{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4JF6VAUUW5LR3KYMJ4IPOFTWBQ","short_pith_number":"pith:4JF6VAUU","schema_version":"1.0","canonical_sha256":"e24bea8294b7571dab0c4f10f716760c3be7065e1f8a74126943ca2f61e30cd5","source":{"kind":"arxiv","id":"1810.00116","version":3},"attestation_state":"computed","paper":{"title":"Improved Gradient-Based Optimization Over Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Arash Vahdat, Bill Macready, Evgeny Andriyash","submitted_at":"2018-09-29T00:07:28Z","abstract_excerpt":"In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirical"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.00116","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-29T00:07:28Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d98716c427c10df83b2267750079abb658891d5d657c75e0fd2491d0383a2f3","abstract_canon_sha256":"53105f78b204616f687d9e6e22783b80e2fe9fb5a9304fcd39a64cf4e338c1bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:17.499220Z","signature_b64":"yM+IBkBtDVLRpz7Gb0NcHYYmcwHi+NBKzZq9vCMcQDFQO2+5SkP+rLTPm2inUn4a1gBez9vA2aBV5wQNYyvoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e24bea8294b7571dab0c4f10f716760c3be7065e1f8a74126943ca2f61e30cd5","last_reissued_at":"2026-05-17T23:43:17.498541Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:17.498541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Gradient-Based Optimization Over Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Arash Vahdat, Bill Macready, Evgeny Andriyash","submitted_at":"2018-09-29T00:07:28Z","abstract_excerpt":"In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00116","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.00116","created_at":"2026-05-17T23:43:17.498635+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00116v3","created_at":"2026-05-17T23:43:17.498635+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00116","created_at":"2026-05-17T23:43:17.498635+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JF6VAUUW5LR","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JF6VAUUW5LR3KYM","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JF6VAUU","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ","json":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ.json","graph_json":"https://pith.science/api/pith-number/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/graph.json","events_json":"https://pith.science/api/pith-number/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/events.json","paper":"https://pith.science/paper/4JF6VAUU"},"agent_actions":{"view_html":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ","download_json":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ.json","view_paper":"https://pith.science/paper/4JF6VAUU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00116&json=true","fetch_graph":"https://pith.science/api/pith-number/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/action/storage_attestation","attest_author":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/action/author_attestation","sign_citation":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/action/citation_signature","submit_replication":"https://pith.science/pith/4JF6VAUUW5LR3KYMJ4IPOFTWBQ/action/replication_record"}},"created_at":"2026-05-17T23:43:17.498635+00:00","updated_at":"2026-05-17T23:43:17.498635+00:00"}