The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Natural Gradient Works Efficiently in Learning
Abstract
When a parameter space has a certain underlying structure, the ordinary gradient of a function does not represent its steepest direction, but the natural gradient does. Information geometry is used for calculating the natural gradients in the parameter space of perceptrons, the space of matrices (for blind source separation), and the space of linear dynamical systems (for blind source deconvolution). The dynamical behavior of natural gradient online learning is analyzed and is proved to be Fisher efficient, implying that it has asymptotically the same performance as the optimal batch estimation of parameters. This suggests that the plateau phenomenon, which appears in the backpropagation learning algorithm of multilayer perceptrons, might disappear or might not be so serious when the natural gradient is used. An adaptive method of updating the learning rate is proposed and analyzed.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
An Information-Maximization Approach to Blind Separation and Blind Deconvolution
Bell, A. J., & Sejnowski, T. J. (1995) · Neural Computation · doi:10.1162/neco.1995.7.6.1129 · Cited by 8,986
Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
Research works printed but not linked: 21
- Amari S., 1967, IEEE Trans., EC-16(3), 299
- 10.1007/BF00365229 · DOI · Paper page
- 10.1007/BF01692059 · DOI
- 10.1016/0893-6080(93)90013-M · DOI
- 10.1090/conm/203/02554 · DOI
- Amari S., IEEE Trans. on Signal Processing.
- 10.2307/3318651 · DOI
- 10.1109/72.125867 · DOI
- 10.1162/neco.1993.5.1.140 · DOI
- 10.1103/PhysRevLett.75.1415 · DOI
- 10.1016/0020-0255(85)90050-7 · DOI
- 10.1109/78.553476 · DOI · Paper page
- 10.1016/0165-1684(94)90029-9 · DOI · Paper page
- 10.1049/el:19961414 · DOI
- 10.1103/PhysRevA.44.2718 · DOI
- 10.1016/0165-1684(91)90079-X · DOI
- 10.1088/0954-898X/5/4/008 · DOI · Paper page
- 10.1103/PhysRevLett.77.4671 · DOI
- Rao C. R., 1945, Bulletin of the Calcutta Mathematical Society, 37, 81
- 10.1103/PhysRevE.52.4225 · DOI
- 10.1103/PhysRevLett.76.2188 · DOI
Cited by
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
Representation Learning: A Review and New Perspectives
Bengio, Y., Courville, A., & Vincent, P. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.50 · Cited by 13,001
Lee, T.-W., Girolami, M., & Sejnowski, T. J. (1999) · Neural Computation · doi:10.1162/089976699300016719 · Cited by 1,967
Practical Recommendations for Gradient-Based Training of Deep Architectures
Bengio, Y. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-35289-8_26 · Cited by 2,259
Metadata
- Authors
- Amari, S.-I.
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 1998-02-01
- Volume
- 10
- Issue
- 2
- Pages
- 251-276
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W1970789124
- Cited by
- 2,681
- References
- 2
- FWCI
- 61.26
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Natural Gradient Works Efficiently in Learning. https://app.cochat.ai/papers/10.1162/089976698300017746
- The paper
- Amari, S.-I. (1998). Natural Gradient Works Efficiently in Learning. Neural Computation. https://doi.org/10.1162/089976698300017746
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
