machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a model inspired by the structure and function of

biological neural network A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks. Biological neural networks have inspired t ...

s in animal

brain The brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head ( cephalization), usually near organs for special ...

s. An ANN consists of connected units or nodes called ''

artificial neuron An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network. Artificial neurons are elementary units in an artificial neural network. The artificial neuron receives one or more inputs (representing ...

s'', which loosely model the

neuron A neuron, neurone, or nerve cell is an membrane potential#Cell excitability, electrically excitable cell (biology), cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous ...

s in a brain. These are connected by ''edges'', which model the

synapse In the nervous system, a synapse is a structure that permits a neuron (or nerve cell) to pass an electrical or chemical signal to another neuron or to the target effector cell. Synapses are essential to the transmission of nervous impulses fr ...

s in a brain. Each artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons. The "signal" is a

real number In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...

, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the '' activation function''. The strength of the signal at each connection is determined by a ''

weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar q ...

'', which adjusts during the learning process. Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the ''input layer'') to the last layer (the ''output layer''), possibly passing through multiple intermediate layers ('' hidden layers''). A network is typically called a deep neural network if it has at least 2 hidden layers. Artificial neural networks are used for various tasks, including predictive modeling, adaptive control, and solving problems in

artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, moveme ...

. They can learn from experience, and can derive conclusions from a complex and seemingly unrelated set of information.

Training

Neural networks are typically trained through

empirical risk minimization Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on their performance. The core idea is that we cannot know exactly how well an a ...

. This method is based on the idea of optimizing the network's parameters to minimize the difference, or empirical risk, between the predicted output and the actual target values in a given dataset. Gradient based methods such as

backpropagation In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions gener ...

are usually used to estimate the parameters of the network. During the training phase, ANNs learn from labeled training data by iteratively updating their parameters to minimize a defined

loss function In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "co ...

. This method allows the network to generalize to unseen data.

History

Historically, digital computers evolved from the

von Neumann model The von Neumann architecture — also known as the von Neumann model or Princeton architecture — is a computer architecture based on a 1945 description by John von Neumann, and by others, in the ''First Draft of a Report on the EDVAC''. The ...

, and operate via the execution of explicit instructions via access to memory by a number of processors. Neural networks, on the other hand, originated from efforts to model information processing in biological systems through the framework of

connectionism Connectionism refers to both an approach in the field of cognitive science that hopes to explain mind, mental phenomena using artificial neural networks (ANN) and to a wide range of techniques and algorithms using ANNs in the context of artificial ...

. Unlike the von Neumann model, connectionist computing does not separate memory and processing. The simplest kind of

feedforward neural network A feedforward neural network (FNN) is an artificial neural network wherein connections between the nodes do ''not'' form a cycle. As such, it is different from its descendant: recurrent neural networks. The feedforward neural network was the ...

(FNN) is a linear network, which consists of a single layer of output nodes; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated at each node. The

mean squared error In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference betwe ...

s between these calculated outputs and the given target values are minimized by creating an adjustment to the weights. This technique has been known for over two centuries as the method of least squares or

linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is ...

. It was used as a means of finding a good rough linear fit to a set of points by Legendre (1805) and

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

(1795) for the prediction of planetary movement.Mansfield Merriman, "A List of Writings Relating to the Method of Least Squares"

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. (23 April 1923 – 14 May 1969) was a logician who worked in the field of computational neuroscience.Smalheiser, Neil R"Walter Pitts", ''Perspectives in Biology and Medicine'', Volume 43, Number 2, Winter 2000, pp. 21 ...

(1943) also considered a non-learning computational model for neural networks. In the late 1940s, D. O. Hebb created a learning

hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can testable, test it. Scientists generally base scientific hypotheses on prev ...

based on the mechanism of

neural plasticity Neuroplasticity, also known as neural plasticity, or brain plasticity, is the ability of neural networks in the brain to change through growth and reorganization. It is when the brain is rewired to function in some way that differs from how it p ...

that became known as

Hebbian learning Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptatio ...

. Hebbian learning is considered to be a 'typical'

unsupervised learning Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and t ...

rule and its later variants were early models for long term potentiation. These ideas started being applied to computational models in 1948 with Turing's "

unorganized machine An unorganized machine is a concept mentioned in a 1948 report in which Alan Turing suggested that the infant human cortex was what he called an "unorganised machine". Overview Turing defined the class of unorganized machines as largely random in ...

s". Farley and Wesley A. Clark were the first to simulate a Hebbian network in 1954 at MIT. They used computational machines, then called "calculators". Other neural network computational machines were created by Rochester, Holland, Habit, and Duda in 1956. In 1958, psychologist Frank Rosenblatt invented the

perceptron In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function which can decide whether or not an ...

, the first implemented artificial neural network, funded by 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 pla ...

. The invention of the perceptron raised public excitement for research in Artificial Neural Networks, causing the US government to drastically increase funding into deep learning research. This led to "the golden age of AI" fueled by the optimistic claims made by computer scientists regarding the ability of perceptrons to emulate human intelligence. For example, in 1957 Herbert Simon famously said:However, this wasn't the case as research stagnated in the United States following the work of

Minsky Minsky (Belarusian: Мінскі; Russian: Минский) is a family name originating in Eastern Europe. People *Hyman Minsky (1919–1996), American economist *Marvin Minsky (1927–2016), American cognitive scientist in the field of Ar ...

and Papert (1969), who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to train useful neural networks. This, along with other factors such as the 1973 Lighthill report by

James Lighthill Sir Michael James Lighthill (23 January 1924 – 17 July 1998) was a British applied mathematician, known for his pioneering work in the field of aeroacoustics and for writing the Lighthill report on artificial intelligence. Biography ...

stating that research in Artificial Intelligence has not "produced the major impact that was then promised," shutting funding in research into the field of AI in all but two universities in the UK and in many major institutions across the world. This ushered an era called the

AI Winter In the history of artificial intelligence, an AI winter is a period of reduced funding and interest in artificial intelligence research.symbolic artificial intelligence In artificial intelligence, symbolic artificial intelligence is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic and search. Sy ...

in the United States and other Western countries. During the AI Winter era, however, research outside the United States continued, especially in Eastern Europe. By the time Minsky and Papert's book on

Perceptrons In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function which can decide whether or not an ...

came out, methods for training multilayer perceptrons (MLPs) were already known. The first deep learning MLP was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, as the

Group Method of Data Handling Group method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models. GMDH is used in such fiel ...

. The first deep learning MLP trained by

stochastic gradient descent Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of ...

was published in 1967 by Shun'ichi Amari. In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes.

Self-organizing map A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher dimensional data set while preserving the ...

s (SOMs) were described by

Teuvo Kohonen Teuvo Kalevi Kohonen (11 July 1934 – 13 December 2021) was a prominent Finnish academic ( Dr. Eng.) and researcher. He was professor emeritus of the Academy of Finland. SOMs are neurophysiologically inspired neural networks that learn low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using

competitive learning Competitive learning is a form of unsupervised learning in artificial neural networks Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural net ...

. The

convolutional neural network In deep learning, a convolutional neural network (CNN, or ConvNet) is a class of artificial neural network (ANN), most commonly applied to analyze visual imagery. CNNs are also known as Shift Invariant or Space Invariant Artificial Neural Netwo ...

(CNN) architecture with convolutional layers and downsampling layers was introduced by Kunihiko Fukushima in 1980. He called it the

neocognitron __NOTOC__ The neocognitron is a hierarchical, multilayered artificial neural network proposed by Kunihiko Fukushima in 1979. It has been used for Japanese Handwriting recognition, handwritten character recognition and other pattern recognition task ...

. In 1969, he also introduced the ReLU (rectified linear unit) activation function. The rectifier has become the most popular activation function for CNNs and

deep neural networks Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised. ...

in general. CNNs have become an essential tool for

computer vision Computer vision is an Interdisciplinarity, interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate t ...

. A key in later advances in artificial neural network research was the

algorithm, an efficient application of the

Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mat ...

chain rule In calculus, the chain rule is a formula that expresses the derivative of the Function composition, composition of two differentiable functions and in terms of the derivatives of and . More precisely, if h=f\circ g is the function such that h(x) ...

(1673) to networks of differentiable nodes. It is also known as the reverse mode of

automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function ...

reverse accumulation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function s ...

, due to

Seppo Linnainmaa Seppo Ilmari Linnainmaa (born 28 September 1945) is a Finnish mathematician and computer scientist. He was born in Pori. In 1974 he obtained the first doctorate ever awarded in computer science at the University of Helsinki. In 1976, he became Ass ...

(1970). The term "back-propagating errors" was introduced in 1962 by Frank Rosenblatt, but he did not have an implementation of this procedure, although Henry J. Kelley and Bryson had

dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

based continuous precursors of backpropagation already in 1960–61 in the context of

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

. In 1973, Dreyfus used backpropagation to adapt

parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

s of controllers in proportion to error gradients. In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard. In 1986

Rumelhart David Everett Rumelhart (June 12, 1942 – March 13, 2011) was an American psychologist who made many contributions to the formal analysis of human cognition, working primarily within the frameworks of mathematical psychology, symbolic artific ...

, Hinton and Williams showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence.David E. Rumelhart, Geoffrey E. Hinton & Ronald J. Williams,
Learning representations by back-propagating errors
," ''Nature'', 323, pages 533–536 1986. In the late 1970s to early 1980s, interest briefly emerged in theoretically investigating the

Ising model The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...

created by Wilhelm Lenz (1920) and

Ernst Ising Ernst Ising (; May 10, 1900 in Cologne, Germany – May 11, 1998 in Peoria, Illinois, USA) was a German physicist, who is best remembered for the development of the Ising model. He was a professor of physics at Bradley University until his r ...

(1925) in relation to . The Ising model is essentially a non-learning artificial

recurrent neural network A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic ...

(RNN) consisting of neuron-like threshold elements. In 1972,

Shun'ichi Amari , is a Japanese scholar born in 1936 in Tokyo, Japan. Overviews He majored in Mathematical Engineering in 1958 from the University of Tokyo then graduated in 1963 from the Graduate School of the University of Tokyo. His M. Eng. in 1960 was en ...

described an adaptive version of this architecture, In 1981, the Ising model was solved exactly by Peter Barth for the general case of closed Cayley trees (with loops) with an arbitrary branching ratio and found to exhibit unusual

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...

behavior in its local-apex and long-range site-site correlations. John Hopfield popularised this architecture in 1982, and it is now known as a

Hopfield network A Hopfield network (or Ising model of a neural network or Ising–Lenz–Little model) is a form of recurrent artificial neural network and a type of spin glass system popularised by John Hopfield in 1982 as described earlier by Little in 1974 b ...

. The time delay neural network (TDNN) of Alex Waibel (1987) combined convolutions and weight sharing and backpropagation. Alexander Waibel et al.,
Phoneme Recognition Using Time-Delay Neural Networks
'' IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume 37, No. 3, pp. 328. – 339 March 1989. In 1988, Wei Zhang et al. applied backpropagation to a CNN (a simplified Neocognitron with convolutional interconnections between the image feature layers and the last fully connected layer) for alphabet recognition. In 1989,

Yann LeCun Yann André LeCun ( , ; originally spelled Le Cun; born 8 July 1960) is a French computer scientist working primarily in the fields of machine learning, computer vision, mobile robotics and computational neuroscience. He is the Silver Professor ...

et al. trained a CNN to recognize handwritten ZIP codes on mail.LeCun ''et al.'', "Backpropagation Applied to Handwritten Zip Code Recognition," ''Neural Computation'', 1, pp. 541–551, 1989. In 1992, max-pooling for CNNs was introduced by Juan Weng et al. to help with least-shift invariance and tolerance to deformation to aid

3D object recognition {{FeatureDetectionCompVisNavbox In computer vision, 3D object recognition involves recognizing and determining 3D information, such as the pose, volume, or shape, of user-chosen 3D objects in a photograph or range scan. Typically, an example o ...

.J. Weng, N. Ahuja and T. S. Huang,
Cresceptron: a self-organizing neural network which grows adaptively
," ''Proc. International Joint Conference on Neural Networks'', Baltimore, Maryland, vol I, pp. 576–581, June 1992.J. Weng, N. Ahuja and T. S. Huang,
Learning recognition and segmentation of 3-D objects from 2-D images
," ''Proc. 4th International Conf. Computer Vision'', Berlin, Germany, pp. 121–128, May 1993.J. Weng, N. Ahuja and T. S. Huang,
Learning recognition and segmentation using the Cresceptron
," ''International Journal of Computer Vision'', vol. 25, no. 2, pp. 105–139, Nov. 1997. LeNet-5 (1998), a 7-level CNN by

et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32x32 pixel images. From 1988 onward,Qian, Ning, and Terrence J. Sejnowski. "Predicting the secondary structure of globular proteins using neural network models." ''Journal of molecular biology'' 202, no. 4 (1988): 865-884.Bohr, Henrik, Jakob Bohr, Søren Brunak, Rodney MJ Cotterill, Benny Lautrup, Leif Nørskov, Ole H. Olsen, and Steffen B. Petersen. "Protein secondary structure and homology by neural networks The α-helices in rhodopsin." ''FEBS letters'' 241, (1988): 223-228 the use of neural networks transformed the field of

protein structure prediction Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is differen ...

, in particular when the first cascading networks were trained on ''profiles'' (matrices) produced by multiple

sequence alignment In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Ali ...

s.Rost, Burkhard, and Chris Sander. "Prediction of protein secondary structure at better than 70% accuracy." ''Journal of molecular biology'' 232, no. 2 (1993): 584-599. In 1991,

Sepp Hochreiter Josef "Sepp" Hochreiter (born 14 February 1967) is a German computer scientist. Since 2018 he has led the Institute for Machine Learning at the Johannes Kepler University of Linz after having led the Institute of Bioinformatics from 2006 to 2018 ...

's diploma thesis S. Hochreiter.,
Untersuchungen zu dynamischen neuronalen Netzen
," ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991. identified and analyzed the

vanishing gradient problem In machine learning, the vanishing gradient problem is encountered when training artificial neural networks with gradient-based learning methods and backpropagation. In such methods, during each iteration of training each of the neural network's ...

and proposed recurrent residual connections to solve it. His thesis was called "one of the most important documents in the history of machine learning" by his supervisor Juergen Schmidhuber. In 1991, Juergen Schmidhuber published adversarial neural networks that contest with each other in the form of a

zero-sum game Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is ...

, where one network's gain is the other network's loss. The first network is a

generative model In statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is incons ...

that models a

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...

over output patterns. The second network learns by

gradient descent In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of ...

to predict the reactions of the environment to these patterns. This was called "artificial curiosity." In 1992, Juergen Schmidhuber proposed a hierarchy of RNNs pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales. This can substantially facilitate downstream deep learning. The RNN hierarchy can be ''collapsed'' into a single RNN, by Knowledge distillation, distilling a higher level ''chunker'' network into a lower level ''automatizer'' network. In the same year he also published an ''alternative to RNNs'' which is a precursor of a ''linear Transformer (machine learning model), Transformer''. It introduces the concept ''internal spotlights of attention'': a slow feedforward neural network learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns. The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), in the form of complementary MOS (CMOS) technology, enabled increasing MOS transistor counts in digital electronics. This provided more processing power for the development of practical artificial neural networks in the 1980s. Neural networks' early successes included in 1995 a (mostly) self-driving car. 1997,

and Juergen Schmidhuber introduced the deep learning method called long short-term memory (LSTM), published in Neural Computation. LSTM recurrent neural networks can learn "very deep learning" tasks with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. The "vanilla LSTM" with forget gate was introduced in 1999 by Felix Gers, Schmidhuber and Fred Cummins. Geoffrey Hinton et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine to model each layer. In 2012, Andrew Ng, Ng and Jeff Dean (computer scientist), Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images. Unsupervised pre-training and increased computing power from GPUs and distributed computing allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning". Variants of the back-propagation algorithm, as well as unsupervised methods by Geoff Hinton and colleagues at the University of Toronto, can be used to train deep, highly nonlinear neural architectures, similar to the 1980 Neocognitron by Kunihiko Fukushima, and the "standard architecture of vision", inspired by the simple and complex cells identified by David H. Hubel and Torsten Wiesel in the primary visual cortex. Computational devices have been created in CMOS for both biophysical simulation and neuromorphic computing. More recent efforts show promise for creating nanodevices for very large scale principal components analyses and convolution. If successful, these efforts could usher in a new era of neural computing that is a step beyond digital computing, because it depends on learning rather than programming language, programming and because it is fundamentally Analog signal, analog rather than Digital data, digital even though the first instantiations may in fact be with CMOS digital devices. Ciresan and colleagues (2010) showed that despite the

, GPUs make backpropagation feasible for many-layered feedforward neural networks.Dominik Scherer, Andreas C. Müller, and Sven Behnke:
Evaluation of Pooling Operations in Convolutional Architectures for Object Recognition
," ''In 20th International Conference Artificial Neural Networks (ICANN)'', pp. 92–101, 2010. . Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in pattern recognition and handwriting recognition. For example, the bi-directional and multi-dimensional long short-term memory (LSTM) of Alex Graves (computer scientist), Graves et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned. Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance on benchmarks such as traffic sign recognition (IJCNN 2012). Radial basis function network, Radial basis function and wavelet networks were introduced in 2013. These can be shown to offer best approximation properties and have been applied in nonlinear system identification and classification applications. In 2014, the adversarial network principle was used in a generative adversarial network (GAN) by Ian Goodfellow et al. Here the adversarial network (discriminator) outputs a value between 1 and 0 depending on the likelihood of the first network's (generator) output is in a given set. This can be used to create realistic deepfakes. Excellent image quality is achieved by Nvidia's StyleGAN (2018) based on the Progressive GAN by Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Here the GAN generator is grown from small to large scale in a pyramidal fashion. In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used the LSTM principle to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet Competition, ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network. In 2017, Ashish Vaswani et al. introduced the modern Transformer architecture in their paper "Attention Is All You Need." It combines this with a softmax operator and a projection matrix. Transformers have increasingly become the model of choice for natural language processing. Many modern large language models such as ChatGPT, GPT-4, and BERT (language model), BERT use it. Transformers are also increasingly being used in

. Ramenzanpour et al. showed in 2020 that analytical and computational techniques derived from statistical physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep neural networks.

Models

ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, abandoning attempts to remain true to their biological precursors. ANNs have the ability to learn and model non-linearities and complex relationships. This is achieved by neurons being connected in various patterns, allowing the output of some neurons to become the input of others. The network forms a Directed graph, directed, weighted graph. An artificial neural network consists of simulated neurons. Each neuron is connected to other Vertex (graph theory), nodes via Glossary of graph theory terms#edge, links like a biological axon-synapse-dendrite connection. All the nodes connected by links take in some data and use it to perform specific operations and tasks on the data. Each link has a weight, determining the strength of one node's influence on another, allowing weights to choose the signal between neurons.

Artificial neurons

ANNs are composed of artificial neurons which are conceptually derived from biological

s. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons. The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final ''output neurons'' of the neural net accomplish the task, such as recognizing an object in an image. To find the output of the neuron we take the weighted sum of all the inputs, weighted by the ''weights'' of the ''connections'' from the inputs to the neuron. We add a ''bias'' term to this sum. This weighted sum is sometimes called the ''activation''. This weighted sum is then passed through a (usually nonlinear) activation function to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.

Organization

The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the ''input layer''. The layer that produces the ultimate result is the ''output layer''. In between them are zero or more ''hidden layers''. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be ''pooling'', where a group of neurons in one layer connects to a single neuron in the next layer, thereby reducing the number of neurons in that layer. Neurons with only such connections form a directed acyclic graph and are known as feedforward neural network, ''feedforward networks''. Alternatively, networks that allow connections between neurons in the same or previous layers are known as Recurrent neural network, ''recurrent networks''.

Hyperparameter

A hyperparameter (machine learning), hyperparameter is a constant

whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size. The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.

Learning

Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a Loss function, cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of Mathematical optimization, optimization theory and statistical estimation.

Learning rate

The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation. A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate. The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.

Cost function

While it is possible to define a cost function ad hoc, frequently the choice is determined by the function's desirable properties (such as Convex function, convexity) or because it arises from the model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost).

Backpropagation

Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the gradient (the derivative) of the loss function, cost function associated with a given state with respect to the weights. The weight updates can be done via

or other methods, such as ''extreme learning machines'', "no-prop" networks, training without backtracking, "weightless" networks, and Holographic associative memory, non-connectionist neural networks.

Learning paradigms

Machine learning is commonly separated into three main learning paradigms, supervised learning,

and reinforcement learning. Each corresponds to a particular learning task.

Supervised learning

Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions. A commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are pattern recognition (also known as classification) and Regression analysis, regression (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for handwriting, speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.

Unsupervised learning

, input data is given along with the cost function, some function of the data

\textstyle x

and the network's output. The cost function is dependent on the task (the model domain) and any ''A priori and a posteriori, a priori'' assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model

\textstyle f(x) = a

where

\textstyle a

is a constant and the cost

\textstyle C=E[(x - f(x))^2]

. Minimizing this cost produces a value of

\textstyle a

that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in Data compression, compression it could be related to the mutual information between

\textstyle x

and

\textstyle f(x)

, whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general Approximation, estimation problems; the applications include Data clustering, clustering, the estimation of statistical distributions, Data compression, compression and Bayesian spam filtering, filtering.

Reinforcement learning

In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In reinforcement learning, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an instantaneous cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly. Formally the environment is modeled as a Markov decision process (MDP) with states

\textstyle \in S

and actions

\textstyle  \in A

. Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution

\textstyle P(c_t, s_t)

, the observation distribution

\textstyle P(x_t, s_t)

and the transition distribution

\textstyle P(s_, s_t, a_t)

, while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the lowest-cost MC. ANNs serve as the learning component in such applications. Dynamic programming coupled with ANNs (giving Neural oscillation, neurodynamic programming) has been applied to problems such as those involved in vehicle routing, video games, natural resource management and medicine because of ANNs ability to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

Self-learning

Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named ''crossbar adaptive array'' (CAA). It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion. Given the memory matrix, W =, , w(a,s), , , the crossbar self-learning algorithm in each iteration performs the following computation: In situation s perform action a; Receive consequence situation s'; Compute emotion of being in consequence situation v(s'); Update crossbar memory w'(a,s) = w(a,s) + v(s'). The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.

Neuroevolution

Neuroevolution can create neural network topologies and weights using evolutionary computation. It is competitive with sophisticated gradient descent approaches. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".

Stochastic neural network

Stochastic neural networks originating from Spin glass#Sherrington–Kirkpatrick model, Sherrington–Kirkpatrick models are a type of artificial neural network built by introducing random variations into the network, either by giving the network's

s Stochastic process, stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for Optimization (mathematics), optimization problems, since the random fluctuations help the network escape from Maxima and minima, local minima. Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks.

Other

In a Bayesian probability, Bayesian framework, a distribution over the set of allowed models is chosen to minimize the cost. Evolutionary methods, gene expression programming, simulated annealing, expectation–maximization algorithm, expectation–maximization, non-parametric methods and particle swarm optimization are other learning algorithms. Convergent recursion is a learning algorithm for cerebellar model articulation controller (CMAC) neural networks.

Modes

Two modes of learning are available: stochastic gradient descent, stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.

Types

ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter is much more complicated but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers. Some of the main breakthroughs include: * Convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data;

(2016). Slides on Deep Learnin
Online
where long short-term memory avoids the

and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition, text-to-speech synthesis, and photo-real talking heads; * Competitive networks such as generative adversarial networks in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game or on deceiving the opponent about the authenticity of an input.

Network design

Using artificial neural networks requires an understanding of their characteristics. * Choice of model: This depends on the data representation and the application. Model parameters include the number, type, and connectedness of network layers, as well as the size of each and the connection type (full, pooling, etc. ). Overly complex models learn slowly. * Machine learning, Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation. * Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust. Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset, and use the results as feedback to teach the NAS network. Available systems include Automated machine learning, AutoML and AutoKeras. Scikit-learn, scikit-learn library provides functions to help with building a deep network from scratch. We can then implement a deep network with TensorFlow or Keras. Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc.

Applications

Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. These include: * Function approximation, or regression analysis, (including Time series#Prediction and forecasting, time series prediction, fitness approximation, and modeling) * Data processing (including filtering, clustering, blind source separation, and compression) * Nonlinear system identification and control (including vehicle control, trajectory prediction, adaptive control, process control, and natural resource management) * Pattern recognition (including radar systems, Facial recognition system, face identification, signal classification, novelty detection, 3D reconstruction, object recognition, and sequential decision making) * Sequence recognition (including Gesture recognition, gesture, Speech recognition, speech, and handwriting recognition, handwritten and printed text recognition) * Sensor data analysis (including image analysis) * Robotics (including directing manipulators and prosthesis, prostheses) * Data mining (including knowledge discovery in databases) * Finance (such as ex-ante models for specific financial long-run forecasts and artificial financial markets) * Quantum chemistry * General game playing * Generative AI * Data visualization * Machine translation * Social network filtering * E-mail spam filtering * Medical diagnosis ANNs have been used to diagnose several types of cancers and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information. ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters and to predict foundation settlements. It can also be useful to mitigate flood by the use of ANNs for modelling rainfall-runoff. ANNs have also been used for building black-box models in geoscience: hydrology, ocean modelling and coastal engineering, and geomorphology. ANNs have been employed in Computer security, cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware, for identifying domains belonging to threat actors and for detecting URLs posing a security risk. Research is underway on ANN systems designed for penetration testing, for detecting botnets, credit cards frauds and network intrusions. ANNs have been proposed as a tool to solve partial differential equations in physics and simulate the properties of many-body open quantum systems. In brain research ANNs have studied short-term behavior of biological neuron models, individual neurons, the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level. It is possible to create a profile of a user's interests from pictures, using artificial neural networks trained for object recognition. Beyond their traditional applications, artificial neural networks are increasingly being utilized in interdisciplinary research, such as materials science. For instance, graph neural networks (GNNs) have demonstrated their capability in scaling deep learning for the discovery of new stable materials by efficiently predicting the total energy of crystals. This application underscores the adaptability and potential of ANNs in tackling complex problems beyond the realms of predictive modeling and artificial intelligence, opening new pathways for scientific discovery and innovation.

Theoretical properties

Computational power

The multilayer perceptron is a UTM theorem, universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters. A specific recurrent architecture with rational number, rational-valued weights (as opposed to full precision

-valued weights) has the power of a universal Turing machine, using a finite number of neurons and standard linear connections. Further, the use of Irrational number, irrational values for weights results in a machine with Hypercomputation, super-Turing power.

Capacity

A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity. Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book which summarizes work by Thomas Cover. The capacity of a network of standard neurons (not convolutional) can be derived by four rules that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the VC dimension. VC Dimension uses the principles of measure theory and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in, the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.

Convergence

Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical. Another issue worthy to mention is that training may cross some Saddle point which may lead the convergence to the wrong direction. The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of Linear model, affine models. Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks. This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions.

Generalization and statistics

Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use cross-validation (statistics), cross-validation and similar techniques to check for the presence of over-training and to select hyperparameters to minimize the generalization error. The second is to use some form of ''regularization (mathematics), regularization''. This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting. Synapse deployment

Supervised neural networks that use a

(MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of network output, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output

stays the same and the network is not modified. By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications. The softmax activation function is: :

y_i=\frac

Criticism

Training

A common criticism of neural networks, particularly in robotics, is that they require too many training samples for real-world operation. Any learning machine needs sufficient representative examples in order to capture the underlying structure that allows it to generalize to new cases. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for cerebellar model articulation controller, CMAC. Dean Pomerleau uses a neural network to train a robotic vehicle to drive on multiple types of roads (single lane, multi-lane, dirt, etc.), and a large amount of his research is devoted to extrapolating multiple training scenarios from a single training experience, and preserving past training diversity so that the system does not become overtrained (if, for example, it is presented with a series of right turns—it should not learn to always turn right).

Theory

A central claim of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed that they are Emergent properties, emergent from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, Alexander Dewdney, a former ''Scientific American'' columnist, commented that as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything". One response to Dewdney is that neural networks have been successfully used to handle many complex and diverse tasks, ranging from autonomously flying aircraft to detecting credit card fraud to mastering the game of Go (game), Go. Technology writer Roger Bridgman commented: Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network. Moreover, recent emphasis on the Explainable artificial intelligence, explainability of AI has contributed towards the development of methods, notably those based on Attention (machine learning), attention mechanisms, for visualizing and explaining learned neural networks. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering generic principles that allow a learning machine to be successful. For example, Bengio and LeCun (2007) wrote an article regarding local vs non-local learning, as well as shallow vs deep architecture. Biological brains use both shallow and deep circuits as reported by brain anatomy,D. J. Felleman and D. C. Van Essen,
Distributed hierarchical processing in the primate cerebral cortex
" ''Cerebral Cortex'', 1, pp. 1–47, 1991. displaying a wide variety of invariance. WengJ. Weng,
Natural and Artificial Intelligence: Introduction to Computational Brain-Mind
," BMI Press, , 2012. argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.

Hardware

Large and effective neural networks require considerable computing resources. While the brain has hardware tailored to the task of processing signals through a Graph (discrete mathematics), graph of neurons, simulating even a simplified neuron on von Neumann architecture may consume vast amounts of Random-access memory, memory and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons which require enormous Central processing unit, CPU power and time. Jürgen Schmidhuber, Schmidhuber noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by General-purpose computing on graphics processing units, GPGPUs (on Graphics processing unit, GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before. The use of accelerators such as Field-programmable gate array, FPGAs and GPUs can reduce training times from months to days. Neuromorphic engineering or a physical neural network addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a Tensor Processing Unit, or TPU.

Practical counterexamples

Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture.

Hybrid approaches

Advocates of Hybrid neural network, hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.

Dataset bias

Neural networks are dependent on the quality of the data they are trained on, thus low quality data with imbalanced representativeness can lead to the model learning and perpetuating societal biases. These inherited biases become especially critical when the ANNs are integrated into real-world scenarios where the training data may be imbalanced due to the scarcity of data for a specific race, gender or other attribute. This imbalance can result in the model having inadequate representation and understanding of underrepresented groups, leading to discriminatory outcomes that exasperate societal inequalities, especially in applications like Facial recognition system, facial recognition, hiring processes, and law enforcement. For example, in 2018, Amazon (company), Amazon had to scrap a recruiting tool because the model favored men over women for jobs in software engineering due to the higher number of male workers in the field. The program would penalize any resume with the word "woman" or the name of any women's college. However, the use of synthetic data can help reduce dataset bias and increase representation in datasets.

Gallery

File:Single layer ann.svg, A single-layer feedforward artificial neural network. Arrows originating from

\scriptstyle x_2

are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output,

y_q

, is calculated as

\scriptstyle y_q = K*(\sum_i(x_i*w_)-b_q).

File:Two layer ann.svg, A two-layer feedforward artificial neural network File:Artificial neural network.svg, An artificial neural network File:Ann dependency (graph).svg, An ANN dependency graph File:Single-layer feedforward artificial neural network.png, A single-layer feedforward artificial neural network with 4 inputs, 6 hidden nodes and 2 outputs. Given position state and direction, it outputs wheel based control values. File:Two-layer feedforward artificial neural network.png, A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden nodes and 2 outputs. Given position state, direction and other environment values, it outputs thruster based control values. File:Cmac.jpg, Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step.

Recent advancements and future directions

Artificial neural networks (ANNs) have undergone significant advancements, particularly in their ability to model complex systems, handle large data sets, and adapt to various types of applications. Their evolution over the past few decades has been marked by a broad range of applications in fields such as image processing, speech recognition, natural language processing, finance, and medicine.

Image processing

In the realm of image processing, ANNs are employed in tasks such as image classification, object recognition, and image segmentation. For instance, deep convolutional neural networks (CNNs) have been important in handwritten digit recognition, achieving state-of-the-art performance. This demonstrates the ability of ANNs to effectively process and interpret complex visual information, leading to advancements in fields ranging from automated surveillance to medical imaging.

Speech recognition

By modeling speech signals, ANNs are used for tasks like speaker identification and speech-to-text conversion. Deep neural network architectures have introduced significant improvements in large vocabulary continuous speech recognition, outperforming traditional techniques. These advancements have enabled the development of more accurate and efficient voice-activated systems, enhancing user interfaces in technology products.

Natural language processing

In natural language processing, ANNs are used for tasks such as text classification, sentiment analysis, and machine translation. They have enabled the development of models that can accurately translate between languages, understand the context and sentiment in textual data, and categorize text based on content. This has implications for automated customer service, content moderation, and language understanding technologies.

Control systems

In the domain of control systems, ANNs are used to model dynamic systems for tasks such as system identification, control design, and optimization. For instance, deep feedforward neural networks are important in system identification and control applications.

Finance

ANNs are used for quantitative investing, stock market prediction and credit scoring: *In investing, ANNs can process vast amounts of financial data, recognize complex patterns, and forecast stock market trends, aiding investors and risk managers in making informed decisions. *In credit scoring, ANNs offer data-driven, personalized assessments of creditworthiness, improving the accuracy of default predictions and automating the lending process. ANNs require high-quality data and careful tuning, and their "black-box" nature can pose challenges in interpretation. Nevertheless, ongoing advancements suggest that ANNs continue to play a role in finance, offering valuable insights and enhancing financial risk management, risk management strategies.

Medicine

ANNs are able to process and analyze vast medical datasets. They enhance diagnostic accuracy, especially by interpreting complex medical imaging for early disease detection, and by predicting patient outcomes for personalized treatment planning. In drug discovery, ANNs speed up the identification of potential drug candidates and predict their efficacy and safety, significantly reducing development time and costs. Additionally, their application in personalized medicine and healthcare data analysis allows tailored therapies and efficient patient care management. Ongoing research is aimed at addressing remaining challenges such as data privacy and model interpretability, as well as expanding the scope of ANN applications in medicine.

Content creation

ANNs such as generative adversarial networks (Generative adversarial network, GAN) and Transformer (machine learning model), transformers are used for content creation across numerous industries. This is because deep learning models are able to learn the style of an artist or musician from huge datasets and generate completely new artworks and music compositions. For instance, DALL-E is a deep neural network trained on 650 million pairs of images and texts across the internet that can create artworks based on text entered by the user. In the field of music, transformers are used to create original music for commercials and documentaries through companies such as AIVA and Jukedeck. In the marketing industry generative models are used to create personalized advertisements for consumers. Additionally, major film companies are partnering with technology companies to analyze the financial success of a film, such as the partnership between Warner Bros and technology company Cinelytic established in 2020. Furthermore, neural networks have found uses in video game creation, where Non Player Characters (NPCs) can make decisions based on all the characters currently in the game.

External links

A Brief Introduction to Neural Networks (D. Kriesel)
- Illustrated, bilingual manuscript about artificial neural networks; Topics so far: Perceptrons, Backpropagation, Radial Basis Functions, Recurrent Neural Networks, Self Organizing Maps, Hopfield Networks.

*[https://web.archive.org/web/20091216110504/http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html Another introduction to ANN]
Next Generation of Neural Networks
- Google Tech Talks
Neural Networks and Information
*

Notes

References

Bibliography

* * * *
PDF
* * * * **created for National Science Foundation, Contract Number EET-8716324, and Defense Advanced Research Projects Agency (DOD), ARPA Order No. 4976 under Contract F33615-87-C-1499. * * * * * * * * * * * * * {{Authority control Computational statistics Artificial neural networks, Classification algorithms Computational neuroscience Market research Mathematical psychology Mathematical and quantitative methods (economics) Bioinspiration

Training

History

Models

Artificial neurons

Organization

Hyperparameter

Learning

Learning rate

Cost function

Backpropagation

Learning paradigms

Supervised learning

Unsupervised learning

Reinforcement learning

Self-learning

Neuroevolution

Stochastic neural network

Other

Modes

Types

Network design

Applications

Theoretical properties

Computational power

Capacity

Convergence

Generalization and statistics

Criticism

Training

Theory

Hardware

Practical counterexamples

Hybrid approaches

Dataset bias

Gallery

Recent advancements and future directions

Image processing

Speech recognition

Natural language processing

Control systems

Finance

Medicine

Content creation

See also

External links

Notes

References

Bibliography