{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X2H72ZXEISJJYPHPLMQR2YSNWD","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":"afd15a6ff35b5a4515ddeb937e45496969719f0276b3ea1cbe5e1e5fdce55668","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-31T02:31:15Z","title_canon_sha256":"142f7fc8cd6d6e230f10fc5b7ed0bc6d088e69ec1c13662f5e40d4cce2f5fcca"},"schema_version":"1.0","source":{"id":"1804.00108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00108","created_at":"2026-05-17T23:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00108v1","created_at":"2026-05-17T23:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00108","created_at":"2026-05-17T23:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"X2H72ZXEISJJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X2H72ZXEISJJYPHP","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X2H72ZXE","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:7873666ff4be20adcc82b92386f0194ed0ff0615322dc60061fb95510e6ec9dd","target":"graph","created_at":"2026-05-17T23:59:09Z","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"},"paper":{"abstract_excerpt":"In this paper we generalize the 1-bit matrix completion problem to higher order tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor $T$ in $\\mathbb{R}^{N} \\times \\mathbb{R}^{N} \\times \\cdots \\times \\mathbb{R}^{N}$ can be estimated efficiently by only $m=O(Nd)$ binary measurements by regularizing its max-qnorm and M-norm as surrogates for its rank. We prove that similar to the matrix case, i.e., when $d=2$, the sample complexity of recovering a low-rank tensor from 1-bit measurements of a subset of its entries is the same as recovering it from unquantized measurements. Mor","authors_text":"Navid Ghadermarzy, Ozgur Yilmaz, Yaniv Plan","cross_cats":["cs.IT","math.IT","math.OC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-31T02:31:15Z","title":"Learning tensors from partial binary measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00108","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":"sha256:56f2a620f4954091d9b95649d393b28f151b5337ccc08ec8fe0fbb9c9251cbc9","target":"record","created_at":"2026-05-17T23:59:09Z","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":"afd15a6ff35b5a4515ddeb937e45496969719f0276b3ea1cbe5e1e5fdce55668","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-31T02:31:15Z","title_canon_sha256":"142f7fc8cd6d6e230f10fc5b7ed0bc6d088e69ec1c13662f5e40d4cce2f5fcca"},"schema_version":"1.0","source":{"id":"1804.00108","kind":"arxiv","version":1}},"canonical_sha256":"be8ffd66e444929c3cef5b211d624db0ec10dca0a7b2c6bb154d871b86e36cc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be8ffd66e444929c3cef5b211d624db0ec10dca0a7b2c6bb154d871b86e36cc2","first_computed_at":"2026-05-17T23:59:09.381552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:09.381552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEJTi6j7RXVidVy+w8BgKUgEKxr/FYyTJ90DpilehHPhn6syyqGiACrdb3IBBJaGICbLHLmliZVyGWSuVUECCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:09.381998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56f2a620f4954091d9b95649d393b28f151b5337ccc08ec8fe0fbb9c9251cbc9","sha256:7873666ff4be20adcc82b92386f0194ed0ff0615322dc60061fb95510e6ec9dd"],"state_sha256":"d3e92b1b118c81d5e171845e44a1d762cdcddd2067acecd77ac092e676b5645c"}