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A Common Framework for Natural Gradient and Taylor based Optimisation using Manifold Theory

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Adnan Haider

Machine Learning · Submitted 26 Mar 2018

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

The authors' main claim Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG.

how it is stated · asserted 0.94 read the record →

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arXiv ID1803.09791 (version 3)
Pith ID3PAOMN2P, Pith's permanent record of this paper and its review
CitationAdnan Haider. "A Common Framework for Natural Gradient and Taylor based Optimisation using Manifold Theory." arXiv:1803.09791 (2018). https://pith.science/paper/3PAOMN2P
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The compiled record

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, 2,258 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.43 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG.

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 This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. contribution 1.00 0.89 0.23 asserted 0.99
s1 Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG. result 0.45 0.59 0.40 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

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

What it cites · 2 sentences without a confident label

Cites as support 1 paper
  • When $X$ possesses such a structure, performing first order optimisation within a trust region defined by $I_θ$ can be shown to produce the update $Δθ =I_θ^-1 ∇F(θ )$ at each iteration [ref] .

    Optimization Methods for Large-Scale Machine Learning · Relating Gradient Descent with Natural Gradient · 0.96

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