A variational formulation for the multilayer perceptron

==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.

Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.

An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. -->==




==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.

Most of the documents in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific publications in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.


2.1 Subsections

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2.2 General guidelines

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*  Symbols denoting vectors and matrices should be indicated in bold type. Scalar variable names should normally be expressed using italics.

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2.4 Supplementary material

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==3 Bibliography<!-- 
Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the document is [1], the second [2], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen 

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==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==




==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.

[2] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.

[3] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.

[4] Author of Part, D. (Year). Title of chapter or part. In A. Editor & B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.

[5] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.

[6] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: http://www.scipedia.com/document.pdf. 
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