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I struggle to find Rosenblatt's perceptron training algorithm in any of his publications from 1957 - 1961, namely:

  1. Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms

  2. The perceptron: A probabilistic model for information storage and organization in the brain

  3. The Perceptron — A Perceiving and Recognizing Automaton

Does anyone know where to find the original learning formula?

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The paper (or report) that formally introduced the perceptron is The Perceptron — A Perceiving and Recognizing Automaton (1957) by Frank Rosenblatt. If you read the first page of this paper, you can immediately understand that's the case. In particular, at some point (page 2, which corresponds to page 5 of the pdf), he writes

Recent theoretical studies by this writer indicate that it should be feasible to construct an electronic or electromechanical system which will learn to recognize similarities or identities between patterns of optical, electrical, or tonal information, in a manner which may be closely analogous to the perceptual processes of a biological brain. The proposed system depends on probabilistic rather than deterministic principles for its operation, and gains its reliability from the properties of statistical measurements obtained from large populations of elements. A system which operates according to these principles will be called a perceptron.

See also Appendix I (page 19, which corresponds to page 22 of the pdf).

The paper The perceptron: A probabilistic model for information storage and organization in the brain (1958) by F. Rosenblatt is apparently an updated and nicer version of the original report.

A more accessible (although not the most intuitive) description of the perceptron model and its learning algorithms can be found in the famous book Perceptrons: An Introduction to Computational Geometry (expanded edition, third printing, 1988) by Minsky and Papert (from page 161 onwards).

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