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In
machine learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
, the perceptron is an algorithm for
supervised learning
In machine learning, supervised learning (SL) is a paradigm where a Statistical model, model is trained using input objects (e.g. a vector of predictor variables) and desired output values (also known as a ''supervisory signal''), which are often ...
of
binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of
linear classifier
In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. Such classifiers work well for practical problems such as document classification, and more generally for prob ...
, i.e. a classification algorithm that makes its predictions based on a
linear predictor function
In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent varia ...
combining a set of
weights with the
feature vector
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a data set. Choosing informative, discriminating, and independent features is crucial to produce effective algorithms for pattern re ...
.
History
The artificial neuron network was invented in 1943 by
Warren McCulloch
Warren Sturgis McCulloch (November 16, 1898 – September 24, 1969) was an American neurophysiologist and cybernetician known for his work on the foundation for certain brain theories and his contribution to the cybernetics movement.Ken Aizawa ...
and
Walter Pitts
Walter Harry Pitts, Jr. (April 23, 1923 – May 14, 1969) was an American logician who worked in the field of computational neuroscience.Smalheiser, Neil R"Walter Pitts", ''Perspectives in Biology and Medicine'', Volume 43, Number 2, Wint ...
in ''
A logical calculus of the ideas immanent in nervous activity
"A Logical Calculus of the Ideas Immanent to Nervous Activity" is a 1943 article written by Warren McCulloch and Walter Pitts. The paper, published in the journal '' The Bulletin of Mathematical Biophysics,'' proposed a mathematical model of the ...
''.
In 1957,
Frank Rosenblatt
Frank Rosenblatt (July 11, 1928July 11, 1971) was an American psychologist notable in the field of artificial intelligence. He is sometimes called the father of deep learning for his pioneering work on artificial neural networks.
Life and career
...
was at the
Cornell Aeronautical Laboratory. He simulated the perceptron on an
IBM 704
The IBM 704 is the model name of a large digital computer, digital mainframe computer introduced by IBM in 1954. Designed by John Backus and Gene Amdahl, it was the first mass-produced computer with hardware for floating-point arithmetic. The I ...
.
Later, he obtained funding by the Information Systems Branch of the United States
Office of Naval Research
The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...
and the
Rome Air Development Center
Rome Laboratory (Rome Air Development Center until 1991) is a U.S. Air Force research laboratory for " command, control, and communications" research and development and is responsible for planning and executing the USAF science and technology pr ...
, to build a custom-made computer, the
Mark I Perceptron. It was first publicly demonstrated on 23 June 1960.
The machine was "part of a previously secret four-year NPIC
he US' National Photographic Interpretation Center">National Photographic Interpretation Center">he US' National Photographic Interpretation Centereffort from 1963 through 1966 to develop this algorithm into a useful tool for photo-interpreters".
Rosenblatt described the details of the perceptron in a 1958 paper. His organization of a perceptron is constructed of three kinds of cells ("units"): AI, AII, R, which stand for "
projection
Projection or projections may refer to:
Physics
* Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction
* The display of images by a projector
Optics, graphics, and carto ...
", "association" and "response". He presented at the first international symposium on AI, ''Mechanisation of Thought Processes'', which took place in 1958 November.
Rosenblatt's project was funded under Contract Nonr-401(40) "Cognitive Systems Research Program", which lasted from 1959 to 1970, and Contract Nonr-2381(00) "Project PARA" ("PARA" means "Perceiving and Recognition Automata"), which lasted from 1957
to 1963.
In 1959, the Institute for Defense Analysis awarded his group a $10,000 contract. By September 1961, the ONR awarded further $153,000 worth of contracts, with $108,000 committed for 1962.
The ONR research manager, Marvin Denicoff, stated that ONR, instead of
ARPA, funded the Perceptron project, because the project was unlikely to produce technological results in the near or medium term. Funding from ARPA go up to the order of millions dollars, while from ONR are on the order of 10,000 dollars. Meanwhile, the head of
IPTO at ARPA, J.C.R. Licklider">Information Processing Techniques Office">IPTO at ARPA, J.C.R. Licklider, was interested in 'self-organizing', 'adaptive' and other biologically-inspired methods in the 1950s; but by the mid-1960s he was openly critical of these, including the perceptron. Instead he strongly favored the logical AI approach of
Simon and Allen Newell">Newell.
Mark I Perceptron machine

The perceptron was intended to be a machine, rather than a program, and while its first implementation was in software for the
IBM 704
The IBM 704 is the model name of a large digital computer, digital mainframe computer introduced by IBM in 1954. Designed by John Backus and Gene Amdahl, it was the first mass-produced computer with hardware for floating-point arithmetic. The I ...
, it was subsequently implemented in custom-built hardware as the
Mark I Perceptron with the project name "Project PARA",
designed for image recognition. The machine is currently in National Museum of American History, Smithsonian National Museum of American History.
The Mark I Perceptron had three layers. One version was implemented as follows:
* An array of 400
photocell
Photodetectors, also called photosensors, are devices that detect light or other forms of electromagnetic radiation and convert it into an electrical signal. They are essential in a wide range of applications, from digital imaging and optical c ...
s arranged in a 20x20 grid, named "sensory units" (S-units), or "input retina". Each S-unit can connect to up to 40 A-units.
* A hidden layer of 512 perceptrons, named "association units" (A-units).
* An output layer of eight perceptrons, named "response units" (R-units).
Rosenblatt called this three-layered perceptron network the ''alpha-perceptron'', to distinguish it from other perceptron models he experimented with.
The S-units are connected to the A-units randomly (according to a table of random numbers) via a plugboard (see photo), to "eliminate any particular intentional bias in the perceptron". The connection weights are fixed, not learned. Rosenblatt was adamant about the random connections, as he believed the retina was randomly connected to the visual cortex, and he wanted his perceptron machine to resemble human visual perception.
The A-units are connected to the R-units, with adjustable weights encoded in
potentiometer
A potentiometer is a three- terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat.
The measuring instrum ...
s, and weight updates during learning were performed by electric motors.
The hardware details are in an operators' manual.
In a 1958 press conference organized by the US Navy, Rosenblatt made statements about the perceptron that caused a heated controversy among the fledgling
AI community; based on Rosenblatt's statements, ''
The New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...
'' reported the perceptron to be "the embryo of an electronic computer that
he Navyexpects will be able to walk, talk, see, write, reproduce itself and be conscious of its existence."
The Photo Division of
Central Intelligence Agency
The Central Intelligence Agency (CIA; ) is a civilian foreign intelligence service of the federal government of the United States tasked with advancing national security through collecting and analyzing intelligence from around the world and ...
, from 1960 to 1964, studied the use of Mark I Perceptron machine for recognizing militarily interesting silhouetted targets (such as planes and ships) in
aerial photos.
''Principles of Neurodynamics'' (1962)
Rosenblatt described his experiments with many variants of the Perceptron machine in a book ''Principles of Neurodynamics'' (1962). The book is a published version of the 1961 report.
Among the variants are:
* "cross-coupling" (connections between units within the same layer) with possibly closed loops,
* "back-coupling" (connections from units in a later layer to units in a previous layer),
* four-layer perceptrons where the last two layers have adjustible weights (and thus a proper multilayer perceptron),
* incorporating time-delays to perceptron units, to allow for processing sequential data,
* analyzing audio (instead of images).
The machine was shipped from Cornell to Smithsonian in 1967, under a government transfer administered by the Office of Naval Research.
''Perceptrons'' (1969)
Although the perceptron initially seemed promising, it was quickly proved that perceptrons could not be trained to recognise many classes of patterns. This caused the field of
neural network
A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...
research to stagnate for many years, before it was recognised that a
feedforward neural network
Feedforward refers to recognition-inference architecture of neural networks. Artificial neural network architectures are based on inputs multiplied by weights to obtain outputs (inputs-to-output): feedforward. Recurrent neural networks, or neur ...
with two or more layers (also called a
multilayer perceptron
In deep learning, a multilayer perceptron (MLP) is a name for a modern feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is ...
) had greater processing power than perceptrons with one layer (also called a
single-layer perceptron).
Single-layer perceptrons are only capable of learning
linearly separable patterns.
For a classification task with some step activation function, a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve many otherwise non-separable problems.
In 1969, a famous book entitled ''
Perceptrons'' by
Marvin Minsky
Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive scientist, cognitive and computer scientist concerned largely with research in artificial intelligence (AI). He co-founded the Massachusetts Institute of Technology ...
and
Seymour Papert
Seymour Aubrey Papert (; 29 February 1928 – 31 July 2016) was a South African-born American mathematician, computer scientist, and educator, who spent most of his career teaching and researching at MIT. He was one of the pioneers of artif ...
showed that it was impossible for these classes of network to learn an
XOR function. It is often incorrectly believed that they also conjectured that a similar result would hold for a multi-layer perceptron network. However, this is not true, as both Minsky and Papert already knew that multi-layer perceptrons were capable of producing an XOR function. (See the page on ''
Perceptrons (book)'' for more information.) Nevertheless, the often-miscited Minsky and Papert text caused a significant decline in interest and funding of neural network research. It took ten more years until neural network research experienced a resurgence in the 1980s.
This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected.
Subsequent work
Rosenblatt continued working on perceptrons despite diminishing funding. The last attempt was Tobermory, built between 1961 and 1967, built for speech recognition. It occupied an entire room.
[Nagy, George. 1963. ]
System and circuit designs for the Tobermory perceptron
'. Technical report number 5, Cognitive Systems Research Program, Cornell University, Ithaca New York. It had 4 layers with 12,000 weights implemented by toroidal
magnetic core
A magnetic core is a piece of magnetism, magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, ele ...
s. By the time of its completion, simulation on digital computers had become faster than purpose-built perceptron machines. He died in a boating accident in 1971.

The
kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by
Freund and
Schapire (1998),
and more recently by
Mohri and Rostamizadeh (2013) who extend previous results and give new and more favorable L1 bounds.
The perceptron is a simplified model of a biological
neuron
A neuron (American English), neurone (British English), or nerve cell, is an membrane potential#Cell excitability, excitable cell (biology), cell that fires electric signals called action potentials across a neural network (biology), neural net ...
. While the complexity of
biological neuron models is often required to fully understand neural behavior, research suggests a perceptron-like linear model can produce some behavior seen in real neurons.
The solution spaces of decision boundaries for all binary functions and learning behaviors are studied in.
Definition
In the modern sense, the perceptron is an algorithm for learning a binary classifier called a
threshold function: a function that maps its input
(a real-valued
vector
Vector most often refers to:
* Euclidean vector, a quantity with a magnitude and a direction
* Disease vector, an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematics a ...
) to an output value
(a single
binary value):
where
is the
Heaviside step-function (where an input of
outputs 1; otherwise 0 is the output ),
is a vector of real-valued weights,
is the
dot product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...
, where is the number of inputs to the perceptron, and is the ''bias''. The bias shifts the decision boundary away from the origin and does not depend on any input value.
Equivalently, since
, we can add the bias term
as another weight
and add a coordinate
to each input
, and then write it as a linear classifier that passes the origin:
The binary value of
(0 or 1) is used to perform binary classification on
as either a positive or a negative instance. Spatially, the bias shifts the position (though not the orientation) of the planar
decision boundary
__NOTOC__
In a statistical-classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the poin ...
.
In the context of neural networks, a perceptron is an
artificial neuron
An artificial neuron is a mathematical function conceived as a model of a biological neuron in a neural network. The artificial neuron is the elementary unit of an ''artificial neural network''.
The design of the artificial neuron was inspired ...
using the
Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Differen ...
as the activation function. The perceptron algorithm is also termed the single-layer perceptron, to distinguish it from a
multilayer perceptron
In deep learning, a multilayer perceptron (MLP) is a name for a modern feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is ...
, which is a misnomer for a more complicated neural network. As a linear classifier, the single-layer perceptron is the simplest
feedforward neural network
Feedforward refers to recognition-inference architecture of neural networks. Artificial neural network architectures are based on inputs multiplied by weights to obtain outputs (inputs-to-output): feedforward. Recurrent neural networks, or neur ...
.
Power of representation
Information theory
From an
information theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
point of view, a single perceptron with ''K'' inputs has a capacity of ''2K''
bits of information.
This result is due to
Thomas Cover.
Specifically let
be the number of ways to linearly separate ''N'' points in ''K'' dimensions, then