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Ahle","submitted_at":"2019-09-03T08:56:59Z","abstract_excerpt":"We construct a matrix $M\\in R^{m\\otimes d^c}$ with just $m=O(c\\,\\lambda\\,\\varepsilon^{-2}\\text{poly}\\log1/\\varepsilon\\delta)$ rows, which preserves the norm $\\|Mx\\|_2=(1\\pm\\varepsilon)\\|x\\|_2$ of all $x$ in any given $\\lambda$ dimensional subspace of $ R^d$ with probability at least $1-\\delta$. This matrix can be applied to tensors $x^{(1)}\\otimes\\dots\\otimes x^{(c)}\\in R^{d^c}$ in $O(c\\, m \\min\\{d,m\\})$ time -- hence the name \"Tensor Sketch\". (Here $x\\otimes y = \\text{asvec}(xy^T) = [x_1y_1, x_1y_2,\\dots,x_1y_m,x_2y_1,\\dots,x_ny_m]\\in R^{nm}$.)\n  This improves upon earlier Tensor Sketch const"},"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":"1909.01821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-09-03T08:56:59Z","cross_cats_sorted":["cs.LG","math.PR","stat.ML"],"title_canon_sha256":"f0030ed4abfc5525f186d51c15bc3ed00c587f6620a12191eb148f8ae9218b6f","abstract_canon_sha256":"99eed06a5637cae78751fa1c4838fb5f489ab75d9b8595e19383e1761152bc36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:20.788038Z","signature_b64":"6ZV1L0SaFANBh0aQz57ic7zFvOS8EeiIs/J+7+KM2mLqar9HTb8MZKvLLNWrL5s8Ib6mkbp4d1qBjtYphyZ0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f235be5e25de4fede4715879248e9bacfd06976c1ec6acfdd069c80adc88e1fc","last_reissued_at":"2026-07-05T00:02:20.787652Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:20.787652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Optimal Tensor Sketch","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML"],"primary_cat":"cs.DS","authors_text":"Jakob B. 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