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75-1005: HDC may refer to: Computing [ edit ] Hyperdimensional computing , with very long vectors Handle of Device Context , part of the GDI API High-Definition Coding , an audio codec /dev/hdc ; a Unix-like ATA device file Law [ edit ] Holder in due course , in commercial law Home Detention Curfew , United Kingdom Music [ edit ] Heavyweight Dub Champion , an American electronic group Herräng Dance Camp , Sweden Organizations [ edit ] Halal Industry Development Corporation , Malaysia Health and Disability Commissioner , New Zealand Health Data Consortium , US Historic Districts Council , New York City, US Honeysuckle Development Corporation , NSW, Australia HDC Hyundai Development Company , South Korea Transportation [ edit ] Haldia Dock Complex , of

150-494: 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 networks in animal brains . An ANN consists of connected units or nodes called artificial neurons , which loosely model the neurons in the brain. These are connected by edges , which model the synapses in the brain. Each artificial neuron receives signals from connected neurons, then processes them and sends

225-411: A 1994 book, did not yet describe the algorithm ). In 1986, David E. Rumelhart et al. popularised backpropagation but did not cite the original work. Kunihiko Fukushima 's convolutional neural network (CNN) architecture of 1979 also introduced max pooling , a popular downsampling procedure for CNNs. CNNs have become an essential tool for computer vision . The time delay neural network (TDNN)

300-471: A CNN named DanNet by Dan Ciresan, Ueli Meier, Jonathan Masci, Luca Maria Gambardella , and Jürgen Schmidhuber achieved for the first time superhuman performance in a visual pattern recognition contest, outperforming traditional methods by a factor of 3. It then won more contests. They also showed how max-pooling CNNs on GPU improved performance significantly. In October 2012, AlexNet by Alex Krizhevsky , Ilya Sutskever , and Geoffrey Hinton won

375-411: A CNN was applied to medical image object segmentation and breast cancer detection in mammograms. LeNet -5 (1998), a 7-level CNN by Yann LeCun et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32×32 pixel images. From 1988 onward, the use of neural networks transformed the field of protein structure prediction , in particular when

450-542: A Hebbian network. Other neural network computational machines were created by Rochester , Holland, Habit and Duda (1956). In 1958, psychologist Frank Rosenblatt described the perceptron, one of the first implemented artificial neural networks, funded by the United States Office of Naval Research . R. D. Joseph (1960) mentions an even earlier perceptron-like device by Farley and Clark: "Farley and Clark of MIT Lincoln Laboratory actually preceded Rosenblatt in

525-401: A binary hypervector (values are +1 or −1) that is as close as possible to some set of dictionary hypervectors. The generated hypervector thus describes all the objects and their attributes in the image. Another algorithm creates probability distributions for the number of objects in each image and their characteristics. These probability distributions describe the likely characteristics of both

600-409: A complex and seemingly unrelated set of information. Neural networks are typically trained through empirical risk minimization . 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 are usually used to estimate

675-461: A constant and the cost C = E [ ( x − f ( x ) ) 2 ] {\displaystyle \textstyle C=E[(x-f(x))^{2}]} . Minimizing this cost produces a value of a {\displaystyle \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 compression it could be related to

750-444: A deep network with eight layers trained by this method, which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates." The first deep learning multilayer perceptron trained by stochastic gradient descent

825-399: A hypervector. A vector could contain information about all the objects in the image, including properties such as color, position, and size. In 2023, Abbas Rahimi et al., used HDC with neural networks to solve Raven's progressive matrices . In 2023, Mike Heddes et Al. under the supervision of Professors Givargis, Nicolau and Veidenbaum created a hyper-dimensional computing library that

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900-582: A neural network model of cognition-emotion relation. It was an example of a debate where an AI system, a recurrent neural network, contributed to an issue in the same time addressed by cognitive psychology. Two early influential works were the Jordan network (1986) and the Elman network (1990), which applied RNN to study cognitive psychology . In the 1980s, backpropagation did not work well for deep RNNs. To overcome this problem, in 1991, Jürgen Schmidhuber proposed

975-572: A particular learning task. 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 (also known as function approximation). Supervised learning

1050-462: A signal to other connected neurons. The "signal" is a real number , 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 , which adjusts during the learning process. Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from

1125-413: A single layer of output nodes with linear activation functions; 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 errors 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

1200-418: 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

1275-560: A working learning algorithm for hidden units, i.e., deep learning . Fundamental research was conducted on ANNs in the 1960s and 1970s. The first working deep learning algorithm was the Group method of data handling , a method to train arbitrarily deep neural networks, published by Alexey Ivakhnenko and Lapa in Ukraine (1965). They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron. A 1971 paper described

1350-434: Is CIRCLE” to “COLOR is RED,” creates a vector that represents a red circle. Permutation rearranges the vector elements. For example, permuting a three-dimensional vector with values labeled x , y and z , can interchange x to y , y to z , and z to x . Events represented by hypervectors A and B can be added, forming one vector, but that would sacrifice the event sequence. Combining addition with permutation preserves

1425-409: Is a constant parameter 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

1500-498: Is also a function ⊗ : H × H → H. The input is two points in H , while the output is a dissimilar point. Multiplying the SHAPE vector with CIRCLE binds the two, representing the idea “SHAPE is CIRCLE”. This vector is "nearly orthogonal" to SHAPE and CIRCLE. The components are recoverable from the vector (e.g., answer the question "is the shape a circle?"). Addition creates a vector that combines concepts. For example, adding “SHAPE

1575-427: 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. In unsupervised learning , input data is given along with the cost function, some function of the data x {\displaystyle \textstyle x} and

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1650-401: Is built on top of PyTorch . HDC algorithms can replicate tasks long completed by deep neural networks , such as classifying images. Classifying an annotated set of handwritten digits uses an algorithm to analyze the features of each image, yielding a hypervector per image. The algorithm then adds the hypervectors for all labeled images of e.g., zero, to create a prototypical hypervector for

1725-567: Is represented by a pattern of values across many dimensions rather than a single constant. HDC can combine hypervectors into new hypervectors using well-defined vector space operations. Groups , rings , and fields over hypervectors become the underlying computing structures with addition, multiplication, permutation, mapping, and inverse as primitive computing operations. All computational tasks are performed in high-dimensional space using simple operations like element-wise additions and dot products . Binding creates ordered point tuples and

1800-641: Is robust to errors such as an individual bit error (a 0 flips to 1 or vice versa) missed by error-correcting mechanisms. Eliminating such error-correcting mechanisms can save up to 25% of compute cost. This is possible because such errors leave the result "close" to the correct vector. Reasoning using vectors is not compromised. HDC is at least 10x more error tolerant than traditional artificial neural networks , which are already orders of magnitude more tolerant than traditional computing. A simple example considers images containing black circles and white squares. Hypervectors can represent SHAPE and COLOR variables and hold

1875-444: 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,

1950-478: Is the class of a particular x i . Given query x q ∈ X the most similar prototype can be found with k ∗ = k ∈ 1 , . . . , K a r g m a x   p ( ϕ ( x q ) ) , ϕ ( c k ) ) {\displaystyle k^{*}=_{k\in 1,...,K}^{argmax}\ p(\phi (x_{q})),\phi (c_{k}))} . The similarity metric ρ

2025-424: Is typically the dot-product. Hypervectors can also be used for reasoning. Raven's progressive matrices presents images of objects in a grid. One position in the grid is blank. The test is to choose from candidate images the one that best fits. A dictionary of hypervectors represents individual objects. Each hypervector represents an object concept with its attributes. For each test image a neural network generates

2100-450: The Boltzmann machine , restricted Boltzmann machine , Helmholtz machine , and the wake-sleep algorithm . These were designed for unsupervised learning of deep generative models. 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 . In 2011,

2175-563: The ReLU (rectified linear unit) activation function . The rectifier has become the most popular activation function for deep learning. Nevertheless, research stagnated in the United States following the work of Minsky and Papert (1969), who emphasized that basic perceptrons were incapable of processing the exclusive-or circuit. This insight was irrelevant for the deep networks of Ivakhnenko (1965) and Amari (1967). In 1976 transfer learning

2250-408: The method of least squares or linear regression . It was used as a means of finding a good rough linear fit to a set of points by Legendre (1805) and Gauss (1795) for the prediction of planetary movement. Historically, digital computers such as the von Neumann model operate via the execution of explicit instructions with access to memory by a number of processors. Some neural networks, on

2325-410: The mutual information between x {\displaystyle \textstyle x} and f ( x ) {\displaystyle \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

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2400-554: The vanishing gradient problem and proposed recurrent residual connections to solve it. He and Schmidhuber introduced long short-term memory (LSTM), which set accuracy records in multiple applications domains. This was not yet the modern version of LSTM, which required the forget gate, which was introduced in 1999. It became the default choice for RNN architecture. During 1985–1995, inspired by statistical mechanics, several architectures and methods were developed by Terry Sejnowski , Peter Dayan , Geoffrey Hinton , etc., including

2475-557: 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. The neurons are typically organized into multiple layers, especially in deep learning . Neurons of one layer connect only to neurons of

2550-473: The "neural sequence chunker" or "neural history compressor" which introduced the important concepts of self-supervised pre-training (the "P" in ChatGPT ) and neural knowledge distillation . In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequent layers in an RNN unfolded in time. In 1991, Sepp Hochreiter 's diploma thesis identified and analyzed

2625-507: The 2010s, the seq2seq model was developed, and attention mechanisms were added. It led to the modern Transformer architecture in 2017 in Attention Is All You Need . It requires computation time that is quadratic in the size of the context window. Jürgen Schmidhuber 's fast weight controller (1992) scales linearly and was later shown to be equivalent to the unnormalized linear Transformer. Transformers have increasingly become

2700-464: The Port of Kolkata, India Hammond Northshore Regional Airport (FAA LID code), Louisiana, US Hill descent control system , of an automobile Other uses [ edit ] Histidine decarboxylase , an enzyme Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title HDC . If an internal link led you here, you may wish to change

2775-428: 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 , weighted graph . An artificial neural network consists of simulated neurons. Each neuron is connected to other nodes via links like a biological axon-synapse-dendrite connection. All

2850-738: The algebra. HDC is suitable for "in-memory computing systems", which compute and hold data on a single chip, avoiding data transfer delays. Analog devices operate at low voltages. They are energy-efficient, but prone to error-generating noise. HDC's can tolerate such errors. Various teams have developed low-power HDC hardware accelerators. Nanoscale memristive devices can be exploited to perform computation. An in-memory hyperdimensional computing system can implement operations on two memristive crossbar engines together with peripheral digital CMOS circuits. Experiments using 760,000 phase-change memory devices performing analog in-memory computing achieved accuracy comparable to software implementations. HDC

2925-466: The art in generative modeling during 2014–2018 period. The GAN principle was originally published in 1991 by Jürgen Schmidhuber who called it "artificial curiosity": two neural networks contest with each other in the form of a zero-sum game , where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict

3000-433: 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. While it is possible to define a cost function ad hoc , frequently the choice is determined by the function's desirable properties (such as convexity ) or because it arises from

3075-803: The concept of zero and repeats this for the other digits. Classifying an unlabeled image involves creating a hypervector for it and comparing it to the reference hypervectors. This comparison identifies the digit that the new image most resembles. Given labeled example set S = { ( x i , y i ) } i = 1 N ,   where   x i ∈ X   and   y i ∈ { c i } i = 1 K {\displaystyle S=\{(x_{i},y_{i})\}_{i=1}^{N},\ {\scriptstyle {\text{where}}}\ x_{i}\in X\ {\scriptstyle {\text{and}}}\ y_{i}\in \{c_{i}\}_{i=1}^{K}}

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3150-575: The context and candidate images. They too are transformed into hypervectors, then algebra predicts the most likely candidate image to fill the slot. This approach achieved 88% accuracy on one problem set, beating neural network–only solutions that were 61% accurate. For 3-by-3 grids, the system was 250x faster than a method that used symbolic logic to reason, because of the size of the associated rulebook. Other applications include bio-signal processing, natural language processing, and robotics. Artificial neural network In machine learning ,

3225-417: The corresponding values: CIRCLE, SQUARE, BLACK and WHITE. Bound hypervectors can hold the pairs BLACK and CIRCLE, etc. High-dimensional space allows many mutually orthogonal vectors. However, If vectors are instead allowed to be nearly orthogonal , the number of distinct vectors in high-dimensional space is vastly larger. HDC uses the concept of distributed representations, in which an object/observation

3300-874: The development of a perceptron-like device." However, "they dropped the subject." The perceptron raised public excitement for research in Artificial Neural Networks, causing the US government to drastically increase funding. This contributed to "the Golden Age of AI" fueled by the optimistic claims made by computer scientists regarding the ability of perceptrons to emulate human intelligence. The first perceptrons did not have adaptive hidden units. However, Joseph (1960) also discussed multilayer perceptrons with an adaptive hidden layer. Rosenblatt (1962) cited and adopted these ideas, also crediting work by H. D. Block and B. W. Knight. Unfortunately, these early efforts did not lead to

3375-405: The error rate is too high, the network typically must be redesigned. Practically this is done by defining a 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

3450-483: The first cascading networks were trained on profiles (matrices) produced by multiple sequence alignments . One origin of RNN was statistical mechanics . In 1972, Shun'ichi Amari proposed to modify the weights of an Ising model by Hebbian learning rule as a model of associative memory, adding in the component of learning. This was popularized as the Hopfield network by John Hopfield (1982). Another origin of RNN

3525-466: 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 two hidden layers. Artificial neural networks are used for various tasks, including predictive modeling , adaptive control , and solving problems in artificial intelligence . They can learn from experience, and can derive conclusions from

3600-442: 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

3675-483: The input data. H is typically restricted to range-limited integers (-v-v) This is analogous to the learning process conducted by fruit flies olfactory system. The input is a roughly 50-dimensional vector corresponding to odor receptor neuron types. The HD representation uses ~2,000-dimensions. HDC algebra reveals the logic of how and why systems makes decisions, unlike artificial neural networks . Physical world objects can be mapped to hypervectors, to be processed by

3750-534: The large-scale ImageNet competition by a significant margin over shallow machine learning methods. Further incremental improvements included the VGG-16 network by Karen Simonyan and Andrew Zisserman and Google's Inceptionv3 . In 2012, Ng and 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

3825-708: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=HDC&oldid=1246585888 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Hyperdimensional computing Data is mapped from the input space to sparse HD space under an encoding function φ : X → H. HD representations are stored in data structures that are subject to corruption by noise/hardware failures. Noisy/corrupted HD representations can still serve as input for learning, classification, etc. They can also be decoded to recover

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3900-427: The model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost). 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 cost function associated with a given state with respect to

3975-433: The model of choice for natural language processing . Many modern large language models such as ChatGPT , GPT-4 , and BERT use this architecture. 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

4050-442: 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,

4125-401: The network's output. The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model f ( x ) = a {\displaystyle \textstyle f(x)=a} where a {\displaystyle \textstyle a} is

4200-441: 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 networks . Alternatively, networks that allow connections between neurons in the same or previous layers are known as recurrent networks . A hyperparameter

4275-401: 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. ANNs are composed of artificial neurons which are conceptually derived from biological neurons . Each artificial neuron has inputs and produces

4350-673: The order; the event sequence can be retrieved by reversing the operations. Bundling combines a set of elements in H as function ⊕ : H ×H → H. The input is two points in H and the output is a third point that is similar to both. Vector symbolic architectures (VSA) provided a systematic approach to high-dimensional symbol representations to support operations such as establishing relationships. Early examples include holographic reduced representations, binary spatter codes, and matrix binding of additive terms. HD computing advanced these models, particularly emphasizing hardware efficiency. In 2018, Eric Weiss showed how to fully represent an image as

4425-412: The other focused on the application of neural networks to artificial intelligence . In the late 1940s, D. O. Hebb proposed a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning . It was used in many early neural networks, such as Rosenblatt's perceptron and the Hopfield network . Farley and Clark (1954) used computational machines to simulate

4500-465: The other hand, originated from efforts to model information processing in biological systems through the framework of connectionism . Unlike the von Neumann model, connectionist computing does not separate memory and processing. Warren McCulloch and Walter Pitts (1943) considered a non-learning computational model for neural networks. This model paved the way for research to split into two approaches. One approach focused on biological processes while

4575-436: 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 optimization theory and statistical estimation . 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

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4650-401: The paradigm of unsupervised learning are in general estimation problems; the applications include clustering , the estimation of statistical distributions , compression and filtering . 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

4725-426: 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 . This method allows the network to generalize to unseen data. Today's deep neural networks are based on early work in statistics over 200 years ago. The simplest kind of feedforward neural network (FNN) is a linear network, which consists of

4800-427: The past. In 1982 a recurrent neural network, with an array architecture (rather than a multilayer perceptron architecture), named Crossbar Adaptive Array used direct recurrent connections from the output to the supervisor (teaching ) inputs. In addition of computing actions (decisions), it computed internal state evaluations (emotions) of the consequence situations. Eliminating the external supervisor, it introduced

4875-615: The reactions of the environment to these patterns. Excellent image quality is achieved by Nvidia 's StyleGAN (2018) based on the Progressive GAN by Tero Karras et al. Here, the GAN generator is grown from small to large scale in a pyramidal fashion. Image generation by GAN reached popular success, and provoked discussions concerning deepfakes . Diffusion models (2015) eclipsed GANs in generative modeling since then, with systems such as DALL·E 2 (2022) and Stable Diffusion (2022). In 2014,

4950-480: The self-learning method in neural networks. In cognitive psychology, the journal American Psychologist in early 1980's carried out a debate on relation between cognition and emotion. Zajonc in 1980 stated that emotion is computed first and is independent from cognition, while Lazarus in 1982 stated that cognition is computed first and is inseparable from emotion. In 1982 the Crossbar Adaptive Array gave

5025-530: The state of the art was training "very deep neural network" with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In 2015, two techniques were developed to train very deep networks: the highway network was published in May 2015, and the residual neural network (ResNet) in December 2015. ResNet behaves like an open-gated Highway Net. During

5100-540: 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

5175-435: The use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning". 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. Generative adversarial network (GAN) ( Ian Goodfellow et al., 2014) became state of

5250-432: The weights. The weight updates can be done via stochastic gradient descent or other methods, such as extreme learning machines , "no-prop" networks, training without backtracking, "weightless" networks, and non-connectionist neural networks . Machine learning is commonly separated into three main learning paradigms, supervised learning , unsupervised learning and reinforcement learning . Each corresponds to

5325-465: Was actually introduced in 1962 by Rosenblatt, but he did not know how to implement this, although Henry J. Kelley had a continuous precursor of backpropagation in 1960 in the context of control theory . In 1970, Seppo Linnainmaa published the modern form of backpropagation in his master thesis (1970). G.M. Ostrovski et al. republished it in 1971. Paul Werbos applied backpropagation to neural networks in 1982 (his 1974 PhD thesis, reprinted in

5400-434: Was introduced in 1987 by Alex Waibel to apply CNN to phoneme recognition. It used convolutions, weight sharing, and backpropagation. In 1988, Wei Zhang applied a backpropagation-trained CNN to alphabet recognition. In 1989, Yann LeCun et al. created a CNN called LeNet for recognizing handwritten ZIP codes on mail. Training required 3 days. In 1990, Wei Zhang implemented a CNN on optical computing hardware. In 1991,

5475-558: Was introduced in neural networks learning. Deep learning architectures for convolutional neural networks (CNNs) with convolutional layers and downsampling layers and weight replication began with the Neocognitron introduced by Kunihiko Fukushima in 1979, though not trained by backpropagation. Backpropagation is an efficient application of the chain rule derived by Gottfried Wilhelm Leibniz in 1673 to networks of differentiable nodes. The terminology "back-propagating errors"

5550-441: Was neuroscience. The word "recurrent" is used to describe loop-like structures in anatomy. In 1901, Cajal observed "recurrent semicircles" in the cerebellar cortex . Hebb considered "reverberating circuit" as an explanation for short-term memory. The McCulloch and Pitts paper (1943) considered neural networks that contains cycles, and noted that the current activity of such networks can be affected by activity indefinitely far in

5625-437: 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 internal representations to classify non-linearily separable pattern classes. Subsequent developments in hardware and hyperparameter tunings have made end-to-end stochastic gradient descent the currently dominant training technique. In 1969, Kunihiko Fukushima introduced

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