Pith Number

pith:IFWQKZQK

pith:2026:IFWQKZQK64MLDVQE3ARFXHPWWQ

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Stochastic global optimization of continuous functions via random walks on Grassmannians

Kartik Gupta, Pradeep Ravikumar, Ramarathnam Venkatesan, Stephen D. Miller

Random walks on Grassmannians converge to global minima of continuous functions at a rate set by a geometric gap parameter.

arxiv:2605.14151 v1 · 2026-05-13 · math.OC

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Record completeness

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Claims

C1strongest claim

We identify a gap parameter -- an analogue of a spectral gap for random walks -- that controls the rate at which the iterates approach the global minimum value. Finally, we argue that the same analysis yields a blind-spot robustness property: sufficiently narrow, deep dips of the loss function have limited influence on the algorithm's trajectory.

C2weakest assumption

The convergence analysis rests on the existence and positivity of the gap parameter defined from the geometric distribution of restricted minima across random k-dimensional subspaces; the abstract provides no explicit construction, bound, or verification procedure for this quantity on arbitrary continuous functions.

C3one line summary

A stochastic global optimizer samples random k-dimensional subspaces, solves the restricted problem on each, and moves to the improved point, with rate controlled by a gap parameter on the distribution of restricted minima.

References

24 extracted · 24 resolved · 1 Pith anchors

[1] Ballinger, B., Blekherman, G., Cohn, H., Giansiracusa, N., Kelly, E., & Schürmann, A. (2009). Experimental Study of Energy-Minimizing Point Configurations on Spheres. Experimental Mathematics, 18(3), 2009 · doi:10.1080/10586458.2009.10129052

[2] Point configurations minimizing harmonic energy on spheres 2021

[3] B. Bekka, P. de la Harpe, and A. Valette. Kazhdan's Property (T) . New Mathematical Monographs. Cambridge University Press, 2008 2008

[4] Thomas Bendokat, Ralf Zimmermann, and P.-A. Absil. A Grassmann manifold handbook: basic geometry and computational aspects. Advances in Computational Mathematics , 50(1), January 2024 2024

[5] Moser, Alina Oprea, Battista Biggio, Marcello Pelillo, and Fabio Roli 2023

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:11.581846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

416d05660af718b1d604d8225b9df6b4232408790ee326942ec2974b2cdc90be

Aliases

arxiv: 2605.14151 · arxiv_version: 2605.14151v1 · doi: 10.48550/arxiv.2605.14151 · pith_short_12: IFWQKZQK64ML · pith_short_16: IFWQKZQK64MLDVQE · pith_short_8: IFWQKZQK

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IFWQKZQK64MLDVQE3ARFXHPWWQ \
  | 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: 416d05660af718b1d604d8225b9df6b4232408790ee326942ec2974b2cdc90be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7b722979913df499b45453b5374ba7d753aa5a97460b5c5c0d3d6767228525c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-13T22:06:50Z",
    "title_canon_sha256": "c0103300bde6bd59e7889744d0df411da80d89caa37cf2f990b0984230f8f0f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14151",
    "kind": "arxiv",
    "version": 1
  }
}