{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:X5XZUHCXM5RUVXNIPHX2WZ7F6Q","short_pith_number":"pith:X5XZUHCX","schema_version":"1.0","canonical_sha256":"bf6f9a1c5767634adda879efab67e5f42ebe2b8ab9addc0e66c8069ed6f55871","source":{"kind":"arxiv","id":"1711.00954","version":2},"attestation_state":"computed","paper":{"title":"Efficient construction of tensor ring representations from sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Lexing Ying, YueHaw Khoo","submitted_at":"2017-11-02T21:59:49Z","abstract_excerpt":"In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions, we propose efficient sampling scheme to obtain $O(d)$ important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has less parameters th"},"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":"1711.00954","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-02T21:59:49Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"84ef04feaaa012f845295ed29826b0bae6448f10cb0e2131ab1c83b16c789615","abstract_canon_sha256":"e90f72afacab355ceef7c8a4b45a03f454693bc06b59e0a5ac152f3f7d85c3e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:08.903000Z","signature_b64":"9O/XPzsEsl1mUZvljzQVmmf+BUB2yndDKtbSKtz5FCFzzW0WY7C+hBLJvGaWJMbRtWs68gSjPT/sJNfLXaeoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6f9a1c5767634adda879efab67e5f42ebe2b8ab9addc0e66c8069ed6f55871","last_reissued_at":"2026-05-17T23:42:08.902502Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:08.902502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient construction of tensor ring representations from sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Lexing Ying, YueHaw Khoo","submitted_at":"2017-11-02T21:59:49Z","abstract_excerpt":"In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions, we propose efficient sampling scheme to obtain $O(d)$ important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has less parameters th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00954","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.00954","created_at":"2026-05-17T23:42:08.902584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.00954v2","created_at":"2026-05-17T23:42:08.902584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00954","created_at":"2026-05-17T23:42:08.902584+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5XZUHCXM5RU","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5XZUHCXM5RUVXNI","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5XZUHCX","created_at":"2026-05-18T12:31:53.515858+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/X5XZUHCXM5RUVXNIPHX2WZ7F6Q","json":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q.json","graph_json":"https://pith.science/api/pith-number/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/graph.json","events_json":"https://pith.science/api/pith-number/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/events.json","paper":"https://pith.science/paper/X5XZUHCX"},"agent_actions":{"view_html":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q","download_json":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q.json","view_paper":"https://pith.science/paper/X5XZUHCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.00954&json=true","fetch_graph":"https://pith.science/api/pith-number/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/action/storage_attestation","attest_author":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/action/author_attestation","sign_citation":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/action/citation_signature","submit_replication":"https://pith.science/pith/X5XZUHCXM5RUVXNIPHX2WZ7F6Q/action/replication_record"}},"created_at":"2026-05-17T23:42:08.902584+00:00","updated_at":"2026-05-17T23:42:08.902584+00:00"}