{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:E6JC2KJG5KTH7CJK54SYP2LD2W","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":"99e1a6a9e6a83ddf40841e1be40b680ea8946457d0b0aced42af9a9115a6f367","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-18T15:33:26Z","title_canon_sha256":"7be20f542c0e979622edbec2f3aff82cc329301a88cc520e9cc41374765dd932"},"schema_version":"1.0","source":{"id":"2101.07123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.07123","created_at":"2026-07-05T02:07:40Z"},{"alias_kind":"arxiv_version","alias_value":"2101.07123v1","created_at":"2026-07-05T02:07:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.07123","created_at":"2026-07-05T02:07:40Z"},{"alias_kind":"pith_short_12","alias_value":"E6JC2KJG5KTH","created_at":"2026-07-05T02:07:40Z"},{"alias_kind":"pith_short_16","alias_value":"E6JC2KJG5KTH7CJK","created_at":"2026-07-05T02:07:40Z"},{"alias_kind":"pith_short_8","alias_value":"E6JC2KJG","created_at":"2026-07-05T02:07:40Z"}],"graph_snapshots":[{"event_id":"sha256:0df0fa9e15328e785609cb99ea066e6f5739b63b8e12b4422d94183d000e53e1","target":"graph","created_at":"2026-07-05T02:07:40Z","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/2101.07123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In reinforcement learning, temporal difference-based algorithms can be sample-inefficient: for instance, with sparse rewards, no learning occurs until a reward is observed. This can be remedied by learning richer objects, such as a model of the environment, or successor states. Successor states model the expected future state occupancy from any given state for a given policy and are related to goal-dependent value functions, which learn how to reach arbitrary states. We formally derive the temporal difference algorithm for successor state and goal-dependent value function learning, either for ","authors_text":"Corentin Tallec, L\\'eonard Blier, Yann Ollivier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-18T15:33:26Z","title":"Learning Successor States and Goal-Dependent Values: A Mathematical Viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07123","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":"sha256:2ff78e294a069ea780ba389ad75e7fc4fdd66541428fda9a8c2e8612f67a1eab","target":"record","created_at":"2026-07-05T02:07:40Z","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":"99e1a6a9e6a83ddf40841e1be40b680ea8946457d0b0aced42af9a9115a6f367","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-18T15:33:26Z","title_canon_sha256":"7be20f542c0e979622edbec2f3aff82cc329301a88cc520e9cc41374765dd932"},"schema_version":"1.0","source":{"id":"2101.07123","kind":"arxiv","version":1}},"canonical_sha256":"27922d2926eaa67f892aef2587e963d583a9c3120da37938af7dfc60c4cc27f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27922d2926eaa67f892aef2587e963d583a9c3120da37938af7dfc60c4cc27f7","first_computed_at":"2026-07-05T02:07:40.508818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:07:40.508818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqwhXO+FpRdlFiPgvYBew9BN8kxpX/QecM7odm6OiuPmcAU78JAyAbEOINzfqSHmIYQlGbrws1Os+qzqudZZDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:07:40.509242Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.07123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ff78e294a069ea780ba389ad75e7fc4fdd66541428fda9a8c2e8612f67a1eab","sha256:0df0fa9e15328e785609cb99ea066e6f5739b63b8e12b4422d94183d000e53e1"],"state_sha256":"b1f9a786abaaaa4b8e5791890895374bde52569763f7e05182008108f60c1471"}