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Characterizing Deep Gaussian Processes via Nonlinear Recurrence Systems

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Anh Tong, Jaesik Choi

Machine Learning · Submitted 19 Oct 2020

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

The authors' main claim The recurrence relations between layers are analytically derived, providing a tighter bound and the rate of convergence of the dynamic systems.

how it is stated · asserted 1.00 read the record →

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arXiv ID2010.09301 (version 3)
Pith IDTLVCWZ2K, Pith's permanent record of this paper and its review
CitationAnh Tong, Jaesik Choi. "Characterizing Deep Gaussian Processes via Nonlinear Recurrence Systems." arXiv:2010.09301 (2020). https://pith.science/paper/TLVCWZ2K
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,366 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.11 · human participants 0.03 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning capacities reduce significantly when the number of layers increases. In this paper, we present a new analysis in DGPs by studying its corresponding nonlinear dynamic systems to explain the issue. Existing work reports the pathology for the squared exponential kernel function. We extend our investigation to four types of common stationary kernel functions. The recurrence relations between layers are analytically derived, providing a tighter bound and the rate of convergence of the dynamic systems. We demonstrate our finding with a number of experimental 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 Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). background 1.00 0.04 0.03 hedged possibility 0.62
s1 However, there exists a pathology of deep Gaussian processes that their learning capacities reduce significantly when the number of layers increases. background 0.91 0.09 0.08 asserted 1.00
s2 In this paper, we present a new analysis in DGPs by studying its corresponding nonlinear dynamic systems to explain the issue. contribution 0.91 0.89 0.09 asserted 0.98
s3 Existing work reports the pathology for the squared exponential kernel function. background 0.93 0.04 0.03 asserted 0.99
s4 We extend our investigation to four types of common stationary kernel functions. contribution 0.85 0.90 0.05 asserted 0.95
s5 The recurrence relations between layers are analytically derived, providing a tighter bound and the rate of convergence of the dynamic systems. result 0.38 0.96 0.33 asserted 1.00
s6 We demonstrate our finding with a number of experimental results. contribution 0.49 0.94 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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  • T body sentences
  • C citations
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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

Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning capacities reduce significantly when the number of layers increases. In this paper, we present a new analysis in DGPs by studying its corresponding nonlinear dynamic systems to explain the issue. Existing work reports the pathology for the squared exponential kernel function. We extend our investigation to four types of common stationary kernel functions. The recurrence relations between layers are analytically derived, providing a tighter bound and the rate of convergence of the dynamic systems. We demonstrate our finding with a number of experimental 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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