{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:H5BTRGSKWRTMZJBB7P2YTHDHVM","short_pith_number":"pith:H5BTRGSK","canonical_record":{"source":{"id":"2112.03257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-06T18:59:52Z","cross_cats_sorted":["cs.AI","cs.CV","cs.NE","cs.RO"],"title_canon_sha256":"8d9ca4e79448dd98e884c06b2864cd04c08574b6b5d7f21901989494f6d60834","abstract_canon_sha256":"47119106df0423d759f1fefbe52980ec731332e425e9edc69990b59cdffd74a1"},"schema_version":"1.0"},"canonical_sha256":"3f43389a4ab466cca421fbf5899c67ab2adc276df499754960e1b723698bebff","source":{"kind":"arxiv","id":"2112.03257","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.03257","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"2112.03257v1","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.03257","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"H5BTRGSKWRTM","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_16","alias_value":"H5BTRGSKWRTMZJBB","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_8","alias_value":"H5BTRGSK","created_at":"2026-07-05T03:38:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:H5BTRGSKWRTMZJBB7P2YTHDHVM","target":"record","payload":{"canonical_record":{"source":{"id":"2112.03257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-06T18:59:52Z","cross_cats_sorted":["cs.AI","cs.CV","cs.NE","cs.RO"],"title_canon_sha256":"8d9ca4e79448dd98e884c06b2864cd04c08574b6b5d7f21901989494f6d60834","abstract_canon_sha256":"47119106df0423d759f1fefbe52980ec731332e425e9edc69990b59cdffd74a1"},"schema_version":"1.0"},"canonical_sha256":"3f43389a4ab466cca421fbf5899c67ab2adc276df499754960e1b723698bebff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:38:09.729646Z","signature_b64":"UvD17o/rjMyMrmP7amlS53KtdnnQlc2hZjlgSEbfY9pYN9vLXFRr/L9s175u0EH9cRYiEUYdlE/ktlebi9D1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f43389a4ab466cca421fbf5899c67ab2adc276df499754960e1b723698bebff","last_reissued_at":"2026-07-05T03:38:09.729059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:38:09.729059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.03257","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KJGtatYC1zLawTmO3fDOxvd3wC/BB16BNg7etRvbAuZyoXMng7fgcD8eGr+rqVMT10Ty+o6Lyjmke9MONLRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:05:57.001334Z"},"content_sha256":"33f37594a6725be0a16dcaf533d5aed8b1e0260f966020abb30426307bd87c55","schema_version":"1.0","event_id":"sha256:33f37594a6725be0a16dcaf533d5aed8b1e0260f966020abb30426307bd87c55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:H5BTRGSKWRTMZJBB7P2YTHDHVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional Regularization for Reinforcement Learning via Learned Fourier Features","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CV","cs.NE","cs.RO"],"primary_cat":"cs.LG","authors_text":"Alexander C. Li, Deepak Pathak","submitted_at":"2021-12-06T18:59:52Z","abstract_excerpt":"We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of our architecture using the Neural Tangent Kernel and theoretically show that tuning the initial variance of the Fourier basis is equivalent to functional regularization of the learned deep network. That is, these learned Fourier features allow for adjusting the degree to which networks underfit or overfit different frequencies in the training data, and hence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.03257","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.03257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7okPwg7Z1hgqP6bfXhQilu6wUskdhptYst00j0l5mGBJ443C4JARySpzSAij+AxfsNXu3seiD41p9swm/JVoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:05:57.001708Z"},"content_sha256":"00680f4aa0a9a31d7f160a494de34750eee9d9f3023c1b089eba021e6b177ca6","schema_version":"1.0","event_id":"sha256:00680f4aa0a9a31d7f160a494de34750eee9d9f3023c1b089eba021e6b177ca6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/bundle.json","state_url":"https://pith.science/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/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":"2026-07-06T15:05:57Z","links":{"resolver":"https://pith.science/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM","bundle":"https://pith.science/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/bundle.json","state":"https://pith.science/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5BTRGSKWRTMZJBB7P2YTHDHVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:H5BTRGSKWRTMZJBB7P2YTHDHVM","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":"47119106df0423d759f1fefbe52980ec731332e425e9edc69990b59cdffd74a1","cross_cats_sorted":["cs.AI","cs.CV","cs.NE","cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-06T18:59:52Z","title_canon_sha256":"8d9ca4e79448dd98e884c06b2864cd04c08574b6b5d7f21901989494f6d60834"},"schema_version":"1.0","source":{"id":"2112.03257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.03257","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"2112.03257v1","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.03257","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"H5BTRGSKWRTM","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_16","alias_value":"H5BTRGSKWRTMZJBB","created_at":"2026-07-05T03:38:09Z"},{"alias_kind":"pith_short_8","alias_value":"H5BTRGSK","created_at":"2026-07-05T03:38:09Z"}],"graph_snapshots":[{"event_id":"sha256:00680f4aa0a9a31d7f160a494de34750eee9d9f3023c1b089eba021e6b177ca6","target":"graph","created_at":"2026-07-05T03:38:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.03257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of our architecture using the Neural Tangent Kernel and theoretically show that tuning the initial variance of the Fourier basis is equivalent to functional regularization of the learned deep network. That is, these learned Fourier features allow for adjusting the degree to which networks underfit or overfit different frequencies in the training data, and hence","authors_text":"Alexander C. Li, Deepak Pathak","cross_cats":["cs.AI","cs.CV","cs.NE","cs.RO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-06T18:59:52Z","title":"Functional Regularization for Reinforcement Learning via Learned Fourier Features"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.03257","kind":"arxiv","version":1},"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":"sha256:33f37594a6725be0a16dcaf533d5aed8b1e0260f966020abb30426307bd87c55","target":"record","created_at":"2026-07-05T03:38:09Z","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":"47119106df0423d759f1fefbe52980ec731332e425e9edc69990b59cdffd74a1","cross_cats_sorted":["cs.AI","cs.CV","cs.NE","cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-06T18:59:52Z","title_canon_sha256":"8d9ca4e79448dd98e884c06b2864cd04c08574b6b5d7f21901989494f6d60834"},"schema_version":"1.0","source":{"id":"2112.03257","kind":"arxiv","version":1}},"canonical_sha256":"3f43389a4ab466cca421fbf5899c67ab2adc276df499754960e1b723698bebff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f43389a4ab466cca421fbf5899c67ab2adc276df499754960e1b723698bebff","first_computed_at":"2026-07-05T03:38:09.729059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:38:09.729059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UvD17o/rjMyMrmP7amlS53KtdnnQlc2hZjlgSEbfY9pYN9vLXFRr/L9s175u0EH9cRYiEUYdlE/ktlebi9D1Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:38:09.729646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.03257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f37594a6725be0a16dcaf533d5aed8b1e0260f966020abb30426307bd87c55","sha256:00680f4aa0a9a31d7f160a494de34750eee9d9f3023c1b089eba021e6b177ca6"],"state_sha256":"75083a4a64d55255348348cd2024ffc8e6c46292d0d178363a2c34927f7467a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KZ82qpGTcEsTxw3BbhWZKWXDNUGcTIQBW8AAo0NWQ/54PUnnGW6pb7qk6Sp7932z31DoHsiJPL+PFK/78cYCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:05:57.003626Z","bundle_sha256":"ef9cd9344bf60cbecd0515c80e134ff8990d72f7ce464a3ab4c92cd9481fa86b"}}