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Noise sensitivity from fractional query algorithms and the axis-aligned Laplacian

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Renan Gross

Computational Complexity · Submitted 25 Jan 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the limiting run-time complexity of a natural class of these algorithms obeys the non-linear partial differential equation $\min_{k}\partial^{2}u/\partial x_{k}^{2}=-2$, and that the individual bit revealment satisfies the Schramm-Steif bound for Fourier weight, connecting noise sensitivity with PDEs.

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arXiv ID2201.10350 (version 1)
Pith ID3VXPVUWO, Pith's permanent record of this paper and its review
CitationRenan Gross. "Noise sensitivity from fractional query algorithms and the axis-aligned Laplacian." arXiv:2201.10350 (2022). https://pith.science/paper/3VXPVUWO
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,984 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.18 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.82 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show that the limiting run-time complexity of a natural class of these algorithms obeys the non-linear partial differential equation $\min_{k}\partial^{2}u/\partial x_{k}^{2}=-2$, and that the individual bit revealment satisfies the Schramm-Steif bound for Fourier weight, connecting noise sensitivity with PDEs. We discuss relations with other decision tree results.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. contribution 1.00 0.84 0.16 hedged possibility 0.92
s1 We show that the limiting run-time complexity of a natural class of these algorithms obeys the non-linear partial differential equation $\min_{k}\partial^{2}u/\partial x_{k}^{2}=-2$, and that the individual bit revealment satisfies the Schramm-Steif bound for Fourier weight, connecting noise sensitivity with PDEs. result 0.97 0.94 0.79 asserted 1.00
s2 We discuss relations with other decision tree results. contribution 0.36 0.52 0.03 unclear 0.75

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from proof or derivation 1.00.

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sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show that the limiting run-time complexity of a natural class of these algorithms obeys the non-linear partial differential equation $\min_{k}\partial^{2}u/\partial x_{k}^{2}=-2$, and that the individual bit revealment satisfies the Schramm-Steif bound for Fourier weight, connecting noise sensitivity with PDEs. We discuss relations with other decision tree results.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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