14:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"e836eff4167e3a8db3a4a3f7e4739eb59f544dfb22aaed71286f23c1906ceb80","abstract_canon_sha256":"4713455966cbe8a9c8036aa32e468f9f312faabed3e0422023e66be8bc2c7b18"},"schema_version":"1.0"},"canonical_sha256":"1164858ec9ddb2854ffa0792c3c1ba51d13d2720edd796c8111f55482518852e","source":{"kind":"arxiv","id":"1902.00744","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00744","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00744v2","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00744","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"pith_short_12","alias_value":"CFSILDWJ3WZI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CFSILDWJ3WZIKT72","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CFSILDWJ","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CFSILDWJ3WZIKT72A6JMHQN2KH","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-02T16:14:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"e836eff4167e3a8db3a4a3f7e4739eb59f544dfb22aaed71286f23c1906ceb80","abstract_canon_sha256":"4713455966cbe8a9c8036aa32e468f9f312faabed3e0422023e66be8bc2c7b18"},"schema_version":"1.0"},"canonical_sha256":"1164858ec9ddb2854ffa0792c3c1ba51d13d2720edd796c8111f55482518852e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:14.634761Z","signature_b64":"5cCjzdVL9XuRtS/ZYxsZX47O39+I2PJ7EAr4ynGsf1JHXR+abOvE4j9kv7CgEWm51EDRJHWY0My1Xo0JOBZxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1164858ec9ddb2854ffa0792c3c1ba51d13d2720edd796c8111f55482518852e","last_reissued_at":"2026-05-17T23:49:14.634114Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:14.634114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00744","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hr6JAFVe3f9gXNqYXV5vvpuRUSMy0wD2d+jI1DcjtQbHiOOnQyd9CFN4BxI0YdS94PuxJV5e0oQgNem9fWHAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:43:32.960494Z"},"content_sha256":"1625bf3352d8c400b3ea92fc4f636902fb0332e94090db4ca1cdf4fe4c8386a2","schema_version":"1.0","event_id":"sha256:1625bf3352d8c400b3ea92fc4f636902fb0332e94090db4ca1cdf4fe4c8386a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CFSILDWJ3WZIKT72A6JMHQN2KH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymmetric Valleys: Beyond Sharp and Flat Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Gao Huang, Haowei He, Yang Yuan","submitted_at":"2019-02-02T16:14:52Z","abstract_excerpt":"Despite the non-convex nature of their loss functions, deep neural networks are known to generalize well when optimized with stochastic gradient descent (SGD). Recent work conjectures that SGD with proper configuration is able to find wide and flat local minima, which have been proposed to be associated with good generalization performance. In this paper, we observe that local minima of modern deep networks are more than being flat or sharp. Specifically, at a local minimum there exist many asymmetric directions such that the loss increases abruptly along one side, and slowly along the opposit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00744","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URreyJntC1S4ZWDpYEJEd4Hd9cpcNrhWmV03g6xSS+KSxODpBeWNoousqmSKzrpr9HOoUqscq3dVncJIlBgACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:43:32.960851Z"},"content_sha256":"0dc16b69ae4af4d9433a27418c6795672b49b78c1e21eb17ddd2c4f58ce265e0","schema_version":"1.0","event_id":"sha256:0dc16b69ae4af4d9433a27418c6795672b49b78c1e21eb17ddd2c4f58ce265e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/bundle.json","state_url":"https://pith.science/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T01:43:32Z","links":{"resolver":"https://pith.science/pith/CFSILDWJ3WZIKT72A6JMHQN2KH","bundle":"https://pith.science/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/bundle.json","state":"https://pith.science/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFSILDWJ3WZIKT72A6JMHQN2KH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CFSILDWJ3WZIKT72A6JMHQN2KH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4713455966cbe8a9c8036aa32e468f9f312faabed3e0422023e66be8bc2c7b18","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-02T16:14:52Z","title_canon_sha256":"e836eff4167e3a8db3a4a3f7e4739eb59f544dfb22aaed71286f23c1906ceb80"},"schema_version":"1.0","source":{"id":"1902.00744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00744","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00744v2","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00744","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"pith_short_12","alias_value":"CFSILDWJ3WZI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CFSILDWJ3WZIKT72","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CFSILDWJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:0dc16b69ae4af4d9433a27418c6795672b49b78c1e21eb17ddd2c4f58ce265e0","target":"graph","created_at":"2026-05-17T23:49:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Despite the non-convex nature of their loss functions, deep neural networks are known to generalize well when optimized with stochastic gradient descent (SGD). Recent work conjectures that SGD with proper configuration is able to find wide and flat local minima, which have been proposed to be associated with good generalization performance. In this paper, we observe that local minima of modern deep networks are more than being flat or sharp. Specifically, at a local minimum there exist many asymmetric directions such that the loss increases abruptly along one side, and slowly along the opposit","authors_text":"Gao Huang, Haowei He, Yang Yuan","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-02T16:14:52Z","title":"Asymmetric Valleys: Beyond Sharp and Flat Local Minima"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00744","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1625bf3352d8c400b3ea92fc4f636902fb0332e94090db4ca1cdf4fe4c8386a2","target":"record","created_at":"2026-05-17T23:49:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4713455966cbe8a9c8036aa32e468f9f312faabed3e0422023e66be8bc2c7b18","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-02T16:14:52Z","title_canon_sha256":"e836eff4167e3a8db3a4a3f7e4739eb59f544dfb22aaed71286f23c1906ceb80"},"schema_version":"1.0","source":{"id":"1902.00744","kind":"arxiv","version":2}},"canonical_sha256":"1164858ec9ddb2854ffa0792c3c1ba51d13d2720edd796c8111f55482518852e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1164858ec9ddb2854ffa0792c3c1ba51d13d2720edd796c8111f55482518852e","first_computed_at":"2026-05-17T23:49:14.634114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:14.634114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5cCjzdVL9XuRtS/ZYxsZX47O39+I2PJ7EAr4ynGsf1JHXR+abOvE4j9kv7CgEWm51EDRJHWY0My1Xo0JOBZxAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:14.634761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1625bf3352d8c400b3ea92fc4f636902fb0332e94090db4ca1cdf4fe4c8386a2","sha256:0dc16b69ae4af4d9433a27418c6795672b49b78c1e21eb17ddd2c4f58ce265e0"],"state_sha256":"e1aeab8c79affc9e8b526ef060844358df7ed93072538177b612edd655b52d07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LycHejUXi9J7JmakKXV3d6PPMxjQHxkaICR0FaMAU1co2pj2p0zLI2IJlRTqbM3kO72dtXiiO8c9jRAiR6IZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:43:32.962835Z","bundle_sha256":"754225d55b86c1b154f16151ea6fc3c6779edab01d3be906f3efa7ae220495d6"}}