Pith Number

pith:FWMC6HOQ

pith:2026:FWMC6HOQYJM6MK3GAERAXDOZRY

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Revisiting CUR Perturbation Analysis: A Local Tangent-Space Expansion

Longxiu Huang

The Fréchet derivative of the rank-truncated CUR map is a sampling-induced oblique tangent-space projector that filters certain perturbations to first order.

arxiv:2605.13437 v1 · 2026-05-13 · math.NA · cs.IT · cs.NA · math.IT

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Claims

C1strongest claim

We show that the Fréchet derivative of the rank-truncated CUR map is a sampling-induced oblique tangent-space projector determined by the selected rows and columns. Consequently, the local recovery error for an underlying low-rank matrix is governed not by the full perturbation norm alone, but by the image of the perturbation under this sampling-induced tangent projector.

C2weakest assumption

The underlying matrix lies near an admissible rank-r matrix with fixed selected indices, so that the rank-truncated CUR map is Fréchet differentiable at that point.

C3one line summary

The Fréchet derivative of rank-truncated CUR is a sampling-induced oblique tangent projector, so perturbations in its kernel are removed to first order.

References

40 extracted · 40 resolved · 0 Pith anchors

[1] Journal of Machine Learning Research , volume=

[2] Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining , pages=

[3] Linear Algebra and its Applications , volume =

[4] Mode-wise tensor decompositions: Multi-dimensional generalizations of

[5] Linear Algebra and its Applications , volume= 2010

Receipt and verification

First computed	2026-05-18T02:44:47.087284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d982f1dd0c259e62b6601220b8dd98e2e8b86083a49306777b250f0eb7923d3

Aliases

arxiv: 2605.13437 · arxiv_version: 2605.13437v1 · doi: 10.48550/arxiv.2605.13437 · pith_short_12: FWMC6HOQYJM6 · pith_short_16: FWMC6HOQYJM6MK3G · pith_short_8: FWMC6HOQ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/FWMC6HOQYJM6MK3GAERAXDOZRY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2d982f1dd0c259e62b6601220b8dd98e2e8b86083a49306777b250f0eb7923d3

Canonical record JSON

{
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    "abstract_canon_sha256": "36aa5034fe1a44fdf80e0d477620c212f03dc39d2f970b9655308d45d26f8940",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.NA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T12:33:17Z",
    "title_canon_sha256": "166633bb8318f1be48a7aa3bb52f9d07bb461ca0243f448eeb5c189f7e74e17e"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}