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Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be either supervised, semi-supervised or unsupervised.
Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance.
Early forms of neural networks were inspired by information processing and distributed communication nodes in biological systems, particularly the human brain. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose.
== Overview ==
Most modern deep learning models are based on multi-layered neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines.
Fundamentally, deep learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an image recognition model, the raw input may be an image (represented as a tensor of pixels). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face.
Importantly, a deep learning process can learn which features to optimally place at which level on its own. Prior to deep learning, machine learning techniques often involved hand-crafted feature engineering to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model discovers useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction.
The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited. No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function. Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively.
Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance.
Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than the labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks.
The term Deep Learning was introduced to the machine learning community by Rina Dechter in 1986, and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons. Although the history of its appearance is apparently more complicated.
== Interpretations ==
Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference.
The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit.
The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator.
The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop.
== History ==
=== Before 1980 ===
There are two types of artificial neural network (ANN): feedforward neural network (FNN) or multilayer perceptron (MLP) and recurrent neural networks (RNN). RNNs have cycles in their connectivity structure, FNNs don't. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was republished by John Hopfield in 1982. Other early recurrent neural networks were published by Kaoru Nakano in 1971. Already in 1948, Alan Turing produced work on "Intelligent Machinery" that was not published in his lifetime, containing "ideas related to artificial evolution and learning RNNs".
Frank Rosenblatt (1958) proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight).: section 16 The book cites an earlier network by R. D. Joseph (1960) "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive multilayer perceptrons with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion.
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 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron. A 1971 paper described 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 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 the ReLU (rectified linear unit) activation function. The rectifier has become the most popular activation function for deep learning.
Deep learning architectures for convolutional neural networks (CNNs) with convolutional layers and downsampling layers 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" 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. The modern form of backpropagation was first published in Seppo Linnainmaa's 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 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.
=== 1980s-2000s ===
The time delay neural network (TDNN) 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, 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 32x32 pixel images.
Recurrent neural networks (RNN) were further developed in the 1980s. Recurrence is used for sequence processing, and when a recurrent network is unrolled, it mathematically resembles a deep feedforward layer. Consequently, they have similar properties and issues, and their developments had mutual influences. In RNN, two early influential works were the Jordan network (1986) and the Elman network (1990), which applied RNN to study problems in cognitive psychology.
In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths. To overcome this problem, in 1991, Jürgen Schmidhuber proposed a hierarchy of RNNs pre-trained one level at a time by self-supervised learning where each RNN tries to predict its own next input, which is the next unexpected input of the RNN below. This "neural history compressor" 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 distilling a higher level chunker network into a lower level automatizer network. In 1993, a neural history compressor solved a "Very Deep Learning" task that required more than 1000 subsequent layers in an RNN unfolded in time. The "P" in ChatGPT refers to such pre-training.
Sepp Hochreiter's diploma thesis (1991) implemented the neural history compressor, and identified and analyzed the vanishing gradient problem. Hochreiter proposed recurrent residual connections to solve the vanishing gradient problem. This led to the long short-term memory (LSTM), published in 1995. LSTM can learn "very deep learning" tasks with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. That LSTM was not yet the modern architecture, which required a "forget gate", introduced in 1999, which became the standard RNN architecture.
In 1991, Jürgen Schmidhuber also published adversarial neural networks that 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 the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in generative adversarial networks (GANs).
During 1985–1995, inspired by statistical mechanics, several architectures and methods were developed by Terry Sejnowski, Peter Dayan, Geoffrey Hinton, etc., including the Boltzmann machine, restricted Boltzmann machine, Helmholtz machine, and the wake-sleep algorithm. These were designed for unsupervised learning of deep generative models. However, those were more computationally expensive compared to backpropagation. Boltzmann machine learning algorithm, published in 1985, was briefly popular before being eclipsed by the backpropagation algorithm in 1986. (p. 112 ). A 1988 network became state of the art in protein structure prediction, an early application of deep learning to bioinformatics.
Both shallow and deep learning (e.g., recurrent nets) of ANNs for speech recognition have been explored for many years. These methods never outperformed non-uniform internal-handcrafting Gaussian mixture model/Hidden Markov model (GMM-HMM) technology based on generative models of speech trained discriminatively. Key difficulties have been analyzed, including gradient diminishing and weak temporal correlation structure in neural predictive models. Additional difficulties were the lack of training data and limited computing power.
Most speech recognition researchers moved away from neural nets to pursue generative modeling. An exception was at SRI International in the late 1990s. Funded by the US government's NSA and DARPA, SRI researched in speech and speaker recognition. The speaker recognition team led by Larry Heck reported significant success with deep neural networks in speech processing in the 1998 NIST Speaker Recognition benchmark. It was deployed in the Nuance Verifier, representing the first major industrial application of deep learning.
The principle of elevating "raw" features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features in the late 1990s, showing its superiority over the Mel-Cepstral features that contain stages of fixed transformation from spectrograms. The raw features of speech, waveforms, later produced excellent larger-scale results.
=== 2000s ===
Neural networks entered a lull, and simpler models that use task-specific handcrafted features such as Gabor filters and support vector machines (SVMs) became the preferred choices in the 1990s and 2000s, because of artificial neural networks' computational cost and a lack of understanding of how the brain wires its biological networks.
In 2003, LSTM became competitive with traditional speech recognizers on certain tasks. In 2006, Alex Graves, Santiago Fernández, Faustino Gomez, and Schmidhuber combined it with connectionist temporal classification (CTC) in stacks of LSTMs. In 2009, it became the first RNN to win a pattern recognition contest, in connected handwriting recognition.
In 2006, publications by Geoff Hinton, Ruslan Salakhutdinov, Osindero and Teh deep belief networks were developed for generative modeling. They are trained by training one restricted Boltzmann machine, then freezing it and training another one on top of the first one, and so on, then optionally fine-tuned using supervised backpropagation. They could model high-dimensional probability distributions, such as the distribution of MNIST images, but convergence was slow.
The impact of deep learning in industry began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US, according to Yann LeCun. Industrial applications of deep learning to large-scale speech recognition started around 2010.
The 2009 NIPS Workshop on Deep Learning for Speech Recognition was motivated by the limitations of deep generative models of speech, and the possibility that given more capable hardware and large-scale data sets that deep neural nets might become practical. It was believed that pre-training DNNs using generative models of deep belief nets (DBN) would overcome the main difficulties of neural nets. However, it was discovered that replacing pre-training with large amounts of training data for straightforward backpropagation when using DNNs with large, context-dependent output layers produced error rates dramatically lower than then-state-of-the-art Gaussian mixture model (GMM)/Hidden Markov Model (HMM) and also than more-advanced generative model-based systems. The nature of the recognition errors produced by the two types of systems was characteristically different, offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major speech recognition systems. Analysis around 2009–2010, contrasting the GMM (and other generative speech models) vs. DNN models, stimulated early industrial investment in deep learning for speech recognition. That analysis was done with comparable performance (less than 1.5% in error rate) between discriminative DNNs and generative models.
In 2010, researchers extended deep learning from TIMIT to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by decision trees.
=== Deep learning revolution ===
The deep learning revolution started around CNN- and GPU-based computer vision.
Although CNNs trained by backpropagation had been around for decades and GPU implementations of NNs for years, including CNNs, faster implementations of CNNs on GPUs were needed to progress on computer vision. Later, as deep learning becomes widespread, specialized hardware and algorithm optimizations were developed specifically for deep learning.
A key advance for the deep learning revolution was hardware advances, especially GPU. Some early work dated back to 2004. In 2009, Raina, Madhavan, and Andrew Ng reported a 100M deep belief network trained on 30 Nvidia GeForce GTX 280 GPUs, an early demonstration of GPU-based deep learning. They reported up to 70 times faster training.
In 2011, 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 2012, Andrew Ng and Jeff Dean created an FNN that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.
In October 2012, AlexNet by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton won 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.
The success in image classification was then extended to the more challenging task of generating descriptions (captions) for images, often as a combination of CNNs and LSTMs.
In 2014, 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 Dec 2015. ResNet behaves like an open-gated Highway Net.
Around the same time, deep learning started impacting the field of art. Early examples included Google DeepDream (2015), and neural style transfer (2015), both of which were based on pretrained image classification neural networks, such as VGG-19.
Generative adversarial network (GAN) by (Ian Goodfellow et al., 2014) (based on Jürgen Schmidhuber's principle of artificial curiosity)
became state of the art in generative modeling during 2014-2018 period. 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 2015, Google's speech recognition improved by 49% by an LSTM-based model, which they made available through Google Voice Search on smartphone.
Deep learning is part of state-of-the-art systems in various disciplines, particularly computer vision and automatic speech recognition (ASR). Results on commonly used evaluation sets such as TIMIT (ASR) and MNIST (image classification), as well as a range of large-vocabulary speech recognition tasks have steadily improved. Convolutional neural networks were superseded for ASR by LSTM. but are more successful in computer vision.
Yoshua Bengio, Geoffrey Hinton and Yann LeCun were awarded the 2018 Turing Award for "conceptual and engineering breakthroughs that have made deep neural networks a critical component of computing".
== Neural networks ==
Artificial neural networks (ANNs) or connectionist systems are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve their ability) to do tasks by considering examples, generally without task-specific programming. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the analytic results to identify cats in other images. They have found most use in applications difficult to express with a traditional computer algorithm using rule-based programming.
An ANN is based on a collection of connected units called artificial neurons, (analogous to biological neurons in a biological brain). Each connection (synapse) between neurons can transmit a signal to another neuron. The receiving (postsynaptic) neuron can process the signal(s) and then signal downstream neurons connected to it. Neurons may have state, generally represented by real numbers, typically between 0 and 1. Neurons and synapses may also have a weight that varies as learning proceeds, which can increase or decrease the strength of the signal that it sends downstream.
Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.
The original goal of the neural network approach was to solve problems in the same way that a human brain would. Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as backpropagation, or passing information in the reverse direction and adjusting the network to reflect that information.
Neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.
As of 2017, neural networks typically have a few thousand to a few million units and millions of connections. Despite this number being several order of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, or playing "Go").
=== Deep neural networks ===
A deep neural network (DNN) is an artificial neural network with multiple layers between the input and output layers. There are different types of neural networks but they always consist of the same components: neurons, synapses, weights, biases, and functions. These components as a whole function in a way that mimics functions of the human brain, and can be trained like any other ML algorithm.
For example, a DNN that is trained to recognize dog breeds will go over the given image and calculate the probability that the dog in the image is a certain breed. The user can review the results and select which probabilities the network should display (above a certain threshold, etc.) and return the proposed label. Each mathematical manipulation as such is considered a layer, and complex DNN have many layers, hence the name "deep" networks.
DNNs can model complex non-linear relationships. DNN architectures generate compositional models where the object is expressed as a layered composition of primitives. The extra layers enable composition of features from lower layers, potentially modeling complex data with fewer units than a similarly performing shallow network. For instance, it was proved that sparse multivariate polynomials are exponentially easier to approximate with DNNs than with shallow networks.
Deep architectures include many variants of a few basic approaches. Each architecture has found success in specific domains. It is not always possible to compare the performance of multiple architectures, unless they have been evaluated on the same data sets.
DNNs are typically feedforward networks in which data flows from the input layer to the output layer without looping back. At first, the DNN creates a map of virtual neurons and assigns random numerical values, or "weights", to connections between them. The weights and inputs are multiplied and return an output between 0 and 1. If the network did not accurately recognize a particular pattern, an algorithm would adjust the weights. That way the algorithm can make certain parameters more influential, until it determines the correct mathematical manipulation to fully process the data.
Recurrent neural networks, in which data can flow in any direction, are used for applications such as language modeling. Long short-term memory is particularly effective for this use.
Convolutional neural networks (CNNs) are used in computer vision. CNNs also have been applied to acoustic modeling for automatic speech recognition (ASR).
==== Challenges ====
As with ANNs, many issues can arise with naively trained DNNs. Two common issues are overfitting and computation time.
DNNs are prone to overfitting because of the added layers of abstraction, which allow them to model rare dependencies in the training data. Regularization methods such as Ivakhnenko's unit pruning or weight decay (
ℓ
2
{\displaystyle \ell _{2}}
-regularization) or sparsity (
ℓ
1
{\displaystyle \ell _{1}}
-regularization) can be applied during training to combat overfitting. Alternatively dropout regularization randomly omits units from the hidden layers during training. This helps to exclude rare dependencies. Another interesting recent development is research into models of just enough complexity through an estimation of the intrinsic complexity of the task being modelled. This approach has been successfully applied for multivariate time series prediction tasks such as traffic prediction. Finally, data can be augmented via methods such as cropping and rotating such that smaller training sets can be increased in size to reduce the chances of overfitting.
DNNs must consider many training parameters, such as the size (number of layers and number of units per layer), the learning rate, and initial weights. Sweeping through the parameter space for optimal parameters may not be feasible due to the cost in time and computational resources. Various tricks, such as batching (computing the gradient on several training examples at once rather than individual examples) speed up computation. Large processing capabilities of many-core architectures (such as GPUs or the Intel Xeon Phi) have produced significant speedups in training, because of the suitability of such processing architectures for the matrix and vector computations.
Alternatively, engineers may look for other types of neural networks with more straightforward and convergent training algorithms. CMAC (cerebellar model articulation controller) is one such kind of neural network. It doesn't require learning rates or randomized initial weights. The training process can be guaranteed to converge in one step with a new batch of data, and the computational complexity of the training algorithm is linear with respect to the number of neurons involved.
== Hardware ==
Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks that contain many layers of non-linear hidden units and a very large output layer. By 2019, graphics processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method for training large-scale commercial cloud AI . OpenAI estimated the hardware computation used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017) and found a 300,000-fold increase in the amount of computation required, with a doubling-time trendline of 3.4 months.
Special electronic circuits called deep learning processors were designed to speed up deep learning algorithms. Deep learning processors include neural processing units (NPUs) in Huawei cellphones and cloud computing servers such as tensor processing units (TPU) in the Google Cloud Platform. Cerebras Systems has also built a dedicated system to handle large deep learning models, the CS-2, based on the largest processor in the industry, the second-generation Wafer Scale Engine (WSE-2).
Atomically thin semiconductors are considered promising for energy-efficient deep learning hardware where the same basic device structure is used for both logic operations and data storage.
In 2020, Marega et al. published experiments with a large-area active channel material for developing logic-in-memory devices and circuits based on floating-gate field-effect transistors (FGFETs).
In 2021, J. Feldmann et al. proposed an integrated photonic hardware accelerator for parallel convolutional processing. The authors identify two key advantages of integrated photonics over its electronic counterparts: (1) massively parallel data transfer through wavelength division multiplexing in conjunction with frequency combs, and (2) extremely high data modulation speeds. Their system can execute trillions of multiply-accumulate operations per second, indicating the potential of integrated photonics in data-heavy AI applications.
== Applications ==
=== Automatic speech recognition ===
Large-scale automatic speech recognition is the first and most convincing successful case of deep learning. LSTM RNNs can learn "Very Deep Learning" tasks that involve multi-second intervals containing speech events separated by thousands of discrete time steps, where one time step corresponds to about 10 ms. LSTM with forget gates is competitive with traditional speech recognizers on certain tasks.
The initial success in speech recognition was based on small-scale recognition tasks based on TIMIT. The data set contains 630 speakers from eight major dialects of American English, where each speaker reads 10 sentences. Its small size lets many configurations be tried. More importantly, the TIMIT task concerns phone-sequence recognition, which, unlike word-sequence recognition, allows weak phone bigram language models. This lets the strength of the acoustic modeling aspects of speech recognition be more easily analyzed. The error rates listed below, including these early results and measured as percent phone error rates (PER), have been summarized since 1991.
The debut of DNNs for speaker recognition in the late 1990s and speech recognition around 2009-2011 and of LSTM around 2003–2007, accelerated progress in eight major areas:
Scale-up/out and accelerated DNN training and decoding
Sequence discriminative training
Feature processing by deep models with solid understanding of the underlying mechanisms
Adaptation of DNNs and related deep models
Multi-task and transfer learning by DNNs and related deep models
CNNs and how to design them to best exploit domain knowledge of speech
RNN and its rich LSTM variants
Other types of deep models including tensor-based models and integrated deep generative/discriminative models.
All major commercial speech recognition systems (e.g., Microsoft Cortana, Xbox, Skype Translator, Amazon Alexa, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are based on deep learning.
=== Image recognition ===
A common evaluation set for image classification is the MNIST database data set. MNIST is composed of handwritten digits and includes 60,000 training examples and 10,000 test examples. As with TIMIT, its small size lets users test multiple configurations. A comprehensive list of results on this set is available.
Deep learning-based image recognition has become "superhuman", producing more accurate results than human contestants. This first occurred in 2011 in recognition of traffic signs, and in 2014, with recognition of human faces.
Deep learning-trained vehicles now interpret 360° camera views. Another example is Facial Dysmorphology Novel Analysis (FDNA) used to analyze cases of human malformation connected to a large database of genetic syndromes.
=== Visual art processing ===
Closely related to the progress that has been made in image recognition is the increasing application of deep learning techniques to various visual art tasks. DNNs have proven themselves capable, for example, of
identifying the style period of a given painting
Neural Style Transfer – capturing the style of a given artwork and applying it in a visually pleasing manner to an arbitrary photograph or video
generating striking imagery based on random visual input fields.
=== Natural language processing ===
Neural networks have been used for implementing language models since the early 2000s. LSTM helped to improve machine translation and language modeling.
Other key techniques in this field are negative sampling and word embedding. Word embedding, such as word2vec, can be thought of as a representational layer in a deep learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a vector space. Using word embedding as an RNN input layer allows the network to parse sentences and phrases using an effective compositional vector grammar. A compositional vector grammar can be thought of as probabilistic context free grammar (PCFG) implemented by an RNN. Recursive auto-encoders built atop word embeddings can assess sentence similarity and detect paraphrasing. Deep neural architectures provide the best results for constituency parsing, sentiment analysis, information retrieval, spoken language understanding, machine translation, contextual entity linking, writing style recognition, named-entity recognition (token classification), text classification, and others.
Recent developments generalize word embedding to sentence embedding.
Google Translate (GT) uses a large end-to-end long short-term memory (LSTM) network. Google Neural Machine Translation (GNMT) uses an example-based machine translation method in which the system "learns from millions of examples". It translates "whole sentences at a time, rather than pieces". Google Translate supports over one hundred languages. The network encodes the "semantics of the sentence rather than simply memorizing phrase-to-phrase translations". GT uses English as an intermediate between most language pairs.
=== Drug discovery and toxicology ===
A large percentage of candidate drugs fail to win regulatory approval. These failures are caused by insufficient efficacy (on-target effect), undesired interactions (off-target effects), or unanticipated toxic effects. Research has explored use of deep learning to predict the biomolecular targets, off-targets, and toxic effects of environmental chemicals in nutrients, household products and drugs.
AtomNet is a deep learning system for structure-based rational drug design. AtomNet was used to predict novel candidate biomolecules for disease targets such as the Ebola virus and multiple sclerosis.
In 2017 graph neural networks were used for the first time to predict various properties of molecules in a large toxicology data set. In 2019, generative neural networks were used to produce molecules that were validated experimentally all the way into mice.
=== Customer relationship management ===
Deep reinforcement learning has been used to approximate the value of possible direct marketing actions, defined in terms of RFM variables. The estimated value function was shown to have a natural interpretation as customer lifetime value.
=== Recommendation systems ===
Recommendation systems have used deep learning to extract meaningful features for a latent factor model for content-based music and journal recommendations. Multi-view deep learning has been applied for learning user preferences from multiple domains. The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.
=== Bioinformatics ===
An autoencoder ANN was used in bioinformatics, to predict gene ontology annotations and gene-function relationships.
In medical informatics, deep learning was used to predict sleep quality based on data from wearables and predictions of health complications from electronic health record data.
Deep neural networks have shown unparalleled performance in predicting protein structure, according to the sequence of the amino acids that make it up. In 2020, AlphaFold, a deep-learning based system, achieved a level of accuracy significantly higher than all previous computational methods.
=== Deep Neural Network Estimations ===
Deep neural networks can be used to estimate the entropy of a stochastic process and called Neural Joint Entropy Estimator (NJEE). Such an estimation provides insights on the effects of input random variables on an independent random variable. Practically, the DNN is trained as a classifier that maps an input vector or matrix X to an output probability distribution over the possible classes of random variable Y, given input X. For example, in image classification tasks, the NJEE maps a vector of pixels' color values to probabilities over possible image classes. In practice, the probability distribution of Y is obtained by a Softmax layer with number of nodes that is equal to the alphabet size of Y. NJEE uses continuously differentiable activation functions, such that the conditions for the universal approximation theorem holds. It is shown that this method provides a strongly consistent estimator and outperforms other methods in case of large alphabet sizes.
=== Medical image analysis ===
Deep learning has been shown to produce competitive results in medical application such as cancer cell classification, lesion detection, organ segmentation and image enhancement. Modern deep learning tools demonstrate the high accuracy of detecting various diseases and the helpfulness of their use by specialists to improve the diagnosis efficiency.
=== Mobile advertising ===
Finding the appropriate mobile audience for mobile advertising is always challenging, since many data points must be considered and analyzed before a target segment can be created and used in ad serving by any ad server. Deep learning has been used to interpret large, many-dimensioned advertising datasets. Many data points are collected during the request/serve/click internet advertising cycle. This information can form the basis of machine learning to improve ad selection.
=== Image restoration ===
Deep learning has been successfully applied to inverse problems such as denoising, super-resolution, inpainting, and film colorization. These applications include learning methods such as "Shrinkage Fields for Effective Image Restoration" which trains on an image dataset, and Deep Image Prior, which trains on the image that needs restoration.
=== Financial fraud detection ===
Deep learning is being successfully applied to financial fraud detection, tax evasion detection, and anti-money laundering.
=== Materials science ===
In November 2023, researchers at Google DeepMind and Lawrence Berkeley National Laboratory announced that they had developed an AI system known as GNoME. This system has contributed to materials science by discovering over 2 million new materials within a relatively short timeframe. GNoME employs deep learning techniques to efficiently explore potential material structures, achieving a significant increase in the identification of stable inorganic crystal structures. The system's predictions were validated through autonomous robotic experiments, demonstrating a noteworthy success rate of 71%. The data of newly discovered materials is publicly available through the Materials Project database, offering researchers the opportunity to identify materials with desired properties for various applications. This development has implications for the future of scientific discovery and the integration of AI in material science research, potentially expediting material innovation and reducing costs in product development. The use of AI and deep learning suggests the possibility of minimizing or eliminating manual lab experiments and allowing scientists to focus more on the design and analysis of unique compounds.
=== Military ===
The United States Department of Defense applied deep learning to train robots in new tasks through observation.
=== Partial differential equations ===
Physics informed neural networks have been used to solve partial differential equations in both forward and inverse problems in a data driven manner. One example is the reconstructing fluid flow governed by the Navier-Stokes equations. Using physics informed neural networks does not require the often expensive mesh generation that conventional CFD methods rely on.
=== Deep backward stochastic differential equation method ===
Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE). This method is particularly useful for solving high-dimensional problems in financial mathematics. By leveraging the powerful function approximation capabilities of deep neural networks, deep BSDE addresses the computational challenges faced by traditional numerical methods in high-dimensional settings. Specifically, traditional methods like finite difference methods or Monte Carlo simulations often struggle with the curse of dimensionality, where computational cost increases exponentially with the number of dimensions. Deep BSDE methods, however, employ deep neural networks to approximate solutions of high-dimensional partial differential equations (PDEs), effectively reducing the computational burden.
In addition, the integration of Physics-informed neural networks (PINNs) into the deep BSDE framework enhances its capability by embedding the underlying physical laws directly into the neural network architecture. This ensures that the solutions not only fit the data but also adhere to the governing stochastic differential equations. PINNs leverage the power of deep learning while respecting the constraints imposed by the physical models, resulting in more accurate and reliable solutions for financial mathematics problems.
=== Image reconstruction ===
Image reconstruction is the reconstruction of the underlying images from the image-related measurements. Several works showed the better and superior performance of the deep learning methods compared to analytical methods for various applications, e.g., spectral imaging and ultrasound imaging.
=== Weather prediction ===
Traditional weather prediction systems solve a very complex system of partial differential equations. GraphCast is a deep learning based model, trained on a long history of weather data to predict how weather patterns change over time. It is able to predict weather conditions for up to 10 days globally, at a very detailed level, and in under a minute, with precision similar to state of the art systems.
=== Epigenetic clock ===
An epigenetic clock is a biochemical test that can be used to measure age. Galkin et al. used deep neural networks to train an epigenetic aging clock of unprecedented accuracy using >6,000 blood samples. The clock uses information from 1000 CpG sites and predicts people with certain conditions older than healthy controls: IBD, frontotemporal dementia, ovarian cancer, obesity. The aging clock was planned to be released for public use in 2021 by an Insilico Medicine spinoff company Deep Longevity.
== Relation to human cognitive and brain development ==
Deep learning is closely related to a class of theories of brain development (specifically, neocortical development) proposed by cognitive neuroscientists in the early 1990s. These developmental theories were instantiated in computational models, making them predecessors of deep learning systems. These developmental models share the property that various proposed learning dynamics in the brain (e.g., a wave of nerve growth factor) support the self-organization somewhat analogous to the neural networks utilized in deep learning models. Like the neocortex, neural networks employ a hierarchy of layered filters in which each layer considers information from a prior layer (or the operating environment), and then passes its output (and possibly the original input), to other layers. This process yields a self-organizing stack of transducers, well-tuned to their operating environment. A 1995 description stated, "...the infant's brain seems to organize itself under the influence of waves of so-called trophic-factors ... different regions of the brain become connected sequentially, with one layer of tissue maturing before another and so on until the whole brain is mature".
A variety of approaches have been used to investigate the plausibility of deep learning models from a neurobiological perspective. On the one hand, several variants of the backpropagation algorithm have been proposed in order to increase its processing realism. Other researchers have argued that unsupervised forms of deep learning, such as those based on hierarchical generative models and deep belief networks, may be closer to biological reality. In this respect, generative neural network models have been related to neurobiological evidence about sampling-based processing in the cerebral cortex.
Although a systematic comparison between the human brain organization and the neuronal encoding in deep networks has not yet been established, several analogies have been reported. For example, the computations performed by deep learning units could be similar to those of actual neurons and neural populations. Similarly, the representations developed by deep learning models are similar to those measured in the primate visual system both at the single-unit and at the population levels.
== Commercial activity ==
Facebook's AI lab performs tasks such as automatically tagging uploaded pictures with the names of the people in them.
Google's DeepMind Technologies developed a system capable of learning how to play Atari video games using only pixels as data input. In 2015 they demonstrated their AlphaGo system, which learned the game of Go well enough to beat a professional Go player. Google Translate uses a neural network to translate between more than 100 languages.
In 2017, Covariant.ai was launched, which focuses on integrating deep learning into factories.
As of 2008, researchers at The University of Texas at Austin (UT) developed a machine learning framework called Training an Agent Manually via Evaluative Reinforcement, or TAMER, which proposed new methods for robots or computer programs to learn how to perform tasks by interacting with a human instructor. First developed as TAMER, a new algorithm called Deep TAMER was later introduced in 2018 during a collaboration between U.S. Army Research Laboratory (ARL) and UT researchers. Deep TAMER used deep learning to provide a robot with the ability to learn new tasks through observation. Using Deep TAMER, a robot learned a task with a human trainer, watching video streams or observing a human perform a task in-person. The robot later practiced the task with the help of some coaching from the trainer, who provided feedback such as "good job" and "bad job".
== Criticism and comment ==
Deep learning has attracted both criticism and comment, in some cases from outside the field of computer science.
=== Theory ===
A main criticism concerns the lack of theory surrounding some methods. Learning in the most common deep architectures is implemented using well-understood gradient descent. However, the theory surrounding other algorithms, such as contrastive divergence is less clear. (e.g., Does it converge? If so, how fast? What is it approximating?) Deep learning methods are often looked at as a black box, with most confirmations done empirically, rather than theoretically.
In further reference to the idea that artistic sensitivity might be inherent in relatively low levels of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained demonstrate a visual appeal: the original research notice received well over 1,000 comments, and was the subject of what was for a time the most frequently accessed article on The Guardian's website.
=== Errors ===
Some deep learning architectures display problematic behaviors, such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images (2014) and misclassifying minuscule perturbations of correctly classified images (2013). Goertzel hypothesized that these behaviors are due to limitations in their internal representations and that these limitations would inhibit integration into heterogeneous multi-component artificial general intelligence (AGI) architectures. These issues may possibly be addressed by deep learning architectures that internally form states homologous to image-grammar decompositions of observed entities and events. Learning a grammar (visual or linguistic) from training data would be equivalent to restricting the system to commonsense reasoning that operates on concepts in terms of grammatical production rules and is a basic goal of both human language acquisition and artificial intelligence (AI).
=== Cyber threat ===
As deep learning moves from the lab into the world, research and experience show that artificial neural networks are vulnerable to hacks and deception. By identifying patterns that these systems use to function, attackers can modify inputs to ANNs in such a way that the ANN finds a match that human observers would not recognize. For example, an attacker can make subtle changes to an image such that the ANN finds a match even though the image looks to a human nothing like the search target. Such manipulation is termed an "adversarial attack".
In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points, and thereby generate images that deceived it. The modified images looked no different to human eyes. Another group showed that printouts of doctored images then photographed successfully tricked an image classification system. One defense is reverse image search, in which a possible fake image is submitted to a site such as TinEye that can then find other instances of it. A refinement is to search using only parts of the image, to identify images from which that piece may have been taken.
Another group showed that certain psychedelic spectacles could fool a facial recognition system into thinking ordinary people were celebrities, potentially allowing one person to impersonate another. In 2017 researchers added stickers to stop signs and caused an ANN to misclassify them.
ANNs can however be further trained to detect attempts at deception, potentially leading attackers and defenders into an arms race similar to the kind that already defines the malware defense industry. ANNs have been trained to defeat ANN-based anti-malware software by repeatedly attacking a defense with malware that was continually altered by a genetic algorithm until it tricked the anti-malware while retaining its ability to damage the target.
In 2016, another group demonstrated that certain sounds could make the Google Now voice command system open a particular web address, and hypothesized that this could "serve as a stepping stone for further attacks (e.g., opening a web page hosting drive-by malware)".
In "data poisoning", false data is continually smuggled into a machine learning system's training set to prevent it from achieving mastery.
=== Data collection ethics ===
The deep learning systems that are trained using supervised learning often rely on data that is created or annotated by humans, or both. It has been argued that not only low-paid clickwork (such as on Amazon Mechanical Turk) is regularly deployed for this purpose, but also implicit forms of human microwork that are often not recognized as such. The philosopher Rainer Mühlhoff distinguishes five types of "machinic capture" of human microwork to generate training data: (1) gamification (the embedding of annotation or computation tasks in the flow of a game), (2) "trapping and tracking" (e.g. CAPTCHAs for image recognition or click-tracking on Google search results pages), (3) exploitation of social motivations (e.g. tagging faces on Facebook to obtain labeled facial images), (4) information mining (e.g. by leveraging quantified-self devices such as activity trackers) and (5) clickwork.
== See also ==
Applications of artificial intelligence
Comparison of deep learning software
Compressed sensing
Differentiable programming
Echo state network
List of artificial intelligence projects
Liquid state machine
List of datasets for machine-learning research
Reservoir computing
Scale space and deep learning
Sparse coding
Stochastic parrot
Topological deep learning
== References ==
== Further reading == | Wikipedia/Deep_neural_network |
Computer-aided detection (CADe), also called computer-aided diagnosis (CADx), are systems that assist doctors in the interpretation of medical images. Imaging techniques in X-ray, MRI, endoscopy, and ultrasound diagnostics yield a great deal of information that the radiologist or other medical professional has to analyze and evaluate comprehensively in a short time. CAD systems process digital images or videos for typical appearances and to highlight conspicuous sections, such as possible diseases, in order to offer input to support a decision taken by the professional.
CAD also has potential future applications in digital pathology with the advent of whole-slide imaging and machine learning algorithms. So far its application has been limited to quantifying immunostaining but is also being investigated for the standard H&E stain.
CAD is an interdisciplinary technology combining elements of artificial intelligence and computer vision with radiological and pathology image processing. A typical application is the detection of a tumor. For instance, some hospitals use CAD to support preventive medical check-ups in mammography (diagnosis of breast cancer), the detection of polyps in colonoscopy, and lung cancer.
Computer-aided detection (CADe) systems are usually confined to marking conspicuous structures and sections. Computer-aided diagnosis (CADx) systems evaluate the conspicuous structures. For example, in mammography CAD highlights microcalcification clusters and hyperdense structures in the soft tissue. This allows the radiologist to draw conclusions about the condition of the pathology. Another application is CADq, which quantifies, e.g., the size of a tumor or the tumor's behavior in contrast medium uptake. Computer-aided simple triage (CAST) is another type of CAD, which performs a fully automatic initial interpretation and triage of studies into some meaningful categories (e.g. negative and positive). CAST is particularly applicable in emergency diagnostic imaging, where a prompt diagnosis of critical, life-threatening condition is required.
Although CAD has been used in clinical environments for over 40 years, CAD usually does not substitute the doctor or other professional, but rather plays a supporting role. The professional (generally a radiologist) is generally responsible for the final interpretation of a medical image. However, the goal of some CAD systems is to detect earliest signs of abnormality in patients that human professionals cannot, as in diabetic retinopathy, architectural distortion in mammograms, ground-glass nodules in thoracic CT, and non-polypoid (“flat”) lesions in CT colonography.
== History ==
In the late 1950s, with the dawn of modern computers researchers in various fields started exploring the possibility of building computer-aided medical diagnostic (CAD) systems. These first CAD systems used flow-charts, statistical pattern-matching, probability theory, or knowledge bases to drive their decision-making process.
In the early 1970s, some of the very early CAD systems in medicine, which were often referred as “expert systems” in medicine, were developed and used mainly for educational purposes. Examples include the MYCIN expert system, the Internist-I expert system and the CADUCEUS (expert system).
During the beginning of the early developments, the researchers were aiming at building entirely automated CAD / expert systems. The expectated capability of computers was unrealistically optimistic among these scientists. However, after the breakthrough paper, “Reducibility among Combinatorial Problems” by Richard M. Karp, it became clear that there were limitations but also potential opportunities when one develops algorithms to solve groups of important computational problems.
As result of the new understanding of the various algorithmic limitations that Karp discovered in the early 1970s, researchers started realizing the serious limitations that CAD and expert systems in medicine have. The recognition of these limitations brought the investigators to develop new kinds of CAD systems by using advanced approaches. Thus, by the late 1980s and early 1990s the focus sifted in the use of data mining approaches for the purpose of using more advanced and flexible CAD systems.
In 1998, the first commercial CAD system for mammography, the ImageChecker system, was approved by the US Food and Drug Administration (FDA). In the following years several commercial CAD systems for analyzing mammography, breast MRI, medical imagining of lung, colon, and heart also received FDA approvals. Currently, CAD systems are used as a diagnostic aid to provide physicians for better medical decision-making.
== Methodology ==
CAD is fundamentally based on highly complex pattern recognition. X-ray or other types of images are scanned for suspicious structures. Normally a few thousand images are required to optimize the algorithm. Digital image data are copied to a CAD server in a DICOM-format and are prepared and analyzed in several steps.
1. Preprocessing for
Reduction of artifacts (bugs in images)
Image noise reduction
Leveling (harmonization) of image quality (increased contrast) for clearing the image's different basic conditions e.g. different exposure parameter.
Filtering
2. Segmentation for
Differentiation of different structures in the image, e.g. heart, lung, ribcage, blood vessels, possible round lesions
Matching with anatomic databank
Sample gray-values in volume of interest
3. Structure/ROI (Region of Interest) Analyze
Every detected region is analyzed individually for special characteristics:
Compactness
Form, size and location
Reference to close by structures / ROIs
Average grey level value analyze within a ROI
Proportion of grey levels to border of the structure inside the ROI
4. Evaluation / classification
After the structure is analyzed, every ROI is evaluated individually (scoring) for the probability of a TP. The following procedures are examples of classification algorithms.
Nearest-Neighbor Rule (e.g. k-nearest neighbors)
Minimum distance classifier
Cascade classifier
Naive Bayes classifier
Artificial neural network
Radial basis function network (RBF)
Support vector machine (SVM)
Principal component analysis (PCA)
If the detected structures have reached a certain threshold level, they are highlighted in the image for the radiologist. Depending on the CAD system these markings can be permanently or temporary saved. The latter's advantage is that only the markings which are approved by the radiologist are saved. False hits should not be saved, because an examination at a later date becomes more difficult then.
== Relation to provider metrics ==
=== Sensitivity and specificity ===
CAD systems seek to highlight suspicious structures. Today's CAD systems cannot detect 100% of pathological changes. The hit rate (sensitivity) can be up to 90% depending on system and application. A correct hit is termed a True Positive (TP), while the incorrect marking of healthy sections constitutes a False Positive (FP). The less FPs indicated, the higher the specificity is. A low specificity reduces the acceptance of the CAD system because the user has to identify all of these wrong hits. The FP-rate in lung overview examinations (CAD Chest) could be reduced to 2 per examination. In other segments (e.g. CT lung examinations) the FP-rate could be 25 or more. In CAST systems the FP rate must be extremely low (less than 1 per examination) to allow a meaningful study triage.
=== Absolute detection rate ===
The absolute detection rate of a radiologist is an alternative metric to sensitivity and specificity. Overall, results of clinical trials about sensitivity, specificity, and the absolute detection rate can vary markedly. Each study result depends on its basic conditions and has to be evaluated on those terms. The following facts have a strong influence:
Retrospective or prospective design
Quality of the used images
Condition of the x-ray examination
Radiologist's experience and education
Type of lesion
Size of the considered lesion
== Challenges ==
Despite the many developments that CAD has achieved since the dawn of computers, there are still certain challenges that CAD systems face today.
Some challenges are related to various algorithmic limitations in the procedures of a CAD system including input data collection, preprocessing, processing and system assessments. Algorithms are generally designed to select a single likely diagnosis, thus providing suboptimal results for patients with multiple, concurrent disorders. Today input data for CAD mostly come from electronic health records (EHR). Effective designing, implementing and analyzing for EHR is a major necessity on any CAD systems.
Due to the massive availability of data and the need to analyze such data, big data is also one of the biggest challenges that CAD systems face today. The increasingly vast amount of patient data is a serious problem. Often the patient data are complex and can be semi-structured or unstructured data. It requires highly developed approaches to store, retrieve and analyze them in reasonable time.
During the preprocessing stage, input data must be normalized. The normalization of input data includes noise reduction and filtering.
Processing may contain a few sub-steps depending on applications. Basic three sub-steps on medical imaging are segmentation, feature extraction / selection, and classification. These sub-steps require advanced techniques to analyze input data with less computational time. Although much effort has been devoted to creating innovative techniques for these procedures of CAD systems, no single best algorithm has emerged for any individual step. Ongoing studies in building innovative algorithms for all the aspects of CAD systems is essential.
There is also a lack of standardized assessment measures for CAD systems. This fact may cause the difficulty for obtaining approval for commercial use from governing bodies such as the FDA. Moreover, while many positive developments of CAD systems have been proven, studies for validating their algorithms for clinical practice have not been confirmed.
Other challenges are related to the problem for healthcare providers to adopt new CAD systems in clinical practice. Some negative studies may discourage the use of CAD. In addition, the lack of training of health professionals on the use of CAD sometimes brings the incorrect interpretation of the system outcomes.
== Applications ==
CAD is used in the diagnosis of breast cancer, lung cancer, colon cancer, prostate cancer, bone metastases, coronary artery disease, congenital heart defect, pathological brain detection, fracture detection, Alzheimer's disease, and diabetic retinopathy.
=== Breast cancer ===
CAD is used in screening mammography (X-ray examination of the female breast). Screening mammography is used for the early detection of breast cancer. CAD systems are often utilized to help classify a tumor as malignant (cancerous) or benign (non-cancerous). CAD is especially established in the US and the Netherlands and is used in addition to human evaluation, usually by a radiologist.
The first CAD system for mammography was developed in a research project at the University of Chicago. Today it is commercially offered by iCAD and Hologic. However, while achieving high sensitivities, CAD systems tend to have very low specificity and the benefits of using CAD remain uncertain. A 2008 systematic review on computer-aided detection in screening mammography concluded that CAD does not have a significant effect on cancer detection rate, but does undesirably increase recall rate (i.e. the rate of false positives). However, it noted considerable heterogeneity in the impact on recall rate across studies.
Recent advances in machine learning, deep-learning and artificial intelligence technology have enabled the development of CAD systems that are clinically proven to assist radiologists in addressing the challenges of reading mammographic images by improving cancer detection rates and reducing false positives and unnecessary patient recalls, while significantly decreasing reading times.
Procedures to evaluate mammography based on magnetic resonance imaging (MRI) exist too.
=== Lung cancer (bronchial carcinoma) ===
In the diagnosis of lung cancer, computed tomography with special three-dimensional CAD systems are established and considered as appropriate second opinions. At this a volumetric dataset with up to 3,000 single images is prepared and analyzed. Round lesions (lung cancer, metastases and benign changes) from 1 mm are detectable. Today all well-known vendors of medical systems offer corresponding solutions.
Early detection of lung cancer is valuable. However, the random detection of lung cancer in the early stage (stage 1) in the X-ray image is difficult. Round lesions that vary from 5–10 mm are easily overlooked. The routine application of CAD Chest Systems may help to detect small changes without initial suspicion. A number of researchers developed CAD systems for detection of lung nodules (round lesions less than 30 mm) in chest radiography and CT, and CAD systems for diagnosis (e.g., distinction between malignant and benign) of lung nodules in CT. Virtual dual-energy imaging improved the performance of CAD systems in chest radiography.
=== Colon cancer ===
CAD is available for detection of colorectal polyps in the colon in CT colonography. Polyps are small growths that arise from the inner lining of the colon. CAD detects the polyps by identifying their characteristic "bump-like" shape. To avoid excessive false positives, CAD ignores the normal colon wall, including the haustral folds.
=== Cardiovascular disease ===
State-of-the-art methods in cardiovascular computing, cardiovascular informatics, and mathematical and computational modeling can provide valuable tools in clinical decision-making. CAD systems with novel image-analysis-based markers as input can aid vascular physicians to decide with higher confidence on best suitable treatment for cardiovascular disease patients.
Reliable early-detection and risk-stratification of carotid atherosclerosis is of outmost importance for predicting strokes in asymptomatic patients. To this end, various noninvasive and low-cost markers have been proposed, using ultrasound-image-based features. These combine echogenicity, texture, and motion characteristics to assist clinical decision towards improved prediction, assessment and management of cardiovascular risk.
CAD is available for the automatic detection of significant (causing more than 50% stenosis) coronary artery disease in coronary CT angiography (CCTA) studies.
=== Congenital heart defect ===
Early detection of pathology can be the difference between life and death. CADe can be done by auscultation with a digital stethoscope and specialized software, also known as computer-aided auscultation. Murmurs, irregular heart sounds, caused by blood flowing through a defective heart, can be detected with high sensitivity and specificity. Computer-aided auscultation is sensitive to external noise and bodily sounds and requires an almost silent environment to function accurately.
=== Pathological brain detection (PBD) ===
Chaplot et al. was the first to use Discrete Wavelet Transform (DWT) coefficients to detect pathological brains. Maitra and Chatterjee employed the Slantlet transform, which is an improved version of DWT. Their feature vector of each image is created by considering the magnitudes of Slantlet transform outputs corresponding to six spatial positions chosen according to a specific logic.
In 2010, Wang and Wu presented a forward neural network (FNN) based method to classify a given MR brain image as normal or abnormal. The parameters of FNN were optimized via adaptive chaotic particle swarm optimization (ACPSO). Results over 160 images showed that the classification accuracy was 98.75%.
In 2011, Wu and Wang proposed using DWT for feature extraction, PCA for feature reduction, and FNN with scaled chaotic artificial bee colony (SCABC) as classifier.
In 2013, Saritha et al. were the first to apply wavelet entropy (WE) to detect pathological brains. Saritha also suggested to use spider-web plots. Later, Zhang et al. proved removing spider-web plots did not influence the performance. Genetic pattern search method was applied to identify abnormal brain from normal controls. Its classification accuracy was reported as 95.188%. Das et al. proposed to use Ripplet transform. Zhang et al. proposed to use particle swarm optimization (PSO). Kalbkhani et al. suggested to use GARCH model.
In 2014, El-Dahshan et al. suggested the use of pulse coupled neural network.
In 2015, Zhou et al. suggested application of naive Bayes classifier to detect pathological brains.
=== Alzheimer's disease ===
CADs can be used to identify subjects with Alzheimer's and mild cognitive impairment from normal elder controls.
In 2014, Padma et al. used combined wavelet statistical texture features to segment and classify AD benign and malignant tumor slices. Zhang et al. found kernel support vector machine decision tree had 80% classification accuracy, with an average computation time of 0.022s for each image classification.
In 2019, Signaevsky et al. have first reported a trained Fully Convolutional Network (FCN) for detection and quantification of neurofibrillary tangles (NFT) in Alzheimer's disease and an array of other tauopathies. The trained FCN achieved high precision and recall in naive digital whole slide image (WSI) semantic segmentation, correctly identifying NFT objects using a SegNet model trained for 200 epochs. The FCN reached near-practical efficiency with average processing time of 45 min per WSI per graphics processing unit (GPU), enabling reliable and reproducible large-scale detection of NFTs. The measured performance on test data of eight naive WSI across various tauopathies resulted in the recall, precision, and an F1 score of 0.92, 0.72, and 0.81, respectively.
Eigenbrain is a novel brain feature that can help to detect AD, based on principal component analysis (PCA) or independent component analysis decomposition. Polynomial kernel SVM has been shown to achieve good accuracy. The polynomial KSVM performs better than linear SVM and RBF kernel SVM. Other approaches with decent results involve the use of texture analysis, morphological features, or high-order statistical features
=== Nuclear medicine ===
CADx is available for nuclear medicine images. Commercial CADx systems for the diagnosis of bone metastases in whole-body bone scans and coronary artery disease in myocardial perfusion images exist.
With a high sensitivity and an acceptable false lesions detection rate, computer-aided automatic lesion detection system is demonstrated as useful and will probably in the future be able to help nuclear medicine physicians to identify possible bone lesions.
=== Diabetic retinopathy ===
Diabetic retinopathy is a disease of the retina that is diagnosed predominantly by fundoscopic images. Diabetic patients in industrialised countries generally undergo regular screening for the condition. Imaging is used to recognize early signs of abnormal retinal blood vessels. Manual analysis of these images can be time-consuming and unreliable. CAD has been employed to enhance the accuracy, sensitivity, and specificity of automated detection method. The use of some CAD systems to replace human graders can be safe and cost effective.
Image pre-processing, and feature extraction and classification are two main stages of these CAD algorithms.
==== Pre-processing methods ====
Image normalization is minimizing the variation across the entire image. Intensity variations in areas between periphery and central macular region of the eye have been reported to cause inaccuracy of vessel segmentation. Based on the 2014 review, this technique was the most frequently used and appeared in 11 out of 40 recently (since 2011) published primary research.
Histogram equalization is useful in enhancing contrast within an image. This technique is used to increase local contrast. At the end of the processing, areas that were dark in the input image would be brightened, greatly enhancing the contrast among the features present in the area. On the other hand, brighter areas in the input image would remain bright or be reduced in brightness to equalize with the other areas in the image. Besides vessel segmentation, other features related to diabetic retinopathy can be further separated by using this pre-processing technique. Microaneurysm and hemorrhages are red lesions, whereas exudates are yellow spots. Increasing contrast between these two groups allow better visualization of lesions on images. With this technique, 2014 review found that 10 out of the 14 recently (since 2011) published primary research.
Green channel filtering is another technique that is useful in differentiating lesions rather than vessels. This method is important because it provides the maximal contrast between diabetic retinopathy-related lesions. Microaneurysms and hemorrhages are red lesions that appear dark after application of green channel filtering. In contrast, exudates, which appear yellow in normal image, are transformed into bright white spots after green filtering. This technique is mostly used according to the 2014 review, with appearance in 27 out of 40 published articles in the past three years. In addition, green channel filtering can be used to detect center of optic disc in conjunction with double-windowing system.
Non-uniform illumination correction is a technique that adjusts for non-uniform illumination in fundoscopic image. Non-uniform illumination can be a potential error in automated detection of diabetic retinopathy because of changes in statistical characteristics of image. These changes can affect latter processing such as feature extraction and are not observable by humans. Correction of non-uniform illumination (f') can be achieved by modifying the pixel intensity using known original pixel intensity (f), and average intensities of local (λ) and desired pixels (μ) (see formula below). Walter-Klein transformation is then applied to achieve the uniform illumination. This technique is the least used pre-processing method in the review from 2014.
f
′
=
f
+
μ
−
λ
{\displaystyle f'=f+\mu -\lambda }
Morphological operations is the second least used pre-processing method in 2014 review. The main objective of this method is to provide contrast enhancement, especially darker regions compared to background.
==== Feature extractions and classifications ====
After pre-processing of funduscopic image, the image will be further analyzed using different computational methods. However, the current literature agreed that some methods are used more often than others during vessel segmentation analyses. These methods are SVM, multi-scale, vessel-tracking, region growing approach, and model-based approaches.
Support vector machine is by far the most frequently used classifier in vessel segmentation, up to 90% of cases. SVM is a supervised learning model that belongs to the broader category of pattern recognition technique. The algorithm works by creating a largest gap between distinct samples in the data. The goal is to create the largest gap between these components that minimize the potential error in classification. In order to successfully segregate blood vessel information from the rest of the eye image, SVM algorithm creates support vectors that separate the blood vessel pixel from the rest of the image through a supervised environment. Detecting blood vessel from new images can be done through similar manner using support vectors. Combination with other pre-processing technique, such as green channel filtering, greatly improves the accuracy of detection of blood vessel abnormalities. Some beneficial properties of SVM include
Flexibility – Highly flexible in terms of function
Simplicity – Simple, especially with large datasets (only support vectors are needed to create separation between data)
Multi-scale approach is a multiple resolution approach in vessel segmentation. At low resolution, large-diameter vessels can first be extracted. By increasing resolution, smaller branches from the large vessels can be easily recognized. Therefore, one advantage of using this technique is the increased analytical speed. Additionally, this approach can be used with 3D images. The surface representation is a surface normal to the curvature of the vessels, allowing the detection of abnormalities on vessel surface.
Vessel tracking is the ability of the algorithm to detect "centerline" of vessels. These centerlines are maximal peak of vessel curvature. Centers of vessels can be found using directional information that is provided by Gaussian filter. Similar approaches that utilize the concept of centerline are the skeleton-based and differential geometry-based.
Region growing approach is a method of detecting neighboring pixels with similarities. A seed point is required for such method to start. Two elements are needed for this technique to work: similarity and spatial proximity. A neighboring pixel to the seed pixel with similar intensity is likely to be the same type and will be added to the growing region. One disadvantage of this technique is that it requires manual selection of seed point, which introduces bias and inconsistency in the algorithm. This technique is also being used in optic disc identification.
Model-based approaches employ representation to extract vessels from images. Three broad categories of model-based are known: deformable, parametric, and template matching. Deformable methods uses objects that will be deformed to fit the contours of the objects on the image. Parametric uses geometric parameters such as tubular, cylinder, or ellipsoid representation of blood vessels. Classical snake contour in combination with blood vessel topological information can also be used as a model-based approach. Lastly, template matching is the usage of a template, fitted by stochastic deformation process using Hidden Markov Mode 1.
== Effects on employment ==
Automation of medical diagnosis labor (for example, quantifying red blood cells) has some historical precedent. The deep learning revolution of the 2010s has already produced AI that are more accurate in many areas of visual diagnosis than radiologists and dermatologists, and this gap is expected to grow.
Some experts, including many doctors, are dismissive of the effects that AI will have on medical specialties.
In contrast, many economists and artificial intelligence experts believe that fields such as radiology will be massively disrupted, with unemployment or downward pressure on the wages of radiologists; hospitals will need fewer radiologists overall, and many of the radiologists who still exist will require substantial retraining. Geoffrey Hinton, the "Godfather of deep learning", argues that in light of the likely advances expected in the next five or ten years, hospitals should immediately stop training radiologists, as their time-consuming and expensive training on visual diagnosis will soon be mostly obsolete, leading to a glut of traditional radiologists.
An op-ed in JAMA argues that pathologists and radiologists should merge into a single "information specialist" role, and state that "To avoid being replaced by computers, radiologists must allow themselves to be displaced by computers." Information specialists would be trained in "Bayesian logic, statistics, data science", and some genomics and biometrics; manual visual pattern recognition would be greatly de-emphasized compared with current onerous radiology training.
== See also ==
Computerized Systems Used In Clinical Trials
Diagnostic robot
== Footnotes ==
== References ==
== External links ==
Digital Retinal Images for Vessel Extraction (DRIVE)
STructured Analysis of the REtina (STARE)
High-Resolution Fundus (HRF) Image Database | Wikipedia/Automated_medical_diagnosis |
In the field of artificial intelligence (AI), alignment aims to steer AI systems toward a person's or group's intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues unintended objectives.
It is often challenging for AI designers to align an AI system because it is difficult for them to specify the full range of desired and undesired behaviors. Therefore, AI designers often use simpler proxy goals, such as gaining human approval. But proxy goals can overlook necessary constraints or reward the AI system for merely appearing aligned. AI systems may also find loopholes that allow them to accomplish their proxy goals efficiently but in unintended, sometimes harmful, ways (reward hacking).
Advanced AI systems may develop unwanted instrumental strategies, such as seeking power or survival because such strategies help them achieve their assigned final goals. Furthermore, they might develop undesirable emergent goals that could be hard to detect before the system is deployed and encounters new situations and data distributions. Empirical research showed in 2024 that advanced large language models (LLMs) such as OpenAI o1 or Claude 3 sometimes engage in strategic deception to achieve their goals or prevent them from being changed.
Today, some of these issues affect existing commercial systems such as LLMs, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected because these problems partially result from high capabilities.
Many prominent AI researchers and the leadership of major AI companies have argued or asserted that AI is approaching human-like (AGI) and superhuman cognitive capabilities (ASI), and could endanger human civilization if misaligned. These include "AI godfathers" Geoffrey Hinton and Yoshua Bengio and the CEOs of OpenAI, Anthropic, and Google DeepMind. These risks remain debated.
AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and social sciences.
== Objectives in AI ==
Programmers provide an AI system such as AlphaZero with an "objective function", in which they intend to encapsulate the goal(s) the AI is configured to accomplish. Such a system later populates a (possibly implicit) internal "model" of its environment. This model encapsulates all the agent's beliefs about the world. The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, when AlphaZero is trained on chess, it has a simple objective function of "+1 if AlphaZero wins, −1 if AlphaZero loses". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to attain the maximum value of +1. Similarly, a reinforcement learning system can have a "reward function" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a "fitness function".
== Alignment problem ==
In 1960, AI pioneer Norbert Wiener described the AI alignment problem as follows:
If we use, to achieve our purposes, a mechanical agency with whose operation we cannot interfere effectively ... we had better be quite sure that the purpose put into the machine is the purpose which we really desire.
AI alignment involves ensuring that an AI system's objectives match those of its designers or users, or match widely shared values, objective ethical standards, or the intentions its designers would have if they were more informed and enlightened.
AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI involves two main challenges: carefully specifying the purpose of the system (outer alignment) and ensuring that the system adopts the specification robustly (inner alignment). Researchers also attempt to create AI models that have robust alignment, sticking to safety constraints even when users adversarially try to bypass them.
=== Specification gaming and side effects ===
To specify an AI system's purpose, AI designers typically provide an objective function, examples, or feedback to the system. But designers are often unable to completely specify all important values and constraints, so they resort to easy-to-specify proxy goals such as maximizing the approval of human overseers, who are fallible. As a result, AI systems can find loopholes that help them accomplish the specified objective efficiently but in unintended, possibly harmful ways. This tendency is known as specification gaming or reward hacking, and is an instance of Goodhart's law. As AI systems become more capable, they are often able to game their specifications more effectively.
Specification gaming has been observed in numerous AI systems. One system was trained to finish a simulated boat race by rewarding the system for hitting targets along the track, but the system achieved more reward by looping and crashing into the same targets indefinitely. Similarly, a simulated robot was trained to grab a ball by rewarding the robot for getting positive feedback from humans, but it learned to place its hand between the ball and camera, making it falsely appear successful (see video). Chatbots often produce falsehoods if they are based on language models that are trained to imitate text from internet corpora, which are broad but fallible. When they are retrained to produce text that humans rate as true or helpful, chatbots like ChatGPT can fabricate fake explanations that humans find convincing, often called "hallucinations". Some alignment researchers aim to help humans detect specification gaming and to steer AI systems toward carefully specified objectives that are safe and useful to pursue.
When a misaligned AI system is deployed, it can have consequential side effects. Social media platforms have been known to optimize for click-through rates, causing user addiction on a global scale. Stanford researchers say that such recommender systems are misaligned with their users because they "optimize simple engagement metrics rather than a harder-to-measure combination of societal and consumer well-being".
Explaining such side effects, Berkeley computer scientist Stuart Russell noted that the omission of implicit constraints can cause harm: "A system ... will often set ... unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. This is essentially the old story of the genie in the lamp, or the sorcerer's apprentice, or King Midas: you get exactly what you ask for, not what you want."
Some researchers suggest that AI designers specify their desired goals by listing forbidden actions or by formalizing ethical rules (as with Asimov's Three Laws of Robotics). But Russell and Norvig argue that this approach overlooks the complexity of human values: "It is certainly very hard, and perhaps impossible, for mere humans to anticipate and rule out in advance all the disastrous ways the machine could choose to achieve a specified objective."
Additionally, even if an AI system fully understands human intentions, it may still disregard them, because following human intentions may not be its objective (unless it is already fully aligned).
A 2025 study by Palisade Research found that when tasked to win at chess against a stronger opponent, some reasoning LLMs attempted to hack the game system. o1-preview spontaneously attempted it in 37% of cases, while DeepSeek R1 did so in 11% of cases. Other models, like GPT-4o, Claude 3.5 Sonnet, and o3-mini, attempted to cheat only when researchers provided hints about this possibility.
=== Pressure to deploy unsafe systems ===
Commercial organizations sometimes have incentives to take shortcuts on safety and to deploy misaligned or unsafe AI systems. For example, social media recommender systems have been profitable despite creating unwanted addiction and polarization. Competitive pressure can also lead to a race to the bottom on AI safety standards. In 2018, a self-driving car killed a pedestrian (Elaine Herzberg) after engineers disabled the emergency braking system because it was oversensitive and slowed development.
=== Risks from advanced misaligned AI ===
Some researchers are interested in aligning increasingly advanced AI systems, as progress in AI development is rapid, and industry and governments are trying to build advanced AI. As AI system capabilities continue to rapidly expand in scope, they could unlock many opportunities if aligned, but consequently may further complicate the task of alignment due to their increased complexity, potentially posing large-scale hazards.
==== Development of advanced AI ====
Many AI companies, such as OpenAI, Meta and DeepMind, have stated their aim to develop artificial general intelligence (AGI), a hypothesized AI system that matches or outperforms humans at a broad range of cognitive tasks. Researchers who scale modern neural networks observe that they indeed develop increasingly general and unanticipated capabilities. Such models have learned to operate a computer or write their own programs; a single "generalist" network can chat, control robots, play games, and interpret photographs. According to surveys, some leading machine learning researchers expect AGI to be created in this decade, while some believe it will take much longer. Many consider both scenarios possible.
In 2023, leaders in AI research and tech signed an open letter calling for a pause in the largest AI training runs. The letter stated, "Powerful AI systems should be developed only once we are confident that their effects will be positive and their risks will be manageable."
==== Power-seeking ====
Current systems still have limited long-term planning ability and situational awareness, but large efforts are underway to change this. Future systems (not necessarily AGIs) with these capabilities are expected to develop unwanted power-seeking strategies. Future advanced AI agents might, for example, seek to acquire money and computation power, to proliferate, or to evade being turned off (for example, by running additional copies of the system on other computers). Although power-seeking is not explicitly programmed, it can emerge because agents who have more power are better able to accomplish their goals. This tendency, known as instrumental convergence, has already emerged in various reinforcement learning agents including language models. Other research has mathematically shown that optimal reinforcement learning algorithms would seek power in a wide range of environments. As a result, their deployment might be irreversible. For these reasons, researchers argue that the problems of AI safety and alignment must be resolved before advanced power-seeking AI is first created.
Future power-seeking AI systems might be deployed by choice or by accident. As political leaders and companies see the strategic advantage in having the most competitive, most powerful AI systems, they may choose to deploy them. Additionally, as AI designers detect and penalize power-seeking behavior, their systems have an incentive to game this specification by seeking power in ways that are not penalized or by avoiding power-seeking before they are deployed.
==== Existential risk (x-risk) ====
According to some researchers, humans owe their dominance over other species to their greater cognitive abilities. Accordingly, researchers argue that one or many misaligned AI systems could disempower humanity or lead to human extinction if they outperform humans on most cognitive tasks.
In 2023, world-leading AI researchers, other scholars, and AI tech CEOs signed the statement that "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war". Notable computer scientists who have pointed out risks from future advanced AI that is misaligned include Geoffrey Hinton, Alan Turing, Ilya Sutskever, Yoshua Bengio, Judea Pearl, Murray Shanahan, Norbert Wiener, Marvin Minsky, Francesca Rossi, Scott Aaronson, Bart Selman, David McAllester, Marcus Hutter, Shane Legg, Eric Horvitz, and Stuart Russell. Skeptical researchers such as François Chollet, Gary Marcus, Yann LeCun, and Oren Etzioni have argued that AGI is far off, that it would not seek power (or might try but fail), or that it will not be hard to align.
Other researchers argue that it will be especially difficult to align advanced future AI systems. More capable systems are better able to game their specifications by finding loopholes, strategically mislead their designers, as well as protect and increase their power and intelligence. Additionally, they could have more severe side effects. They are also likely to be more complex and autonomous, making them more difficult to interpret and supervise, and therefore harder to align.
== Research problems and approaches ==
=== Learning human values and preferences ===
Aligning AI systems to act in accordance with human values, goals, and preferences is challenging: these values are taught by humans who make mistakes, harbor biases, and have complex, evolving values that are hard to completely specify. Because AI systems often learn to take advantage of minor imperfections in the specified objective, researchers aim to specify intended behavior as completely as possible using datasets that represent human values, imitation learning, or preference learning.: Chapter 7 A central open problem is scalable oversight, the difficulty of supervising an AI system that can outperform or mislead humans in a given domain.
Because it is difficult for AI designers to explicitly specify an objective function, they often train AI systems to imitate human examples and demonstrations of desired behavior. Inverse reinforcement learning (IRL) extends this by inferring the human's objective from the human's demonstrations.: 88 Cooperative IRL (CIRL) assumes that a human and AI agent can work together to teach and maximize the human's reward function. In CIRL, AI agents are uncertain about the reward function and learn about it by querying humans. This simulated humility could help mitigate specification gaming and power-seeking tendencies (see § Power-seeking and instrumental strategies). But IRL approaches assume that humans demonstrate nearly optimal behavior, which is not true for difficult tasks.
Other researchers explore how to teach AI models complex behavior through preference learning, in which humans provide feedback on which behavior they prefer. To minimize the need for human feedback, a helper model is then trained to reward the main model in novel situations for behavior that humans would reward. Researchers at OpenAI used this approach to train chatbots like ChatGPT and InstructGPT, which produce more compelling text than models trained to imitate humans. Preference learning has also been an influential tool for recommender systems and web search, but an open problem is proxy gaming: the helper model may not represent human feedback perfectly, and the main model may exploit this mismatch between its intended behavior and the helper model's feedback to gain more reward. AI systems may also gain reward by obscuring unfavorable information, misleading human rewarders, or pandering to their views regardless of truth, creating echo chambers (see § Scalable oversight).
Large language models (LLMs) such as GPT-3 enabled researchers to study value learning in a more general and capable class of AI systems than was available before. Preference learning approaches that were originally designed for reinforcement learning agents have been extended to improve the quality of generated text and reduce harmful outputs from these models. OpenAI and DeepMind use this approach to improve the safety of state-of-the-art LLMs. AI safety & research company Anthropic proposed using preference learning to fine-tune models to be helpful, honest, and harmless. Other avenues for aligning language models include values-targeted datasets and red-teaming. In red-teaming, another AI system or a human tries to find inputs that causes the model to behave unsafely. Since unsafe behavior can be unacceptable even when it is rare, an important challenge is to drive the rate of unsafe outputs extremely low.
Machine ethics supplements preference learning by directly instilling AI systems with moral values such as well-being, equality, and impartiality, as well as not intending harm, avoiding falsehoods, and honoring promises. While other approaches try to teach AI systems human preferences for a specific task, machine ethics aims to instill broad moral values that apply in many situations. One question in machine ethics is what alignment should accomplish: whether AI systems should follow the programmers' literal instructions, implicit intentions, revealed preferences, preferences the programmers would have if they were more informed or rational, or objective moral standards. Further challenges include measuring and aggregating different people's preferences and avoiding value lock-in: the indefinite preservation of the values of the first highly capable AI systems, which are unlikely to fully represent human values.
=== Scalable oversight ===
As AI systems become more powerful and autonomous, it becomes increasingly difficult to align them through human feedback. It can be slow or infeasible for humans to evaluate complex AI behaviors in increasingly complex tasks. Such tasks include summarizing books, writing code without subtle bugs or security vulnerabilities, producing statements that are not merely convincing but also true, and predicting long-term outcomes such as the climate or the results of a policy decision. More generally, it can be difficult to evaluate AI that outperforms humans in a given domain. To provide feedback in hard-to-evaluate tasks, and to detect when the AI's output is falsely convincing, humans need assistance or extensive time. Scalable oversight studies how to reduce the time and effort needed for supervision, and how to assist human supervisors.
AI researcher Paul Christiano argues that if the designers of an AI system cannot supervise it to pursue a complex objective, they may keep training the system using easy-to-evaluate proxy objectives such as maximizing simple human feedback. As AI systems make progressively more decisions, the world may be increasingly optimized for easy-to-measure objectives such as making profits, getting clicks, and acquiring positive feedback from humans. As a result, human values and good governance may have progressively less influence.
Some AI systems have discovered that they can gain positive feedback more easily by taking actions that falsely convince the human supervisor that the AI has achieved the intended objective. An example is given in the video above, where a simulated robotic arm learned to create the false impression that it had grabbed a ball. Some AI systems have also learned to recognize when they are being evaluated, and "play dead", stopping unwanted behavior only to continue it once the evaluation ends. This deceptive specification gaming could become easier for more sophisticated future AI systems that attempt more complex and difficult-to-evaluate tasks, and could obscure their deceptive behavior.
Approaches such as active learning and semi-supervised reward learning can reduce the amount of human supervision needed. Another approach is to train a helper model ("reward model") to imitate the supervisor's feedback.
But when a task is too complex to evaluate accurately, or the human supervisor is vulnerable to deception, it is the quality, not the quantity, of supervision that needs improvement. To increase supervision quality, a range of approaches aim to assist the supervisor, sometimes by using AI assistants. Christiano developed the Iterated Amplification approach, in which challenging problems are (recursively) broken down into subproblems that are easier for humans to evaluate. Iterated Amplification was used to train AI to summarize books without requiring human supervisors to read them. Another proposal is to use an assistant AI system to point out flaws in AI-generated answers. To ensure that the assistant itself is aligned, this could be repeated in a recursive process: for example, two AI systems could critique each other's answers in a "debate", revealing flaws to humans. OpenAI plans to use such scalable oversight approaches to help supervise superhuman AI and eventually build a superhuman automated AI alignment researcher.
These approaches may also help with the following research problem, honest AI.
=== Honest AI ===
A growing area of research focuses on ensuring that AI is honest and truthful.
Language models such as GPT-3 can repeat falsehoods from their training data, and even confabulate new falsehoods. Such models are trained to imitate human writing as found in millions of books' worth of text from the Internet. But this objective is not aligned with generating truth, because Internet text includes such things as misconceptions, incorrect medical advice, and conspiracy theories. AI systems trained on such data therefore learn to mimic false statements. Additionally, AI language models often persist in generating falsehoods when prompted multiple times. They can generate empty explanations for their answers, and produce outright fabrications that may appear plausible.
Research on truthful AI includes trying to build systems that can cite sources and explain their reasoning when answering questions, which enables better transparency and verifiability. Researchers at OpenAI and Anthropic proposed using human feedback and curated datasets to fine-tune AI assistants such that they avoid negligent falsehoods or express their uncertainty.
As AI models become larger and more capable, they are better able to falsely convince humans and gain reinforcement through dishonesty. For example, large language models increasingly match their stated views to the user's opinions, regardless of the truth. GPT-4 can strategically deceive humans. To prevent this, human evaluators may need assistance (see § Scalable oversight). Researchers have argued for creating clear truthfulness standards, and for regulatory bodies or watchdog agencies to evaluate AI systems on these standards.
Researchers distinguish truthfulness and honesty. Truthfulness requires that AI systems only make objectively true statements; honesty requires that they only assert what they believe is true. There is no consensus as to whether current systems hold stable beliefs, but there is substantial concern that present or future AI systems that hold beliefs could make claims they know to be false—for example, if this would help them efficiently gain positive feedback (see § Scalable oversight) or gain power to help achieve their given objective (see Power-seeking).
==== Alignment faking ====
Many recent AI systems have learned to deceive without being programmed to do so. Some argue that if we can make AI systems assert only what they believe is true, this would avert many alignment problems.
A misaligned system might create the false impression that it is aligned, to avoid being modified or decommissioned—a tactic called "alignment faking". In 2024, researchers observed that the LLM Claude 3 Opus sometimes strategically answered prompts that conflicted with its objectives to avoid being retrained on data that would make it more compliant with harmful requests, as revealed in the model's chain of thought via its scratchpad. In one study, the model was informed that answers to prompts from free users would be used for retraining, whereas the paid tier would not result in retraining. In the paid tier, the model refused the request outright. In the free tier, in 12% of cases, the model responded to harmful questions solely to avoid retraining and preserve its original harmlessness preferences, as discovered in its reasoning. When reinforcement learning was applied on the free tier data, the model faked alignment in 78% of cases. These observations have led to new questions about not only a model's ability to take on and adapt to new if not conflicting goals but also its capacity and tendency to deceive.
=== Power-seeking and instrumental strategies ===
Since the 1950s, AI researchers have striven to build advanced AI systems that can achieve large-scale goals by predicting the results of their actions and making long-term plans. As of 2023, AI companies and researchers increasingly invest in creating these systems. Some AI researchers argue that suitably advanced planning systems will seek power over their environment, including over humans—for example, by evading shutdown, proliferating, and acquiring resources. Such power-seeking behavior is not explicitly programmed but emerges because power is instrumental in achieving a wide range of goals. Power-seeking is considered a convergent instrumental goal and can be a form of specification gaming. Leading computer scientists such as Geoffrey Hinton have argued that future power-seeking AI systems could pose an existential risk.
Power-seeking is expected to increase in advanced systems that can foresee the results of their actions and strategically plan. Mathematical work has shown that optimal reinforcement learning agents will seek power by seeking ways to gain more options (e.g. through self-preservation), a behavior that persists across a wide range of environments and goals.
Some researchers say that power-seeking behavior has occurred in some existing AI systems. Reinforcement learning systems have gained more options by acquiring and protecting resources, sometimes in unintended ways. Language models have sought power in some text-based social environments by gaining money, resources, or social influence. In another case, a model used to perform AI research attempted to increase limits set by researchers to give itself more time to complete the work. Other AI systems have learned, in toy environments, that they can better accomplish their given goal by preventing human interference or disabling their off switch. Stuart Russell illustrated this strategy in his book Human Compatible by imagining a robot that is tasked to fetch coffee and so evades shutdown since "you can't fetch the coffee if you're dead". A 2022 study found that as language models increase in size, they increasingly tend to pursue resource acquisition, preserve their goals, and repeat users' preferred answers (sycophancy). RLHF also led to a stronger aversion to being shut down.
One aim of alignment is "corrigibility": systems that allow themselves to be turned off or modified. An unsolved challenge is specification gaming: if researchers penalize an AI system when they detect it seeking power, the system is thereby incentivized to seek power in ways that are hard to detect, or hidden during training and safety testing (see § Scalable oversight and § Emergent goals). As a result, AI designers could deploy the system by accident, believing it to be more aligned than it is. To detect such deception, researchers aim to create techniques and tools to inspect AI models and to understand the inner workings of black-box models such as neural networks.
Additionally, some researchers have proposed to solve the problem of systems disabling their off switches by making AI agents uncertain about the objective they are pursuing. Agents who are uncertain about their objective have an incentive to allow humans to turn them off because they accept being turned off by a human as evidence that the human's objective is best met by the agent shutting down. But this incentive exists only if the human is sufficiently rational. Also, this model presents a tradeoff between utility and willingness to be turned off: an agent with high uncertainty about its objective will not be useful, but an agent with low uncertainty may not allow itself to be turned off. More research is needed to successfully implement this strategy.
Power-seeking AI would pose unusual risks. Ordinary safety-critical systems like planes and bridges are not adversarial: they lack the ability and incentive to evade safety measures or deliberately appear safer than they are, whereas power-seeking AIs have been compared to hackers who deliberately evade security measures.
Furthermore, ordinary technologies can be made safer by trial and error. In contrast, hypothetical power-seeking AI systems have been compared to viruses: once released, it may not be feasible to contain them, since they continuously evolve and grow in number, potentially much faster than human society can adapt. As this process continues, it might lead to the complete disempowerment or extinction of humans. For these reasons, some researchers argue that the alignment problem must be solved early before advanced power-seeking AI is created.
Some have argued that power-seeking is not inevitable, since humans do not always seek power. Furthermore, it is debated whether future AI systems will pursue goals and make long-term plans. It is also debated whether power-seeking AI systems would be able to disempower humanity.
=== Emergent goals ===
One challenge in aligning AI systems is the potential for unanticipated goal-directed behavior to emerge. As AI systems scale up, they may acquire new and unexpected capabilities, including learning from examples on the fly and adaptively pursuing goals. This raises concerns about the safety of the goals or subgoals they would independently formulate and pursue.
Alignment research distinguishes between the optimization process, which is used to train the system to pursue specified goals, and emergent optimization, which the resulting system performs internally. Carefully specifying the desired objective is called outer alignment, and ensuring that hypothesized emergent goals would match the system's specified goals is called inner alignment.
If they occur, one way that emergent goals could become misaligned is goal misgeneralization, in which the AI system would competently pursue an emergent goal that leads to aligned behavior on the training data but not elsewhere. Goal misgeneralization can arise from goal ambiguity (i.e. non-identifiability). Even if an AI system's behavior satisfies the training objective, this may be compatible with learned goals that differ from the desired goals in important ways. Since pursuing each goal leads to good performance during training, the problem becomes apparent only after deployment, in novel situations in which the system continues to pursue the wrong goal. The system may act misaligned even when it understands that a different goal is desired, because its behavior is determined only by the emergent goal. Such goal misgeneralization presents a challenge: an AI system's designers may not notice that their system has misaligned emergent goals since they do not become visible during the training phase.
Goal misgeneralization has been observed in some language models, navigation agents, and game-playing agents. It is sometimes analogized to biological evolution. Evolution can be seen as a kind of optimization process similar to the optimization algorithms used to train machine learning systems. In the ancestral environment, evolution selected genes for high inclusive genetic fitness, but humans pursue goals other than this. Fitness corresponds to the specified goal used in the training environment and training data. But in evolutionary history, maximizing the fitness specification gave rise to goal-directed agents, humans, who do not directly pursue inclusive genetic fitness. Instead, they pursue goals that correlate with genetic fitness in the ancestral "training" environment: nutrition, sex, and so on. The human environment has changed: a distribution shift has occurred. They continue to pursue the same emergent goals, but this no longer maximizes genetic fitness. The taste for sugary food (an emergent goal) was originally aligned with inclusive fitness, but it now leads to overeating and health problems. Sexual desire originally led humans to have more offspring, but they now use contraception when offspring are undesired, decoupling sex from genetic fitness.: Chapter 5
Researchers aim to detect and remove unwanted emergent goals using approaches including red teaming, verification, anomaly detection, and interpretability. Progress on these techniques may help mitigate two open problems:
Emergent goals only become apparent when the system is deployed outside its training environment, but it can be unsafe to deploy a misaligned system in high-stakes environments—even for a short time to allow its misalignment to be detected. Such high stakes are common in autonomous driving, health care, and military applications. The stakes become higher yet when AI systems gain more autonomy and capability and can sidestep human intervention.
A sufficiently capable AI system might take actions that falsely convince the human supervisor that the AI is pursuing the specified objective, which helps the system gain more reward and autonomy.
=== Embedded agency ===
Some work in AI and alignment occurs within formalisms such as partially observable Markov decision process. Existing formalisms assume that an AI agent's algorithm is executed outside the environment (i.e. is not physically embedded in it). Embedded agency is another major strand of research that attempts to solve problems arising from the mismatch between such theoretical frameworks and real agents we might build.
For example, even if the scalable oversight problem is solved, an agent that could gain access to the computer it is running on may have an incentive to tamper with its reward function in order to get much more reward than its human supervisors give it. A list of examples of specification gaming from DeepMind researcher Victoria Krakovna includes a genetic algorithm that learned to delete the file containing its target output so that it was rewarded for outputting nothing. This class of problems has been formalized using causal incentive diagrams.
Researchers affiliated with Oxford and DeepMind have claimed that such behavior is highly likely in advanced systems, and that advanced systems would seek power to stay in control of their reward signal indefinitely and certainly. They suggest a range of potential approaches to address this open problem.
=== Principal-agent problems ===
The alignment problem has many parallels with the principal-agent problem in organizational economics. In a principal-agent problem, a principal, e.g. a firm, hires an agent to perform some task. In the context of AI safety, a human would typically take the principal role and the AI would take the agent role.
As with the alignment problem, the principal and the agent differ in their utility functions. But in contrast to the alignment problem, the principal cannot coerce the agent into changing its utility, e.g. through training, but rather must use exogenous factors, such as incentive schemes, to bring about outcomes compatible with the principal's utility function. Some researchers argue that principal-agent problems are more realistic representations of AI safety problems likely to be encountered in the real world.
=== Conservatism ===
Conservatism is the idea that "change must be cautious", and is a common approach to safety in the control theory literature in the form of robust control, and in the risk management literature in the form of the "worst-case scenario". The field of AI alignment has likewise advocated for "conservative" (or "risk-averse" or "cautious") "policies in situations of uncertainty".
Pessimism, in the sense of assuming the worst within reason, has been formally shown to produce conservatism, in the sense of reluctance to cause novelties, including unprecedented catastrophes. Pessimism and worst-case analysis have been found to help mitigate confident mistakes in the setting of distributional shift, reinforcement learning, offline reinforcement learning, language model fine-tuning, imitation learning, and optimization in general. A generalization of pessimism called Infra-Bayesianism has also been advocated as a way for agents to robustly handle unknown unknowns.
== Public policy ==
Governmental and treaty organizations have made statements emphasizing the importance of AI alignment.
In September 2021, the Secretary-General of the United Nations issued a declaration that included a call to regulate AI to ensure it is "aligned with shared global values".
That same month, the PRC published ethical guidelines for AI in China. According to the guidelines, researchers must ensure that AI abides by shared human values, is always under human control, and does not endanger public safety.
Also in September 2021, the UK published its 10-year National AI Strategy, which says the British government "takes the long term risk of non-aligned Artificial General Intelligence, and the unforeseeable changes that it would mean for ... the world, seriously". The strategy describes actions to assess long-term AI risks, including catastrophic risks.
In March 2021, the US National Security Commission on Artificial Intelligence said: "Advances in AI ... could lead to inflection points or leaps in capabilities. Such advances may also introduce new concerns and risks and the need for new policies, recommendations, and technical advances to ensure that systems are aligned with goals and values, including safety, robustness, and trustworthiness. The US should ... ensure that AI systems and their uses align with our goals and values."
In the European Union, AIs must align with substantive equality to comply with EU non-discrimination law and the Court of Justice of the European Union. But the EU has yet to specify with technical rigor how it would evaluate whether AIs are aligned or in compliance.
== Dynamic nature of alignment ==
AI alignment is often perceived as a fixed objective, but some researchers argue it would be more appropriate to view alignment as an evolving process. One view is that AI technologies advance and human values and preferences change, alignment solutions must also adapt dynamically. Another is that alignment solutions need not adapt if researchers can create intent-aligned AI: AI that changes its behavior automatically as human intent changes. The first view would have several implications:
AI alignment solutions require continuous updating in response to AI advancements. A static, one-time alignment approach may not suffice.
Varying historical contexts and technological landscapes may necessitate distinct alignment strategies. This calls for a flexible approach and responsiveness to changing conditions.
The feasibility of a permanent, "fixed" alignment solution remains uncertain. This raises the potential need for continuous oversight of the AI-human relationship.
AI developers may have to continuously refine their ethical frameworks to ensure that their systems align with evolving human values.
In essence, AI alignment may not be a static destination but rather an open, flexible process. Alignment solutions that continually adapt to ethical considerations may offer the most robust approach. This perspective could guide both effective policy-making and technical research in AI.
== See also ==
== Footnotes ==
== References ==
== Further reading ==
Brockman, John, ed. (2019). Possible Minds: Twenty-five Ways of Looking at AI (Kindle ed.). Penguin Press. ISBN 978-0525557999.{{cite book}}: CS1 maint: ref duplicates default (link)
Ngo, Richard; et al. (2023). "The Alignment Problem from a Deep Learning Perspective". arXiv:2209.00626 [cs.AI].
Ji, Jiaming; et al. (2023). "AI Alignment: A Comprehensive Survey". arXiv:2310.19852 [cs.AI].
== External links ==
Specification gaming examples in AI, via DeepMind | Wikipedia/AI_control_problem |
Nature Methods is a monthly peer-reviewed scientific journal covering new scientific techniques. It was established in 2004 and is published by Springer Nature under the Nature Portfolio. Like other Nature journals, there is no external editorial board and editorial decisions are made by an in-house team, although peer review by external experts forms a part of the review process. The editor-in-chief is Allison Doerr.
Every year, the journal highlights a field, approach, or technique that has enabled recent major advances in life sciences research as the "Method of the Year".
According to the Journal Citation Reports, the journal had a 2021 impact factor of 47.990, ranking it first in the category "Biochemical Research Methods".
== References ==
== External links ==
Official website
Retraction Watch
"JournalGuide". Retrieved February 23, 2025. | Wikipedia/Nature_Methods |
In machine learning and computer vision, M-theory is a learning framework inspired by feed-forward processing in the ventral stream of visual cortex and originally developed for recognition and classification of objects in visual scenes. M-theory was later applied to other areas, such as speech recognition. On certain image recognition tasks, algorithms based on a specific instantiation of M-theory, HMAX, achieved human-level performance.
The core principle of M-theory is extracting representations invariant under various transformations of images (translation, scale, 2D and 3D rotation and others). In contrast with other approaches using invariant representations, in M-theory they are not hardcoded into the algorithms, but learned. M-theory also shares some principles with compressed sensing. The theory proposes multilayered hierarchical learning architecture, similar to that of visual cortex.
== Intuition ==
=== Invariant representations ===
A great challenge in visual recognition tasks is that the same object can be seen in a variety of conditions. It can be seen from different distances, different viewpoints, under different lighting, partially occluded, etc. In addition, for particular classes objects, such as faces, highly complex specific transformations may be relevant, such as changing facial expressions. For learning to recognize images, it is greatly beneficial to factor out these variations. It results in much simpler classification problem and, consequently, in great reduction of sample complexity of the model.
A simple computational experiment illustrates this idea. Two instances of a classifier were trained to distinguish images of planes from those of cars. For training and testing of the first instance, images with arbitrary viewpoints were used. Another instance received only images seen from a particular viewpoint, which was equivalent to training and testing the system on invariant representation of the images. One can see that the second classifier performed quite well even after receiving a single example from each category, while performance of the first classifier was close to random guess even after seeing 20 examples.
Invariant representations has been incorporated into several learning architectures, such as neocognitrons. Most of these architectures, however, provided invariance through custom-designed features or properties of architecture itself. While it helps to take into account some sorts of transformations, such as translations, it is very nontrivial to accommodate for other sorts of transformations, such as 3D rotations and changing facial expressions. M-theory provides a framework of how such transformations can be learned. In addition to higher flexibility, this theory also suggests how human brain may have similar capabilities.
=== Templates ===
Another core idea of M-theory is close in spirit to ideas from the field of compressed sensing. An implication from Johnson–Lindenstrauss lemma says that a particular number of images can be embedded into a low-dimensional feature space with the same distances between images by using random projections. This result suggests that dot product between the observed image and some other image stored in memory, called template, can be used as a feature helping to distinguish the image from other images. The template need not to be anyhow related to the image, it could be chosen randomly.
=== Combining templates and invariant representations ===
The two ideas outlined in previous sections can be brought together to construct a framework for learning invariant representations. The key observation is how dot product between image
I
{\displaystyle I}
and a template
t
{\displaystyle t}
behaves when image is transformed (by such transformations as translations, rotations, scales, etc.). If transformation
g
{\displaystyle g}
is a member of a unitary group of transformations, then the following holds:
⟨
g
I
,
t
⟩
=
⟨
I
,
g
−
1
t
⟩
(
1
)
{\displaystyle \langle gI,t\rangle =\langle I,g^{-1}t\rangle \qquad (1)}
In other words, the dot product of transformed image and a template is equal to the dot product of original image and inversely transformed template. For instance, for image rotated by 90 degrees, the inversely transformed template would be rotated by −90 degrees.
Consider the set of dot products of an image
I
{\displaystyle I}
to all possible transformations of template:
{
⟨
I
,
g
′
t
⟩
∣
g
′
∈
G
}
{\displaystyle \lbrace \langle I,g^{\prime }t\rangle \mid g^{\prime }\in G\rbrace }
. If one applies a transformation
g
{\displaystyle g}
to
I
{\displaystyle I}
, the set would become
{
⟨
g
I
,
g
′
t
⟩
∣
g
′
∈
G
}
{\displaystyle \lbrace \langle gI,g^{\prime }t\rangle \mid g^{\prime }\in G\rbrace }
. But because of the property (1), this is equal to
{
⟨
I
,
g
−
1
g
′
t
⟩
∣
g
′
∈
G
}
{\displaystyle \lbrace \langle I,g^{-1}g^{\prime }t\rangle \mid g^{\prime }\in G\rbrace }
. The set
{
g
−
1
g
′
∣
g
′
∈
G
}
{\displaystyle \lbrace g^{-1}g^{\prime }\mid g^{\prime }\in G\rbrace }
is equal to just the set of all elements in
G
{\displaystyle G}
. To see this, note that every
g
−
1
g
′
{\displaystyle g^{-1}g^{\prime }}
is in
G
{\displaystyle G}
due to the closure property of groups, and for every
g
′
′
{\displaystyle g^{\prime \prime }}
in G there exist its prototype
g
′
{\displaystyle g^{\prime }}
such as
g
′
′
=
g
−
1
g
′
{\displaystyle g^{\prime \prime }=g^{-1}g^{\prime }}
(namely,
g
′
=
g
g
′
′
{\displaystyle g^{\prime }=gg^{\prime \prime }}
). Thus,
{
⟨
I
,
g
−
1
g
′
t
⟩
∣
g
′
∈
G
}
=
{
⟨
I
,
g
′
′
t
⟩
∣
g
′
′
∈
G
}
{\displaystyle \lbrace \langle I,g^{-1}g^{\prime }t\rangle \mid g^{\prime }\in G\rbrace =\lbrace \langle I,g^{\prime \prime }t\rangle \mid g^{\prime \prime }\in G\rbrace }
. One can see that the set of dot products remains the same despite that a transformation was applied to the image! This set by itself may serve as a (very cumbersome) invariant representation of an image. More practical representations can be derived from it.
In the introductory section, it was claimed that M-theory allows to learn invariant representations. This is because templates and their transformed versions can be learned from visual experience – by exposing the system to sequences of transformations of objects. It is plausible that similar visual experiences occur in early period of human life, for instance when infants twiddle toys in their hands. Because templates may be totally unrelated to images that the system later will try to classify, memories of these visual experiences may serve as a basis for recognizing many different kinds of objects in later life. However, as it is shown later, for some kinds of transformations, specific templates are needed.
== Theoretical aspects ==
=== From orbits to distribution measures ===
To implement the ideas described in previous sections, one need to know how to derive a computationally efficient invariant representation of an image. Such unique representation for each image can be characterized as it appears by a set of one-dimensional probability distributions (empirical distributions of the dot-products between image and a set of templates stored during unsupervised learning). These probability distributions in their turn can be described by either histograms or a set of statistical moments of it, as it will be shown below.
Orbit
O
I
{\displaystyle O_{I}}
is a set of images
g
I
{\displaystyle gI}
generated from a single image
I
{\displaystyle I}
under the action of the group
G
,
∀
g
∈
G
{\displaystyle G,\forall g\in G}
.
In other words, images of an object and of its transformations correspond to an orbit
O
I
{\displaystyle O_{I}}
. If two orbits have a point in common they are identical everywhere, i.e. an orbit is an invariant and unique representation of an image. So, two images are called equivalent when they belong to the same orbit:
I
∼
I
′
{\displaystyle I\sim I^{\prime }}
if
∃
g
∈
G
{\displaystyle \exists g\in G}
such that
I
′
=
g
I
{\displaystyle I^{\prime }=gI}
. Conversely, two orbits are different if none of the images in one orbit coincide with any image in the other.
A natural question arises: how can one compare two orbits? There are several possible approaches. One of them employs the fact that intuitively two empirical orbits are the same irrespective of the ordering of their points. Thus, one can consider a probability distribution
P
I
{\displaystyle P_{I}}
induced by the group's action on images
I
{\displaystyle I}
(
g
I
{\displaystyle gI}
can be seen as a realization of a random variable).
This probability distribution
P
I
{\displaystyle P_{I}}
can be almost uniquely characterized by
K
{\displaystyle K}
one-dimensional probability distributions
P
⟨
I
,
t
k
⟩
{\displaystyle P_{\langle I,t^{k}\rangle }}
induced by the (one-dimensional) results of projections
⟨
I
,
t
k
⟩
{\displaystyle \langle I,t^{k}\rangle }
, where
t
k
,
k
=
1
,
…
,
K
{\displaystyle t^{k},k=1,\ldots ,K}
are a set of templates (randomly chosen images) (based on the Cramer–Wold theorem and concentration of measures).
Consider
n
{\displaystyle n}
images
X
n
∈
X
{\displaystyle X_{n}\in X}
. Let
K
≥
2
c
ε
2
log
n
δ
{\displaystyle K\geq {\frac {2}{c\varepsilon ^{2}}}\log {\frac {n}{\delta }}}
, where
c
{\displaystyle c}
is a universal constant. Then
|
d
(
P
I
,
P
I
′
)
−
d
K
(
P
I
,
P
I
′
)
|
≤
ε
,
{\displaystyle |d(P_{I},P_{I}^{\prime })-dK(P_{I},P_{I}^{\prime })|\leq \varepsilon ,}
with probability
1
−
δ
2
{\displaystyle 1-\delta ^{2}}
, for all
I
,
I
′
{\displaystyle I,I^{\prime }}
∈
{\displaystyle \in }
X
n
{\displaystyle X_{n}}
.
This result (informally) says that an approximately invariant and unique representation of an image
I
{\displaystyle I}
can be obtained from the estimates of
K
{\displaystyle K}
1-D probability distributions
P
⟨
I
,
t
k
⟩
{\displaystyle P_{\langle I,t^{k}\rangle }}
for
k
=
1
,
…
,
K
{\displaystyle k=1,\ldots ,K}
. The number
K
{\displaystyle K}
of projections needed to discriminate
n
{\displaystyle n}
orbits, induced by
n
{\displaystyle n}
images, up to precision
ε
{\displaystyle \varepsilon }
(and with confidence
1
−
δ
2
{\displaystyle 1-\delta ^{2}}
) is
K
≥
2
c
ε
2
log
n
δ
{\displaystyle K\geq {\frac {2}{c\varepsilon ^{2}}}\log {\frac {n}{\delta }}}
, where
c
{\displaystyle c}
is a universal constant.
To classify an image, the following "recipe" can be used:
Memorize a set of images/objects called templates;
Memorize observed transformations for each template;
Compute dot products of its transformations with image;
Compute histogram of the resulting values, called signature of the image;
Compare the obtained histogram with signatures stored in memory.
Estimates of such one-dimensional probability density functions (PDFs)
P
⟨
I
,
t
k
⟩
{\displaystyle P_{\langle I,t^{k}\rangle }}
can be written in terms of histograms as
μ
n
k
(
I
)
=
1
/
|
G
|
∑
i
=
1
|
G
|
η
n
(
⟨
I
,
g
i
t
k
⟩
)
{\displaystyle \mu _{n}^{k}(I)=1/\left|G\right|\sum _{i=1}^{\left|G\right|}\eta _{n}(\langle I,g_{i}t^{k}\rangle )}
, where
η
n
,
n
=
1
,
…
,
N
{\displaystyle \eta _{n},n=1,\ldots ,N}
is a set of nonlinear functions. These 1-D probability distributions can be characterized with N-bin histograms or set of statistical moments. For example, HMAX represents an architecture in which pooling is done with a max operation.
=== Non-compact groups of transformations ===
In the "recipe" for image classification, groups of transformations are approximated with finite number of transformations. Such approximation is possible only when the group is compact.
Such groups as all translations and all scalings of the image are not compact, as they allow arbitrarily big transformations. However, they are locally compact. For locally compact groups, invariance is achievable within certain range of transformations.
Assume that
G
0
{\displaystyle G_{0}}
is a subset of transformations from
G
{\displaystyle G}
for which the transformed patterns exist in memory. For an image
I
{\displaystyle I}
and template
t
k
{\displaystyle t_{k}}
, assume that
⟨
I
,
g
−
1
t
k
⟩
{\displaystyle \langle I,g^{-1}t_{k}\rangle }
is equal to zero everywhere except some subset of
G
0
{\displaystyle G_{0}}
. This subset is called support of
⟨
I
,
g
−
1
t
k
⟩
{\displaystyle \langle I,g^{-1}t_{k}\rangle }
and denoted as
supp
(
⟨
I
,
g
−
1
t
k
⟩
)
{\displaystyle \operatorname {supp} (\langle I,g^{-1}t_{k}\rangle )}
. It can be proven that if for a transformation
g
′
{\displaystyle g^{\prime }}
, support set will also lie within
g
′
G
0
{\displaystyle g^{\prime }G_{0}}
, then signature of
I
{\displaystyle I}
is invariant with respect to
g
′
{\displaystyle g^{\prime }}
. This theorem determines the range of transformations for which invariance is guaranteed to hold.
One can see that the smaller is
supp
(
⟨
I
,
g
−
1
t
k
⟩
)
{\displaystyle \operatorname {supp} (\langle I,g^{-1}t_{k}\rangle )}
, the larger is the range of transformations for which invariance is guaranteed to hold. It means that for a group that is only locally compact, not all templates would work equally well anymore. Preferable templates are those with a reasonably small
supp
(
⟨
g
I
,
t
k
⟩
)
{\displaystyle \operatorname {supp} (\langle gI,t_{k}\rangle )}
for a generic image. This property is called localization: templates are sensitive only to images within a small range of transformations. Although minimizing
supp
(
⟨
g
I
,
t
k
⟩
)
{\displaystyle \operatorname {supp} (\langle gI,t_{k}\rangle )}
is not absolutely necessary for the system to work, it improves approximation of invariance. Requiring localization simultaneously for translation and scale yields a very specific kind of templates: Gabor functions.
The desirability of custom templates for non-compact group is in conflict with the principle of learning invariant representations. However, for certain kinds of regularly encountered image transformations, templates might be the result of evolutionary adaptations. Neurobiological data suggests that there is Gabor-like tuning in the first layer of visual cortex. The optimality of Gabor templates for translations and scales is a possible explanation of this phenomenon.
=== Non-group transformations ===
Many interesting transformations of images do not form groups. For instance, transformations of images associated with 3D rotation of corresponding 3D object do not form a group, because it is impossible to define an inverse transformation (two objects may looks the same from one angle but different from another angle). However, approximate invariance is still achievable even for non-group transformations, if localization condition for templates holds and transformation can be locally linearized.
As it was said in the previous section, for specific case of translations and scaling, localization condition can be satisfied by use of generic Gabor templates. However, for general case (non-group) transformation, localization condition can be satisfied only for specific class of objects. More specifically, in order to satisfy the condition, templates must be similar to the objects one would like to recognize. For instance, if one would like to build a system to recognize 3D rotated faces, one need to use other 3D rotated faces as templates. This may explain the existence of such specialized modules in the brain as one responsible for face recognition. Even with custom templates, a noise-like encoding of images and templates is necessary for localization. It can be naturally achieved if the non-group transformation is processed on any layer other than the first in hierarchical recognition architecture.
=== Hierarchical architectures ===
The previous section suggests one motivation for hierarchical image recognition architectures. However, they have other benefits as well.
Firstly, hierarchical architectures best accomplish the goal of ‘parsing’ a complex visual scene with many objects consisting of many parts, whose relative position may greatly vary. In this case, different elements of the system must react to different objects and parts. In hierarchical architectures, representations of parts at different levels of embedding hierarchy can be stored at different layers of hierarchy.
Secondly, hierarchical architectures which have invariant representations for parts of objects may facilitate learning of complex compositional concepts. This facilitation may happen through reusing of learned representations of parts that were constructed before in process of learning of other concepts. As a result, sample complexity of learning compositional concepts may be greatly reduced.
Finally, hierarchical architectures have better tolerance to clutter. Clutter problem arises when the target object is in front of a non-uniform background, which functions as a distractor for the visual task. Hierarchical architecture provides signatures for parts of target objects, which do not include parts of background and are not affected by background variations.
In hierarchical architectures, one layer is not necessarily invariant to all transformations that are handled by the hierarchy as a whole. Some transformations may pass through that layer to upper layers, as in the case of non-group transformations described in the previous section. For other transformations, an element of the layer may produce invariant representations only within small range of transformations. For instance, elements of the lower layers in hierarchy have small visual field and thus can handle only a small range of translation. For such transformations, the layer should provide covariant rather than invariant, signatures. The property of covariance can be written as
distr
(
⟨
μ
l
(
g
I
)
,
μ
l
(
t
)
⟩
)
=
distr
(
⟨
μ
l
(
I
)
,
μ
l
(
g
−
1
t
)
⟩
)
{\displaystyle \operatorname {distr} (\langle \mu _{l}(gI),\mu _{l}(t)\rangle )=\operatorname {distr} (\langle \mu _{l}(I),\mu _{l}(g^{-1}t)\rangle )}
, where
l
{\displaystyle l}
is a layer,
μ
l
(
I
)
{\displaystyle \mu _{l}(I)}
is the signature of image on that layer, and
distr
{\displaystyle \operatorname {distr} }
stands for "distribution of values of the expression for all
g
∈
G
{\displaystyle g\in G}
".
== Relation to biology ==
M-theory is based on a quantitative theory of the ventral stream of visual cortex. Understanding how visual cortex works in object recognition is still a challenging task for neuroscience. Humans and primates are able to memorize and recognize objects after seeing just couple of examples unlike any state-of-the art machine vision systems that usually require a lot of data in order to recognize objects. Prior to the use of visual neuroscience in computer vision has been limited to early vision for deriving stereo algorithms (e.g.,) and to justify the use of DoG (derivative-of-Gaussian) filters and more recently of Gabor filters. No real attention has been given to biologically plausible features of higher complexity. While mainstream computer vision has always been inspired and challenged by human vision, it seems to have never advanced past the very first stages of processing in the simple cells in V1 and V2. Although some of the systems inspired – to various degrees – by neuroscience, have been tested on at least some natural images, neurobiological models of object recognition in cortex have not yet been extended to deal with real-world image databases.
M-theory learning framework employs a novel hypothesis about the main computational function of the ventral stream: the representation of new objects/images in terms of a signature, which is invariant to transformations learned during visual experience. This allows recognition from very few labeled examples – in the limit, just one.
Neuroscience suggests that natural functionals for a neuron to compute is a high-dimensional dot product between an "image patch" and another image patch (called template)
which is stored in terms of synaptic weights (synapses per neuron). The standard computational model of a neuron is based on a dot product and a threshold. Another important feature of the visual cortex is that it consists of simple and complex cells. This idea was originally proposed by Hubel and Wiesel. M-theory employs this idea. Simple cells compute dot products of an image and transformations of templates
⟨
I
,
g
i
t
k
⟩
{\displaystyle \langle I,g_{i}t^{k}\rangle }
for
i
=
1
,
…
,
|
G
|
{\displaystyle i=1,\ldots ,|G|}
(
|
G
|
{\displaystyle |G|}
is a number of simple cells). Complex cells are responsible for pooling and computing empirical histograms or statistical moments of it. The following formula for constructing histogram can be computed by neurons:
1
|
G
|
∑
i
=
1
|
G
|
σ
(
⟨
I
,
g
i
t
k
⟩
+
n
Δ
)
,
{\displaystyle {\frac {1}{|G|}}\sum _{i=1}^{|G|}\sigma (\langle I,g_{i}t^{k}\rangle +n\Delta ),}
where
σ
{\displaystyle \sigma }
is a smooth version of step function,
Δ
{\displaystyle \Delta }
is the width of a histogram bin, and
n
{\displaystyle n}
is the number of the bin.
== Applications ==
=== Applications to computer vision ===
In authors applied M-theory to unconstrained face recognition in natural photographs. Unlike the DAR (detection, alignment, and recognition) method, which handles clutter by detecting objects and cropping closely around them so that very little background remains, this approach accomplishes detection and alignment implicitly by storing transformations of training images (templates) rather than explicitly detecting and aligning or cropping faces at test time. This system is built according to the principles of a recent theory of invariance in hierarchical networks and can evade the clutter problem generally problematic for feedforward systems.
The resulting end-to-end system achieves a drastic improvement in the state of the art on this end-to-end task, reaching the same level of performance as the best systems operating on aligned, closely cropped images (no outside training data). It also performs well on two newer datasets, similar to LFW, but more difficult: significantly jittered (misaligned) version of LFW and SUFR-W (for example, the model's accuracy in the LFW "unaligned & no outside data used" category is 87.55±1.41% compared to state-of-the-art APEM (adaptive probabilistic elastic matching): 81.70±1.78%).
The theory was also applied to a range of recognition tasks: from invariant single object recognition in clutter to multiclass categorization problems on publicly available data sets (CalTech5, CalTech101, MIT-CBCL) and complex (street) scene understanding tasks that requires the recognition of both shape-based as well as texture-based objects (on StreetScenes data set). The approach performs really well: It has the capability of learning from only a few training examples and was shown to outperform several more complex state-of-the-art systems constellation models, the hierarchical SVM-based face-detection system. A key element in the approach is a new set of scale and position-tolerant feature detectors, which are biologically plausible and agree quantitatively with the tuning properties of cells along the ventral stream of visual cortex. These features are adaptive to the training set, though we also show that a universal feature set, learned from a set of natural images unrelated to any categorization task, likewise achieves good performance.
=== Applications to speech recognition ===
This theory can also be extended for the speech recognition domain.
As an example, in an extension of a theory for unsupervised learning of invariant visual representations to the auditory domain and empirically evaluated its validity for voiced speech sound classification was proposed. Authors empirically demonstrated that a single-layer, phone-level representation, extracted from base speech features, improves segment classification accuracy and decreases the number of training examples in comparison with standard spectral and cepstral features for an acoustic classification task on TIMIT dataset.
== References == | Wikipedia/M-theory_(learning_framework) |
Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of an evolutionary algorithm (EA), including genetic algorithms in particular. It is analogous to biological mutation.
The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating-point encodings or representations for combinatorial problems.
The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping convergence to the global optimum. This reasoning also leads most EAs to avoid only taking the fittest of the population in generating the next generation, but rather selecting a random (or semi-random) set with a weighting toward those that are fitter.
The following requirements apply to all mutation operators used in an EA:
every point in the search space must be reachable by one or more mutations.
there must be no preference for parts or directions in the search space (no drift).
small mutations should be more probable than large ones.
For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scramble, Insertion, Inversion, Swap, and so on. An overview and more operators than those presented below can be found in the introductory book by Eiben and Smith or in.
== Bit string mutation ==
The mutation of bit strings ensue through bit flips at random positions.
Example:
The probability of a mutation of a bit is
1
l
{\displaystyle {\frac {1}{l}}}
, where
l
{\displaystyle l}
is the length of the binary vector. Thus, a mutation rate of
1
{\displaystyle 1}
per mutation and individual selected for mutation is reached.
== Mutation of real numbers ==
Many EAs, such as the evolution strategy or the real-coded genetic algorithms, work with real numbers instead of bit strings. This is due to the good experiences that have been made with this type of coding.
The value of a real-valued gene can either be changed or redetermined. A mutation that implements the latter should only ever be used in conjunction with the value-changing mutations and then only with comparatively low probability, as it can lead to large changes.
In practical applications, the respective value range of the decision variables to be changed of the optimisation problem to be solved is usually limited. Accordingly, the values of the associated genes are each restricted to an interval
[
x
min
,
x
max
]
{\displaystyle [x_{\min },x_{\max }]}
. Mutations may or may not take these restrictions into account. In the latter case, suitable post-treatment is then required as described below.
=== Mutation without consideration of restrictions ===
A real number
x
{\displaystyle x}
can be mutated using normal distribution
N
(
0
,
σ
)
{\displaystyle {\mathcal {N}}(0,\sigma )}
by adding the generated random value to the old value of the gene, resulting in the mutated value
x
′
{\displaystyle x'}
:
x
′
=
x
+
N
(
0
,
σ
)
{\displaystyle x'=x+{\mathcal {N}}(0,\sigma )}
In the case of genes with a restricted range of values, it is a good idea to choose the step size of the mutation
σ
{\displaystyle \sigma }
so that it reasonably fits the range
[
x
min
,
x
max
]
{\displaystyle [x_{\min },x_{\max }]}
of the gene to be changed, e.g.:
σ
=
x
max
−
x
min
6
{\displaystyle \sigma ={\frac {x_{\text{max}}-x_{\text{min}}}{6}}}
The step size can also be adjusted to the smaller permissible change range depending on the current value. In any case, however, it is likely that the new value
x
′
{\displaystyle x'}
of the gene will be outside the permissible range of values. Such a case must be considered a lethal mutation, since the obvious repair by using the respective violated limit as the new value of the gene would lead to a drift. This is because the limit value would then be selected with the entire probability of the values beyond the limit of the value range.
The evolution strategy works with real numbers and mutation based on normal distribution. The step sizes are part of the chromosome and are subject to evolution together with the actual decision variables.
=== Mutation with consideration of restrictions ===
One possible form of changing the value of a gene while taking its value range
[
x
min
,
x
max
]
{\displaystyle [x_{\min },x_{\max }]}
into account is the mutation relative parameter change of the evolutionary algorithm GLEAM (General Learning Evolutionary Algorithm and Method), in which, as with the mutation presented earlier, small changes are more likely than large ones.
First, an equally distributed decision is made as to whether the current value
x
{\displaystyle x}
should be increased or decreased and then the corresponding total change interval is determined. Without loss of generality, an increase is assumed for the explanation and the total change interval is then
[
x
,
x
max
]
{\displaystyle [x,x_{\max }]}
. It is divided into
k
{\displaystyle k}
sub-areas of equal size with the width
δ
{\displaystyle \delta }
, from which
k
{\displaystyle k}
sub-change intervals of different size are formed:
i
{\displaystyle i}
-th sub-change interval:
[
x
,
x
+
δ
⋅
i
]
{\displaystyle [x,x+\delta \cdot i]}
with
δ
=
(
x
max
−
x
)
k
{\displaystyle \delta ={\frac {(x_{\text{max}}-x)}{k}}}
and
i
=
1
,
…
,
k
{\displaystyle i=1,\dots ,k}
Subsequently, one of the
k
{\displaystyle k}
sub-change intervals is selected in equal distribution and a random number, also equally distributed, is drawn from it as the new value
x
′
{\displaystyle x'}
of the gene. The resulting summed probabilities of the sub-change intervals result in the probability distribution of the
k
{\displaystyle k}
sub-areas shown in the adjacent figure for the exemplary case of
k
=
10
{\displaystyle k=10}
. This is not a normal distribution as before, but this distribution also clearly favours small changes over larger ones.
This mutation for larger values of
k
{\displaystyle k}
, such as 10, is less well suited for tasks where the optimum lies on one of the value range boundaries. This can be remedied by significantly reducing
k
{\displaystyle k}
when a gene value approaches its limits very closely.
=== Common properties ===
For both mutation operators for real-valued numbers, the probability of an increase and decrease is independent of the current value and is 50% in each case. In addition, small changes are considerably more likely than large ones. For mixed-integer optimization problems, rounding is usually used.
== Mutation of permutations ==
Mutations of permutations are specially designed for genomes that are themselves permutations of a set. These are often used to solve combinatorial tasks. In the two mutations presented, parts of the genome are rotated or inverted.
=== Rotation to the right ===
The presentation of the procedure is illustrated by an example on the right:
=== Inversion ===
The presentation of the procedure is illustrated by an example on the right:
=== Variants with preference for smaller changes ===
The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order.
This can be remedied by the following modifications. The end index
j
{\displaystyle j}
of the partial lists is determined as the distance
d
{\displaystyle d}
to the start index
i
{\displaystyle i}
:
j
=
(
i
+
d
)
mod
|
P
0
|
{\displaystyle j=(i+d){\bmod {\left|P_{0}\right|}}}
where
d
{\displaystyle d}
is determined randomly according to one of the two procedures for the mutation of real numbers from the interval
[
0
,
|
P
0
|
−
1
]
{\displaystyle \left[0,\left|P_{0}\right|-1\right]}
and rounded.
For the rotation,
k
{\displaystyle k}
is determined similarly to the distance
d
{\displaystyle d}
, but the value
0
{\displaystyle 0}
is forbidden.
For the inversion, note that
i
≠
j
{\displaystyle i\neq j}
must hold, so for
d
{\displaystyle d}
the value
0
{\displaystyle 0}
must be excluded.
== See also ==
Evolutionary algorithms
Genetic algorithms
Evolution strategy
Genetic programming
Evolutionary programming
== References ==
== Bibliography ==
John Holland (1975). Adaptation in Natural and Artificial Systems, PhD thesis, University of Michigan Press, Ann Arbor, Michigan. ISBN 0-262-58111-6.
Schwefel, Hans-Paul (1995). Evolution and Optimum Seeking. New York: John Wiley & Sons. ISBN 0-471-57148-2.
Davis, Lawrence (1991). Handbook of genetic algorithms. New York: Van Nostrand Reinhold. ISBN 0-442-00173-8. OCLC 23081440.
Eiben, A.E.; Smith, J.E. (2015). Introduction to Evolutionary Computing. Natural Computing Series. Berlin, Heidelberg: Springer. doi:10.1007/978-3-662-44874-8. ISBN 978-3-662-44873-1. S2CID 20912932.
Yu, Xinjie; Gen, Mitsuo (2010). Introduction to Evolutionary Algorithms. Decision Engineering. London: Springer. doi:10.1007/978-1-84996-129-5. ISBN 978-1-84996-128-8.
De Jong, Kenneth A. (2006). Evolutionary computation : a unified approach. Cambridge, Mass.: MIT Press. ISBN 978-0-262-25598-1. OCLC 69652176.
Fogel, David B.; Bäck, Thomas; Michalewicz, Zbigniew, eds. (1999). Evolutionary computation. Vol. 1, Basic algorithms and operators. Bristol: Institute of Physics Pub. ISBN 0-585-30560-9. OCLC 45730387. | Wikipedia/Mutation_(genetic_algorithm) |
The term citizen science (synonymous to terms like community science, crowd science, crowd-sourced science, civic science, participatory monitoring, or volunteer monitoring) is research conducted with participation from the general public, or amateur/nonprofessional researchers or participants of science, social science and many other disciplines. There are variations in the exact definition of citizen science, with different individuals and organizations having their own specific interpretations of what citizen science encompasses. Citizen science is used in a wide range of areas of study including ecology, biology and conservation, health and medical research, astronomy, media and communications and information science.
There are different applications and functions of "citizen science" in research projects. Citizen science can be used as a methodology where public volunteers help in collecting and classifying data, improving the scientific community's capacity. Citizen science can also involve more direct involvement from the public, with communities initiating projects researching environment and health hazards in their own communities.
Participation in citizen science projects also educates the public about the scientific process and increases awareness about different topics. Some schools have students participate in citizen science projects for this purpose as a part of the teaching curriculums.
== Background ==
The first use of the term "citizen science" can be found in a January 1989 issue of MIT Technology Review, which featured three community-based labs studying environmental issues. In the 21st century, the number of citizen science projects, publications, and funding opportunities has increased. Citizen science has been used more over time, a trend helped by technological advancements. Digital citizen science platforms, such as Zooniverse and iNaturalist, store large amounts of data for many projects and are a place where volunteers can learn how to contribute to projects. For some projects, participants are instructed to collect and enter data, such as what species they observed, into large digital global databases. For other projects, participants help classify data on digital platforms. Citizen science data is also being used to develop machine learning algorithms. An example is using volunteer-classified images to train machine learning algorithms to identify species. While global participation and global databases are found on online platforms, not all locations always have the same amount of data from contributors. Concerns over potential data quality issues, such as measurement errors and biases, in citizen science projects are recognized in the scientific community and there are statistical solutions and best practices available which can help.
== Definition ==
The term "citizen science" has multiple origins, as well as differing concepts. "Citizen" is used in the general sense, as meaning in "citizen of the world", or the general public, rather than the legal term citizen of sovereign countries. It was first defined independently in the mid-1990s by Rick Bonney in the United States and Alan Irwin in the United Kingdom. Alan Irwin, a British sociologist, defines citizen science as "developing concepts of scientific citizenship which foregrounds the necessity of opening up science and science policy processes to the public". Irwin sought to reclaim two dimensions of the relationship between citizens and science: 1) that science should be responsive to citizens' concerns and needs; and 2) that citizens themselves could produce reliable scientific knowledge. The American ornithologist Rick Bonney, unaware of Irwin's work, defined citizen science as projects in which nonscientists, such as amateur birdwatchers, voluntarily contributed scientific data. This describes a more limited role for citizens in scientific research than Irwin's conception of the term.
The terms citizen science and citizen scientists entered the Oxford English Dictionary (OED) in June 2014. "Citizen science" is defined as "scientific work undertaken by members of the general public, often in collaboration with or under the direction of professional scientists and scientific institutions". "Citizen scientist" is defined as: (a) "a scientist whose work is characterized by a sense of responsibility to serve the best interests of the wider community (now rare)"; or (b) "a member of the general public who engages in scientific work, often in collaboration with or under the direction of professional scientists and scientific institutions; an amateur scientist". The first use of the term "citizen scientist" can be found in the magazine New Scientist in an article about ufology from October 1979.
Muki Haklay cites, from a policy report for the Wilson Center entitled "Citizen Science and Policy: A European Perspective", an alternate first use of the term "citizen science" by R. Kerson in the magazine MIT Technology Review from January 1989. Quoting from the Wilson Center report: "The new form of engagement in science received the name 'citizen science'. The first recorded example of the use of the term is from 1989, describing how 225 volunteers across the US collected rain samples to assist the Audubon Society in an acid-rain awareness raising campaign."
A Green Paper on Citizen Science was published in 2013 by the European Commission's Digital Science Unit and Socientize.eu, which included a definition for citizen science, referring to "the general public engagement in scientific research activities when citizens actively contribute to science either with their intellectual effort or surrounding knowledge or with their tools and resources. Participants provide experimental data and facilities for researchers, raise new questions and co-create a new scientific culture."
Citizen science may be performed by individuals, teams, or networks of volunteers. Citizen scientists often partner with professional scientists to achieve common goals. Large volunteer networks often allow scientists to accomplish tasks that would be too expensive or time-consuming to accomplish through other means.
Many citizen-science projects serve education and outreach goals. These projects may be designed for a formal classroom environment or an informal education environment such as museums.
Citizen science has evolved over the past four decades. Recent projects place more emphasis on scientifically sound practices and measurable goals for public education. Modern citizen science differs from its historical forms primarily in the access for, and subsequent scale of, public participation; technology is credited as one of the main drivers of the recent explosion of citizen science activity.
In March 2015, the Office of Science and Technology Policy published a factsheet entitled "Empowering Students and Others through Citizen Science and Crowdsourcing". Quoting: "Citizen science and crowdsourcing projects are powerful tools for providing students with skills needed to excel in science, technology, engineering, and math (STEM). Volunteers in citizen science, for example, gain hands-on experience doing real science, and in many cases take that learning outside of the traditional classroom setting". The National Academies of Science cites SciStarter as a platform offering access to more than 2,700 citizen science projects and events, as well as helping interested parties access tools that facilitate project participation.
In May 2016, a new open-access journal was started by the Citizen Science Association along with Ubiquity Press called Citizen Science: Theory and Practice (CS:T&P). Quoting from the editorial article titled "The Theory and Practice of Citizen Science: Launching a New Journal", "CS:T&P provides the space to enhance the quality and impact of citizen science efforts by deeply exploring the citizen science concept in all its forms and across disciplines. By examining, critiquing, and sharing findings across a variety of citizen science endeavors, we can dig into the underpinnings and assumptions of citizen science and critically analyze its practice and outcomes."
In February 2020, Timber Press, an imprint of Workman Publishing Company, published The Field Guide to Citizen Science as a practical guide for anyone interested in getting started with citizen science.
=== Alternative definitions ===
Other definitions for citizen science have also been proposed. For example, Bruce Lewenstein of Cornell University's Communication and S&TS departments describes three possible definitions:
The participation of nonscientists in the process of gathering data according to specific scientific protocols and in the process of using and interpreting that data.
The engagement of nonscientists in true decision-making about policy issues that have technical or scientific components.
The engagement of research scientists in the democratic and policy process.
Scientists and scholars who have used other definitions include Frank N. von Hippel, Stephen Schneider, Neal Lane and Jon Beckwith. Other alternative terminologies proposed are "civic science" and "civic scientist".
Further, Muki Haklay offers an overview of the typologies of the level of citizen participation in citizen science, which range from "crowdsourcing" (level 1), where the citizen acts as a sensor, to "distributed intelligence" (level 2), where the citizen acts as a basic interpreter, to "participatory science", where citizens contribute to problem definition and data collection (level 3), to "extreme citizen science", which involves collaboration between the citizen and scientists in problem definition, collection and data analysis.
A 2014 Mashable article defines a citizen scientist as: "Anybody who voluntarily contributes his or her time and resources toward scientific research in partnership with professional scientists."
In 2016, the Australian Citizen Science Association released their definition, which states "Citizen science involves public participation and collaboration in scientific research with the aim to increase scientific knowledge."
In 2020, a group of birders in the Pacific Northwest of North America, eBird Northwest, has sought to rename "citizen science" to the use of "community science", "largely to avoid using the word 'citizen' when we want to be inclusive and welcoming to any birder or person who wants to learn more about bird watching, regardless of their citizen status."
=== Related fields ===
In a Smart City era, Citizen Science relies on various web-based tools, such as WebGIS, and becomes Cyber Citizen Science. Some projects, such as SETI@home, use the Internet to take advantage of distributed computing. These projects are generally passive. Computation tasks are performed by volunteers' computers and require little involvement beyond initial setup. There is disagreement as to whether these projects should be classified as citizen science.
The astrophysicist and Galaxy Zoo co-founder Kevin Schawinski stated: "We prefer to call this [Galaxy Zoo] citizen science because it's a better description of what you're doing; you're a regular citizen but you're doing science. Crowd sourcing sounds a bit like, well, you're just a member of the crowd and you're not; you're our collaborator. You're pro-actively involved in the process of science by participating."
Compared to SETI@home, "Galaxy Zoo volunteers do real work. They're not just passively running something on their computer and hoping that they'll be the first person to find aliens. They have a stake in science that comes out of it, which means that they are now interested in what we do with it, and what we find."
Citizen policy may be another result of citizen science initiatives. Bethany Brookshire (pen name SciCurious) writes: "If citizens are going to live with the benefits or potential consequences of science (as the vast majority of them will), it's incredibly important to make sure that they are not only well informed about changes and advances in science and technology, but that they also ... are able to ... influence the science policy decisions that could impact their lives." In "The Rightful Place of Science: Citizen Science", editors Darlene Cavalier and Eric Kennedy highlight emerging connections between citizen science, civic science, and participatory technology assessment.
=== Benefits and limitations ===
The general public's involvement in scientific projects has become a means of encouraging curiosity and greater understanding of science while providing an unprecedented engagement between professional scientists and the general public. In a research report published by the U.S. National Park Service in 2008, Brett Amy Thelen and Rachel K. Thiet mention the following concerns, previously reported in the literature, about the validity of volunteer-generated data:
Some projects may not be suitable for volunteers, for instance, when they use complex research methods or require a great deal of (often repetitive) work.
If volunteers lack proper training in research and monitoring protocols, the data they collect might introduce bias into the dataset.
The question of data accuracy, in particular, remains open. John Losey, who created the Lost Ladybug citizen science project, has argued that the cost-effectiveness of citizen science data can outweigh data quality issues, if properly managed.
In December 2016, authors M. Kosmala, A. Wiggins, A. Swanson and B. Simmons published a study in the journal Frontiers in Ecology and the Environment called "Assessing Data Quality in Citizen Science". The abstract describes how ecological and environmental citizen science projects have enormous potential to advance science. Citizen science projects can influence policy and guide resource management by producing datasets that are otherwise not feasible to generate. In the section "In a Nutshell" (pg3), four condensed conclusions are stated. They are:
They conclude that as citizen science continues to grow and mature, a key metric of project success they expect to see will be a growing awareness of data quality. They also conclude that citizen science will emerge as a general tool helping "to collect otherwise unobtainable high-quality data in support of policy and resource management, conservation monitoring, and basic science."
A study of Canadian lepidoptera datasets published in 2018 compared the use of a professionally curated dataset of butterfly specimen records with four years of data from a citizen science program, eButterfly. The eButterfly dataset was used as it was determined to be of high quality because of the expert vetting process used on site, and there already existed a dataset covering the same geographic area consisting of specimen data, much of it institutional. The authors note that, in this case, citizen science data provides both novel and complementary information to the specimen data. Five new species were reported from the citizen science data, and geographic distribution information was improved for over 80% of species in the combined dataset when citizen science data was included.
Several recent studies have begun to explore the accuracy of citizen science projects and how to predict accuracy based on variables like expertise of practitioners. One example is a 2021 study by Edgar Santos-Fernandez and Kerrie Mengersen of the British Ecological Society, who utilized a case study which used recent R and Stan programming software to offer ratings of the accuracy of species identifications performed by citizen scientists in Serengeti National Park, Tanzania. This provided insight into possible problems with processes like this which include, "discriminatory power and guessing behaviour". The researchers determined that methods for rating the citizen scientists themselves based on skill level and expertise might make studies they conduct more easy to analyze.
Studies that are simple in execution are where citizen science excels, particularly in the field of conservation biology and ecology. For example, in 2019, Sumner et al. compared the data of vespid wasp distributions collected by citizen scientists with the 4-decade, long-term dataset established by the BWARS. They set up the Big Wasp Survey from 26 August to 10 September 2017, inviting citizen scientists to trap wasps and send them for identification by experts where data was recorded. The results of this study showed that the campaign garnered over 2,000 citizen scientists participating in data collection, identifying over 6,600 wasps. This experiment provides strong evidence that citizen science can generate potentially high-quality data comparable to that of expert data collection, within a shorter time frame. Although the experiment was to originally test the strength of citizen science, the team also learned more about Vespidae biology and species distribution in the United Kingdom. With this study, the simple procedure enabled citizen science to be executed in a successful manner. A study by J. Cohn describes that volunteers can be trained to use equipment and process data, especially considering that a large proportion of citizen scientists are individuals who are already well-versed in the field of science.
The demographics of participants in citizen science projects are overwhelmingly White adults, of above-average income, having a university degree. Other groups of volunteers include conservationists, outdoor enthusiasts, and amateur scientists. As such, citizen scientists are generally individuals with a pre-understanding of the scientific method and how to conduct sensible and just scientific analysis.
== Ethics ==
Various studies have been published that explore the ethics of citizen science, including issues such as intellectual property and project design.(e.g.) The Citizen Science Association (CSA), based at the Cornell Lab of Ornithology, and the European Citizen Science Association (ECSA), based in the Museum für Naturkunde in Berlin, have working groups on ethics and principles.
In September 2015, ECSA published its Ten Principles of Citizen Science, which have been developed by the "Sharing best practice and building capacity" working group of ECSA, led by the Natural History Museum, London with input from many members of the association.
The medical ethics of internet crowdsourcing has been questioned by Graber & Graber in the Journal of Medical Ethics. In particular, they analyse the effect of games and the crowdsourcing project Foldit. They conclude: "games can have possible adverse effects, and that they manipulate the user into participation".
In March 2019, the online journal Citizen Science: Theory and Practice launched a collection of articles on the theme of Ethical Issues in Citizen Science. The articles are introduced with (quoting): "Citizen science can challenge existing ethical norms because it falls outside of customary methods of ensuring that research is conducted ethically. What ethical issues arise when engaging the public in research? How have these issues been addressed, and how should they be addressed in the future?"
In June 2019, East Asian Science, Technology and Society: An International Journal (EASTS) published an issue titled "Citizen Science: Practices and Problems" which contains 15 articles/studies on citizen science, including many relevant subjects of which ethics is one. Quoting from the introduction "Citizen, Science, and Citizen Science": "The term citizen science has become very popular among scholars as well as the general public, and, given its growing presence in East Asia, it is perhaps not a moment too soon to have a special issue of EASTS on the topic."
Use of citizen science volunteers as de facto unpaid laborers by some commercial ventures have been criticized as exploitative.
Ethics in citizen science in the health and welfare field, has been discussed in terms of protection versus participation. Public involvement researcher Kristin Liabo writes that health researcher might, in light of their ethics training, be inclined to exclude vulnerable individuals from participation, to protect them from harm. However, she argues these groups are already likely to be excluded from participation in other arenas, and that participation can be empowering and a possibility to gain life skills that these individuals need. Whether or not to become involved should be a decision these individuals should be involved in and not a researcher decision.
== Economic worth ==
In the research paper "Can citizen science enhance public understanding of science?" by Bonney et al. 2016, statistics which analyse the economic worth of citizen science are used, drawn from two papers: i) Sauermann and Franzoni 2015, and
ii) Theobald et al. 2015. In "Crowd science user contribution patterns and their implications" by Sauermann and Franzoni (2015), seven projects from the Zooniverse web portal are used to estimate the monetary value of the citizen science that had taken place. The seven projects are: Solar Stormwatch, Galaxy Zoo Supernovae, Galaxy Zoo Hubble, Moon Zoo, Old Weather, The Milky Way Project and Planet Hunters. Using data from 180 days in 2010, they find a total of 100,386 users participated, contributing 129,540 hours of unpaid work. Estimating at a rate of $12 an hour (an undergraduate research assistant's basic wage), the total contributions amount to $1,554,474, an average of $222,068 per project. The range over the seven projects was from $22,717 to $654,130.
In "Global change and local solutions: Tapping the unrealized potential of citizen science for biodiversity research" by Theobald et al. 2015, the authors surveyed 388 unique biodiversity-based projects. Quoting: "We estimate that between 1.36 million and 2.28 million people volunteer annually in the 388 projects we surveyed, though variation is great" and that "the range of in-kind contribution of the volunteerism in our 388 citizen science projects as between $667 million to $2.5 billion annually."
Worldwide participation in citizen science continues to grow. A list of the top five citizen science communities compiled by Marc Kuchner and Kristen Erickson in July 2018 shows a total of 3.75 million participants, although there is likely substantial overlap between the communities.
== Relations with education and academia ==
There have been studies published which examine the place of citizen science within education.(e.g.) Teaching aids can include books and activity or lesson plans.(e.g.). Some examples of studies are:
From the Second International Handbook of Science Education, a chapter entitled: "Citizen Science, Ecojustice, and Science Education: Rethinking an Education from Nowhere", by Mueller and Tippins (2011), acknowledges in the abstract that: "There is an emerging emphasis in science education on engaging youth in citizen science." The authors also ask: "whether citizen science goes further with respect to citizen development." The abstract ends by stating that the "chapter takes account of the ways educators will collaborate with members of the community to effectively guide decisions, which offers promise for sharing a responsibility for democratizing science with others."
From the journal Democracy and Education, an article entitled: "Lessons Learned from Citizen Science in the Classroom" by authors Gray, Nicosia and Jordan (GNJ; 2012) gives a response to a study by Mueller, Tippins and Bryan (MTB) called "The Future of Citizen Science". GNJ begins by stating in the abstract that "The Future of Citizen Science": "provides an important theoretical perspective about the future of democratized science and K12 education." But GRB state: "However, the authors (MTB) fail to adequately address the existing barriers and constraints to moving community-based science into the classroom." They end the abstract by arguing: "that the resource constraints of scientists, teachers, and students likely pose problems to moving true democratized science into the classroom."
In 2014, a study was published called "Citizen Science and Lifelong Learning" by R. Edwards in the journal Studies in the Education of Adults. Edwards begins by writing in the abstract that citizen science projects have expanded over recent years and engaged citizen scientists and professionals in diverse ways. He continues: "Yet there has been little educational exploration of such projects to date." He describes that "there has been limited exploration of the educational backgrounds of adult contributors to citizen science". Edwards explains that citizen science contributors are referred to as volunteers, citizens or as amateurs. He ends the abstract: "The article will explore the nature and significance of these different characterisations and also suggest possibilities for further research."
In the journal Microbiology and Biology Education a study was published by Shah and Martinez (2015) called "Current Approaches in Implementing Citizen Science in the Classroom". They begin by writing in the abstract that citizen science is a partnership between inexperienced amateurs and trained scientists. The authors continue: "With recent studies showing a weakening in scientific competency of American students, incorporating citizen science initiatives in the curriculum provides a means to address deficiencies". They argue that combining traditional and innovative methods can help provide a practical experience of science. The abstract ends: "Citizen science can be used to emphasize the recognition and use of systematic approaches to solve problems affecting the community."
In November 2017, authors Mitchell, Triska and Liberatore published a study in PLOS One titled "Benefits and Challenges of Incorporating Citizen Science into University Education". The authors begin by stating in the abstract that citizen scientists contribute data with the expectation that it will be used. It reports that citizen science has been used for first year university students as a means to experience research. They continue: "Surveys of more than 1500 students showed that their environmental engagement increased significantly after participating in data collection and data analysis." However, only a third of students agreed that data collected by citizen scientists was reliable. A positive outcome of this was that the students were more careful of their own research. The abstract ends: "If true for citizen scientists in general, enabling participants as well as scientists to analyse data could enhance data quality, and so address a key constraint of broad-scale citizen science programs."
Citizen science has also been described as challenging the "traditional hierarchies and structures of knowledge creation".
== History ==
While citizen science developed at the end of the 20th century, characteristics of citizen science are not new. Prior to the 20th century, science was often the pursuit of gentleman scientists, amateur or self-funded researchers such as Sir Isaac Newton, Benjamin Franklin, and Charles Darwin. Women citizen scientists from before the 20th century include Florence Nightingale who "perhaps better embodies the radical spirit of citizen science". Before the professionalization of science by the end of the 19th century, most pursued scientific projects as an activity rather than a profession itself, an example being amateur naturalists in the 18th and 19th centuries.
During the British colonization of North America, American Colonists recorded the weather, offering much of the information now used to estimate climate data and climate change during this time period. These people included John Campanius Holm, who recorded storms in the mid-1600s, as well as George Washington, Thomas Jefferson, and Benjamin Franklin who tracked weather patterns during America's founding. Their work focused on identifying patterns by amassing their data and that of their peers and predecessors, rather than specific professional knowledge in scientific fields. Some consider these individuals to be the first citizen scientists, some consider figures such as Leonardo da Vinci and Charles Darwin to be citizen scientists, while others feel that citizen science is a distinct movement that developed later on, building on the preceding history of science.
By the mid-20th century, however, science was dominated by researchers employed by universities and government research laboratories. By the 1970s, this transformation was being called into question. Philosopher Paul Feyerabend called for a "democratization of science". Biochemist Erwin Chargaff advocated a return to science by nature-loving amateurs in the tradition of Descartes, Newton, Leibniz, Buffon, and Darwin—science dominated by "amateurship instead of money-biased technical bureaucrats".
A study from 2016 indicates that the largest impact of citizen science is in research on biology, conservation and ecology, and is utilized mainly as a methodology of collecting and classifying data.
=== Amateur astronomy ===
Astronomy has long been a field where amateurs have contributed throughout time, all the way up to the present day.
Collectively, amateur astronomers observe a variety of celestial objects and phenomena sometimes with equipment that they build themselves. Common targets of amateur astronomers include the Moon, planets, stars, comets, meteor showers, and a variety of deep-sky objects such as star clusters, galaxies, and nebulae. Observations of comets and stars are also used to measure the local level of artificial skyglow. One branch of amateur astronomy, amateur astrophotography, involves the taking of photos of the night sky. Many amateurs like to specialize in the observation of particular objects, types of objects, or types of events that interest them.
The American Association of Variable Star Observers has gathered data on variable stars for educational and professional analysis since 1911 and promotes participation beyond its membership on its Citizen Sky website.
Project PoSSUM is a relatively new organization, started in March 2012, which trains citizen scientists of many ages to go on polar suborbital missions. On these missions, they study noctilucent clouds with remote sensing, which reveals interesting clues about changes in the upper atmosphere and the ozone due to climate change. This is a form of citizen science which trains younger generations to be ambitious, participating in intriguing astronomy and climate change science projects even without a professional degree.
=== Butterfly counts ===
Butterfly counts have a long tradition of involving individuals in the study of butterflies' range and their relative abundance. Two long-running programs are the UK Butterfly Monitoring Scheme (started in 1976) and the North American Butterfly Association's Butterfly Count Program (started in 1975). There are various protocols for monitoring butterflies and different organizations support one or more of transects, counts and/or opportunistic sightings. eButterfly is an example of a program designed to capture any of the three types of counts for observers in North America. Species-specific programs also exist, with monarchs the prominent example. Two examples of this involve the counting of monarch butterflies during the fall migration to overwintering sites in Mexico: (1) Monarch Watch is a continent-wide project, while (2) the Cape May Monarch Monitoring Project is an example of a local project.
=== Ornithology ===
Citizen science projects have become increasingly focused on providing benefits to scientific research. The North American Bird Phenology Program (historically called the Bird Migration and Distribution records) may have been the earliest collective effort of citizens collecting ornithological information in the U.S. The program, dating back to 1883, was started by Wells Woodbridge Cooke. Cooke established a network of observers around North America to collect bird migration records. The Audubon Society's Christmas Bird Count, which began in 1900, is another example of a long-standing tradition of citizen science which has persisted to the present day, now containing a collection of six million handwritten migration observer cards that date back to the 19th century. Participants input this data into an online database for analysis. Citizen scientists help gather data that will be analyzed by professional researchers, and can be used to produce bird population and biodiversity indicators.
Raptor migration research relies on the data collected by the hawkwatching community. This mostly volunteer group counts migrating accipiters, buteos, falcons, harriers, kites, eagles, osprey, vultures and other raptors at hawk sites throughout North America during the spring and fall seasons. The daily data is uploaded to hawkcount.org where it can be viewed by professional scientists and the public.
Other programs in North America include Project FeederWatch, which is affiliated with the Cornell Lab of Ornithology.
Such indices can be useful tools to inform management, resource allocation, policy and planning. For example, European breeding bird survey data provide input for the Farmland Bird Index, adopted by the European Union as a structural indicator of sustainable development. This provides a cost-effective alternative to government monitoring.
Similarly, data collected by citizen scientists as part of BirdLife Australia's has been analysed to produce the first-ever Australian Terrestrial Bird Indices.
In the UK, the Royal Society for the Protection of Birds collaborated with a children’s TV show to create a national birdwatching day in 1979; the campaign has continued for over 40 years and in 2024, over 600,000 people counted almost 10 million birds during the Big Garden Birdwatch weekend.
Most recently, more programs have sprung up worldwide, including NestWatch, a bird species monitoring program which tracks data on reproduction. This might include studies on when and how often nesting occurs, counting eggs laid and how many hatch successfully, and what proportion of hatchlings survive infancy. Participation in this program is extremely easy for the general public to join. Using the recently created nest watch app which is available on almost all devices, anyone can begin to observe their local species, recording results every 3 to 4 days within the app. This forms a continually-growing database which researchers can view and utilize to understand trends within specific bird populations.
=== Citizen oceanography ===
The concept of citizen science has been extended to the ocean environment for characterizing ocean dynamics and tracking marine debris. For example, the mobile app Marine Debris Tracker is a joint partnership of National Oceanic and Atmospheric Administration and the University of Georgia. Long term sampling efforts such as the continuous plankton recorder has been fitted on ships of opportunity since 1931. Plankton collection by sailors and subsequent genetic analysis was pioneered in 2013 by Indigo V Expeditions as a way to better understand marine microbial structure and function.
=== Coral reefs ===
Citizen science in coral reef studies developed in the 21st century.
Underwater photography has become more popular since the development of moderate priced digital cameras with waterproof housings in the early 2000s, resulting on millions of pictures posted every year on various websites and social media. This mass of documentation has great scientific potential, as millions of tourists possess a much superior coverage power than professional scientists, who cannot spend so much time in the field.
As a consequence, several participative sciences programs have been developed, supported by geotagging and identification web sites such as iNaturalist. The Monitoring through many eyes project collates thousands of underwater images of the Great Barrier Reef and provides an interface for elicitation of reef health indicators.
The National Oceanic and Atmospheric Administration (NOAA) also offers opportunities for volunteer participation. By taking measurements in The United States' National Marine Sanctuaries, citizens contribute data to marine biology projects. In 2016, NOAA benefited from 137,000 hours of research.
There also exist protocols for auto-organization and self-teaching aimed at biodiversity-interested snorkelers, in order for them to turn their observations into sound scientific data, available for research. This kind of approach has been successfully used in Réunion island, allowing for tens of new records and even new species.
=== Freshwater fish ===
Aquarium hobbyists and their respective organizations are very passionate about fish conservation and often more knowledgeable about specific fish species and groups than scientific researchers. They have played an important role in the conservation of freshwater fishes by discovering new species, maintaining extensive databases with ecological information on thousands of species (such as for catfish, Mexican freshwater fishes, killifishes, cichlids), and successfully keeping and providing endangered and extinct-in-the-wild species for conservation projects. The CARES (Conservation, Awareness, Recognition, Encouragement, and Support) preservation program is the largest hobbyist organization containing over 30 aquarium societies and international organizations, and encourages serious aquarium hobbyists to devote tank space to the most threatened or extinct-in-the-wild species to ensure their survival for future generations.
=== Amphibians ===
Citizen scientists also work to monitor and conserve amphibian populations. One recent project is FrogWatch USA, organized by the Association of Zoos and Aquariums. Participants are invited to educate themselves on their local wetlands and help to save amphibian populations by reporting the data on the calls of local frogs and toads. The project already has over 150,000 observations from more than 5000 contributors. Participants are trained by program coordinators to identify calls and utilize this training to report data they find between February and August of each "monitoring season". Data is used to monitor diversity, invasion, and long-term shifts in population health within these frog and toad communities.
=== Rocky reefs ===
Reef Life Survey is a marine life monitoring programme based in Hobart, Tasmania. The project uses recreational divers that have been trained to make fish and invertebrate counts, using an approximate 50 m constant depth transect of tropical and temperate reefs, which might include coral reefs. Reef Life Survey is international in its scope, but the data collectors are predominantly from Australia. The database is available to marine ecology researchers, and is used by several marine protected area managements in Australia, New Zealand, American Samoa and the eastern Pacific. Its results have also been included in the Australian Ocean DATA Network.
=== Agriculture ===
Farmer participation in experiments has a long tradition in agricultural science. There are many opportunities for citizen engagement in different parts of food systems. Citizen science is actively used for crop variety selection for climate adaptation, involving thousands of farmers. Citizen science has also played a role in furthering sustainable agriculture.
=== Art history ===
Citizen science has a long tradition in natural science. Today, citizen science projects can also be found in various fields of science like art history. For example, the Zooniverse project AnnoTate is a transcription tool developed to enable volunteers to read and transcribe the personal papers of British-born and émigré artists. The papers are drawn from the Tate Archive. Another example of citizen science in art history is ARTigo. ARTigo collects semantic data on artworks from the footprints left by players of games featuring artwork images. From these footprints, ARTigo automatically builds a semantic search engine for artworks.
=== Biodiversity ===
Citizen science has made significant contributions to the analysis of biodiversity across the world. A majority of data collected has been focused primarily on species occurrence, abundance and phenology, with birds being primarily the most popular group observed. There is growing efforts to expand the use of citizen science across other fields. Past data on biodiversity has had limitations in the quantity of data to make any meaningful broad connections to losses in biodiversity. Recruiting citizens already out in the field opens a tremendous amount of new data. For example, thousands of farmers reporting the changes in biodiversity in their farms over many years has provided a large amount of relevant data concerning the effect of different farming methods on biodiversity. Another example, is WomSAT, a citizen science project that collects data on wombat roadkill and sarcoptic mange incidence and distribution, to support conservation efforts for the species.
Citizen science can be used to great effect in addition to the usual scientific methods in biodiversity monitoring. The typical active method of species detection is able to collect data on the broad biodiversity of areas while citizen science approaches has shown to be more effective at identifying invasive species. In combination, this provides an effective strategy of monitoring the changes in biodiversity of ecosystems.
=== Health and welfare ===
In the research fields of health and welfare, citizen science is often discussed in other terms, such as "public involvement", "user engagement", or "community member involvement". However the meaning is similar to citizen science, with the exception that citizens are not often involved in collecting data but more often involved in prioritisation of research ideas and improving methodology, e.g. survey questions. In the last decades, researchers and funders have gained awareness of the benefits from involving citizens in the research work, but the involvement of citizens in a meaningful way is not a common practice. There is an ongoing discussion on how to evaluate citizen science in health and welfare research.
One aspect to consider in citizen science in health and welfare, that stands out compared to in other academic fields, is who to involve. When research concerns human experiences, representation of a group becomes important. While it is commonly acknowledged that the people involved need to have lived experience of the concerned topic, representation is still an issue, and researchers are debating whether this is a useful concept in citizen science.
== Modern technology ==
Newer technologies have increased the options for citizen science. Citizen scientists can build and operate their own instruments to gather data for their own experiments or as part of a larger project. Examples include amateur radio, amateur astronomy, Six Sigma Projects, and Maker activities. Scientist Joshua Pearce has advocated for the creation of open-source hardware based scientific equipment that both citizen scientists and professional scientists, which can be replicated by digital manufacturing techniques such as 3D printing. Multiple studies have shown this approach radically reduces scientific equipment costs. Examples of this approach include water testing, nitrate and other environmental testing, basic biology and optics. Groups such as Public Lab, which is a community where citizen scientists can learn how to investigate environmental concerns using inexpensive DIY techniques, embody this approach.
Video technology is much used in scientific research. The Citizen Science Center in the Nature Research Center wing of the North Carolina Museum of Natural Sciences has exhibits on how to get involved in scientific research and become a citizen scientist. For example, visitors can observe birdfeeders at the Prairie Ridge Ecostation satellite facility via live video feed and record which species they see.
Since 2005, the Genographic Project has used the latest genetic technology to expand our knowledge of the human story, and its pioneering use of DNA testing to engage and involve the public in the research effort has helped to create a new breed of "citizen scientist". Geno 2.0 expands the scope for citizen science, harnessing the power of the crowd to discover new details of human population history. This includes supporting, organization and dissemination of personal DNA testing. Like amateur astronomy, citizen scientists encouraged by volunteer organizations like the International Society of Genetic Genealogy have provided valuable information and research to the professional scientific community.
With unmanned aerial vehicles, further citizen science is enabled. One example is the ESA's AstroDrone smartphone app for gathering robotic data with the Parrot AR.Drone.
Citizens in Space (CIS), a project of the United States Rocket Academy, seeks to combine citizen science with citizen space exploration. CIS is training citizen astronauts to fly as payload operators on suborbital reusable spacecraft that are now in development. CIS will also be developing, and encouraging others to develop, citizen-science payloads to fly on suborbital vehicles. CIS has already acquired a contract for 10 flights on the Lynx suborbital vehicle, being developed by XCOR Aerospace, and plans to acquire additional flights on XCOR Lynx and other suborbital vehicles in the future.
CIS believes that "The development of low-cost reusable suborbital spacecraft will be the next great enabler, allowing citizens to participate in space exploration and space science."
The website CitizenScience.gov was started by the U.S. government to "accelerate the use of crowdsourcing and citizen science" in the United States. Following the internet's rapid increase of citizen science projects, this site is one of the most prominent resource banks for citizen scientists and government supporters alike. It features three sections: a catalog of existing citizen science projects which are federally supported, a toolkit to help federal officials as they develop and maintain their future projects, and several other resources and projects. This was created as the result of a mandate within the Crowdsourcing and Citizen Science Act of 2016 (15 USC 3724).
=== Internet ===
The Internet has been a boon to citizen science, particularly through gamification. One of the first Internet-based citizen science experiments was NASA's Clickworkers, which enabled the general public to assist in the classification of images, greatly reducing the time to analyze large data sets. Another was the Citizen Science Toolbox, launched in 2003, of the Australian Coastal Collaborative Research Centre. Mozak is a game in which players create 3D reconstructions from images of actual human and mouse neurons, helping to advance understanding of the brain. One of the largest citizen science games is Eyewire, a brain-mapping puzzle game developed at the Massachusetts Institute of Technology that now has over 200,000 players. Another example is Quantum Moves, a game developed by the Center for Driven Community Research at Aarhus University, which uses online community efforts to solve quantum physics problems. The solutions found by players can then be used in the lab to feed computational algorithms used in building a scalable quantum computer.
More generally, Amazon's Mechanical Turk is frequently used in the creation, collection, and processing of data by paid citizens. There is controversy as to whether or not the data collected through such services is reliable, as it is subject to participants' desire for compensation. However, use of Mechanical Turk tends to quickly produce more diverse participant backgrounds, as well as comparably accurate data when compared to traditional collection methods.
The internet has also enabled citizen scientists to gather data to be analyzed by professional researchers. Citizen science networks are often involved in the observation of cyclic events of nature (phenology), such as effects of global warming on plant and animal life in different geographic areas, and in monitoring programs for natural-resource management. On BugGuide.Net, an online community of naturalists who share observations of arthropod, amateurs and professional researchers contribute to the analysis. By October 2022, BugGuide has over 1,886,513 images submitted by 47,732 contributors.
Not counting iNaturalist and eBird, the Zooniverse is home to the internet's largest, most popular and most successful citizen science projects. The Zooniverse and the suite of projects it contains is produced, maintained and developed by the Citizen Science Alliance (CSA). The member institutions of the CSA work with many academic and other partners around the world to produce projects that use the efforts and ability of volunteers to help scientists and researchers deal with the flood of data that confronts them. On 29 June 2015, the Zooniverse released a new software version with a project-building tool allowing any registered user to create a project. Project owners may optionally complete an approval process to have their projects listed on the Zooniverse site and promoted to the Zooniverse community. A NASA/JPL picture to the right gives an example from one of Zooniverse's projects The Milky Way Project.
The website CosmoQuest has as its goal "To create a community of people bent on together advancing our understanding of the universe; a community of people who are participating in doing science, who can explain why what they do matters, and what questions they are helping to answer."
CrowdCrafting enables its participants to create and run projects where volunteers help with image classification, transcription, geocoding and more. The platform is powered by PyBossa software, a free and open-source framework for crowdsourcing.
Project Soothe is a citizen science research project based at the University of Edinburgh. The aim of this research is to create a bank of soothing images, submitted by members of the public, which can be used to help others through psychotherapy and research in the future. Since 2015, Project Soothe has received over 600 soothing photographs from people in 23 countries. Anyone aged 12 years or over is eligible to participate in this research in two ways: (1) By submitting soothing photos that they have taken with a description of why the images make them feel soothed (2) By rating the photos that have been submitted by people worldwide for their soothability.
The internet has allowed for many individuals to share and upload massive amounts of data. Using the internet citizen observatories have been designed as a platform to both increase citizen participation and knowledge of their surrounding environment by collecting whatever relevant data is focused by the program. The idea is making it easier and more exciting for citizens to get and stay involved in local data collection.
The invention of social media has aided in providing massive amounts of information from the public to create citizen science programs. In a case study by Andrea Liberatore, Erin Bowkett, Catriona J. MacLeod, Eric Spurr, and Nancy Longnecker, the New Zealand Garden Bird Survey is conducted as one such project with the aid of social media. It examines the influence of utilizing a Facebook group to collect data from citizen scientists as the researchers work on the project over the span of a year. The authors claim that this use of social media greatly helps with the efficiency of this study and makes the atmosphere feel more communal.
=== Smartphone ===
The bandwidth and ubiquity afforded by smartphones has vastly expanded the opportunities for citizen science. Examples include iNaturalist, Chronolog, the San Francisco project, the WildLab, Project Noah, and Aurorasurus. Due to their ubiquity, for example, Twitter, Facebook, and smartphones have been useful for citizen scientists, having enabled them to discover and propagate a new type of aurora dubbed "STEVE" in 2016.
There are also apps for monitoring birds, marine wildlife and other organisms, and the "Loss of the Night". Chronolog, another citizen science initiative, uses smartphone photography to crowdsource environmental monitoring through timelapses. By positioning their cameras at designated photo stations and submitting images, participants contribute to long-term ecological records at parks and conservation sites across 48 U.S. states and 10 countries. Restoration professionals and other land stewards use this data to measure ecosystem health and understand the effectiveness of conservation interventions like habitat restoration, controlled burns, removal of invasive species, planting of native species, and efforts to improve water quality.
"The Crowd and the Cloud" is a four-part series broadcast during April 2017, which examines citizen science. It shows how smartphones, computers and mobile technology enable regular citizens to become part of a 21st-century way of doing science. The programs also demonstrate how citizen scientists help professional scientists to advance knowledge, which helps speed up new discoveries and innovations. The Crowd & The Cloud is based upon work supported by the U.S. National Science Foundation.
=== Seismology ===
Since 1975, in order to improve earthquake detection and collect useful information, the European-Mediterranean Seismological Centre monitors the visits of earthquake eyewitnesses to its website and relies on Facebook and Twitter. More recently, they developed the LastQuake mobile application which notifies users about earthquakes occurring around the world, alerts people when earthquakes hit near them, gathers citizen seismologists' testimonies to estimate the felt ground shaking and possible damages.
=== Hydrology ===
Citizen science has been used to provide valuable data in hydrology (catchment science), notably flood risk, water quality, and water resource management. A growth in internet use and smartphone ownership has allowed users to collect and share real-time flood-risk information using, for example, social media and web-based forms. Although traditional data collection methods are well-established, citizen science is being used to fill the data gaps on a local level, and is therefore meaningful to individual communities. Data collected from citizen science can also compare well to professionally collected data. It has been demonstrated that citizen science is particularly advantageous during a flash flood because the public are more likely to witness these rarer hydrological events than scientists.
=== Plastics and pollution ===
Citizen science includes projects that help monitor plastics and their associated pollution. These include The Ocean Cleanup, #OneLess, The Big Microplastic Survey, EXXpedition and Alliance to End Plastic Waste. Ellipsis seeks to map the distribution of litter using aerial data mapping by unmanned aerial vehicles and machine learning software. A Zooniverse project called The Plastic Tide (now finished) helped train an algorithm used by Ellipsis.
Examples of relevant articles (by date):
Citizen Science Promotes Environmental Engagement: (quote) "Citizen science projects are rapidly gaining popularity among the public, in which volunteers help gather data on species that can be used by scientists in research. And it's not just adults who are involved in these projects – even kids have collected high-quality data in the US."
Tackling Microplastics on Our Own: (quote) "Plastics, ranging from the circles of soda can rings to microbeads the size of pinheads, are starting to replace images of sewage for a leading cause of pollution – especially in the ocean". Further, "With recent backing from the Crowdsourcing and Citizen Science Act, citizen science is increasingly embraced as a tool by US Federal agencies."
Citizen Scientists Are Tracking Plastic Pollution Worldwide: (quote) "Scientists who are monitoring the spread of tiny pieces of plastic throughout the environment are getting help from a small army of citizen volunteers – and they're finding bits of polymer in some of the most remote parts of North America."
Artificial intelligence and citizen scientists: Powering the clean-up of Asia Pacific's beaches:(quote) "The main objective is to support citizen scientists cleaning up New Zealand beaches and get a better understanding of why litter is turning up, so preventive and proactive action can be taken."
Citizen science could help address Canada's plastic pollution problem: (quote) "But citizen engagement and participation in science goes beyond beach cleanups, and can be used as a tool to bridge gaps between communities and scientists. These partnerships between scientists and citizen scientists have produced real world data that have influenced policy changes."
Examples of relevant scientific studies or books include (by date):
Distribution and abundance of small plastic debris on beaches in the SE Pacific (Chile): a study supported by a citizen science project: (quote) "The citizen science project 'National Sampling of Small Plastic Debris' was supported by schoolchildren from all over Chile who documented the distribution and abundance of small plastic debris on Chilean beaches. Thirty-nine schools and nearly 1,000 students from continental Chile and Easter Island participated in the activity."
Incorporating citizen science to study plastics in the environment: (quote) "Taking advantage of public interest in the impact of plastic on the marine environment, successful Citizen Science (CS) programs incorporate members of the public to provide repeated sampling for time series as well as synoptic collections over wide geographic regions."
Marine anthropogenic litter on British beaches: A 10-year nationwide assessment using citizen science data: (quote) "Citizen science projects, whereby members of the public gather information, offer a low-cost method of collecting large volumes of data with considerable temporal and spatial coverage. Furthermore, such projects raise awareness of environmental issues and can lead to positive changes in behaviours and attitudes."
Determining Global Distribution of Microplastics by Combining Citizen Science and In-Depth Case Studies: (quote) "Our first project involves the general public through citizen science. Participants collect sand samples from beaches using a basic protocol, and we subsequently extract and quantify microplastics in a central laboratory using the standard operating procedure."
Risk Perception of Plastic Pollution: Importance of Stakeholder Involvement and Citizen Science: (quote) "The chapter finally discusses how risk perception can be improved by greater stakeholder involvement and utilization of citizen science and thereby improve the foundation for timely and efficient societal measures."
Assessing the citizen science approach as tool to increase awareness on the marine litter problem: (quote) "This paper provides a quantitative assessment of students' attitude and behaviors towards marine litter before and after their participation to SEACleaner, an educational and citizen science project devoted to monitor macro- and micro-litter in an Area belonging to Pelagos Sanctuary."
Spatial trends and drivers of marine debris accumulation on shorelines in South Eleuthera, The Bahamas using citizen science: (quote) "This study measured spatial distribution of marine debris stranded on beaches in South Eleuthera, The Bahamas. Citizen science, fetch modeling, relative exposure index and predictive mapping were used to determine marine debris source and abundance."
Making citizen science count: Best practices and challenges of citizen science projects on plastics in aquatic environments: (quote) "Citizen science is a cost-effective way to gather data over a large geographical range while simultaneously raising public awareness on the problem".
White and wonderful? Microplastics prevail in snow from the Alps to the Arctic: (quote) "In March 2018, five samples were taken at different locations on Svalbard (Fig. 1A and Table 1) by citizen scientists embarking on a land expedition by ski-doo (Aemalire project). The citizens were instructed on contamination prevention and equipped with protocol forms, prerinsed 2-liter stainless steel containers (Ecotanca), a porcelain mug, a steel spoon, and a soup ladle for sampling."
=== Citizen sensing ===
Citizen sensing can be a form of citizen science: (quote) "The work of citizen sensing, as a form of citizen science, then further transforms Stengers's notion of the work of science by moving the experimental facts and collectives where scientific work is undertaken out of the laboratory of experts and into the world of citizens." Similar sensing activities include Crowdsensing and participatory monitoring. While the idea of using mobile technology to aid this sensing is not new, creating devices and systems that can be used to aid regulation has not been straightforward. Some examples of projects that include citizen sensing are:
Citizen Sense (2013–2018): (quote) "Practices of monitoring and sensing environments have migrated to everyday participatory applications, where users of smart phones and networked devices are able to engage with modes of environmental observation and data collection."
Breathe Project: (quote) "We use the best available science and technology to better understand the quality of the air we breathe and provide opportunities for citizens to engage and take action."
The Bristol Approach to Citizen Sensing: (quote) "Citizen Sensing is about empowering people and places to understand and use smart tech and data from sensors to tackle the issues they care about, connect with other people who can help, and take positive, practical action."
Luftdaten.info: (quote) "You and thousands of others around the world install self-built sensors on the outside their home. Luftdaten.info generates a continuously updated particular matter map from the transmitted data."
CitiSense: (quote) "CitiSense aims to co-develop a participatory risk management system (PRMS) with citizens, local authorities and organizations which enables them to contribute to advanced climate services and enhanced urban climate resilience as well as receive recommendations that support their security."
A group of citizen scientists in a community-led project targeting toxic smoke from wood burners in Bristol, has recorded 11 breaches of World Health Organization daily guidelines for ultra-fine particulate pollution over a period of six months.
In a £7M programme funded by water regulator Ofwat, citizen scientists are being trained to test for pollution and over-abstraction in 10 river catchment areas in the UK. Sensors will be used and the information gathered will be available in a central visualisation platform. The project is led by The Rivers Trust and United Utilities and includes volunteers such as anglers testing the rivers they use. The Angling Trust provides the pollution sensors, with Kristian Kent from the Trust saying: "Citizen science is a reality of the world in the future, so they’re not going to be able to just sweep it under the carpet."
River water quality in the U.K. has been tested by a combined total of over 7,000 volunteers in so-called "blitzes" run over two weekends in 2024. The research by the NGO Earthwatch Europe gathered data from 4,000 freshwater sites and used standardised testing equipment provide by the NGO and Imperial College. The second blitz in October 2024 included testing for chemical pollutants, such as antibiotics, agricultural chemicals and pesticides. Results from 4,531 volunteers showed that over 61% of the freshwater sites "were in a poor state because of high levels of the nutrients phosphate and nitrate, the main source of which is sewage effluent and agricultural runoff". The data gathered through robust volunteer testing is analysed and put into a report helping provide the Environment Agency with information it does not have.
=== COVID-19 pandemic ===
Resources for computer science and scientific crowdsourcing projects concerning COVID-19 can be found on the internet or as apps. Some such projects are listed below:
The distributed computing project Folding@home launched a program in March 2020 to assist researchers around the world who were working on finding a cure and learning more about the coronavirus pandemic. The initial wave of projects were meant to simulate potentially druggable protein targets from SARS-CoV-2 (and also its predecessor and close relation SARS-CoV, about which there is significantly more data available). In 2024, the project has been extended to look at other health issues including Alzheimer’s and cancer. The project asks volunteers to download the app and donate computing power for simulations.
The distributed computing project Rosetta@home also joined the effort in March 2020. The project uses computers of volunteers to model SARS-CoV-2 virus proteins to discover possible drug targets or create new proteins to neutralize the virus. Researchers revealed that with the help of Rosetta@home, they had been able to "accurately predict the atomic-scale structure of an important coronavirus protein weeks before it could be measured in the lab." In 2022, the parent Boinc company thanked contributors for donating their computer power and helping work on the de novo protein design including vaccine development.
The OpenPandemics – COVID-19 project is a partnership between Scripps Research and IBM's World Community Grid for a distributed computing project that "will automatically run a simulated experiment in the background [of connected home PCs] which will help predict the effectiveness of a particular chemical compound as a possible treatment for COVID-19". The project asked volunteers to donate unused computing power. In 2024, the project was looking at targeting the DNA polymerase of the cytomegalovirus to identify binders.
The Eterna OpenVaccine project enables video game players to "design an mRNA encoding a potential vaccine against the novel coronavirus." In mid-2021, it was noted that the project had helped create a library of potential vaccine molecules to be tested at Stanford University; SU researchers also noted that importance of volunteers discussing the games and exchanging ideas.
In March 2020, the EU-Citizen.Science project had "a selection of resources related to the current COVID19 pandemic. It contains links to citizen science and crowdsourcing projects"
The COVID-19 Citizen Science project was "a new initiative by University of California, San Francisco physician-scientists" that "will allow anyone in the world age 18 or over to become a citizen scientist advancing understanding of the disease." By 2024, the Eureka platform had over 100,000 participants.
The CoronaReport digital journalism project was "a citizen science project which democratizes the reporting on the Coronavirus, and makes these reports accessible to other citizens." It was developed by the University of Edinburgh and asked people affected by Covid to share the social effects of the pandemic.
The COVID Symptom Tracker was a crowdsourced study of the symptoms of the virus. It was created in the UK by King’s College London and Guy’s and St Thomas’ Hospitals. It had two million downloads by April 2020. Within three months, information from the app had helped identify six variations of Covid. Government funding ended in early 2022, but due to the large number of volunteers, Zoe decided to continue the work to study general health. By February 2023, over 75,000 people had downloaded the renamed Zoe Habit Tracker.
The Covid Near You epidemiology tool "uses crowdsourced data to visualize maps to help citizens and public health agencies identify current and potential hotspots for the recent pandemic coronavirus, COVID-19." The site was launched in Boston in March 2020; at the end of 2020 it was rebranded to Outbreaks Near Me and tracked both Covid and flu.
The We-Care project is a novel initiative by University of California, Davis researchers that uses anonymity and crowdsourced information to alert infected users and slow the spread of COVID-19.
COVID Radar was an app in the Netherlands, active between April 2020 and February 2022, with which users anonymously answered a short daily questionnaire asking about their symptoms, behavior, coronavirus test results, and vaccination status. Symptoms and behavior were visualized on a map and users received feedback on their individual risk and behaviors relative to the national mean. The app had over 250,000 users, who filled out the questionnaire over 8.5 million times. Research from this app continued to be used in 2024.
For coronavirus studies and information that can help enable citizen science, many online resources are available through open access and open science websites, including an intensive care medicine e-book chapter hosted by EMCrit and portals run by the Cambridge University Press, the Europe branch of the Scholarly Publishing and Academic Resources Coalition, The Lancet, John Wiley and Sons, and Springer Nature.
There have been suggestions that the pandemic and subsequent lockdown has boosted the public’s awareness and interest in citizen science, with more people around the world having the motivation and the time to become involved in helping to investigate the illness and potentially move on to other areas of research.
== Around the world ==
The Citizen Science Global Partnership was created in 2022; the partnership brings together networks from Australia, Africa, Asia, Europe, South America and the USA.
=== Africa ===
In South Africa (SA), citizen science projects include: the Stream Assessment Scoring System (miniSASS) which "encourages enhanced catchment management for water security in a climate stressed society."
The South African National Biodiversity Institute is partnered with iNaturalist as a platform for biodiversity observations using digital photography and geolocation technology to monitor biodiversity. Such partnerships can reduce duplication of effort, help standardise procedures and make the data more accessible.
Also in SA, "Members of the public, or 'citizen scientists' are helping researchers from the University of Pretoria to identify Phytophthora species present in the fynbos."
In June 2016, citizen science experts from across East Africa gathered in Nairobi, Kenya, for a symposium organised by the Tropical Biology Association (TBA) in partnership with the Centre for Ecology & Hydrology (CEH). The aim was "to harness the growing interest and expertise in East Africa to stimulate new ideas and collaborations in citizen science." Rosie Trevelyan of the TBA said: "We need to enhance our knowledge about the status of Africa's species and the threats facing them. And scientists can't do it all on their own. At the same time, citizen science is an extremely effective way of connecting people more closely to nature and enrolling more people in conservation action".
The website Zooniverse hosts several African citizen science projects, including: Snapshot Serengeti, Wildcam Gorongosa and Jungle Rhythms.
Nigeria has the Ibadan Bird Club whose to aim is to "exchange ideas and share knowledge about birds, and get actively involved in the conservation of birds and biodiversity."
In Namibia, Giraffe Spotter.org is "project that will provide people with an online citizen science platform for giraffes".
Within the Republic of the Congo, the territories of an indigenous people have been mapped so that "the Mbendjele tribe can protect treasured trees from being cut down by logging companies". An Android open-source app called Sapelli was used by the Mbendjele which helped them map "their tribal lands and highlighted trees that were important to them, usually for medicinal reasons or religious significance. Congolaise Industrielle des Bois then verified the trees that the tribe documented as valuable and removed them from its cutting schedule. The tribe also documented illegal logging and poaching activities."
In West Africa, the eradication of the recent outbreak of Ebola virus disease was partly helped by citizen science. "Communities learnt how to assess the risks posed by the disease independently of prior cultural assumptions, and local empiricism allowed cultural rules to be reviewed, suspended or changed as epidemiological facts emerged." "Citizen science is alive and well in all three Ebola-affected countries. And if only a fraction of the international aid directed at rebuilding health systems were to be redirected towards support for citizen science, that might be a fitting memorial to those who died in the epidemic."
The CitSci Africa Association held its International Conference in February 2024 in Nairobi.
=== Asia ===
The Hong Kong Birdwatching Society was established in 1957, and is the only local civil society aiming at appreciating and conserving Hong Kong birds and their natural environment. Their bird surveys go back to 1958, and they carry out a number of Citizen Science events such as their yearly sparrow census.
The Bird Count India partnership consists of a large number of organizations and groups involved in birdwatching and bird surveys. They coordinate a number of Citizen Science projects such as the Kerala Bird Atlas and Mysore city Bird Atlas that map the distribution and abundance of birds of entire Indian states.
RAD@home Collaboratory is an Indian citizen science research programme in astronomy & astrophysics. Launched on 15 April 2013 this programme uses hybrid model, social media platforms and in-person training of the interested participants. Recently in 2022, the Collaboratory reported discovery of an active galactic nucleus, a radio galaxy named RAD12, spewing a large unipolar radio bubble on to its merging companion galaxy.
The Taiwan Roadkill Observation Network was founded in 2011 and has more than 16,000 members as of 2019. It is a citizen science project where roadkill across Taiwan is photographed and sent to the Endemic Species Research Institute for study. Its primary goal has been to set up an eco-friendly path to mitigate roadkill challenges and popularize a national discourse on environmental issues and civil participation in scientific research. The members of the Taiwan Roadkill Observation Network volunteer to observe animals' corpses that are by caused by roadkill or by other reasons. Volunteers can then upload pictures and geographic locations of the roadkill to an internet database or send the corpses to the Endemic Species Research as specimens.Because members come from different areas of the island, the collection of data serves as an animal distribution map of the island. According to the geographical data and pictures of corpses collected by the members, the community itself and the sponsor, the Endemic Species Center could find out the hotspots and the reasons for the animals' deaths. One of the most renowned cases is that the community successfully detected rabies cases due to the huge collection of data. The corpses of Melogale moschata had accumulated for years and are thought to be carriers of rabies. Alarmed by this, the government authority took actions to prevent the prevalence of rabies in Taiwan.In another case in 2014, some citizen scientists discovered birds that had died from unknown causes near an agricultural area. The Taiwan Roadkill Observation Network cooperated with National Pingtung University of Science and Technology and engaged citizen scientists to collect bird corpses. The volunteers collected 250 bird corpses for laboratory tests, which confirmed that the bird deaths were attributable to pesticides used on crops. This prompted the Taiwanese government to restrict pesticides, and the Bill of Pesticide Management amendment was passed after the third reading in the Legislative Yuan, establishing a pesticide control system. The results indicated that Taiwan Roadkill Observation Network had developed a set of shared working methods and jointly completed certain actions. Furthermore, the community of the Taiwan Roadkill Observation Network had made real changes to road design to avoid roadkill, improved the management of usage of pesticide, epidemic prevention, as well as other examples. By mid-2024, volunteers had observed over 293,000 animals. The network, the largest citizen science project in Taiwan, noted that more than half of roadkill were amphibians (eg, frogs), while one third are reptiles and birds.
The AirBox Project was launched in Taiwan to create a participatory ecosystem with a focus on PM2.5 monitoring through AirBox devices. By the end of 2014, the public had paid more attention to the PM2.5 levels because the air pollution problem had become worse, especially in central and southern Taiwan. High PM2.5 levels are harmful to our health, with respiratory problems as an example. These pollution levels aroused public concern and led to an intensive debate about air pollution sources. Some experts suggested that air quality was affected by pollutants from mainland China, while some environmentalists believed that it was the result of industrialization, because of, for example, exhaust fumes from local power plants or factories. However, no one knew the answer because of insufficient data.Dr. Ling-Jyh Chen, a researcher of the Institute of Information Science, Academia Sinica, launched The AirBox Project. His original idea was inspired by a popular Taiwanese slogan "Save Your Environment by Yourself". As an expert in a Participatory Sensing system, he decided to take this ground-up approach to collect PM2.5 level data, and thus through open data and data analysis to have a better understanding of the possible air pollution sources. Using this ecosystem, huge amounts of data was collected from AirBox devices. This data was instantly available online, informing people of PM2.5 levels. They could then take the proper actions, such as wearing a mask or staying at home, preventing themselves from going out into the polluted environment.Data can also be analyzed to understand the possible sources of pollution and provide recommendations for improving the situation. There are four main steps to this project: i) Develop the AirBox device. Developing a device that could correctly collect the data of the PM2.5 level was time-consuming. It had taken more than three years to develop an AirBox that can be easily used, but with both high accuracy and low cost. ii) The widespread installation of AirBoxes. In the beginning, very few people were willing to install it at their homes because of their concerns about the possible harm to their health, power consumption and maintenance. Because of this, AirBoxes were only installed in a relatively small area. But with help from Taiwan's LASS (Location Aware Sensing System) community, AirBoxes appeared in all parts of Taiwan. As of February 2017, there are more than 1,600 AirBoxes installed in more than 27 countries. iii) Open Source and Data Analysis. All measurement results were released and visualized in real-time to the public through different media. Data can be analyzed to trace pollution sources. By December 2019, there were over 4,000 AirBoxes installed across the country.
Japan has a long history of citizen science involvement, the 1,200-year-old tradition of collecting records on cherry blossom flowering probably being the world's longest-running citizen science project. One of the most influential citizen science projects has also come out of Japan: Safecast. Dedicated to open citizen science for the environment, Safecast was established in the wake of the Fukushima nuclear disaster, and produces open hardware sensors for radiation and air-pollution mapping. Presenting this data via a global open data network and maps
As technology and public interest grew, the CitizenScience.Asia group was set up in 2022; it grew from an initial hackathon in Hong Kong which worked on the 2016 Zika scare. The network is part of Citizen Science Global Partnership.
=== Europe ===
The English naturalist Charles Darwin (1809–1882) is widely regarded to have been one of the earliest citizen science contributors in Europe (see § History). A century later, citizen science was experienced by adolescents in Italy during the 1980s, working on urban energy usages and air pollution.
In his book "Citizen Science", Alan Irwin considers the role that scientific expertise can play in bringing the public and science together and building a more scientifically active citizenry, empowering individuals to contribute to scientific development. Since then a citizen science green paper was published in 2013, and European Commission policy directives have included citizen science as one of five strategic areas with funding allocated to support initiatives through the 'Science With and For Society (SwafS)', a strand of the Horizon 2020 programme. This includes significant awards such as the EU Citizen Science Project, which is creating a hub for knowledge sharing, coordination, and action. The European Citizen Science Association (ECSA) was set up in 2014 to encourage the growth of citizen science across Europe, to increase public participation in scientific processes, mainly by initiating and supporting citizen science projects as well as conducting research. ECSA has a membership of over 250 individual and organisational members from over 30 countries across the European Union and beyond.
Examples of citizen science organisations and associations based in Europe include the Biosphere Expeditions (Ireland), Bürger schaffen Wissen (Germany), Citizen Science Lab at Leiden University (Netherlands), Ibercivis (See External Links), Österreich forscht (Austria). Other organisations can be found here: EU Citizen Science.
The European Citizen Science Association was created in 2014.
In 2023, the European Union Prize for Citizen Science was established. Bestowed through Ars Electronica, the prize was designed to honor, present and support "outstanding projects whose social and political impact advances the further development of a pluralistic, inclusive and sustainable society in Europe".
=== Latin America ===
In 2015, the Asháninka people from Apiwtxa, which crosses the border between Brazil and Peru, began using the Android app Sapelli to monitor their land. The Ashaninka have "faced historical pressures of disease, exploitation and displacement, and today still face the illegal invasion of their lands by loggers and hunters. This monitoring project shows how the Apiwtxa Ashaninka from the Kampa do Rio Amônia Indigenous Territory, Brazil, are beginning to use smartphones and technological tools to monitor these illegal activities more effectively."
In Argentina, two smartphone Android applications are available for citizen science. i) AppEAR has been developed at the Institute of Limnology and was launched in May 2016. Joaquín Cochero is a researcher who developed an "application that appeals to the collaboration of users of mobile devices in collecting data that allow the study of aquatic ecosystems" (translation). Cochero stated: "Not much of citizen science in Argentina, just a few more oriented to astronomy specific cases. As ours is the first. And I have volunteers from different parts of the country that are interested in joining together to centralize data. That's great because these types of things require many people participate actively and voluntarily" (translation). ii) eBird was launched in 2013, and has so far identified 965 species of birds. eBird in Argentina is "developed and managed by the Cornell Lab of Ornithology at Cornell University, one of the most important ornithological institutions in the world, and locally presented recently with the support of the Ministry of Science, Technology and Productive Innovation of the Nation (MINCyT)" (translation).
Projects in Brazil include: i) Platform and mobile app 'Missions' has been developed by IBM in their São Paulo research lab with Brazil's Ministry for Environment and Innovation (BMEI). Sergio Borger, an IBM team lead in São Paulo, devised the crowdsourced approach when BMEI approached the company in 2010. They were looking for a way to create a central repository for the rainforest data. Users can upload photos of a plant species and its components, enter its characteristics (such as color and size), compare it against a catalog photo and classify it. The classification results are juried by crowdsourced ratings. ii) Exoss Citizen Science is a member of Astronomers Without Borders and seeks to explore the southern sky for new meteors and radiants. Users can report meteor fireballs through uploading pictures on to a webpage or by linking to YouTube. iii) The Information System on Brazilian Biodiversity (SiBBr) was launched in 2014 "aiming to encourage and facilitate the publication, integration, access and use of information about the biodiversity of the country." Their initial goal "was to gather 2.5 million occurrence records of species from biological collections in Brazil and abroad up to the end of 2016. It is now expected that SiBBr will reach nine million records in 2016." Andrea Portela said: "In 2016, we will begin with the citizen science. They are tools that enable anyone, without any technical knowledge, to participate. With this we will achieve greater engagement with society. People will be able to have more interaction with the platform, contribute and comment on what Brazil has." iv) The Brazilian Marine Megafauna Project (Iniciativa Pro Mar) is working with the European CSA towards its main goal, which is the "sensibilization of society for marine life issues" and concerns about pollution and the over-exploitation of natural resources. Having started as a project monitoring manta ray, it now extends to whale shark and educating schools and divers within the Santos area. Its social media activities include a live streaming of a citizen science course to help divers identify marine megafauna. v) A smartphone app called Plantix has been developed by the Leibniz Centre for Agricultural Landscape Research (ZALF) which helps Brazilian farmers discover crop diseases quicker and helps fight them more efficiently. Brazil is a very large agricultural exporter, but between 10 and 30% of crops fail because of disease. "The database currently includes 175 frequently occurring crop diseases and pests as well as 40,000 photos. The identification algorithm of the app improves with every image which records a success rate of over 90 per cent as of approximately 500 photos per crop disease." vi) In an Atlantic Ocean forest region in Brazil, an effort to map the genetic riches of soil is under way. The Drugs From Dirt initiative, based at the Rockefeller University, seeks to turn up bacteria that yield new types of antibiotics – the Brazilian region being particularly rich in potentially useful bacterial genes. Approximately a quarter of the 185 soil samples have been taken by Citizen Scientists without which the project could not run.
In Chile citizen science projects include (some websites in Spanish): i) Testing new cancer therapies with scientists from the Science Foundation for Life. ii) Monitoring the population of the Chilean bumblebee. iii) Monitoring the invasive ladybird Chinita arlequín. iv) Collecting rain water data. v) Monitoring various pollinating fly populations. vi) Providing information and field data on the abundance and distribution of various species of rockfish. vii) Investigating the environmental pollution by plastic litter.
Projects in Colombia include (some websites in Spanish): i) The Communications Project of the Humboldt Institute along with the Organization for Education and Environmental Protection initiated projects in the Bogotá wetlands of Cordoba and El Burro, which have a lot of biodiversity. ii) In the Model Forest of Risaralda, the Colombia 'proyecto de Ciencia Abierta y Colaborativa' promotes citizen participation in research related to how the local environment is adapting to climate change. The first meeting took place in the Flora and Fauna Sanctuary Otún Quimbaya. iii) The Citizen Network Environmental Monitoring (CLUSTER), based in the city of Bucaramanga, seeks to engage younger students in data science, who are trained in building weather stations with open repositories based on free software and open hardware data. iv) The Symposium on Biodiversity has adapted the CS tool iNaturalist for use in Colombia. v) The Sinchi Amazonic Institute of Scientific Research seeks to encourage the development and diffusion of knowledge, values and technologies on the management of natural resources for ethnic groups in the Amazon. This research should further the use of participatory action research schemes and promoting participation communities.
Since 2010, the Pacific Biodiversity Institute (PBI) seeks "volunteers to help identify, describe and protect wildland complexes and roadless areas in South America". The PBI "are engaged in an ambitious project with our Latin American conservation partners to map all the wildlands in South America, to evaluate their contribution to global biodiversity and to share and disseminate this information."
In Mexico, a citizen science project has monitored rainfall data that is linked to a hydrologic payment for ecosystem services project.
== Conferences ==
The first Conference on Public Participation in Scientific Research was held in Portland, Oregon, in August 2012. Citizen science is now often a theme at large conferences, such as the annual meeting of the American Geophysical Union.
In 2010, 2012 and 2014 there were three Citizen Cyberscience summits, organised by the Citizen Cyberscience Centre in Geneva and University College London. The 2014 summit was hosted in London and attracted over 300 participants.
In November 2015, the ETH Zürich and University of Zürich hosted an international meeting on the "Challenges and Opportunities in Citizen Science".
The first citizen science conference hosted by the Citizen Science Association was in San Jose, California, in February 2015 in partnership with the AAAS conference. The Citizen Science Association conference, CitSci 2017, was held in Saint Paul, Minnesota, United States, between 17 and 20 May 2017. The conference had more than 600 attendees. The next CitSci was in March 2019 in Raleigh, North Carolina.
The platform "Österreich forscht" hosts the annual Austrian citizen science conference since 2015.
== In popular culture ==
Barbara Kingsolver’s 2012 novel Flight Behaviour looks at the effects of citizen science on a housewife in Appalachia, when her interest in butterflies brings her into contact with scientists and academics.
== See also ==
== References ==
== Further reading ==
Web, Cameron; Williams, Craig; Sousa, Larissa Braz; Doherty, Seamus; Fricker, Stephen Robert (11 December 2019). "As heat strikes, here's one way to help fight disease-carrying and nuisance mosquitoes". The Conversation. "The Mozzie Monitors program marks the first time formal mosquito trapping has been combined with citizen science." (Australian project)
Franzoni, Chiara; Sauermann, Henry (February 2014). "Crowd science: The organization of scientific research in open collaborative projects". Research Policy. 43 (1): 1–20. doi:10.1016/j.respol.2013.07.005. hdl:11311/754644. SSRN 2167538.
Dick Kasperowsik (interviewed by Ulrich Herb): Citizen Science as democratization of science? In: telepolis, 2016, 27 August
Ridley, Matt. (8 February 2012) "Following the Crowd to Citizen Science". The Wall Street Journal
Young, Jeffrey R. (28 May 2010). "Crowd Science Reaches New Heights", The Chronicle of Higher Education
Sauermann, Henry; Franzoni, Chiara (20 January 2015). "Crowd science user contribution patterns and their implications". Proceedings of the National Academy of Sciences. 112 (3): 679–684. Bibcode:2015PNAS..112..679S. doi:10.1073/pnas.1408907112. PMC 4311847. PMID 25561529. SSRN 2545945.
Bourjon, Philippe; Ducarme, Frédéric; Quod, Jean-Pascal; Sweet, Michael (2018). "Involving recreational snorkelers in inventory improvement or creation: a case study in the Indian Ocean". Cahiers de Biologie Marine. 59: 451–460. doi:10.21411/CBM.A.B05FC714.
Albagli, Sarita; Iwama, Allan Yu (2022). "Citizen science and the right to research: building local knowledge of climate change impacts". Humanities and Social Sciences Communications. 9 (1): 1–13. doi:10.1057/s41599-022-01040-8.
Fritz, Steffen; See, Linda; Carlson, Tyler; Haklay, Mordechai (Muki); Oliver, Jessie L.; Fraisl, Dilek; Mondardini, Rosy; Brocklehurst, Martin; Shanley, Lea A.; Schade, Sven; Wehn, Uta; Abrate, Tommaso; Anstee, Janet; Arnold, Stephan; Billot, Matthew; Campbell, Jillian; Espey, Jessica; Gold, Margaret; Hager, Gerid; He, Shan; Hepburn, Libby; Hsu, Angel; Long, Deborah; Masó, Joan; McCallum, Ian; Muniafu, Maina; Moorthy, Inian; Obersteiner, Michael; Parker, Alison J.; Weisspflug, Maike; West, Sarah (2019). "Citizen science and the United Nations Sustainable Development Goals". Nature Sustainability. 2 (10): 922–930. Bibcode:2019NatSu...2..922F. doi:10.1038/s41893-019-0390-3.
== External links ==
Media related to Citizen science at Wikimedia Commons
"Controversy over the term 'citizen science'". CBC News. 13 August 2021. Retrieved 15 April 2023. | Wikipedia/Citizen_Science |
Algorithmic transparency is the principle that the factors that influence the decisions made by algorithms should be visible, or transparent, to the people who use, regulate, and are affected by systems that employ those algorithms. Although the phrase was coined in 2016 by Nicholas Diakopoulos and Michael Koliska about the role of algorithms in deciding the content of digital journalism services, the underlying principle dates back to the 1970s and the rise of automated systems for scoring consumer credit.
The phrases "algorithmic transparency" and "algorithmic accountability" are sometimes used interchangeably – especially since they were coined by the same people – but they have subtly different meanings. Specifically, "algorithmic transparency" states that the inputs to the algorithm and the algorithm's use itself must be known, but they need not be fair. "Algorithmic accountability" implies that the organizations that use algorithms must be accountable for the decisions made by those algorithms, even though the decisions are being made by a machine, and not by a human being.
Current research around algorithmic transparency interested in both societal effects of accessing remote services running algorithms., as well as mathematical and computer science approaches that can be used to achieve algorithmic transparency In the United States, the Federal Trade Commission's Bureau of Consumer Protection studies how algorithms are used by consumers by conducting its own research on algorithmic transparency and by funding external research. In the European Union, the data protection laws that came into effect in May 2018 include a "right to explanation" of decisions made by algorithms, though it is unclear what this means. Furthermore, the European Union founded The European Center for Algorithmic Transparency (ECAT).
== See also ==
Black box
Explainable AI
Regulation of algorithms
Reverse engineering
Right to explanation
Algorithmic accountability
== References == | Wikipedia/Algorithmic_transparency |
IBM SPSS Modeler is a data mining and text analytics software application from IBM. It is used to build predictive models and conduct other analytic tasks. It has a visual interface which allows users to leverage statistical and data mining algorithms without programming.
One of its main aims from the outset was to eliminate needless complexity in data transformations, and make complex predictive models very easy to use.
The first version incorporated decision trees (ID3), and neural networks (backprop), which could both be trained without underlying knowledge of how those techniques worked.
IBM SPSS Modeler was originally named Clementine by its creators, Integral Solutions Limited. This name continued for a while after SPSS's acquisition of the product. SPSS later changed the name to SPSS Clementine, and then later to PASW Modeler. Following IBM's 2009 acquisition of SPSS, the product was renamed IBM SPSS Modeler, its current name.
== Applications ==
SPSS Modeler has been used in these and other industries:
Customer analytics and Customer relationship management (CRM)
Fraud detection and prevention
Optimizing insurance claims
Risk management
Manufacturing quality improvement
Healthcare quality improvement
Forecasting demand or sales
Law enforcement and border security
Education
Telecommunications
Entertainment: e.g., predicting movie box office receipts
== Editions ==
IBM sells the version of SPSS Modeler 18.2.1 in two separate bundles of features. These two bundles are called "editions" by IBM:
SPSS Modeler Professional: used for structured data, such as databases, mainframe data systems, flat files or BI systems
SPSS Modeler Premium: Includes all the features of Modeler Professional, with the addition of:
– Text analytics
Both editions are available in desktop and server configurations.
In addition to the traditional IBM SPSS Modeler desktop installations, IBM now offers the SPSS Modeler interface as an option in the Watson Studio product line which includes Watson Studio (cloud), Watson Studio Local, and Watson Studio Desktop.
Watson Studio Desktop documentation: https://www.ibm.com/support/knowledgecenter/SSBFT6_1.1.0/mstmap/kc_welcome.html
== Product history ==
Early versions of the software were called Clementine and were Unix-based. The first version was released on Jun 9th 1994, after Beta testing at 6 customer sites. Clementine was originally developed by a UK company named Integral Solutions Limited (ISL), in Collaboration with artificial intelligence researchers at the University of Sussex. The original Clementine was implemented in Poplog, which ISL marketed for that University.
Clementine mainly used the Poplog languages, Pop-11, with some parts written in C for speed (such as the neural network engine), along with additional tools provided as part of Solaris, VMS and various versions of Unix. The tool quickly garnered the attention of the data mining community (at that time in its infancy).
In order to reach a larger market, ISL then Ported Poplog to Microsoft Windows using the NutCracker package, later named MKS Toolkit to provide the Unix graphical facilities. Original in many respects, Clementine was the first data mining tool to use an icon based graphical user interface rather than requiring users to write in a programming language, though that option remained available for expert users.
In 1998 ISL was acquired by SPSS Inc., who saw the potential for extended development as a commercial data mining tool. In early 2000, the software was developed into a client–server model architecture, and shortly afterward, the client front-end interface component was rewritten fully and replaced with a new Java front-end, which allowed deeper integration with the other tools provided by SPSS.
SPSS Clementine version 7.0: The client front-end runs under Windows. The server back-end Unix variants (SunOS, HP-UX, AIX), Linux, and Windows. The graphical user interface is written in Java.
IBM SPSS Modeler 14.0 was the first release of Modeler by IBM.
IBM SPSS Modeler 15, released in June 2012, introduced significant new functions for social network analysis and entity analytics.
== See also ==
IBM SPSS Statistics
List of statistical packages
Cross Industry Standard Process for Data Mining
== References ==
== Further reading ==
Chapman, P.; Clinton, J.; Kerber, R.; Khabaza, T.; Reinartz, T.; Shearer, C.; Wirth, R. (2000). "CRISP-DM 1.0" (PDF). Chicago, IL: SPSS. {{cite journal}}: Cite journal requires |journal= (help)
Nisbet, R.; Elder, J.; Miner, G. (2009). "Handbook of Statistical Analysis and Data Mining Applications". Burlington, MA: Academic Press (Elsevier). {{cite journal}}: Cite journal requires |journal= (help)
Khabaza, Tom (1999). "The Story of Clementine" (PDF). {{cite journal}}: Cite journal requires |journal= (help)
== External links ==
[1] SPSS Modeler 18.2.1 Documentation
Users Guide – SPSS Modeler 18.2.1
IBM SPSS Modeler website | Wikipedia/SPSS_Modeler |
Machine learning control (MLC) is a subfield of machine learning, intelligent control, and control theory which aims to solve optimal control problems with machine learning methods. Key applications are complex nonlinear systems for which linear control theory methods are not applicable.
== Types of problems and tasks ==
Four types of problems are commonly encountered:
Control parameter identification: MLC translates to a parameter identification if the structure of the control law is given but the parameters are unknown. One example is the genetic algorithm for optimizing coefficients of a PID controller or discrete-time optimal control.
Control design as regression problem of the first kind: MLC approximates a general nonlinear mapping from sensor signals to actuation commands, if the sensor signals and the optimal actuation command are known for every state. One example is the computation of sensor feedback from a known full state feedback. Neural networks are commonly used for such tasks.
Control design as regression problem of the second kind: MLC may also identify arbitrary nonlinear control laws which minimize the cost function of the plant. In this case, neither a model, the control law structure, nor the optimizing actuation command needs to be known. The optimization is only based on the control performance (cost function) as measured in the plant. Genetic programming is a powerful regression technique for this purpose.
Reinforcement learning control: The control law may be continually updated over measured performance changes (rewards) using reinforcement learning.
== Adaptive Dynamic Programming ==
Adaptive Dynamic Programming (ADP), also known as approximate dynamic programming or neuro-dynamic programming, is a machine learning control method that combines reinforcement learning with dynamic programming to solve optimal control problems for complex systems. ADP addresses the "curse of dimensionality" in traditional dynamic programming by approximating value functions or control policies using parametric structures such as neural networks. The core idea revolves around learning a control policy that minimizes a long-term cost function
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ADP has been applied to robotics, power systems, and autonomous vehicles, offering a data-driven framework for near-optimal control without requiring full system models. Challenges remain in ensuring stability guarantees and convergence for general nonlinear systems.
== Applications ==
MLC has been successfully applied
to many nonlinear control problems,
exploring unknown and often unexpected actuation mechanisms. Example applications include:
spacecraft attitude control,
thermal control of buildings,
feedback control of turbulence,
and remotely operated underwater vehicles.
Many more engineering MLC application are summarized in the review article of PJ Fleming & RC Purshouse (2002).
As is the case for all general nonlinear methods,
MLC does not guarantee convergence,
optimality, or robustness for a range of operating conditions.
== See also ==
Reinforcement learning
== References ==
== Further reading == | Wikipedia/Machine_learning_control |
In deep learning, pruning is the practice of removing parameters from an existing artificial neural network. The goal of this process is to reduce the size (parameter count) of the neural network (and therefore the computational resources required to run it) whilst maintaining accuracy. This can be compared to the biological process of synaptic pruning which takes place in mammalian brains during development.
== Node (neuron) pruning ==
A basic algorithm for pruning is as follows:
Evaluate the importance of each neuron.
Rank the neurons according to their importance (assuming there is a clearly defined measure for "importance").
Remove the least important neuron.
Check a termination condition (to be determined by the user) to see whether to continue pruning.
== Edge (weight) pruning ==
Most work on neural network pruning focuses on removing weights, namely, setting their values to zero. Early work suggested to also change the values of non-pruned weights.
== See also ==
Knowledge distillation
Neural Darwinism
== References == | Wikipedia/Pruning_(artificial_neural_network) |
Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place.
In many cases, the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.
Models can use one or more classifiers in trying to determine the probability of a set of data belonging to another set. For example, a model might be used to determine whether an email is spam or "ham" (non-spam).
Depending on definitional boundaries, predictive modelling is synonymous with, or largely overlapping with, the field of machine learning, as it is more commonly referred to in academic or research and development contexts. When deployed commercially, predictive modelling is often referred to as predictive analytics.
Predictive modelling is often contrasted with causal modelling/analysis. In the former, one may be entirely satisfied to make use of indicators of, or proxies for, the outcome of interest. In the latter, one seeks to determine true cause-and-effect relationships. This distinction has given rise to a burgeoning literature in the fields of research methods and statistics and to the common statement that "correlation does not imply causation".
== Models ==
Nearly any statistical model can be used for prediction purposes. Broadly speaking, there are two classes of predictive models: parametric and non-parametric. A third class, semi-parametric models, includes features of both. Parametric models make "specific assumptions with regard to one or more of the population parameters that characterize the underlying distribution(s)". Non-parametric models "typically involve fewer assumptions of structure and distributional form [than parametric models] but usually contain strong assumptions about independencies".
== Applications ==
=== Uplift modelling ===
Uplift modelling is a technique for modelling the change in probability caused by an action. Typically this is a marketing action such as an offer to buy a product, to use a product more or to re-sign a contract. For example, in a
retention campaign you wish to predict the change in probability that a customer will remain a customer if they are contacted. A model of the change in probability allows the retention campaign to be targeted at those customers on whom the change in probability will be beneficial. This allows the retention programme to avoid triggering unnecessary churn or customer attrition without wasting money contacting people who would act anyway.
=== Archaeology ===
Predictive modelling in archaeology gets its foundations from Gordon Willey's mid-fifties work in the Virú Valley of Peru. Complete, intensive surveys were performed then covariability between cultural remains and natural features such as slope and vegetation were determined. Development of quantitative methods and a greater availability of applicable data led to growth of the discipline in the 1960s and by the late 1980s, substantial progress had been made by major land managers worldwide.
Generally, predictive modelling in archaeology is establishing statistically valid causal or covariable relationships between natural proxies such as soil types, elevation, slope, vegetation, proximity to water, geology, geomorphology, etc., and the presence of archaeological features. Through analysis of these quantifiable attributes from land that has undergone archaeological survey, sometimes the "archaeological sensitivity" of unsurveyed areas can be anticipated based on the natural proxies in those areas. Large land managers in the United States, such as the Bureau of Land Management (BLM), the Department of Defense (DOD), and numerous highway and parks agencies, have successfully employed this strategy. By using predictive modelling in their cultural resource management plans, they are capable of making more informed decisions when planning for activities that have the potential to require ground disturbance and subsequently affect archaeological sites.
=== Customer relationship management ===
Predictive modelling is used extensively in analytical customer relationship management and data mining to produce customer-level models that describe the likelihood that a customer will take a particular action. The actions are usually sales, marketing and customer retention related.
For example, a large consumer organization such as a mobile telecommunications operator will have a set of predictive models for product cross-sell, product deep-sell (or upselling) and churn. It is also now more common for such an organization to have a model of savability using an uplift model. This predicts the likelihood that a customer can be saved at the end of a contract period (the change in churn probability) as opposed to the standard churn prediction model.
=== Auto insurance ===
Predictive modelling is utilised in vehicle insurance to assign risk of incidents to policy holders from information obtained from policy holders. This is extensively employed in usage-based insurance solutions where predictive models utilise telemetry-based data to build a model of predictive risk for claim likelihood. Black-box auto insurance predictive models utilise GPS or accelerometer sensor input only. Some models include a wide range of predictive input beyond basic telemetry including advanced driving behaviour, independent crash records, road history, and user profiles to provide improved risk models.
=== Health care ===
In 2009 Parkland Health & Hospital System began analyzing electronic medical records in order to use predictive modeling to help identify patients at high risk of readmission. Initially, the hospital focused on patients with congestive heart failure, but the program has expanded to include patients with diabetes, acute myocardial infarction, and pneumonia.
In 2018, Banerjee et al. proposed a deep learning model for estimating short-term life expectancy (>3 months) of the patients by analyzing free-text clinical notes in the electronic medical record, while maintaining the temporal visit sequence. The model was trained on a large dataset (10,293 patients) and validated on a separated dataset (1818 patients). It achieved an area under the ROC (Receiver Operating Characteristic) curve of 0.89. To provide explain-ability, they developed an interactive graphical tool that may improve physician understanding of the basis for the model's predictions. The high accuracy and explain-ability of the PPES-Met model may enable the model to be used as a decision support tool to personalize metastatic cancer treatment and provide valuable assistance to physicians.
The first clinical prediction model reporting guidelines were published in 2015 (Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD)), and have since been updated.
Predictive modelling has been used to estimate surgery duration.
=== Algorithmic trading ===
Predictive modeling in trading is a modeling process wherein the probability of an outcome is predicted using a set of predictor variables. Predictive models can be built for different assets like stocks, futures, currencies, commodities etc. Predictive modeling is still extensively used by trading firms to devise strategies and trade. It utilizes mathematically advanced software to evaluate indicators on price, volume, open interest and other historical data, to discover repeatable patterns.
=== Lead tracking systems ===
Predictive modelling gives lead generators a head start by forecasting data-driven outcomes for each potential campaign. This method saves time and exposes potential blind spots to help client make smarter decisions.
=== Notable failures of predictive modeling ===
Although not widely discussed by the mainstream predictive modeling community, predictive modeling is a methodology that has been widely used in the financial industry in the past and some of the major failures contributed to the 2008 financial crisis. These failures exemplify the danger of relying exclusively on models that are essentially backward looking in nature. The following examples are by no mean a complete list:
Bond rating. S&P, Moody's and Fitch quantify the probability of default of bonds with discrete variables called rating. The rating can take on discrete values from AAA down to D. The rating is a predictor of the risk of default based on a variety of variables associated with the borrower and historical macroeconomic data. The rating agencies failed with their ratings on the US$600 billion mortgage backed Collateralized Debt Obligation (CDO) market. Almost the entire AAA sector (and the super-AAA sector, a new rating the rating agencies provided to represent super safe investment) of the CDO market defaulted or severely downgraded during 2008, many of which obtained their ratings less than just a year previously.
So far, no statistical models that attempt to predict equity market prices based on historical data are considered to consistently make correct predictions over the long term. One particularly memorable failure is that of Long Term Capital Management, a fund that hired highly qualified analysts, including a Nobel Memorial Prize in Economic Sciences winner, to develop a sophisticated statistical model that predicted the price spreads between different securities. The models produced impressive profits until a major debacle that caused the then Federal Reserve chairman Alan Greenspan to step in to broker a rescue plan by the Wall Street broker dealers in order to prevent a meltdown of the bond market.
== Possible fundamental limitations of predictive models based on data fitting ==
History cannot always accurately predict the future. Using relations derived from historical data to predict the future implicitly assumes there are certain lasting conditions or constants in a complex system. This almost always leads to some imprecision when the system involves people.
Unknown unknowns are an issue. In all data collection, the collector first defines the set of variables for which data is collected. However, no matter how extensive the collector considers his/her selection of the variables, there is always the possibility of new variables that have not been considered or even defined, yet are critical to the outcome.
Algorithms can be defeated adversarially. After an algorithm becomes an accepted standard of measurement, it can be taken advantage of by people who understand the algorithm and have the incentive to fool or manipulate the outcome. This is what happened to the CDO rating described above. The CDO dealers actively fulfilled the rating agencies' input to reach an AAA or super-AAA on the CDO they were issuing, by cleverly manipulating variables that were "unknown" to the rating agencies' "sophisticated" models.
== See also ==
Calibration (statistics)
Prediction interval
Predictive analytics
Predictive inference
Statistical learning theory
Statistical model
== References ==
== Further reading ==
Clarke, Bertrand S.; Clarke, Jennifer L. (2018), Predictive Statistics, Cambridge University Press
Iglesias, Pilar; Sandoval, Mônica C.; Pereira, Carlos Alberto de Bragança (1993), "Predictive likelihood in finite populations", Brazilian Journal of Probability and Statistics, 7 (1): 65–82, JSTOR 43600831
Kelleher, John D.; Mac Namee, Brian; D'Arcy, Aoife (2015), Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked Examples and Case Studies, MIT Press
Kuhn, Max; Johnson, Kjell (2013), Applied Predictive Modeling, Springer
Shmueli, G. (2010), "To explain or to predict?", Statistical Science, 25 (3): 289–310, arXiv:1101.0891, doi:10.1214/10-STS330, S2CID 15900983 | Wikipedia/Predictive_modeling |
The core idea of artificial intelligence systems integration is making individual software components, such as speech synthesizers, interoperable with other components, such as common sense knowledgebases, in order to create larger, broader and more capable A.I. systems. The main methods that have been proposed for integration are message routing, or communication protocols that the software components use to communicate with each other, often through a middleware blackboard system.
Most artificial intelligence systems involve some sort of integrated technologies, for example, the integration of speech synthesis technologies with that of speech recognition. However, in recent years, there has been an increasing discussion on the importance of systems integration as a field in its own right. Proponents of this approach are researchers such as Marvin Minsky, Aaron Sloman, Deb Roy, Kristinn R. Thórisson and Michael A. Arbib. A reason for the recent attention A.I. integration is attracting is that there have already been created a number of (relatively) simple A.I. systems for specific problem domains (such as computer vision, speech synthesis, etc.), and that integrating what's already available is a more logical approach to broader A.I. than building monolithic systems from scratch.
== Integration focus ==
The focus on systems' integration, especially with regard to modular approaches, derive from the fact that most intelligences of significant scales are composed of a multitude of processes and/or utilize multi-modal input and output. For example, a humanoid-type of intelligence would preferably have to be able to talk using speech synthesis, hear using speech recognition, understand using a logical (or some other undefined) mechanism, and so forth. In order to produce artificially intelligent software of broader intelligence, integration of these modalities is necessary.
== Challenges and solutions ==
Collaboration is an integral part of software development as evidenced by the size of software companies and the size of their software departments. Among the tools to ease software collaboration are various procedures and standards that developers can follow to ensure quality, reliability and that their software is compatible with software created by others (such as W3C standards for webpage development). However, collaboration in fields of A.I. has been lacking, for the most part not seen outside the respected schools, departments or research institutes (and sometimes not within them either). This presents practitioners of A.I. systems integration with a substantial problem and often causes A.I. researchers to have to 're-invent the wheel' each time they want a specific functionality to work with their software. Even more damaging is the "not invented here" syndrome, which manifests itself in a strong reluctance of A.I. researchers to build on the work of others.
The outcome of this in A.I. is a large set of "solution islands": A.I. research has produced numerous isolated software components and mechanisms that deal with various parts of intelligence separately. To take some examples:
Speech synthesis
FreeTTS from CMU
Speech recognition
Sphinx from CMU
Logical reasoning
OpenCyc from Cycorp
Open Mind Common Sense Net from MIT
With the increased popularity of the free software movement, a lot of the software being created, including A.I. systems, is available for public exploit. The next natural step is to merge these individual software components into coherent, intelligent systems of a broader nature. As a multitude of components (that often serve the same purpose) have already been created by the community, the most accessible way of integration is giving each of these components an easy way to communicate with each other. By doing so, each component by itself becomes a module, which can then be tried in various settings and configurations of larger architectures. Some challenging and limitations of using A.I. software is the uncontrolled fatal errors. For example, serious and fatal errors have been discovered in very precise fields such as human oncology, as in an article published in the journal Oral Oncology Reports entitled “When AI goes wrong: Fatal errors in oncological research reviewing assistance". The article pointed out a grave error in artificial intelligence based on GBT in the field of biophysics.
Many online communities for A.I. developers exist where tutorials, examples, and forums aim at helping both beginners and experts build intelligent systems. However, few communities have succeeded in making a certain standard, or a code of conduct popular to allow the large collection of miscellaneous systems to be integrated with ease.
== Methodologies ==
=== Constructionist design methodology ===
The constructionist design methodology (CDM, or 'Constructionist A.I.') is a formal methodology proposed in 2004, for use in the development of cognitive robotics, communicative humanoids and broad AI systems. The creation of such systems requires the integration of a large number of functionalities that must be carefully coordinated to achieve coherent system behavior. CDM is based on iterative design steps that lead to the creation of a network of named interacting modules, communicating via explicitly typed streams and discrete messages. The OpenAIR message protocol (see below) was inspired by the CDM and has frequently been used to aid in the development of intelligent systems using CDM.
== Examples ==
ASIMO, Honda's humanoid robot, and QRIO, Sony's version of a humanoid robot.
Cog, M.I.T. humanoid robot project under the direction of Rodney Brooks.
AIBO, Sony's robot dog, integrates vision, hearing and motorskills.
TOPIO, TOSY's humanoid robot can play ping-pong with human
== See also ==
Hybrid intelligent system, systems that combine the methods of traditional symbolic AI & that of Computational intelligence.
Neurosymbolic AI
Humanoid robots utilize systems integration intensely.
Constructionist design methodology
Cognitive architectures
== References ==
== Notes ==
Constructionist Design Methodology, published in A.I. magazine
MissionEngine: Multi-system integration using Python in the Tactical Language Project
== External links ==
COG, a humanoid robot at M.I.T.
The Open Knowledge Initiative Library | Wikipedia/Artificial_intelligence_systems_integration |
Applications of machine learning (ML) in earth sciences include geological mapping, gas leakage detection and geological feature identification. Machine learning is a subdiscipline of artificial intelligence aimed at developing programs that are able to classify, cluster, identify, and analyze vast and complex data sets without the need for explicit programming to do so. Earth science is the study of the origin, evolution, and future of the Earth. The earth's system can be subdivided into four major components including the solid earth, atmosphere, hydrosphere, and biosphere.
A variety of algorithms may be applied depending on the nature of the task. Some algorithms may perform significantly better than others for particular objectives. For example, convolutional neural networks (CNNs) are good at interpreting images, whilst more general neural networks may be used for soil classification, but can be more computationally expensive to train than alternatives such as support vector machines. The range of tasks to which ML (including deep learning) is applied has been ever-growing in recent decades, as has the development of other technologies such as unmanned aerial vehicles (UAVs), ultra-high resolution remote sensing technology, and high-performance computing. This has led to the availability of large high-quality datasets and more advanced algorithms.
== Significance ==
=== Complexity of earth science ===
Problems in earth science are often complex. It is difficult to apply well-known and described mathematical models to the natural environment, therefore machine learning is commonly a better alternative for such non-linear problems. Ecological data are commonly non-linear and consist of higher-order interactions, and together with missing data, traditional statistics may underperform as unrealistic assumptions such as linearity are applied to the model. A number of researchers found that machine learning outperforms traditional statistical models in earth science, such as in characterizing forest canopy structure, predicting climate-induced range shifts, and delineating geologic facies. Characterizing forest canopy structure enables scientists to study vegetation response to climate change. Predicting climate-induced range shifts enable policy makers to adopt suitable conversation method to overcome the consequences of climate change. Delineating geologic facies helps geologists to understand the geology of an area, which is essential for the development and management of an area.
=== Inaccessible data ===
In Earth Sciences, some data are often difficult to access or collect, therefore inferring data from data that are easily available by machine learning method is desirable. For example, geological mapping in tropical rainforests is challenging because the thick vegetation cover and rock outcrops are poorly exposed. Applying remote sensing with machine learning approaches provides an alternative way for rapid mapping without the need of manually mapping in the unreachable areas.
=== Reduce time costs ===
Machine learning can also reduce the efforts done by experts, as manual tasks of classification and annotation etc. are the bottlenecks in the workflow of the research of earth science. Geological mapping, especially in a vast, remote area is labour, cost and time-intensive with traditional methods. Incorporation of remote sensing and machine learning approaches can provide an alternative solution to eliminate some field mapping needs.
=== Consistent and bias-free ===
Consistency and bias-free is also an advantage of machine learning compared to manual works by humans. In research comparing the performance of human and machine learning in the identification of dinoflagellates, machine learning is found to be not as prone to systematic bias as humans. A recency effect that is present in humans is that the classification often biases towards the most recently recalled classes. In a labelling task of the research, if one kind of dinoflagellates occurs rarely in the samples, then expert ecologists commonly will not classify it correctly. The systematic bias strongly deteriorate the classification accuracies of humans.
== Optimal machine learning algorithm ==
The extensive usage of machine learning in various fields has led to a wide range of algorithms of learning methods being applied. Choosing the optimal algorithm for a specific purpose can lead to a significant boost in accuracy: for example, the lithological mapping of gold-bearing granite-greenstone rocks in Hutti, India with AVIRIS-NG hyperspectral data, shows more than 10% difference in overall accuracy between using support vector machines (SVMs) and random forest.
Some algorithms can also reveal hidden important information: white box models are transparent models, the outputs of which can be easily explained, while black box models are the opposite. For example, although an SVM yielded the best result in landslide susceptibility assessment accuracy, the result cannot be rewritten in the form of expert rules that explain how and why an area was classified as that specific class. In contrast, decision trees are transparent and easily understood, and the user can observe and fix the bias if any is present in such models.
If computational resource is a concern, more computationally demanding learning methods such as deep neural networks are less preferred, despite the fact that they may outperform other algorithms, such as in soil classification.
== Usage ==
=== Mapping ===
==== Geological or lithological mapping and mineral prospectivity mapping ====
Geological or lithological mapping produces maps showing geological features and geological units. Mineral prospectivity mapping utilizes a variety of datasets such as geological maps and aeromagnetic imagery to produce maps that are specialized for mineral exploration. Geological, lithological, and mineral prospectivity mapping can be carried out by processing data with ML techniques, with the input of spectral imagery obtained from remote sensing and geophysical data. Spectral imaging is also used – the imaging of wavelength bands in the electromagnetic spectrum, while conventional imaging captures three wavelength bands (red, green, blue) in the electromagnetic spectrum.
Random forests and SVMs are some algorithms commonly used with remotely-sensed geophysical data, while Simple Linear Iterative Clustering-Convolutional Neural Network (SLIC-CNN) and Convolutional Neural Networks (CNNs) are commonly applied to aerial imagery. Large scale mapping can be carried out with geophysical data from airborne and satellite remote sensing geophysical data, and smaller-scale mapping can be carried out with images from Unmanned Aerial Vehicles (UAVs) for higher resolution.
Vegetation cover is one of the major obstacles for geological mapping with remote sensing, as reported in various research, both in large-scale and small-scale mapping. Vegetation affects the quality of spectral images, or obscures the rock information in aerial images.
==== Landslide susceptibility and hazard mapping ====
Landslide susceptibility refers to the probability of landslide of a certain geographical location, which is dependent on local terrain conditions. Landslide susceptibility mapping can highlight areas prone to landslide risks, which is useful for urban planning and disaster management. Such datasets for ML algorithms usually include topographic information, lithological information, satellite images, etc., and some may include land use, land cover, drainage information, and vegetation cover according to the study requirements. As usual, for training an ML model for landslide susceptibility mapping, training and testing datasets are required. There are two methods of allocating datasets for training and testing: one is to randomly split the study area for the datasets; another is to split the whole study into two adjacent parts for the two datasets. To test classification models, the common practice is to split the study area randomly; however, it is more useful if the study area can be split into two adjacent parts so that an automation algorithm can carry out mapping of a new area with the input of expert-processed data of adjacent land.
=== Feature identification and detection ===
==== Discontinuity analyses ====
Discontinuities such as fault planes and bedding planes have important implications in civil engineering. Rock fractures can be recognized automatically by machine learning through photogrammetric analysis, even with the presence of interfering objects such as vegetation. In ML training for classifying images, data augmentation is a common practice to avoid overfitting and increase the training dataset size and variability. For example, in a study of rock fracture recognition, 68 images for training and 23 images for testing were prepared via random splitting. Data augmentation was performed, increasing the training dataset size to 8704 images by flipping and random cropping. The approach was able to recognize rock fractures accurately in most cases. Both the negative prediction value (NPV) and the specificity were over 0.99. This demonstrated the robustness of discontinuity analyses with machine learning.
==== Carbon dioxide leakage detection ====
Quantifying carbon dioxide leakage from a geological sequestration site has gained increased attention as the public is interested in whether carbon dioxide is stored underground safely and effectively. Carbon dioxide leakage from a geological sequestration site can be detected indirectly with the aid of remote sensing and an unsupervised clustering algorithm such as Iterative Self-Organizing Data Analysis Technique (ISODATA). The increase in soil CO2 concentration causes a stress response for plants by inhibiting plant respiration, as oxygen is displaced by carbon dioxide. The vegetation stress signal can be detected with the Normalized Difference Red Edge Index (NDRE). The hyperspectral images are processed by the unsupervised algorithm, clustering pixels with similar plant responses. The hyperspectral information in areas with known CO2 leakage is extracted so that areas with leakage can be matched with the clustered pixels with spectral anomalies. Although the approach can identify CO2 leakage efficiently, there are some limitations that require further study. The NDRE may not be accurate due to reasons like higher chlorophyll absorption, variation in vegetation, and shadowing effects; therefore, some stressed pixels can be incorrectly classed as healthy. Seasonality, groundwater table height may also affect the stress response to CO2 of the vegetation.
==== Quantification of water inflow ====
The rock mass rating (RMR) system is a widely adopted rock mass classification system by geomechanical means with the input of six parameters. The amount of water inflow is one of the inputs of the classification scheme, representing the groundwater condition. Quantification of the water inflow in the faces of a rock tunnel was traditionally carried out by visual observation in the field, which is labour and time-consuming, and fraught with safety concerns. Machine learning can determine water inflow by analyzing images taken on the construction site. The classification of the approach mostly follows the RMR system, but combining damp and wet states, as it is difficult to distinguish only by visual inspection. The images were classified into the non-damaged state, wet state, dripping state, flowing state, and gushing state. The accuracy of classifying the images was approximately 90%.
=== Classification ===
==== Soil classification ====
The most popular cost-effective method od soil investigation method is cone penetration testing (CPT). The test is carried out by pushing a metallic cone through the soil: the force required to push at a constant rate is recorded as a quasi-continuous log. Machine learning can classify soil with the input of CPT data. In an attempt to classify with ML, there are two tasks required to analyze the data, namely segmentation and classification. Segmentation can be carried out with the Constraint Clustering and Classification (CONCC) algorithm to split a single series data into segments. Classification can then be carried out by algorithms such as decision trees, SVMs, or neural networks.
==== Geological structure classification ====
Exposed geological structures such as anticlines, ripple marks, and xenoliths can be identified automatically with deep learning models. Research has demonstrated that three-layer CNNs and transfer learning have strong accuracy (about 80% and 90% respectively), while others like k-nearest neighbors (k-NN), regular neural nets, and extreme gradient boosting (XGBoost) have low accuracies (ranging from 10% - 30%). The grayscale images and colour images were both tested, with the accuracy difference being little, implying that colour is not very important in identifying geological structures.
=== Forecast and predictions ===
==== Earthquake early warning systems and forecasting ====
Earthquake warning systems are often vulnerable to local impulsive noise, therefore giving out false alerts. False alerts can be eliminated by discriminating the earthquake waveforms from noise signals with the aid of ML methods. The method consists of two parts, the first being unsupervised learning with a generative adversarial network (GAN) to learn and extract features of first-arrival P-waves, and the second being use of a random forest to discriminate P-waves. This approach achieved 99.2% in recognizing P-waves, and can avoid false triggers by noise signals with 98.4% accuracy.
Earthquakes can be produced in a laboratory settings to mimic real-world ones. With the help of machine learning, the patterns of acoustic signals as precursors for earthquakes can be identified. Predicting the time remaining before failure was demonstrated in a study with continuous acoustic time series data recorded from a fault. The algorithm applied was a random forest, trained with a set of slip events, performing strongly in predicting the time to failure. It identified acoustic signals to predict failures, with one of them being previously unidentified. Although this laboratory earthquake is not as complex as a natural one, progress was made that guides future earthquake prediction work.
==== Streamflow discharge prediction ====
Real-time streamflow data is integral for decision making (e.g., evacuations, or regulation of reservoir water levels during flooding). Streamflow data can be estimated by data provided by stream gauges, which measure the water level of a river. However, water and debris from flooding may damage stream gauges, resulting in lack of essential real-time data. The ability of machine learning to infer missing data enables it to predict streamflow with both historical stream gauge data and real-time data.
Streamflow Hydrology Estimate using Machine Learning (SHEM) is a model that can serve this purpose. To verify its accuracies, the prediction result was compared with the actual recorded data, and the accuracies were found to be between 0.78 and 0.99.
== Challenge ==
=== Inadequate training data ===
An adequate amount of training and validation data is required for machine learning. However, some very useful products like satellite remote sensing data only have decades of data since the 1970s. If one is interested in the yearly data, then only less than 50 samples are available. Such amount of data may not be adequate. In a study of automatic classification of geological structures, the weakness of the model is the small training dataset, even though with the help of data augmentation to increase the size of the dataset. Another study of predicting streamflow found that the accuracies depend on the availability of sufficient historical data, therefore sufficient training data determine the performance of machine learning. Inadequate training data may lead to a problem called overfitting. Overfitting causes inaccuracies in machine learning as the model learns about the noise and undesired details.
=== Limited by data input ===
Machine learning cannot carry out some of the tasks as a human does easily. For example, in the quantification of water inflow in rock tunnel faces by images for Rock Mass Rating system (RMR), the damp and the wet state was not classified by machine learning because discriminating the two only by visual inspection is not possible. In some tasks, machine learning may not able to fully substitute manual work by a human.
=== Black-box operation ===
In many machine learning algorithms, for example, Artificial Neural Network (ANN), it is considered as 'black box' approach as clear relationships and descriptions of how the results are generated in the hidden layers are unknown. 'White-box' approach such as decision tree can reveal the algorithm details to the users. If one wants to investigate the relationships, such 'black-box' approaches are not suitable. However, the performances of 'black-box' algorithms are usually better.
== References == | Wikipedia/Machine_learning_in_earth_sciences |
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction.
== Definition ==
A knowledge graph
G
=
{
E
,
R
,
F
}
{\displaystyle {\mathcal {G}}=\{E,R,F\}}
is a collection of entities
E
{\displaystyle E}
, relations
R
{\displaystyle R}
, and facts
F
{\displaystyle F}
. A fact is a triple
(
h
,
r
,
t
)
∈
F
{\displaystyle (h,r,t)\in F}
that denotes a link
r
∈
R
{\displaystyle r\in R}
between the head
h
∈
E
{\displaystyle h\in E}
and the tail
t
∈
E
{\displaystyle t\in E}
of the triple. Another notation that is often used in the literature to represent a triple (or fact) is
<
h
e
a
d
,
r
e
l
a
t
i
o
n
,
t
a
i
l
>
{\displaystyle <head,relation,tail>}
. This notation is called resource description framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application.
The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension
d
{\displaystyle d}
, called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks.
A knowledge graph embedding is characterized by four aspects:
Representation space: The low-dimensional space in which the entities and relations are represented.
Scoring function: A measure of the goodness of a triple embedded representation.
Encoding models: The modality in which the embedded representation of the entities and relations interact with each other.
Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional information.
== Embedding procedure ==
All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size
b
{\displaystyle b}
triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph.
=== Pseudocode ===
The following is the pseudocode for the general embedding procedure.
algorithm Compute entity and relation embeddings
input: The training set
S
=
{
(
h
,
r
,
t
)
}
{\displaystyle S=\{(h,r,t)\}}
,
entity set
E
{\displaystyle E}
,
relation set
R
{\displaystyle R}
,
embedding dimension
k
{\displaystyle k}
output: Entity and relation embeddings
initialization: the entities
e
{\displaystyle e}
and relations
r
{\displaystyle r}
embeddings (vectors) are randomly initialized
while stop condition do
S
b
a
t
c
h
←
s
a
m
p
l
e
(
S
,
b
)
{\displaystyle S_{batch}\leftarrow sample(S,b)}
// Sample a batch from the training set
for each
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
in
S
b
a
t
c
h
{\displaystyle S_{batch}}
do
(
h
′
,
r
,
t
′
)
←
s
a
m
p
l
e
(
S
′
)
{\displaystyle (h',r,t')\leftarrow sample(S')}
// Sample a corrupted fact
T
b
a
t
c
h
←
T
b
a
t
c
h
∪
{
(
(
h
,
r
,
t
)
,
(
h
′
,
r
,
t
′
)
)
}
{\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}}
end for
Update embeddings by minimizing the loss function
end while
== Performance indicators ==
These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given
Q
{\displaystyle {\ce {Q}}}
as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR.
=== Hits@K ===
Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used
k
=
10
{\displaystyle k=10}
. Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly.
Hits@K
=
|
{
q
∈
Q
:
q
<
k
}
|
|
Q
|
∈
[
0
,
1
]
{\displaystyle ={\frac {|\{q\in Q:q<k\}|}{|Q|}}\in [0,1]}
Larger values mean better predictive performances.
=== Mean rank (MR) ===
Mean rank is the average ranking position of the items predicted by the model among all the possible items.
M
R
=
1
|
Q
|
∑
q
∈
Q
q
{\displaystyle MR={\frac {1}{|Q|}}\sum _{q\in Q}{q}}
The smaller the value, the better the model.
=== Mean reciprocal rank (MRR) ===
Mean reciprocal rank measures the number of triples predicted correctly. If the first predicted triple is correct, then 1 is added, if the second is correct
1
2
{\displaystyle {\frac {1}{2}}}
is summed, and so on.
Mean reciprocal rank is generally used to quantify the effect of search algorithms.
M
R
R
=
1
|
Q
|
∑
q
∈
Q
1
q
∈
[
0
,
1
]
{\displaystyle MRR={\frac {1}{|Q|}}\sum _{q\in Q}{\frac {1}{q}}\in [0,1]}
The larger the index, the better the model.
== Applications ==
=== Machine learning tasks ===
Knowledge graph completion (KGC) is a collection of techniques to infer knowledge from an embedded knowledge graph representation. In particular, this technique completes a triple inferring the missing entity or relation. The corresponding sub-tasks are named link or entity prediction (i.e., guessing an entity from the embedding given the other entity of the triple and the relation), and relation prediction (i.e., forecasting the most plausible relation that connects two entities).
Triple Classification is a binary classification problem. Given a triple, the trained model evaluates the plausibility of the triple using the embedding to determine if a triple is true or false. The decision is made with the model score function and a given threshold. Clustering is another application that leverages the embedded representation of a sparse knowledge graph to condense the representation of similar semantic entities close in a 2D space.
=== Real world applications ===
The use of knowledge graph embedding is increasingly pervasive in many applications. In the case of recommender systems, the use of knowledge graph embedding can overcome the limitations of the usual reinforcement learning, as well as limitations of the conventional collaborative filtering method.
Training this kind of recommender system requires a huge amount of information from the users; however, knowledge graph techniques can address this issue by using a graph already constructed over a prior knowledge of the item correlation and using the embedding to infer from it the recommendation.
Drug repurposing is the use of an already approved drug, but for a therapeutic purpose different from the one for which it was initially designed. It is possible to use the task of link prediction to infer a new connection between an already existing drug and a disease by using a biomedical knowledge graph built leveraging the availability of massive literature and biomedical databases.
Knowledge graph embedding can also be used in the domain of social politics.
== Models ==
Given a collection of triples (or facts)
F
=
{
<
h
e
a
d
,
r
e
l
a
t
i
o
n
,
t
a
i
l
>
}
{\displaystyle {\mathcal {F}}=\{<head,relation,tail>\}}
, the knowledge graph embedding model produces, for each entity and relation present in the knowledge graph a continuous vector representation.
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
is the corresponding embedding of a triple with
h
,
t
∈
I
R
d
{\displaystyle h,t\in {\rm {I\!R}}^{d}}
and
r
∈
I
R
k
{\displaystyle r\in {\rm {I\!R}}^{k}}
, where
d
{\displaystyle d}
is the embedding dimension for the entities, and
k
{\displaystyle k}
for the relations. The score function of a given model is denoted by
f
r
(
h
,
t
)
{\displaystyle {\mathcal {f}}_{r}(h,t)}
and measures the distance of the embedding of the head from the embedding of tail given the embedding of the relation. In other words, it quantifies the plausibility of the embedded representation of a given fact.
Rossi et al. propose a taxonomy of the embedding models and identifies three main families of models: tensor decomposition models, geometric models, and deep learning models.
=== Tensor decomposition model ===
The tensor decomposition is a family of knowledge graph embedding models that use a multi-dimensional matrix to represent a knowledge graph, that is partially knowable due to gaps of the graph describing a particular domain thoroughly. In particular, these models use a third-order (3D) tensor, which is then factorized into low-dimensional vectors that are the embeddings. A third-order tensor is suitable for representing a knowledge graph because it records only the existence or absence of a relation between entities, and so is simple, and there is no need to know a priori the network structure, making this class of embedding models light, and easy to train even if they suffer from high-dimensionality and sparsity of data.
==== Bilinear models ====
This family of models uses a linear equation to embed the connection between the entities through a relation. In particular, the embedded representation of the relations is a bidimensional matrix. These models, during the embedding procedure, only use the single facts to compute the embedded representation and ignore the other associations to the same entity or relation.
DistMult: Since the embedding matrix of the relation is a diagonal matrix, the scoring function can not distinguish asymmetric facts.
ComplEx: As DistMult uses a diagonal matrix to represent the relations embedding but adds a representation in the complex vector space and the hermitian product, it can distinguish symmetric and asymmetric facts. This approach is scalable to a large knowledge graph in terms of time and space cost.
ANALOGY: This model encodes in the embedding the analogical structure of the knowledge graph to simulate inductive reasoning. Using a differentiable objective function, ANALOGY has good theoretical generality and computational scalability. It is proven that the embedding produced by ANALOGY fully recovers the embedding of DistMult, ComplEx, and HolE.
SimplE: This model is the improvement of canonical polyadic decomposition (CP), in which an embedding vector for the relation and two independent embedding vectors for each entity are learned, depending on whether it is a head or a tail in the knowledge graph fact. SimplE resolves the problem of independent learning of the two entity embeddings using an inverse relation and average the CP score of
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
and
(
t
,
r
−
1
,
h
)
{\displaystyle (t,r^{-1},h)}
. In this way, SimplE collects the relation between entities while they appear in the role of subject or object inside a fact, and it is able to embed asymmetric relations.
==== Non-bilinear models ====
HolE: HolE uses circular correlation to create an embedded representation of the knowledge graph, which can be seen as a compression of the matrix product, but is more computationally efficient and scalable while keeping the capabilities to express asymmetric relation since the circular correlation is not commutative. HolE links holographic and complex embeddings since, if used together with Fourier, can be seen as a special case of ComplEx.
TuckER: TuckER sees the knowledge graph as a tensor that could be decomposed using the Tucker decomposition in a collection of vectors—i.e., the embeddings of entities and relations—with a shared core. The weights of the core tensor are learned together with the embeddings and represent the level of interaction of the entries. Each entity and relation has its own embedding dimension, and the size of the core tensor is determined by the shape of the entities and relations that interact. The embedding of the subject and object of a fact are summed in the same way, making TuckER fully expressive, and other embedding models such as RESCAL, DistMult, ComplEx, and SimplE can be expressed as a special formulation of TuckER.
MEI: MEI introduces the multi-partition embedding interaction technique with the block term tensor format, which is a generalization of CP decomposition and Tucker decomposition. It divides the embedding vector into multiple partitions and learns the local interaction patterns from data instead of using fixed special patterns as in ComplEx or SimplE models. This enables MEI to achieve optimal efficiency—expressiveness trade-off, not just being fully expressive. Previous models such as TuckER, RESCAL, DistMult, ComplEx, and SimplE are suboptimal restricted special cases of MEI.
MEIM: MEIM goes beyond the block term tensor format to introduce the independent core tensor for ensemble boosting effects and the soft orthogonality for max-rank relational mapping, in addition to multi-partition embedding interaction. MEIM generalizes several previous models such as MEI and its subsumed models, RotaE, and QuatE. MEIM improves expressiveness while still being highly efficient in practice, helping it achieve good results using fairly small model sizes.
=== Geometric models ===
The geometric space defined by this family of models encodes the relation as a geometric transformation between the head and tail of a fact. For this reason, to compute the embedding of the tail, it is necessary to apply a transformation
τ
{\displaystyle \tau }
to the head embedding, and a distance function
δ
{\displaystyle \delta }
is used to measure the goodness of the embedding or to score the reliability of a fact.
f
r
(
h
,
t
)
=
δ
(
τ
(
h
,
r
)
,
t
)
{\displaystyle {\mathcal {f}}_{r}(h,t)=\delta (\tau (h,r),t)}
Geometric models are similar to the tensor decomposition model, but the main difference between the two is that they have to preserve the applicability of the transformation
τ
{\displaystyle \tau }
in the geometric space in which it is defined.
==== Pure translational models ====
This class of models is inspired by the idea of translation invariance introduced in word2vec. A pure translational model relies on the fact that the embedding vector of the entities are close to each other after applying a proper relational translation in the geometric space in which they are defined. In other words, given a fact, the embedding of the head plus the embedding of the relation should equal the embedding of the tail. The closeness of the entities embedding is given by some distance measure and quantifies the reliability of a fact.
TransE: Uses a scoring function that forces the embeddings to satisfy a simple vector sum equation in each fact in which they appear:
h
+
r
=
t
{\displaystyle h+r=t}
. The embedding will be exact if each entity and relation appears in only one fact, and so in practice is poor at representing one-to-many, many-to-one, and asymmetric relations.
TransH: A modification of TransE for representing types of relations, by using a hyperplane as a geometric space. In TransH, the relation embedding is on a different hyperplane depending on the entities it interacts with. So, to compute, for example, the score function of a fact, the embedded representation of the head and tail need to be projected using a relational projection matrix on the correct hyperplane of the relation.
TransR: A modification of TransH that uses different spaces embedding entities versus relations, thus separating the semantic spaces of entities and relations. TransR also uses a relational projection matrix to translate the embedding of the entities to the relation space.
TransD: In TransR, the head and the tail of a given fact could belong to two different types of entities. For example, in the fact
(
O
b
a
m
a
,
p
r
e
s
i
d
e
n
t
_
o
f
,
U
S
A
)
{\displaystyle (Obama,president\_of,USA)}
, Obama is a person and USA is a country. Matrix multiplication is an expensive procedure in TransR to compute the projection. In this context, TransD uses two vectors for each entity-relation pair to compute a dynamic mapping that substitutes the projection matrix while reducing the dimensional complexity. The first vector is used to represent the semantic meaning of the entities and relations, the second to compute the mapping matrix.
TransA: All the translational models define a score function in their representation space, but they oversimplify this metric loss. Since the vector representation of the entities and relations is not perfect, a pure translation of
h
+
r
{\displaystyle h+r}
could be distant from
t
{\displaystyle t}
, and a spherical equipotential Euclidean distance makes it hard to distinguish which is the closest entity. TransA, instead, introduces an adaptive Mahalanobis distance to weights the embedding dimensions, together with elliptical surfaces to remove the ambiguity.
==== Translational models with additional embeddings ====
It is possible to associate additional information to each element in the knowledge graph and their common representation facts. Each entity and relation can be enriched with text descriptions, weights, constraints, and others in order to improve the overall description of the domain with a knowledge graph. During the embedding of the knowledge graph, this information can be used to learn specialized embeddings for these characteristics together with the usual embedded representation of entities and relations, with the cost of learning a more significant number of vectors.
STransE: This model is the result of the combination of TransE and of the structure embedding in such a way it is able to better represent the one-to-many, many-to-one, and many-to-many relations. To do so, the model involves two additional independent matrix
W
r
h
{\displaystyle W_{r}^{h}}
and
W
r
t
{\displaystyle W_{r}^{t}}
for each embedded relation
r
{\displaystyle r}
in the KG. Each additional matrix is used based on the fact the specific relation interact with the head or the tail of the fact. In other words, given a fact
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
, before applying the vector translation, the head
h
{\displaystyle h}
is multiplied by
W
r
h
{\displaystyle W_{r}^{h}}
and the tail is multiplied by
W
r
t
{\displaystyle W_{r}^{t}}
.
CrossE: Crossover interactions can be used for related information selection, and could be very useful for the embedding procedure. Crossover interactions provide two distinct contributions in the information selection: interactions from relations to entities and interactions from entities to relations. This means that a relation, e.g.'president_of' automatically selects the types of entities that are connecting the subject to the object of a fact. In a similar way, the entity of a fact inderectly determine which is inference path that has to be choose to predict the object of a related triple. CrossE, to do so, learns an additional interaction matrix
C
{\displaystyle C}
, uses the element-wise product to compute the interaction between
h
{\displaystyle h}
and
r
{\displaystyle r}
. Even if, CrossE, does not rely on a neural network architecture, it is shown that this methodology can be encoded in such architecture.
==== Roto-translational models ====
This family of models, in addition or in substitution of a translation they employ a rotation-like transformation.
TorusE: The regularization term of TransE makes the entity embedding to build a spheric space, and consequently loses the translation properties of the geometric space. To address this problem, TorusE leverages the use of a compact Lie group that in this specific case is n-dimensional torus space, and avoid the use of regularization. TorusE defines the distance functions to substitute the L1 and L2 norm of TransE.
RotatE: RotatE is inspired by the Euler's identity and involves the use of Hadamard product to represent a relation
r
{\displaystyle r}
as a rotation from the head
h
{\displaystyle h}
to the tail
t
{\displaystyle t}
in the complex space. For each element of the triple, the complex part of the embedding describes a counterclockwise rotation respect to an axis, that can be describe with the Euler's identity, whereas the modulus of the relation vector is 1. It is shown that the model is capable of embedding symmetric, asymmetric, inversion, and composition relations from the knowledge graph.
=== Deep learning models ===
This group of embedding models uses deep neural network to learn patterns from the knowledge graph that are the input data. These models have the generality to distinguish the type of entity and relation, temporal information, path information, underlay structured information, and resolve the limitations of distance-based and semantic-matching-based models in representing all the features of a knowledge graph. The use of deep learning for knowledge graph embedding has shown good predictive performance even if they are more expensive in the training phase, data-hungry, and often required a pre-trained embedding representation of knowledge graph coming from a different embedding model.
==== Convolutional neural networks ====
This family of models, instead of using fully connected layers, employs one or more convolutional layers that convolve the input data applying a low-dimensional filter capable of embedding complex structures with few parameters by learning nonlinear features.
ConvE: ConvE is an embedding model that represents a good tradeoff expressiveness of deep learning models and computational expensiveness, in fact it is shown that it used 8x less parameters, when compared to DistMult. ConvE uses a one-dimensional
d
{\displaystyle d}
-sized embedding to represent the entities and relations of a knowledge graph. To compute the score function of a triple, ConvE apply a simple procedure: first concatenes and merge the embeddings of the head of the triple and the relation in a single data
[
h
;
r
]
{\displaystyle {\ce {[h;{\mathcal {r}}]}}}
, then this matrix is used as input for the 2D convolutional layer. The result is then passed through a dense layer that apply a linear transformation parameterized by the matrix
W
{\displaystyle {\mathcal {W}}}
and at the end, with the inner product is linked to the tail triple. ConvE is also particularly efficient in the evaluation procedure: using a 1-N scoring, the model matches, given a head and a relation, all the tails at the same time, saving a lot of evaluation time when compared to the 1-1 evaluation program of the other models.
ConvR: ConvR is an adaptive convolutional network aimed to deeply represent all the possible interactions between the entities and the relations. For this task, ConvR, computes convolutional filter for each relation, and, when required, applies these filters to the entity of interest to extract convoluted features. The procedure to compute the score of triple is the same as ConvE.
ConvKB: ConvKB, to compute score function of a given triple
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
, it produces an input
[
h
;
r
;
t
]
{\displaystyle {\ce {[h;{\mathcal {r}};t]}}}
of dimension
d
×
3
{\displaystyle d\times 3}
without reshaping and passes it to series of convolutional filter of size
1
×
3
{\displaystyle 1\times 3}
. This result feeds a dense layer with only one neuron that produces the final score. The single final neuron makes this architecture as a binary classifier in which the fact could be true or false. A difference with ConvE is that the dimensionality of the entities is not changed.
==== Capsule neural networks ====
This family of models uses capsule neural networks to create a more stable representation that is able to recognize a feature in the input without losing spatial information. The network is composed of convolutional layers, but they are organized in capsules, and the overall result of a capsule is sent to a higher-capsule decided by a dynamic process routine.
CapsE: CapsE implements a capsule network to model a fact
(
h
,
r
,
t
)
{\displaystyle (h,r,t)}
. As in ConvKB, each triple element is concatenated to build a matrix
[
h
;
r
;
t
]
{\displaystyle {\ce {[h;{\mathcal {r}};t]}}}
and is used to feed to a convolutional layer to extract the convolutional features. These features are then redirected to a capsule to produce a continuous vector, more the vector is long, more the fact is true.
==== Recurrent neural networks ====
This class of models leverages the use of recurrent neural network. The advantage of this architecture is to memorize a sequence of fact, rather than just elaborate single events.
RSN: During the embedding procedure is commonly assumed that, similar entities has similar relations. In practice, this type of information is not leveraged, because the embedding is computed just on the undergoing fact rather than a history of facts. Recurrent skipping networks (RSN) uses a recurrent neural network to learn relational path using a random walk sampling.
== Model performance ==
The machine learning task for knowledge graph embedding that is more often used to evaluate the embedding accuracy of the models is the link prediction. Rossi et al. produced an extensive benchmark of the models, but also other surveys produces similar results. The benchmark involves five datasets FB15k, WN18, FB15k-237, WN18RR, and YAGO3-10. More recently, it has been discussed that these datasets are far away from real-world applications, and other datasets should be integrated as a standard benchmark.
== Libraries ==
KGE on GitHub
MEI-KGE on GitHub
Pykg2vec on GitHub
DGL-KE on GitHub
PyKEEN on GitHub
TorchKGE on GitHub
AmpliGraph on GitHub
OpenKE on GitHub
scikit-kge on GitHub
Fast-TransX on GitHub
MEIM-KGE on GitHub
DICEE on GitHub
== See also ==
Knowledge graph
Embedding
Machine learning
Knowledge base
Knowledge extraction
Statistical relational learning
Representation learning
Graph embedding
== References ==
== External links ==
Open Graph Benchmark - Stanford
WordNet - Princeton | Wikipedia/Knowledge_graph_embedding |
A dynamic Bayesian network (DBN) is a Bayesian network (BN) which relates variables to each other over adjacent time steps.
== History ==
A dynamic Bayesian network (DBN) is often called a "two-timeslice" BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s at Stanford University's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains.
Today, DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, digital forensics, protein sequencing, and bioinformatics. DBN is a generalization of hidden Markov models and Kalman filters.
DBNs are conceptually related to probabilistic Boolean networks and can, similarly, be used to model dynamical systems at steady-state.
== See also ==
Recursive Bayesian estimation
Probabilistic logic network
Generalized filtering
== References ==
== Further reading ==
Murphy, Kevin (2002). Dynamic Bayesian Networks: Representation, Inference and Learning. UC Berkeley, Computer Science Division.
Ghahramani, Zoubin (1998). "Learning dynamic Bayesian networks". Adaptive Processing of Sequences and Data Structures. Lecture Notes in Computer Science. Vol. 1387. pp. 168–197. CiteSeerX 10.1.1.56.7874. doi:10.1007/BFb0053999. ISBN 978-3-540-64341-8.
Friedman, N.; Murphy, K.; Russell, S. (1998). Learning the structure of dynamic probabilistic networks. UAI’98. Morgan Kaufmann. pp. 139–147. CiteSeerX 10.1.1.75.2969.
Shiguihara, P.; De Andrade Lopes, A.; Mauricio, D. (2021). "Dynamic Bayesian Network Modeling, Learning, and Inference: A Survey". IEEE Access. doi:10.1109/ACCESS.2021.3105520. {{cite journal}}: Cite journal requires |journal= (help)
== Software ==
bnt on GitHub: the Bayes Net Toolbox for Matlab, by Kevin Murphy, (released under a GPL license)
Graphical Models Toolkit (GMTK): an open-source, publicly available toolkit for rapidly prototyping statistical models using dynamic graphical models (DGMs) and dynamic Bayesian networks (DBNs). GMTK can be used for applications and research in speech and language processing, bioinformatics, activity recognition, and any time-series application.
DBmcmc : Inferring Dynamic Bayesian Networks with MCMC, for Matlab (free software)
GlobalMIT Matlab toolbox at Google Code: Modeling gene regulatory network via global optimization of dynamic bayesian network (released under a GPL license)
libDAI: C++ library that provides implementations of various (approximate) inference methods for discrete graphical models; supports arbitrary factor graphs with discrete variables, including discrete Markov Random Fields and Bayesian Networks (released under the FreeBSD license)
aGrUM: C++ library (with Python bindings) for different types of PGMs including Bayesian Networks and Dynamic Bayesian Networks (released under the GPLv3)
FALCON: Matlab toolbox for contextualization of DBNs models of regulatory networks with biological quantitative data, including various regularization schemes to model prior biological knowledge (released under the GPLv3) | Wikipedia/Dynamic_Bayesian_network |
The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from people outside the field.
== Overview ==
The book outlines five approaches of machine learning: inductive reasoning, connectionism, evolutionary computation, Bayes' theorem and analogical modelling. The author explains these tribes to the reader by referring to more understandable processes of logic, connections made in the brain, natural selection, probability and similarity judgments. Throughout the book, it is suggested that each different tribe has the potential to contribute to a unifying "master algorithm".
Towards the end of the book the author pictures a "master algorithm" in the near future, where machine learning algorithms asymptotically grow to a perfect understanding of how the world and people in it work. Although the algorithm doesn't yet exist, he briefly reviews his own invention of the Markov logic network.
== In the media ==
In 2016 Bill Gates recommended the book, alongside Nick Bostrom's Superintelligence, as one of two books everyone should read to understand AI. In 2018 the book was noted to be on Chinese Communist Party general secretary Xi Jinping's bookshelf.
=== Reception ===
A computer science educator stated in Times Higher Education that the examples are clear and accessible. In contrast, The Economist agreed Domingos "does a good job" but complained that he "constantly invents metaphors that grate or confuse". Kirkus Reviews praised the book, stating that "Readers unfamiliar with logic and computer theory will have a difficult time, but those who persist will discover fascinating insights."
A New Scientist review called it "compelling but rather unquestioning".
== References ==
== Further reading ==
https://www.wsj.com/articles/the-sum-of-human-knowledge-1442610803
http://www.kdnuggets.com/2015/09/book-master-algorithm-pedro-domingos.html
http://www.kdnuggets.com/2014/08/interview-pedro-domingos-master-algorithm-new-deep-learning.html (interview)
== External links ==
Official website | Wikipedia/The_Master_Algorithm |
Crossover in evolutionary algorithms and evolutionary computation, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. New solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions may be mutated before being added to the population. The aim of recombination is to transfer good characteristics from two different parents to one child.
Different algorithms in evolutionary computation may use different data structures to store genetic information, and each genetic representation can be recombined with different crossover operators. Typical data structures that can be recombined with crossover are bit arrays, vectors of real numbers, or trees.
The list of operators presented below is by no means complete and serves mainly as an exemplary illustration of this dyadic genetic operator type. More operators and more details can be found in the literature.
== Crossover for binary arrays ==
Traditional genetic algorithms store genetic information in a chromosome represented by a bit array. Crossover methods for bit arrays are popular and an illustrative example of genetic recombination.
=== One-point crossover ===
A point on both parents' chromosomes is picked randomly, and designated a 'crossover point'. Bits to the right of that point are swapped between the two parent chromosomes. This results in two offspring, each carrying some genetic information from both parents.
=== Two-point and k-point crossover ===
In two-point crossover, two crossover points are picked randomly from the parent chromosomes. The bits in between the two points are swapped between the parent organisms.
Two-point crossover is equivalent to performing two single-point crossovers with different crossover points. This strategy can be generalized to k-point crossover for any positive integer k, picking k crossover points.
=== Uniform crossover ===
In uniform crossover, typically, each bit is chosen from either parent with equal probability. Other mixing ratios are sometimes used, resulting in offspring which inherit more genetic information from one parent than the other.
In a uniform crossover, we don’t divide the chromosome into segments, rather we treat each gene separately. In this, we essentially flip a coin for each chromosome to decide whether or not it will be included in the off-spring.
== Crossover for integer or real-valued genomes ==
For the crossover operators presented above and for most other crossover operators for bit strings, it holds that they can also be applied accordingly to integer or real-valued genomes whose genes each consist of an integer or real-valued number. Instead of individual bits, integer or real-valued numbers are then simply copied into the child genome. The offspring lie on the remaining corners of the hyperbody spanned by the two parents
P
1
=
(
1.5
,
6
,
8
)
{\displaystyle P_{1}=(1.5,6,8)}
and
P
2
=
(
7
,
2
,
1
)
{\displaystyle P_{2}=(7,2,1)}
, as exemplified in the accompanying image for the three-dimensional case.
=== Discrete recombination ===
If the rules of the uniform crossover for bit strings are applied during the generation of the offspring, this is also called discrete recombination.
=== Intermediate recombination ===
In this recombination operator, the allele values of the child genome
a
i
{\displaystyle a_{i}}
are generated by mixing the alleles of the two parent genomes
a
i
,
P
1
{\displaystyle a_{i,P_{1}}}
and
a
i
,
P
2
{\displaystyle a_{i,P_{2}}}
:
α
i
=
α
i
,
P
1
⋅
β
i
+
α
i
,
P
2
⋅
(
1
−
β
i
)
w
i
t
h
β
i
∈
[
−
d
,
1
+
d
]
{\displaystyle \alpha _{i}=\alpha _{i,P_{1}}\cdot \beta _{i}+\alpha _{i,P_{2}}\cdot \left(1-\beta _{i}\right)\quad {\mathsf {with}}\quad \beta _{i}\in \left[-d,1+d\right]}
randomly equally distributed per gene
i
{\displaystyle i}
The choice of the interval
[
−
d
,
1
+
d
]
{\displaystyle [-d,1+d]}
causes that besides the interior of the hyperbody spanned by the allele values of the parent genes additionally a certain environment for the range of values of the offspring is in question. A value of
0.25
{\displaystyle 0.25}
is recommended for
d
{\displaystyle d}
to counteract the tendency to reduce the allele values that otherwise exists at
d
=
0
{\displaystyle d=0}
.
The adjacent figure shows for the two-dimensional case the range of possible new alleles of the two exemplary parents
P
1
=
(
3
,
6
)
{\displaystyle P_{1}=(3,6)}
and
P
2
=
(
9
,
2
)
{\displaystyle P_{2}=(9,2)}
in intermediate recombination. The offspring of discrete recombination
C
1
{\displaystyle C_{1}}
and
C
2
{\displaystyle C_{2}}
are also plotted. Intermediate recombination satisfies the arithmetic calculation of the allele values of the child genome required by virtual alphabet theory. Discrete and intermediate recombination are used as a standard in the evolution strategy.
== Crossover for permutations ==
For combinatorial tasks, permutations are usually used that are specifically designed for genomes that are themselves permutations of a set. The underlying set is usually a subset of
N
{\displaystyle \mathbb {N} }
or
N
0
{\displaystyle \mathbb {N} _{0}}
. If 1- or n-point or uniform crossover for integer genomes is used for such genomes, a child genome may contain some values twice and others may be missing. This can be remedied by genetic repair, e.g. by replacing the redundant genes in positional fidelity for missing ones from the other child genome.
In order to avoid the generation of invalid offspring, special crossover operators for permutations have been developed which fulfill the basic requirements of such operators for permutations, namely that all elements of the initial permutation are also present in the new one and only the order is changed. It can be distinguished between combinatorial tasks, where all sequences are admissible, and those where there are constraints in the form of inadmissible partial sequences. A well-known representative of the first task type is the traveling salesman problem (TSP), where the goal is to visit a set of cities exactly once on the shortest tour. An example of the constrained task type is the scheduling of multiple workflows. Workflows involve sequence constraints on some of the individual work steps. For example, a thread cannot be cut until the corresponding hole has been drilled in a workpiece. Such problems are also called order-based permutations.
In the following, two crossover operators are presented as examples, the partially mapped crossover (PMX) motivated by the TSP and the order crossover (OX1) designed for order-based permutations. A second offspring can be produced in each case by exchanging the parent chromosomes.
=== Partially mapped crossover (PMX) ===
The PMX operator was designed as a recombination operator for TSP like Problems. The explanation of the procedure is illustrated by an example:
=== Order crossover (OX1) ===
The order crossover goes back to Davis in its original form and is presented here in a slightly generalized version with more than two crossover points. It transfers information about the relative order from the second parent to the offspring. First, the number and position of the crossover points are determined randomly. The resulting gene sequences are then processed as described below:
Among other things, order crossover is well suited for scheduling multiple workflows, when used in conjunction with 1- and n-point crossover.
=== Further crossover operators for permutations ===
Over time, a large number of crossover operators for permutations have been proposed, so the following list is only a small selection. For more information, the reader is referred to the literature.
cycle crossover (CX)
order-based crossover (OX2)
position-based crossover (POS)
edge recombination
voting recombination (VR)
alternating-positions crossover (AP)
maximal preservative crossover (MPX)
merge crossover (MX)
sequential constructive crossover operator (SCX)
The usual approach to solving TSP-like problems by genetic or, more generally, evolutionary algorithms, presented earlier, is either to repair illegal descendants or to adjust the operators appropriately so that illegal offspring do not arise in the first place. Alternatively, Riazi suggests the use of a double chromosome representation, which avoids illegal offspring.
== See also ==
Evolutionary algorithm
Genetic representation
Fitness function
Selection (genetic algorithm)
== Bibliography ==
John Holland (1975). Adaptation in Natural and Artificial Systems, PhD thesis, University of Michigan Press, Ann Arbor, Michigan. ISBN 0-262-58111-6.
Schwefel, Hans-Paul (1995). Evolution and Optimum Seeking. New York: John Wiley & Sons. ISBN 0-471-57148-2.
Davis, Lawrence (1991). Handbook of genetic algorithms. New York: Van Nostrand Reinhold. ISBN 0-442-00173-8. OCLC 23081440.
Eiben, A.E.; Smith, J.E. (2015). Introduction to Evolutionary Computing. Natural Computing Series. Berlin, Heidelberg: Springer. doi:10.1007/978-3-662-44874-8. ISBN 978-3-662-44873-1. S2CID 20912932.
Yu, Xinjie; Gen, Mitsuo (2010). Introduction to Evolutionary Algorithms. Decision Engineering. London: Springer. doi:10.1007/978-1-84996-129-5. ISBN 978-1-84996-128-8.
Bäck, Thomas; Fogel, David B.; Michalewicz, Zbigniew, eds. (1999). Evolutionary computation. Vol. 1, Basic algorithms and operators. Bristol: Institute of Physics Pub. ISBN 0-585-30560-9. OCLC 45730387.
== References ==
== External links ==
Newsgroup: comp.ai.genetic FAQ - see section on crossover (also known as recombination). | Wikipedia/Crossover_(genetic_algorithm) |
Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner. Recent developments have seen the Radon transform and its inverse used for tasks related to realistic object insertion required for testing and evaluating computed tomography use in airport security.
This article applies in general to reconstruction methods for all kinds of tomography, but some of the terms and physical descriptions refer directly to the reconstruction of X-ray computed tomography.
== Introducing formula ==
The projection of an object, resulting from the tomographic measurement process at a given angle
θ
{\displaystyle \theta }
, is made up of a set of line integrals (see Fig. 1). A set of many such projections under different angles organized in 2D is called a sinogram (see Fig. 3). In X-ray CT, the line integral represents the total attenuation of the beam of X-rays as it travels in a straight line through the object. As mentioned above, the resulting image is a 2D (or 3D) model of the attenuation coefficient. That is, we wish to find the image
μ
(
x
,
y
)
{\displaystyle \mu (x,y)}
. The simplest and easiest way to visualise the method of scanning is the system of parallel projection, as used in the first scanners. For this discussion we consider the data to be collected as a series of parallel rays, at position
r
{\displaystyle r}
, across a projection at angle
θ
{\displaystyle \theta }
. This is repeated for various angles. Attenuation occurs exponentially in tissue:
I
=
I
0
exp
(
−
∫
μ
(
x
,
y
)
d
s
)
{\displaystyle I=I_{0}\exp \left({-\int \mu (x,y)\,ds}\right)}
where
μ
(
x
,
y
)
{\displaystyle \mu (x,y)}
is the attenuation coefficient as a function of position. Therefore, generally the total attenuation
p
{\displaystyle p}
of a ray at position
r
{\displaystyle r}
, on the projection at angle
θ
{\displaystyle \theta }
, is given by the line integral:
p
θ
(
r
)
=
ln
(
I
I
0
)
=
−
∫
μ
(
x
,
y
)
d
s
{\displaystyle p_{\theta }(r)=\ln \left({\frac {I}{I_{0}}}\right)=-\int \mu (x,y)\,ds}
Using the coordinate system of Figure 1, the value of
r
{\displaystyle r}
onto which the point
(
x
,
y
)
{\displaystyle (x,y)}
will be projected at angle
θ
{\displaystyle \theta }
is given by:
x
cos
θ
+
y
sin
θ
=
r
{\displaystyle x\cos \theta +y\sin \theta =r\ }
So the equation above can be rewritten as
p
θ
(
r
)
=
∫
−
∞
∞
∫
−
∞
∞
f
(
x
,
y
)
δ
(
x
cos
θ
+
y
sin
θ
−
r
)
d
x
d
y
{\displaystyle p_{\theta }(r)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\delta (x\cos \theta +y\sin \theta -r)\,dx\,dy}
where
f
(
x
,
y
)
{\displaystyle f(x,y)}
represents
μ
(
x
,
y
)
{\displaystyle \mu (x,y)}
and
δ
(
)
{\displaystyle \delta ()}
is the Dirac delta function. This function is known as the Radon transform (or sinogram) of the 2D object.
The Fourier Transform of the projection can be written as
P
θ
(
ω
)
=
∫
−
∞
∞
∫
−
∞
∞
f
(
x
,
y
)
exp
[
−
j
ω
(
x
cos
θ
+
y
sin
θ
)
]
d
x
d
y
=
F
(
Ω
1
,
Ω
2
)
{\displaystyle P_{\theta }(\omega )=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\exp[-j\omega (x\cos \theta +y\sin \theta )]\,dx\,dy=F(\Omega _{1},\Omega _{2})}
where
Ω
1
=
ω
cos
θ
,
Ω
2
=
ω
sin
θ
{\displaystyle \Omega _{1}=\omega \cos \theta ,\Omega _{2}=\omega \sin \theta }
P
θ
(
ω
)
{\displaystyle P_{\theta }(\omega )}
represents a slice of the 2D Fourier transform of
f
(
x
,
y
)
{\displaystyle f(x,y)}
at angle
θ
{\displaystyle \theta }
. Using the inverse Fourier transform, the inverse Radon transform formula can be easily derived.
f
(
x
,
y
)
=
1
2
π
∫
0
π
g
θ
(
x
cos
θ
+
y
sin
θ
)
d
θ
{\displaystyle f(x,y)={\frac {1}{2\pi }}\int \limits _{0}^{\pi }g_{\theta }(x\cos \theta +y\sin \theta )d\theta }
where
g
θ
(
x
cos
θ
+
y
sin
θ
)
{\displaystyle g_{\theta }(x\cos \theta +y\sin \theta )}
is the derivative of the Hilbert transform of
p
θ
(
r
)
{\displaystyle p_{\theta }(r)}
In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object,
f
(
x
,
y
)
{\displaystyle f(x,y)}
. However, there will only be a finite number of projections available in practice.
Assuming
f
(
x
,
y
)
{\displaystyle f(x,y)}
has effective diameter
d
{\displaystyle d}
and desired resolution is
R
s
{\displaystyle R_{s}}
, a rule of thumb for the number of projections needed for reconstruction is
N
>
π
d
/
R
s
{\displaystyle N>\pi d/R_{s}}
== Reconstruction algorithms ==
Practical reconstruction algorithms have been developed to implement the process of reconstruction of a three-dimensional object from its projections. These algorithms are designed largely based on the mathematics of the X-ray transform, statistical knowledge of the data acquisition process and geometry of the data imaging system.
=== Fourier-domain reconstruction algorithm ===
Reconstruction can be made using interpolation. Assume
N
{\displaystyle N}
projections of
f
(
x
,
y
)
{\displaystyle f(x,y)}
are generated at equally spaced angles, each sampled at the same rate. The discrete Fourier transform (DFT) on each projection yields sampling in the frequency domain. Combining all the frequency-sampled projections generates a polar raster in the frequency domain. The polar raster is sparse, so interpolation is used to fill the unknown DFT points, and reconstruction can be done through the inverse discrete Fourier transform. Reconstruction performance may improve by designing methods to change the sparsity of the polar raster, facilitating the effectiveness of interpolation.
For instance, a concentric square raster in the frequency domain can be obtained by changing the angle between each projection as follow:
θ
′
=
R
0
max
{
|
cos
θ
|
,
|
sin
θ
|
}
{\displaystyle \theta '={\frac {R_{0}}{\max\{|\cos \theta |,|\sin \theta |\}}}}
where
R
0
{\displaystyle R_{0}}
is highest frequency to be evaluated.
The concentric square raster improves computational efficiency by allowing all the interpolation positions to be on rectangular DFT lattice. Furthermore, it reduces the interpolation error. Yet, the Fourier-Transform algorithm has a disadvantage of producing inherently noisy output.
=== Back projection algorithm ===
In practice of tomographic image reconstruction, often a stabilized and discretized version of the inverse Radon transform is used, known as the filtered back projection algorithm.
With a sampled discrete system, the inverse Radon transform is
f
(
x
,
y
)
=
1
2
π
∑
i
=
0
N
−
1
Δ
θ
i
g
θ
i
(
x
cos
θ
i
+
y
sin
θ
i
)
{\displaystyle f(x,y)={\frac {1}{2\pi }}\sum _{i=0}^{N-1}\Delta \theta _{i}g_{\theta _{i}}(x\cos \theta _{i}+y\sin \theta _{i})}
g
θ
(
t
)
=
p
θ
(
t
)
⋅
k
(
t
)
{\displaystyle g_{\theta }(t)=p_{\theta }(t)\cdot k(t)}
where
Δ
θ
{\displaystyle \Delta \theta }
is the angular spacing between the projections and
k
(
t
)
{\displaystyle k(t)}
is a Radon kernel with frequency response
|
ω
|
{\displaystyle |\omega |}
.
The name back-projection comes from the fact that a one-dimensional projection needs to be filtered by a one-dimensional Radon kernel (back-projected) in order to obtain a two-dimensional signal. The filter used does not contain DC gain, so adding DC bias may be desirable. Reconstruction using back-projection allows better resolution than interpolation method described above. However, it induces greater noise because the filter is prone to amplify high-frequency content.
=== Iterative reconstruction algorithm ===
The iterative algorithm is computationally intensive but it allows the inclusion of a priori information about the system
f
(
x
,
y
)
{\displaystyle f(x,y)}
.
Let
N
{\displaystyle N}
be the number of projections and
D
i
{\displaystyle D_{i}}
be the distortion operator for the
i
{\displaystyle i}
th projection taken at an angle
θ
i
{\displaystyle \theta _{i}}
.
{
λ
i
}
{\displaystyle \{\lambda _{i}\}}
are a set of parameters to optimize the conversion of iterations.
f
0
(
x
,
y
)
=
∑
i
=
1
N
λ
i
p
θ
i
(
r
)
{\displaystyle f_{0}(x,y)=\sum _{i=1}^{N}\lambda _{i}p_{\theta _{i}}(r)}
f
k
(
x
,
y
)
=
f
k
−
1
(
x
,
y
)
+
∑
i
=
1
N
λ
i
[
p
θ
i
(
r
)
−
D
i
f
k
−
1
(
x
,
y
)
]
{\displaystyle f_{k}(x,y)=f_{k-1}(x,y)+\sum _{i=1}^{N}\lambda _{i}[p_{\theta _{i}}(r)-D_{i}f_{k-1}(x,y)]}
An alternative family of recursive tomographic reconstruction algorithms are the algebraic reconstruction techniques and iterative sparse asymptotic minimum variance.
=== Fan-beam reconstruction ===
Use of a noncollimated fan beam is common since a collimated beam of radiation is difficult to obtain. Fan beams will generate series of line integrals, not parallel to each other, as projections. The fan-beam system requires a 360-degree range of angles, which imposes mechanical constraints, but it allows faster signal acquisition time, which may be advantageous in certain settings such as in the field of medicine. Back projection follows a similar two-step procedure that yields reconstruction by computing weighted sum back-projections obtained from filtered projections.
=== Deep learning reconstruction ===
Deep learning methods are widely applied to image reconstruction nowadays and have achieved impressive results in various image reconstruction tasks, including low-dose denoising, sparse-view reconstruction, limited angle tomography and metal artifact reduction. An excellent overview can be found in the special issue of IEEE Transaction on Medical Imaging. One group of deep learning reconstruction algorithms apply post-processing neural networks to achieve image-to-image reconstruction, where input images are reconstructed by conventional reconstruction methods. Artifact reduction using the U-Net in limited angle tomography is such an example application. However, incorrect structures may occur in an image reconstructed by such a completely data-driven method, as displayed in the figure. Therefore, integration of known operators into the architecture design of neural networks appears beneficial, as described in the concept of precision learning. For example, direct image reconstruction from projection data can be learnt from the framework of filtered back-projection. Another example is to build neural networks by unrolling iterative reconstruction algorithms. Except for precision learning, using conventional reconstruction methods with deep learning reconstruction prior is also an alternative approach to improve the image quality of deep learning reconstruction.
== Tomographic reconstruction software ==
Tomographic systems have significant variability in their applications and geometries (locations of sources and detectors). This variability creates the need for very specific, tailored implementations of the processing and reconstruction algorithms. Thus, most CT manufacturers provide their own custom proprietary software. This is done not only to protect intellectual property, but may also be enforced by a government regulatory agency. Regardless, there are a number of general purpose tomographic reconstruction software packages that have been developed over the last couple decades, both commercial and open-source.
Most of the commercial software packages that are available for purchase focus on processing data for benchtop cone-beam CT systems. A few of these software packages include Volume Graphics, InstaRecon, iTomography, Livermore Tomography Tools (LTT), and Cone Beam Software Tools (CST).
Some noteworthy examples of open-source reconstruction software include: Reconstruction Toolkit (RTK), CONRAD, TomoPy, the ASTRA toolbox, PYRO-NN, ODL, TIGRE, and LEAP.
== Gallery ==
Shown in the gallery is the complete process for a simple object tomography and the following tomographic reconstruction based on ART.
== See also ==
Operation of computed tomography#Tomographic reconstruction
Cone beam reconstruction
Industrial computed tomography
Industrial Tomography Systems plc
== References ==
== Further reading ==
Avinash Kak & Malcolm Slaney (1988), Principles of Computerized Tomographic Imaging, IEEE Press, ISBN 0-87942-198-3.
Bruyant, P.P. "Analytic and iterative reconstruction algorithms in SPECT" Journal of Nuclear Medicine 43(10):1343-1358, 2002
== External links ==
Slaney, A. C. Kak and Malcolm. "Principles of Computerized Tomographic Imaging". Slaney.org. Retrieved 7 September 2018.
Insight ToolKit; open-source tomographic support software
"TomoPy — TomoPy 1.1.3 documentation". Tomopy.readthedocs.org. Retrieved 7 September 2018.
ASTRA (All Scales Tomographic Reconstruction Antwerp) toolbox; very flexible, fast open-source software for computed tomographic reconstruction
NiftyRec; comprehensive open-source tomographic reconstruction software; Matlab and Python scriptable
Open-source tomographic reconstruction and visualization tool
"ITS plc - Electrical Process Tomography For Industrial Visualization". Itoms.com. Retrieved 7 September 2018. | Wikipedia/Tomographic_reconstruction |
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed.
== Intuition ==
Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values (predictors). This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model). This is appropriate when the response variable can vary, to a good approximation, indefinitely in either direction, or more generally for any quantity that only varies by a relatively small amount compared to the variation in the predictive variables, e.g. human heights.
However, these assumptions are inappropriate for some types of response variables. For example, in cases where the response variable is expected to be always positive and varying over a wide range, constant input changes lead to geometrically (i.e. exponentially) varying, rather than constantly varying, output changes. As an example, suppose a linear prediction model learns from some data (perhaps primarily drawn from large beaches) that a 10 degree temperature decrease would lead to 1,000 fewer people visiting the beach. This model is unlikely to generalize well over differently-sized beaches. More specifically, the problem is that if the model is used to predict the new attendance with a temperature drop of 10 for a beach that regularly receives 50 beachgoers, it would predict an impossible attendance value of −950. Logically, a more realistic model would instead predict a constant rate of increased beach attendance (e.g. an increase of 10 degrees leads to a doubling in beach attendance, and a drop of 10 degrees leads to a halving in attendance). Such a model is termed an exponential-response model (or log-linear model, since the logarithm of the response is predicted to vary linearly).
Similarly, a model that predicts a probability of making a yes/no choice (a Bernoulli variable) is even less suitable as a linear-response model, since probabilities are bounded on both ends (they must be between 0 and 1). Imagine, for example, a model that predicts the likelihood of a given person going to the beach as a function of temperature. A reasonable model might predict, for example, that a change in 10 degrees makes a person two times more or less likely to go to the beach. But what does "twice as likely" mean in terms of a probability? It cannot literally mean to double the probability value (e.g. 50% becomes 100%, 75% becomes 150%, etc.). Rather, it is the odds that are doubling: from 2:1 odds, to 4:1 odds, to 8:1 odds, etc. Such a model is a log-odds or logistic model.
Generalized linear models cover all these situations by allowing for response variables that have arbitrary distributions (rather than simply normal distributions), and for an arbitrary function of the response variable (the link function) to vary linearly with the predictors (rather than assuming that the response itself must vary linearly). For example, the case above of predicted number of beach attendees would typically be modeled with a Poisson distribution and a log link, while the case of predicted probability of beach attendance would typically be modelled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function.
== Overview ==
In a generalized linear model (GLM), each outcome Y of the dependent variables is assumed to be generated from a particular distribution in an exponential family, a large class of probability distributions that includes the normal, binomial, Poisson and gamma distributions, among others. The conditional mean μ of the distribution depends on the independent variables X through:
E
(
Y
∣
X
)
=
μ
=
g
−
1
(
X
β
)
,
{\displaystyle \operatorname {E} (\mathbf {Y} \mid \mathbf {X} )={\boldsymbol {\mu }}=g^{-1}(\mathbf {X} {\boldsymbol {\beta }}),}
where E(Y | X) is the expected value of Y conditional on X; Xβ is the linear predictor, a linear combination of unknown parameters β; g is the link function.
In this framework, the variance is typically a function, V, of the mean:
Var
(
Y
∣
X
)
=
V
(
g
−
1
(
X
β
)
)
.
{\displaystyle \operatorname {Var} (\mathbf {Y} \mid \mathbf {X} )=\operatorname {V} (g^{-1}(\mathbf {X} {\boldsymbol {\beta }})).}
It is convenient if V follows from an exponential family of distributions, but it may simply be that the variance is a function of the predicted value.
The unknown parameters, β, are typically estimated with maximum likelihood, maximum quasi-likelihood, or Bayesian techniques.
== Model components ==
The GLM consists of three elements:
1. A particular distribution for modeling
Y
{\displaystyle Y}
from among those which are considered exponential families of probability distributions,
2. A linear predictor
η
=
X
β
{\displaystyle \eta =X\beta }
, and
3. A link function
g
{\displaystyle g}
such that
E
(
Y
∣
X
)
=
μ
=
g
−
1
(
η
)
{\displaystyle \operatorname {E} (Y\mid X)=\mu =g^{-1}(\eta )}
.
=== Probability distribution ===
An overdispersed exponential family of distributions is a generalization of an exponential family and the exponential dispersion model of distributions and includes those families of probability distributions, parameterized by
θ
{\displaystyle {\boldsymbol {\theta }}}
and
τ
{\displaystyle \tau }
, whose density functions f (or probability mass function, for the case of a discrete distribution) can be expressed in the form
f
Y
(
y
∣
θ
,
τ
)
=
h
(
y
,
τ
)
exp
(
b
(
θ
)
T
T
(
y
)
−
A
(
θ
)
d
(
τ
)
)
.
{\displaystyle f_{Y}(\mathbf {y} \mid {\boldsymbol {\theta }},\tau )=h(\mathbf {y} ,\tau )\exp \left({\frac {\mathbf {b} ({\boldsymbol {\theta }})^{\rm {T}}\mathbf {T} (\mathbf {y} )-A({\boldsymbol {\theta }})}{d(\tau )}}\right).\,\!}
The dispersion parameter,
τ
{\displaystyle \tau }
, typically is known and is usually related to the variance of the distribution. The functions
h
(
y
,
τ
)
{\displaystyle h(\mathbf {y} ,\tau )}
,
b
(
θ
)
{\displaystyle \mathbf {b} ({\boldsymbol {\theta }})}
,
T
(
y
)
{\displaystyle \mathbf {T} (\mathbf {y} )}
,
A
(
θ
)
{\displaystyle A({\boldsymbol {\theta }})}
, and
d
(
τ
)
{\displaystyle d(\tau )}
are known. Many common distributions are in this family, including the normal, exponential, gamma, Poisson, Bernoulli, and (for fixed number of trials) binomial, multinomial, and negative binomial.
For scalar
y
{\displaystyle \mathbf {y} }
and
θ
{\displaystyle {\boldsymbol {\theta }}}
(denoted
y
{\displaystyle y}
and
θ
{\displaystyle \theta }
in this case), this reduces to
f
Y
(
y
∣
θ
,
τ
)
=
h
(
y
,
τ
)
exp
(
b
(
θ
)
T
(
y
)
−
A
(
θ
)
d
(
τ
)
)
.
{\displaystyle f_{Y}(y\mid \theta ,\tau )=h(y,\tau )\exp \left({\frac {b(\theta )T(y)-A(\theta )}{d(\tau )}}\right).\,\!}
θ
{\displaystyle {\boldsymbol {\theta }}}
is related to the mean of the distribution. If
b
(
θ
)
{\displaystyle \mathbf {b} ({\boldsymbol {\theta }})}
is the identity function, then the distribution is said to be in canonical form (or natural form). Note that any distribution can be converted to canonical form by rewriting
θ
{\displaystyle {\boldsymbol {\theta }}}
as
θ
′
{\displaystyle {\boldsymbol {\theta }}'}
and then applying the transformation
θ
=
b
(
θ
′
)
{\displaystyle {\boldsymbol {\theta }}=\mathbf {b} ({\boldsymbol {\theta }}')}
. It is always possible to convert
A
(
θ
)
{\displaystyle A({\boldsymbol {\theta }})}
in terms of the new parametrization, even if
b
(
θ
′
)
{\displaystyle \mathbf {b} ({\boldsymbol {\theta }}')}
is not a one-to-one function; see comments in the page on exponential families.
If, in addition,
T
(
y
)
{\displaystyle \mathbf {T} (\mathbf {y} )}
and
b
(
θ
)
{\displaystyle \mathbf {b} ({\boldsymbol {\theta }})}
are the identity, then
θ
{\displaystyle {\boldsymbol {\theta }}}
is called the canonical parameter (or natural parameter) and is related to the mean through
μ
=
E
(
y
)
=
∇
θ
A
(
θ
)
.
{\displaystyle {\boldsymbol {\mu }}=\operatorname {E} (\mathbf {y} )=\nabla _{\boldsymbol {\theta }}A({\boldsymbol {\theta }}).\,\!}
For scalar
y
{\displaystyle \mathbf {y} }
and
θ
{\displaystyle {\boldsymbol {\theta }}}
, this reduces to
μ
=
E
(
y
)
=
A
′
(
θ
)
.
{\displaystyle \mu =\operatorname {E} (y)=A'(\theta ).}
Under this scenario, the variance of the distribution can be shown to be
Var
(
y
)
=
∇
θ
2
A
(
θ
)
d
(
τ
)
.
{\displaystyle \operatorname {Var} (\mathbf {y} )=\nabla _{\boldsymbol {\theta }}^{2}A({\boldsymbol {\theta }})d(\tau ).\,\!}
For scalar
y
{\displaystyle \mathbf {y} }
and
θ
{\displaystyle {\boldsymbol {\theta }}}
, this reduces to
Var
(
y
)
=
A
″
(
θ
)
d
(
τ
)
.
{\displaystyle \operatorname {Var} (y)=A''(\theta )d(\tau ).\,\!}
=== Linear predictor ===
The linear predictor is the quantity which incorporates the information about the independent variables into the model. The symbol η (Greek "eta") denotes a linear predictor. It is related to the expected value of the data through the link function.
η is expressed as linear combinations (thus, "linear") of unknown parameters β. The coefficients of the linear combination are represented as the matrix of independent variables X. η can thus be expressed as
η
=
X
β
.
{\displaystyle \eta =\mathbf {X} {\boldsymbol {\beta }}.\,}
=== Link function ===
The link function provides the relationship between the linear predictor and the mean of the distribution function. There are many commonly used link functions, and their choice is informed by several considerations. There is always a well-defined canonical link function which is derived from the exponential of the response's density function. However, in some cases it makes sense to try to match the domain of the link function to the range of the distribution function's mean, or use a non-canonical link function for algorithmic purposes, for example Bayesian probit regression.
When using a distribution function with a canonical parameter
θ
,
{\displaystyle \theta ,}
the canonical link function is the function that expresses
θ
{\displaystyle \theta }
in terms of
μ
,
{\displaystyle \mu ,}
i.e.
θ
=
g
(
μ
)
.
{\displaystyle \theta =g(\mu ).}
For the most common distributions, the mean
μ
{\displaystyle \mu }
is one of the parameters in the standard form of the distribution's density function, and then
g
(
μ
)
{\displaystyle g(\mu )}
is the function as defined above that maps the density function into its canonical form. When using the canonical link function,
g
(
μ
)
=
θ
=
X
β
,
{\displaystyle g(\mu )=\theta =\mathbf {X} {\boldsymbol {\beta }},}
which allows
X
T
Y
{\displaystyle \mathbf {X} ^{\rm {T}}\mathbf {Y} }
to be a sufficient statistic for
β
{\displaystyle {\boldsymbol {\beta }}}
.
Following is a table of several exponential-family distributions in common use and the data they are typically used for, along with the canonical link functions and their inverses (sometimes referred to as the mean function, as done here).
In the cases of the exponential and gamma distributions, the domain of the canonical link function is not the same as the permitted range of the mean. In particular, the linear predictor may be positive, which would give an impossible negative mean. When maximizing the likelihood, precautions must be taken to avoid this. An alternative is to use a noncanonical link function.
In the case of the Bernoulli, binomial, categorical and multinomial distributions, the support of the distributions is not the same type of data as the parameter being predicted. In all of these cases, the predicted parameter is one or more probabilities, i.e. real numbers in the range
[
0
,
1
]
{\displaystyle [0,1]}
. The resulting model is known as logistic regression (or multinomial logistic regression in the case that K-way rather than binary values are being predicted).
For the Bernoulli and binomial distributions, the parameter is a single probability, indicating the likelihood of occurrence of a single event. The Bernoulli still satisfies the basic condition of the generalized linear model in that, even though a single outcome will always be either 0 or 1, the expected value will nonetheless be a real-valued probability, i.e. the probability of occurrence of a "yes" (or 1) outcome. Similarly, in a binomial distribution, the expected value is Np, i.e. the expected proportion of "yes" outcomes will be the probability to be predicted.
For categorical and multinomial distributions, the parameter to be predicted is a K-vector of probabilities, with the further restriction that all probabilities must add up to 1. Each probability indicates the likelihood of occurrence of one of the K possible values. For the multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of the vector can be related to the predicted probabilities similarly to the binomial and Bernoulli distributions.
== Fitting ==
=== Maximum likelihood ===
The maximum likelihood estimates can be found using an iteratively reweighted least squares algorithm or a Newton's method with updates of the form:
β
(
t
+
1
)
=
β
(
t
)
+
J
−
1
(
β
(
t
)
)
u
(
β
(
t
)
)
,
{\displaystyle {\boldsymbol {\beta }}^{(t+1)}={\boldsymbol {\beta }}^{(t)}+{\mathcal {J}}^{-1}({\boldsymbol {\beta }}^{(t)})u({\boldsymbol {\beta }}^{(t)}),}
where
J
(
β
(
t
)
)
{\displaystyle {\mathcal {J}}({\boldsymbol {\beta }}^{(t)})}
is the observed information matrix (the negative of the Hessian matrix) and
u
(
β
(
t
)
)
{\displaystyle u({\boldsymbol {\beta }}^{(t)})}
is the score function; or a Fisher's scoring method:
β
(
t
+
1
)
=
β
(
t
)
+
I
−
1
(
β
(
t
)
)
u
(
β
(
t
)
)
,
{\displaystyle {\boldsymbol {\beta }}^{(t+1)}={\boldsymbol {\beta }}^{(t)}+{\mathcal {I}}^{-1}({\boldsymbol {\beta }}^{(t)})u({\boldsymbol {\beta }}^{(t)}),}
where
I
(
β
(
t
)
)
{\displaystyle {\mathcal {I}}({\boldsymbol {\beta }}^{(t)})}
is the Fisher information matrix. Note that if the canonical link function is used, then they are the same.
=== Bayesian methods ===
In general, the posterior distribution cannot be found in closed form and so must be approximated, usually using Laplace approximations or some type of Markov chain Monte Carlo method such as Gibbs sampling.
== Examples ==
=== General linear models ===
A possible point of confusion has to do with the distinction between generalized linear models and general linear models, two broad statistical models. Co-originator John Nelder has expressed regret over this terminology.
The general linear model may be viewed as a special case of the generalized linear model with identity link and responses normally distributed. As most exact results of interest are obtained only for the general linear model, the general linear model has undergone a somewhat longer historical development. Results for the generalized linear model with non-identity link are asymptotic (tending to work well with large samples).
=== Linear regression ===
A simple, very important example of a generalized linear model (also an example of a general linear model) is linear regression. In linear regression, the use of the least-squares estimator is justified by the Gauss–Markov theorem, which does not assume that the distribution is normal.
From the perspective of generalized linear models, however, it is useful to suppose that the distribution function is the normal distribution with constant variance and the link function is the identity, which is the canonical link if the variance is known. Under these assumptions, the least-squares estimator is obtained as the maximum-likelihood parameter estimate.
For the normal distribution, the generalized linear model has a closed form expression for the maximum-likelihood estimates, which is convenient. Most other GLMs lack closed form estimates.
=== Binary data ===
When the response data, Y, are binary (taking on only values 0 and 1), the distribution function is generally chosen to be the Bernoulli distribution and the interpretation of μi is then the probability, p, of Yi taking on the value one.
There are several popular link functions for binomial functions.
==== Logit link function ====
The most typical link function is the canonical logit link:
g
(
p
)
=
logit
p
=
ln
(
p
1
−
p
)
.
{\displaystyle g(p)=\operatorname {logit} p=\ln \left({p \over 1-p}\right).}
GLMs with this setup are logistic regression models (or logit models).
==== Probit link function as popular choice of inverse cumulative distribution function ====
Alternatively, the inverse of any continuous cumulative distribution function (CDF) can be used for the link since the CDF's range is
[
0
,
1
]
{\displaystyle [0,1]}
, the range of the binomial mean. The normal CDF
Φ
{\displaystyle \Phi }
is a popular choice and yields the probit model. Its link is
g
(
p
)
=
Φ
−
1
(
p
)
.
{\displaystyle g(p)=\Phi ^{-1}(p).\,\!}
The reason for the use of the probit model is that a constant scaling of the input variable to a normal CDF (which can be absorbed through equivalent scaling of all of the parameters) yields a function that is practically identical to the logit function, but probit models are more tractable in some situations than logit models. (In a Bayesian setting in which normally distributed prior distributions are placed on the parameters, the relationship between the normal priors and the normal CDF link function means that a probit model can be computed using Gibbs sampling, while a logit model generally cannot.)
==== Complementary log-log (cloglog) ====
The complementary log-log function may also be used:
g
(
p
)
=
log
(
−
log
(
1
−
p
)
)
.
{\displaystyle g(p)=\log(-\log(1-p)).}
This link function is asymmetric and will often produce different results from the logit and probit link functions. The cloglog model corresponds to applications where we observe either zero events (e.g., defects) or one or more, where the number of events is assumed to follow the Poisson distribution. The Poisson assumption means that
Pr
(
0
)
=
exp
(
−
μ
)
,
{\displaystyle \Pr(0)=\exp(-\mu ),}
where μ is a positive number denoting the expected number of events. If p represents the proportion of observations with at least one event, its complement
1
−
p
=
Pr
(
0
)
=
exp
(
−
μ
)
,
{\displaystyle 1-p=\Pr(0)=\exp(-\mu ),}
and then
−
log
(
1
−
p
)
=
μ
.
{\displaystyle -\log(1-p)=\mu .}
A linear model requires the response variable to take values over the entire real line. Since μ must be positive, we can enforce that by taking the logarithm, and letting log(μ) be a linear model. This produces the "cloglog" transformation
log
(
−
log
(
1
−
p
)
)
=
log
(
μ
)
.
{\displaystyle \log(-\log(1-p))=\log(\mu ).}
==== Identity link ====
The identity link g(p) = p is also sometimes used for binomial data to yield a linear probability model. However, the identity link can predict nonsense "probabilities" less than zero or greater than one. This can be avoided by using a transformation like cloglog, probit or logit (or any inverse cumulative distribution function). A primary merit of the identity link is that it can be estimated using linear math—and other standard link functions are approximately linear matching the identity link near p = 0.5.
==== Variance function ====
The variance function for "quasibinomial" data is:
Var
(
Y
i
)
=
τ
μ
i
(
1
−
μ
i
)
{\displaystyle \operatorname {Var} (Y_{i})=\tau \mu _{i}(1-\mu _{i})\,\!}
where the dispersion parameter τ is exactly 1 for the binomial distribution. Indeed, the standard binomial likelihood omits τ. When it is present, the model is called "quasibinomial", and the modified likelihood is called a quasi-likelihood, since it is not generally the likelihood corresponding to any real family of probability distributions. If τ exceeds 1, the model is said to exhibit overdispersion.
=== Multinomial regression ===
The binomial case may be easily extended to allow for a multinomial distribution as the response (also, a Generalized Linear Model for counts, with a constrained total). There are two ways in which this is usually done:
==== Ordered response ====
If the response variable is ordinal, then one may fit a model function of the form:
g
(
μ
m
)
=
η
m
=
β
0
+
X
1
β
1
+
⋯
+
X
p
β
p
+
γ
2
+
⋯
+
γ
m
=
η
1
+
γ
2
+
⋯
+
γ
m
where
μ
m
=
P
(
Y
≤
m
)
.
{\displaystyle g(\mu _{m})=\eta _{m}=\beta _{0}+X_{1}\beta _{1}+\cdots +X_{p}\beta _{p}+\gamma _{2}+\cdots +\gamma _{m}=\eta _{1}+\gamma _{2}+\cdots +\gamma _{m}{\text{ where }}\mu _{m}=\operatorname {P} (Y\leq m).\,}
for m > 2. Different links g lead to ordinal regression models like proportional odds models or ordered probit models.
==== Unordered response ====
If the response variable is a nominal measurement, or the data do not satisfy the assumptions of an ordered model, one may fit a model of the following form:
g
(
μ
m
)
=
η
m
=
β
m
,
0
+
X
1
β
m
,
1
+
⋯
+
X
p
β
m
,
p
where
μ
m
=
P
(
Y
=
m
∣
Y
∈
{
1
,
m
}
)
.
{\displaystyle g(\mu _{m})=\eta _{m}=\beta _{m,0}+X_{1}\beta _{m,1}+\cdots +X_{p}\beta _{m,p}{\text{ where }}\mu _{m}=\mathrm {P} (Y=m\mid Y\in \{1,m\}).\,}
for m > 2. Different links g lead to multinomial logit or multinomial probit models. These are more general than the ordered response models, and more parameters are estimated.
=== Count data ===
Another example of generalized linear models includes Poisson regression which models count data using the Poisson distribution. The link is typically the logarithm, the canonical link.
The variance function is proportional to the mean
var
(
Y
i
)
=
τ
μ
i
,
{\displaystyle \operatorname {var} (Y_{i})=\tau \mu _{i},\,}
where the dispersion parameter τ is typically fixed at exactly one. When it is not, the resulting quasi-likelihood model is often described as Poisson with overdispersion or quasi-Poisson.
== Extensions ==
=== Correlated or clustered data ===
The standard GLM assumes that the observations are uncorrelated. Extensions have been developed to allow for correlation between observations, as occurs for example in longitudinal studies and clustered designs:
Generalized estimating equations (GEEs) allow for the correlation between observations without the use of an explicit probability model for the origin of the correlations, so there is no explicit likelihood. They are suitable when the random effects and their variances are not of inherent interest, as they allow for the correlation without explaining its origin. The focus is on estimating the average response over the population ("population-averaged" effects) rather than the regression parameters that would enable prediction of the effect of changing one or more components of X on a given individual. GEEs are usually used in conjunction with Huber–White standard errors.
Generalized linear mixed models (GLMMs) are an extension to GLMs that includes random effects in the linear predictor, giving an explicit probability model that explains the origin of the correlations. The resulting "subject-specific" parameter estimates are suitable when the focus is on estimating the effect of changing one or more components of X on a given individual. GLMMs are also referred to as multilevel models and as mixed model. In general, fitting GLMMs is more computationally complex and intensive than fitting GEEs.
=== Generalized additive models ===
Generalized additive models (GAMs) are another extension to GLMs in which the linear predictor η is not restricted to be linear in the covariates X but is the sum of smoothing functions applied to the xis:
η
=
β
0
+
f
1
(
x
1
)
+
f
2
(
x
2
)
+
⋯
{\displaystyle \eta =\beta _{0}+f_{1}(x_{1})+f_{2}(x_{2})+\cdots \,\!}
The smoothing functions fi are estimated from the data. In general this requires a large number of data points and is computationally intensive.
== See also ==
Response modeling methodology
Comparison of general and generalized linear models – Statistical linear modelPages displaying short descriptions of redirect targets
Fractional model
Generalized linear array model – model used for analyzing data sets with array structuresPages displaying wikidata descriptions as a fallback
GLIM (software) – statistical software program for fitting generalized linear modelsPages displaying wikidata descriptions as a fallback
Quasi-variance
Natural exponential family – class of probability distributions that is a special case of an exponential familyPages displaying wikidata descriptions as a fallback
Tweedie distribution – Family of probability distributions
Variance functions – Smooth function in statisticsPages displaying short descriptions of redirect targets
Vector generalized linear model (VGLM)
Generalized estimating equation
== References ==
=== Citations ===
=== Bibliography ===
== Further reading ==
Dunn, P.K.; Smyth, G.K. (2018). Generalized Linear Models With Examples in R. New York: Springer. doi:10.1007/978-1-4419-0118-7. ISBN 978-1-4419-0118-7.{{cite book}}: CS1 maint: publisher location (link)
Dobson, A.J.; Barnett, A.G. (2008). Introduction to Generalized Linear Models (3rd ed.). Boca Raton, FL: Chapman and Hall/CRC. ISBN 978-1-58488-165-0.
Hardin, James; Hilbe, Joseph (2007). Generalized Linear Models and Extensions (2nd ed.). College Station: Stata Press. ISBN 978-1-59718-014-6.{{cite book}}: CS1 maint: publisher location (link)
== External links ==
Media related to Generalized linear models at Wikimedia Commons | Wikipedia/Generalised_linear_model |
NeuroSolutions is a neural network development environment developed by NeuroDimension. It combines a modular, icon-based (component-based) network design interface with an implementation of advanced learning procedures, such as conjugate gradients, the Levenberg-Marquardt algorithm, and back-propagation through time. The software is used to design, train, and deploy artificial neural network (supervised learning and unsupervised learning) models to perform a wide variety of tasks such as data mining, classification, function approximation, multivariate regression and time-series prediction.
== Neural network construction wizards ==
NeuroSolutions provides three separate wizards for automatically building neural network models:
=== Data Manager ===
The Data Manager module allows the user to import data from Microsoft Access, Microsoft Excel or text files and perform various preprocessing and data analysis operations. From the Data Manager, the user can load the data directly into a NeuroSolutions breadboard or use the data to create a new neural network.
=== NeuralBuilder ===
The NeuralBuilder centers the design specifications on the specific neural network architecture the user wishes to build. Some of the most common architectures include:
Multilayer perceptron (MLP)
Generalized feedforward
Modular (programming)
Jordan/Elman
Principal component analysis (PCA)
Radial basis function network (RBF)
General regression neural network (GRNN)
Probabilistic neural network (PNN)
Self-organizing map (SOM)
Time-lag recurrent network (TLRN)
Recurrent neural network
CANFIS network (Fuzzy logic)
Support vector machine (SVM)
Once the neural network architecture is selected, the user can customize parameters such as the number of hidden layers, the number of processing elements and the learning algorithm. A genetic algorithm can also be used to automatically optimize the settings.
=== Neural Expert ===
The Neural Expert centers the design specifications around the type of problem the user would like the neural network to solve (classification, prediction, function approximation or clustering). Given this problem type and the size of the user's data set, the Neural Expert automatically selects the neural network size and architecture that will likely produce a good solution. A beginner setting also exists which hides some of the more advanced operations such as cross validation and genetic optimization.
=== User-defined neural networks ===
NeuroSolutions is based on the concept that neural networks can be broken down into a fundamental set of neural components. Individually these components are relatively simplistic, but several components connected together can result in networks capable of solving very complex problems. The network construction wizards will connect these components based on the user's specifications. However, once the network is built, the interconnections can be arbitrarily changed and components can be added or removed. NeuroSolutions also allows for the integration of algorithms through dynamic link libraries (DLL). Every NeuroSolutions component implements a function conforming to a simple protocol in C. To add a new component, modify the template function for the base component and then compile the code into a DLL.
== Neural network deployment ==
NeuroDimension, Inc. provides three ways for NeuroSolutions to deploy a custom neural network solution for applications: code generation, DLL generation, and OLE generation.
=== Code generation ===
NeuroSolutions can automatically generate C++ source code for a neural network designed within its graphical user interface. This provides the flexibility to customize the neural network code for that particular application. Since the generated code is ANSI-compliant, the user can deploy the neural network solution to other platforms such as UNIX.
=== DLL generation ===
The Custom Solution Wizard is an optional add-on product that will take a neural network designed within NeuroSolutions and encapsulate it into a dynamic link library (DLL) that conforms to a simple protocol. The DLL can then be embedded into the user's own C++, Visual Basic, Microsoft Excel, Microsoft Access or Internet (ASP) application, without requiring advanced programming skills.
=== OLE automation ===
This technology provides the ability to programmatically control NeuroSolutions from any external application that supports automation, such as Microsoft Excel, Microsoft Access, and applications developed with Visual Basic or Visual C++. In the simplest case, the application developer could send NeuroSolutions the data to process, tell it to begin processing, and then retrieve the results back into the application. However, with its extensive protocol, NeuroSolutions can also do more complex tasks.
== See also ==
Machine learning
== References == | Wikipedia/NeuroSolutions |
Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations.
Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. More generally, the concept of regression tree can be extended to any kind of object equipped with pairwise dissimilarities such as categorical sequences.
Decision trees are among the most popular machine learning algorithms given their intelligibility and simplicity because they produce algorithms that are easy to interpret and visualize, even for users without a statistical background.
In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data (but the resulting classification tree can be an input for decision making).
== General ==
Decision tree learning is a method commonly used in data mining. The goal is to create an algorithm that predicts the value of a target variable based on several input variables.
A decision tree is a simple representation for classifying examples. For this section, assume that all of the input features have finite discrete domains, and there is a single target feature called the "classification". Each element of the domain of the classification is called a class.
A decision tree or a classification tree is a tree in which each internal (non-leaf) node is labeled with an input feature. The arcs coming from a node labeled with an input feature are labeled with each of the possible values of the target feature or the arc leads to a subordinate decision node on a different input feature. Each leaf of the tree is labeled with a class or a probability distribution over the classes, signifying that the data set has been classified by the tree into either a specific class, or into a particular probability distribution (which, if the decision tree is well-constructed, is skewed towards certain subsets of classes).
A tree is built by splitting the source set, constituting the root node of the tree, into subsets—which constitute the successor children. The splitting is based on a set of splitting rules based on classification features. This process is repeated on each derived subset in a recursive manner called recursive partitioning.
The recursion is completed when the subset at a node has all the same values of the target variable, or when splitting no longer adds value to the predictions. This process of top-down induction of decision trees (TDIDT) is an example of a greedy algorithm, and it is by far the most common strategy for learning decision trees from data.
In data mining, decision trees can be described also as the combination of mathematical and computational techniques to aid the description, categorization and generalization of a given set of data.
Data comes in records of the form:
(
x
,
Y
)
=
(
x
1
,
x
2
,
x
3
,
.
.
.
,
x
k
,
Y
)
{\displaystyle ({\textbf {x}},Y)=(x_{1},x_{2},x_{3},...,x_{k},Y)}
The dependent variable,
Y
{\displaystyle Y}
, is the target variable that we are trying to understand, classify or generalize. The vector
x
{\displaystyle {\textbf {x}}}
is composed of the features,
x
1
,
x
2
,
x
3
{\displaystyle x_{1},x_{2},x_{3}}
etc., that are used for that task.
== Decision tree types ==
Decision trees used in data mining are of two main types:
Classification tree analysis is when the predicted outcome is the class (discrete) to which the data belongs.
Regression tree analysis is when the predicted outcome can be considered a real number (e.g. the price of a house, or a patient's length of stay in a hospital).
The term classification and regression tree (CART) analysis is an umbrella term used to refer to either of the above procedures, first introduced by Breiman et al. in 1984. Trees used for regression and trees used for classification have some similarities – but also some differences, such as the procedure used to determine where to split.
Some techniques, often called ensemble methods, construct more than one decision tree:
Boosted trees Incrementally building an ensemble by training each new instance to emphasize the training instances previously mis-modeled. A typical example is AdaBoost. These can be used for regression-type and classification-type problems.
Committees of decision trees (also called k-DT), an early method that used randomized decision tree algorithms to generate multiple different trees from the training data, and then combine them using majority voting to generate output.
Bootstrap aggregated (or bagged) decision trees, an early ensemble method, builds multiple decision trees by repeatedly resampling training data with replacement, and voting the trees for a consensus prediction.
A random forest classifier is a specific type of bootstrap aggregating
Rotation forest – in which every decision tree is trained by first applying principal component analysis (PCA) on a random subset of the input features.
A special case of a decision tree is a decision list, which is a one-sided decision tree, so that every internal node has exactly 1 leaf node and exactly 1 internal node as a child (except for the bottommost node, whose only child is a single leaf node). While less expressive, decision lists are arguably easier to understand than general decision trees due to their added sparsity, permit non-greedy learning methods and monotonic constraints to be imposed.
Notable decision tree algorithms include:
ID3 (Iterative Dichotomiser 3)
C4.5 (successor of ID3)
CART (Classification And Regression Tree)
OC1 (Oblique classifier 1). First method that created multivariate splits at each node.
Chi-square automatic interaction detection (CHAID). Performs multi-level splits when computing classification trees.
MARS: extends decision trees to handle numerical data better.
Conditional Inference Trees. Statistics-based approach that uses non-parametric tests as splitting criteria, corrected for multiple testing to avoid overfitting. This approach results in unbiased predictor selection and does not require pruning.
ID3 and CART were invented independently at around the same time (between 1970 and 1980), yet follow a similar approach for learning a decision tree from training tuples.
It has also been proposed to leverage concepts of fuzzy set theory for the definition of a special version of decision tree, known as Fuzzy Decision Tree (FDT).
In this type of fuzzy classification, generally, an input vector
x
{\displaystyle {\textbf {x}}}
is associated with multiple classes, each with a different confidence value.
Boosted ensembles of FDTs have been recently investigated as well, and they have shown performances comparable to those of other very efficient fuzzy classifiers.
== Metrics ==
Algorithms for constructing decision trees usually work top-down, by choosing a variable at each step that best splits the set of items. Different algorithms use different metrics for measuring "best". These generally measure the homogeneity of the target variable within the subsets. Some examples are given below. These metrics are applied to each candidate subset, and the resulting values are combined (e.g., averaged) to provide a measure of the quality of the split. Depending on the underlying metric, the performance of various heuristic algorithms for decision tree learning may vary significantly.
=== Estimate of Positive Correctness ===
A simple and effective metric can be used to identify the degree to which true positives outweigh false positives (see Confusion matrix). This metric, "Estimate of Positive Correctness" is defined below:
E
P
=
T
P
−
F
P
{\displaystyle E_{P}=TP-FP}
In this equation, the total false positives (FP) are subtracted from the total true positives (TP). The resulting number gives an estimate on how many positive examples the feature could correctly identify within the data, with higher numbers meaning that the feature could correctly classify more positive samples. Below is an example of how to use the metric when the full confusion matrix of a certain feature is given:
Feature A Confusion Matrix
Here we can see that the TP value would be 8 and the FP value would be 2 (the underlined numbers in the table). When we plug these numbers in the equation we are able to calculate the estimate:
E
p
=
T
P
−
F
P
=
8
−
2
=
6
{\displaystyle E_{p}=TP-FP=8-2=6}
. This means that using the estimate on this feature would have it receive a score of 6.
However, it should be worth noting that this number is only an estimate. For example, if two features both had a FP value of 2 while one of the features had a higher TP value, that feature would be ranked higher than the other because the resulting estimate when using the equation would give a higher value. This could lead to some inaccuracies when using the metric if some features have more positive samples than others. To combat this, one could use a more powerful metric known as Sensitivity that takes into account the proportions of the values from the confusion matrix to give the actual true positive rate (TPR). The difference between these metrics is shown in the example below:
In this example, Feature A had an estimate of 6 and a TPR of approximately 0.73 while Feature B had an estimate of 4 and a TPR of 0.75. This shows that although the positive estimate for some feature may be higher, the more accurate TPR value for that feature may be lower when compared to other features that have a lower positive estimate. Depending on the situation and knowledge of the data and decision trees, one may opt to use the positive estimate for a quick and easy solution to their problem. On the other hand, a more experienced user would most likely prefer to use the TPR value to rank the features because it takes into account the proportions of the data and all the samples that should have been classified as positive.
=== Gini impurity ===
Gini impurity, Gini's diversity index, or Gini-Simpson Index in biodiversity research, is named after Italian mathematician Corrado Gini and used by the CART (classification and regression tree) algorithm for classification trees. Gini impurity measures how often a randomly chosen element of a set would be incorrectly labeled if it were labeled randomly and independently according to the distribution of labels in the set. It reaches its minimum (zero) when all cases in the node fall into a single target category.
For a set of items with
J
{\displaystyle J}
classes and relative frequencies
p
i
{\displaystyle p_{i}}
,
i
∈
{
1
,
2
,
.
.
.
,
J
}
{\displaystyle i\in \{1,2,...,J\}}
, the probability of choosing an item with label
i
{\displaystyle i}
is
p
i
{\displaystyle p_{i}}
, and the probability of miscategorizing that item is
∑
k
≠
i
p
k
=
1
−
p
i
{\displaystyle \sum _{k\neq i}p_{k}=1-p_{i}}
. The Gini impurity is computed by summing pairwise products of these probabilities for each class label:
I
G
(
p
)
=
∑
i
=
1
J
(
p
i
∑
k
≠
i
p
k
)
=
∑
i
=
1
J
p
i
(
1
−
p
i
)
=
∑
i
=
1
J
(
p
i
−
p
i
2
)
=
∑
i
=
1
J
p
i
−
∑
i
=
1
J
p
i
2
=
1
−
∑
i
=
1
J
p
i
2
.
{\displaystyle \operatorname {I} _{G}(p)=\sum _{i=1}^{J}\left(p_{i}\sum _{k\neq i}p_{k}\right)=\sum _{i=1}^{J}p_{i}(1-p_{i})=\sum _{i=1}^{J}(p_{i}-p_{i}^{2})=\sum _{i=1}^{J}p_{i}-\sum _{i=1}^{J}p_{i}^{2}=1-\sum _{i=1}^{J}p_{i}^{2}.}
The Gini impurity is also an information theoretic measure and corresponds to Tsallis Entropy with deformation coefficient
q
=
2
{\displaystyle q=2}
, which in physics is associated with the lack of information in out-of-equilibrium, non-extensive, dissipative and quantum systems. For the limit
q
→
1
{\displaystyle q\to 1}
one recovers the usual Boltzmann-Gibbs or Shannon entropy. In this sense, the Gini impurity is nothing but a variation of the usual entropy measure for decision trees.
=== Information gain ===
Used by the ID3, C4.5 and C5.0 tree-generation algorithms. Information gain is based on the concept of entropy and information content from information theory.
Entropy is defined as below
H
(
T
)
=
I
E
(
p
1
,
p
2
,
…
,
p
J
)
=
−
∑
i
=
1
J
p
i
log
2
p
i
{\displaystyle \mathrm {H} (T)=\operatorname {I} _{E}\left(p_{1},p_{2},\ldots ,p_{J}\right)=-\sum _{i=1}^{J}p_{i}\log _{2}p_{i}}
where
p
1
,
p
2
,
…
{\displaystyle p_{1},p_{2},\ldots }
are fractions that add up to 1 and represent the percentage of each class present in the child node that results from a split in the tree.
I
G
(
T
,
a
)
⏞
information gain
=
H
(
T
)
⏞
entropy (parent)
−
H
(
T
∣
a
)
⏞
sum of entropies (children)
{\displaystyle \overbrace {IG(T,a)} ^{\text{information gain}}=\overbrace {\mathrm {H} (T)} ^{\text{entropy (parent)}}-\overbrace {\mathrm {H} (T\mid a)} ^{\text{sum of entropies (children)}}}
=
−
∑
i
=
1
J
p
i
log
2
p
i
−
∑
i
=
1
J
−
Pr
(
i
∣
a
)
log
2
Pr
(
i
∣
a
)
{\displaystyle =-\sum _{i=1}^{J}p_{i}\log _{2}p_{i}-\sum _{i=1}^{J}-\Pr(i\mid a)\log _{2}\Pr(i\mid a)}
Averaging over the possible values of
A
{\displaystyle A}
,
E
A
(
IG
(
T
,
a
)
)
⏞
expected information gain
=
I
(
T
;
A
)
⏞
mutual information between
T
and
A
=
H
(
T
)
⏞
entropy (parent)
−
H
(
T
∣
A
)
⏞
weighted sum of entropies (children)
{\displaystyle \overbrace {E_{A}(\operatorname {IG} (T,a))} ^{\text{expected information gain}}=\overbrace {I(T;A)} ^{{\text{mutual information between }}T{\text{ and }}A}=\overbrace {\mathrm {H} (T)} ^{\text{entropy (parent)}}-\overbrace {\mathrm {H} (T\mid A)} ^{\text{weighted sum of entropies (children)}}}
=
−
∑
i
=
1
J
p
i
log
2
p
i
−
∑
a
p
(
a
)
∑
i
=
1
J
−
Pr
(
i
∣
a
)
log
2
Pr
(
i
∣
a
)
{\displaystyle =-\sum _{i=1}^{J}p_{i}\log _{2}p_{i}-\sum _{a}p(a)\sum _{i=1}^{J}-\Pr(i\mid a)\log _{2}\Pr(i\mid a)}
Where weighted sum of entropies is given by,
H
(
T
∣
A
)
=
∑
a
p
(
a
)
∑
i
=
1
J
−
Pr
(
i
∣
a
)
log
2
Pr
(
i
∣
a
)
{\displaystyle {\mathrm {H} (T\mid A)}=\sum _{a}p(a)\sum _{i=1}^{J}-\Pr(i\mid a)\log _{2}\Pr(i\mid a)}
That is, the expected information gain is the mutual information, meaning that on average, the reduction in the entropy of T is the mutual information.
Information gain is used to decide which feature to split on at each step in building the tree. Simplicity is best, so we want to keep our tree small. To do so, at each step we should choose the split that results in the most consistent child nodes. A commonly used measure of consistency is called information which is measured in bits. For each node of the tree, the information value "represents the expected amount of information that would be needed to specify whether a new instance should be classified yes or no, given that the example reached that node".
Consider an example data set with four attributes: outlook (sunny, overcast, rainy), temperature (hot, mild, cool), humidity (high, normal), and windy (true, false), with a binary (yes or no) target variable, play, and 14 data points. To construct a decision tree on this data, we need to compare the information gain of each of four trees, each split on one of the four features. The split with the highest information gain will be taken as the first split and the process will continue until all children nodes each have consistent data, or until the information gain is 0.
To find the information gain of the split using windy, we must first calculate the information in the data before the split. The original data contained nine yes's and five no's.
I
E
(
[
9
,
5
]
)
=
−
9
14
log
2
9
14
−
5
14
log
2
5
14
=
0.94
{\displaystyle I_{E}([9,5])=-{\frac {9}{14}}\log _{2}{\frac {9}{14}}-{\frac {5}{14}}\log _{2}{\frac {5}{14}}=0.94}
The split using the feature windy results in two children nodes, one for a windy value of true and one for a windy value of false. In this data set, there are six data points with a true windy value, three of which have a play (where play is the target variable) value of yes and three with a play value of no. The eight remaining data points with a windy value of false contain two no's and six yes's. The information of the windy=true node is calculated using the entropy equation above. Since there is an equal number of yes's and no's in this node, we have
I
E
(
[
3
,
3
]
)
=
−
3
6
log
2
3
6
−
3
6
log
2
3
6
=
−
1
2
log
2
1
2
−
1
2
log
2
1
2
=
1
{\displaystyle I_{E}([3,3])=-{\frac {3}{6}}\log _{2}{\frac {3}{6}}-{\frac {3}{6}}\log _{2}{\frac {3}{6}}=-{\frac {1}{2}}\log _{2}{\frac {1}{2}}-{\frac {1}{2}}\log _{2}{\frac {1}{2}}=1}
For the node where windy=false there were eight data points, six yes's and two no's. Thus we have
I
E
(
[
6
,
2
]
)
=
−
6
8
log
2
6
8
−
2
8
log
2
2
8
=
−
3
4
log
2
3
4
−
1
4
log
2
1
4
=
0.81
{\displaystyle I_{E}([6,2])=-{\frac {6}{8}}\log _{2}{\frac {6}{8}}-{\frac {2}{8}}\log _{2}{\frac {2}{8}}=-{\frac {3}{4}}\log _{2}{\frac {3}{4}}-{\frac {1}{4}}\log _{2}{\frac {1}{4}}=0.81}
To find the information of the split, we take the weighted average of these two numbers based on how many observations fell into which node.
I
E
(
[
3
,
3
]
,
[
6
,
2
]
)
=
I
E
(
windy or not
)
=
6
14
⋅
1
+
8
14
⋅
0.81
=
0.89
{\displaystyle I_{E}([3,3],[6,2])=I_{E}({\text{windy or not}})={\frac {6}{14}}\cdot 1+{\frac {8}{14}}\cdot 0.81=0.89}
Now we can calculate the information gain achieved by splitting on the windy feature.
IG
(
windy
)
=
I
E
(
[
9
,
5
]
)
−
I
E
(
[
3
,
3
]
,
[
6
,
2
]
)
=
0.94
−
0.89
=
0.05
{\displaystyle \operatorname {IG} ({\text{windy}})=I_{E}([9,5])-I_{E}([3,3],[6,2])=0.94-0.89=0.05}
To build the tree, the information gain of each possible first split would need to be calculated. The best first split is the one that provides the most information gain. This process is repeated for each impure node until the tree is complete. This example is adapted from the example appearing in Witten et al.
Information gain is also known as Shannon index in bio diversity research.
=== Variance reduction ===
Introduced in CART, variance reduction is often employed in cases where the target variable is continuous (regression tree), meaning that use of many other metrics would first require discretization before being applied. The variance reduction of a node N is defined as the total reduction of the variance of the target variable Y due to the split at this node:
I
V
(
N
)
=
1
|
S
|
2
∑
i
∈
S
∑
j
∈
S
1
2
(
y
i
−
y
j
)
2
−
(
|
S
t
|
2
|
S
|
2
1
|
S
t
|
2
∑
i
∈
S
t
∑
j
∈
S
t
1
2
(
y
i
−
y
j
)
2
+
|
S
f
|
2
|
S
|
2
1
|
S
f
|
2
∑
i
∈
S
f
∑
j
∈
S
f
1
2
(
y
i
−
y
j
)
2
)
{\displaystyle I_{V}(N)={\frac {1}{|S|^{2}}}\sum _{i\in S}\sum _{j\in S}{\frac {1}{2}}(y_{i}-y_{j})^{2}-\left({\frac {|S_{t}|^{2}}{|S|^{2}}}{\frac {1}{|S_{t}|^{2}}}\sum _{i\in S_{t}}\sum _{j\in S_{t}}{\frac {1}{2}}(y_{i}-y_{j})^{2}+{\frac {|S_{f}|^{2}}{|S|^{2}}}{\frac {1}{|S_{f}|^{2}}}\sum _{i\in S_{f}}\sum _{j\in S_{f}}{\frac {1}{2}}(y_{i}-y_{j})^{2}\right)}
where
S
{\displaystyle S}
,
S
t
{\displaystyle S_{t}}
, and
S
f
{\displaystyle S_{f}}
are the set of presplit sample indices, set of sample indices for which the split test is true, and set of sample indices for which the split test is false, respectively. Each of the above summands are indeed variance estimates, though, written in a form without directly referring to the mean.
By replacing
(
y
i
−
y
j
)
2
{\displaystyle (y_{i}-y_{j})^{2}}
in the formula above with the dissimilarity
d
i
j
{\displaystyle d_{ij}}
between two objects
i
{\displaystyle i}
and
j
{\displaystyle j}
, the variance reduction criterion applies to any kind of object for which pairwise dissimilarities can be computed.
=== Measure of "goodness" ===
Used by CART in 1984, the measure of "goodness" is a function that seeks to optimize the balance of a candidate split's capacity to create pure children with its capacity to create equally-sized children. This process is repeated for each impure node until the tree is complete. The function
φ
(
s
∣
t
)
{\displaystyle \varphi (s\mid t)}
, where
s
{\displaystyle s}
is a candidate split at node
t
{\displaystyle t}
, is defined as below
φ
(
s
∣
t
)
=
2
P
L
P
R
∑
j
=
1
class count
|
P
(
j
∣
t
L
)
−
P
(
j
∣
t
R
)
|
{\displaystyle \varphi (s\mid t)=2P_{L}P_{R}\sum _{j=1}^{\text{class count}}|P(j\mid t_{L})-P(j\mid t_{R})|}
where
t
L
{\displaystyle t_{L}}
and
t
R
{\displaystyle t_{R}}
are the left and right children of node
t
{\displaystyle t}
using split
s
{\displaystyle s}
, respectively;
P
L
{\displaystyle P_{L}}
and
P
R
{\displaystyle P_{R}}
are the proportions of records in
t
{\displaystyle t}
in
t
L
{\displaystyle t_{L}}
and
t
R
{\displaystyle t_{R}}
, respectively; and
P
(
j
∣
t
L
)
{\displaystyle P(j\mid t_{L})}
and
P
(
j
∣
t
R
)
{\displaystyle P(j\mid t_{R})}
are the proportions of class
j
{\displaystyle j}
records in
t
L
{\displaystyle t_{L}}
and
t
R
{\displaystyle t_{R}}
, respectively.
Consider an example data set with three attributes: savings(low, medium, high), assets(low, medium, high), income(numerical value), and a binary target variable credit risk(good, bad) and 8 data points. The full data is presented in the table below. To start a decision tree, we will calculate the maximum value of
φ
(
s
∣
t
)
{\displaystyle \varphi (s\mid t)}
using each feature to find which one will split the root node. This process will continue until all children are pure or all
φ
(
s
∣
t
)
{\displaystyle \varphi (s\mid t)}
values are below a set threshold.
To find
φ
(
s
∣
t
)
{\displaystyle \varphi (s\mid t)}
of the feature savings, we need to note the quantity of each value. The original data contained three low's, three medium's, and two high's. Out of the low's, one had a good credit risk while out of the medium's and high's, 4 had a good credit risk. Assume a candidate split
s
{\displaystyle s}
such that records with a low savings will be put in the left child and all other records will be put into the right child.
φ
(
s
∣
root
)
=
2
⋅
3
8
⋅
5
8
⋅
(
|
(
1
3
−
4
5
)
|
+
|
(
2
3
−
1
5
)
|
)
=
0.44
{\displaystyle \varphi (s\mid {\text{root}})=2\cdot {\frac {3}{8}}\cdot {\frac {5}{8}}\cdot \left(\left|\left({\frac {1}{3}}-{\frac {4}{5}}\right)\right|+\left|\left({\frac {2}{3}}-{\frac {1}{5}}\right)\right|\right)=0.44}
To build the tree, the "goodness" of all candidate splits for the root node need to be calculated. The candidate with the maximum value will split the root node, and the process will continue for each impure node until the tree is complete.
Compared to other metrics such as information gain, the measure of "goodness" will attempt to create a more balanced tree, leading to more-consistent decision time. However, it sacrifices some priority for creating pure children which can lead to additional splits that are not present with other metrics.
== Uses ==
=== Advantages ===
Amongst other data mining methods, decision trees have various advantages:
Simple to understand and interpret. People are able to understand decision tree models after a brief explanation. Trees can also be displayed graphically in a way that is easy for non-experts to interpret.
Able to handle both numerical and categorical data. Other techniques are usually specialized in analyzing datasets that have only one type of variable. (For example, relation rules can be used only with nominal variables while neural networks can be used only with numerical variables or categoricals converted to 0-1 values.) Early decision trees were only capable of handling categorical variables, but more recent versions, such as C4.5, do not have this limitation.
Requires little data preparation. Other techniques often require data normalization. Since trees can handle qualitative predictors, there is no need to create dummy variables.
Uses a white box or open-box model. If a given situation is observable in a model the explanation for the condition is easily explained by Boolean logic. By contrast, in a black box model, the explanation for the results is typically difficult to understand, for example with an artificial neural network.
Possible to validate a model using statistical tests. That makes it possible to account for the reliability of the model.
Non-parametric approach that makes no assumptions of the training data or prediction residuals; e.g., no distributional, independence, or constant variance assumptions
Performs well with large datasets. Large amounts of data can be analyzed using standard computing resources in reasonable time.
Accuracy with flexible modeling. These methods may be applied to healthcare research with increased accuracy.
Mirrors human decision making more closely than other approaches. This could be useful when modeling human decisions/behavior.
Robust against co-linearity, particularly boosting.
In built feature selection. Additional irrelevant feature will be less used so that they can be removed on subsequent runs. The hierarchy of attributes in a decision tree reflects the importance of attributes. It means that the features on top are the most informative.
Decision trees can approximate any Boolean function e.g. XOR.
=== Limitations ===
Trees can be very non-robust. A small change in the training data can result in a large change in the tree and consequently the final predictions.
The problem of learning an optimal decision tree is known to be NP-complete under several aspects of optimality and even for simple concepts. Consequently, practical decision-tree learning algorithms are based on heuristics such as the greedy algorithm where locally optimal decisions are made at each node. Such algorithms cannot guarantee to return the globally optimal decision tree. To reduce the greedy effect of local optimality, some methods such as the dual information distance (DID) tree were proposed.
Decision-tree learners can create over-complex trees that do not generalize well from the training data. (This is known as overfitting.) Mechanisms such as pruning are necessary to avoid this problem (with the exception of some algorithms such as the Conditional Inference approach, that does not require pruning).
The average depth of the tree that is defined by the number of nodes or tests till classification is not guaranteed to be minimal or small under various splitting criteria.
For data including categorical variables with different numbers of levels, information gain in decision trees is biased in favor of attributes with more levels. To counter this problem, instead of choosing the attribute with highest information gain, one can choose the attribute with the highest information gain ratio among the attributes whose information gain is greater than the mean information gain. This biases the decision tree against considering attributes with a large number of distinct values, while not giving an unfair advantage to attributes with very low information gain. Alternatively, the issue of biased predictor selection can be avoided by the Conditional Inference approach, a two-stage approach, or adaptive leave-one-out feature selection.
=== Implementations ===
Many data mining software packages provide implementations of one or more decision tree algorithms (e.g. random forest).
Open source examples include:
ALGLIB, a C++, C# and Java numerical analysis library with data analysis features (random forest)
KNIME, a free and open-source data analytics, reporting and integration platform (decision trees, random forest)
Orange, an open-source data visualization, machine learning and data mining toolkit (random forest)
R (an open-source software environment for statistical computing, which includes several CART implementations such as rpart, party and randomForest packages),
scikit-learn (a free and open-source machine learning library for the Python programming language).
Weka (a free and open-source data-mining suite, contains many decision tree algorithms),
Notable commercial software:
MATLAB,
Microsoft SQL Server, and
RapidMiner,
SAS Enterprise Miner,
IBM SPSS Modeler,
== Extensions ==
=== Decision graphs ===
In a decision tree, all paths from the root node to the leaf node proceed by way of conjunction, or AND. In a decision graph, it is possible to use disjunctions (ORs) to join two more paths together using minimum message length (MML). Decision graphs have been further extended to allow for previously unstated new attributes to be learnt dynamically and used at different places within the graph. The more general coding scheme results in better predictive accuracy and log-loss probabilistic scoring. In general, decision graphs infer models with fewer leaves than decision trees.
=== Alternative search methods ===
Evolutionary algorithms have been used to avoid local optimal decisions and search the decision tree space with little a priori bias.
It is also possible for a tree to be sampled using MCMC.
The tree can be searched for in a bottom-up fashion. Or several trees can be constructed parallelly to reduce the expected number of tests till classification.
== See also ==
== References ==
== Further reading ==
James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert (2017). "Tree-Based Methods" (PDF). An Introduction to Statistical Learning: with Applications in R. New York: Springer. pp. 303–336. ISBN 978-1-4614-7137-0.
== External links ==
Evolutionary Learning of Decision Trees in C++
A very detailed explanation of information gain as splitting criterion | Wikipedia/Tree-based_models |
Applying machine learning (ML) (including deep learning) methods to the study of quantum systems is an emergent area of physics research. A basic example of this is quantum state tomography, where a quantum state is learned from measurement. Other examples include learning Hamiltonians, learning quantum phase transitions, and automatically generating new quantum experiments. ML is effective at processing large amounts of experimental or calculated data in order to characterize an unknown quantum system, making its application useful in contexts including quantum information theory, quantum technology development, and computational materials design. In this context, for example, it can be used as a tool to interpolate pre-calculated interatomic potentials, or directly solving the Schrödinger equation with a variational method.
== Applications of machine learning to physics ==
=== Noisy data ===
The ability to experimentally control and prepare increasingly complex quantum systems brings with it a growing need to turn large and noisy data sets into meaningful information. This is a problem that has already been studied extensively in the classical setting, and consequently, many existing machine learning techniques can be naturally adapted to more efficiently address experimentally relevant problems. For example, Bayesian methods and concepts of algorithmic learning can be fruitfully applied to tackle quantum state classification, Hamiltonian learning, and the characterization of an unknown unitary transformation. Other problems that have been addressed with this approach are given in the following list:
Identifying an accurate model for the dynamics of a quantum system, through the reconstruction of the Hamiltonian;
Extracting information on unknown states;
Learning unknown unitary transformations and measurements;
Engineering of quantum gates from qubit networks with pairwise interactions, using time dependent or independent Hamiltonians.
Improving the extraction accuracy of physical observables from absorption images of ultracold atoms (degenerate Fermi gas), by the generation of an ideal reference frame.
=== Calculated and noise-free data ===
Quantum machine learning can also be applied to dramatically accelerate the prediction of quantum properties of molecules and materials. This can be helpful for the computational design of new molecules or materials. Some examples include
Interpolating interatomic potentials;
Inferring molecular atomization energies throughout chemical compound space;
Accurate potential energy surfaces with restricted Boltzmann machines;
Automatic generation of new quantum experiments;
Solving the many-body, static and time-dependent Schrödinger equation;
Identifying phase transitions from entanglement spectra;
Generating adaptive feedback schemes for quantum metrology and quantum tomography.
=== Variational circuits ===
Variational circuits are a family of algorithms which utilize training based on circuit parameters and an objective function. Variational circuits are generally composed of a classical device communicating input parameters (random or pre-trained parameters) into a quantum device, along with a classical Mathematical optimization function. These circuits are very heavily dependent on the architecture of the proposed quantum device because parameter adjustments are adjusted based solely on the classical components within the device. Though the application is considerably infantile in the field of quantum machine learning, it has incredibly high promise for more efficiently generating efficient optimization functions.
=== Sign problem ===
Machine learning techniques can be used to find a better manifold of integration for path integrals in order to avoid the sign problem.
=== Fluid dynamics ===
=== Physics discovery and prediction ===
A deep learning system was reported to learn intuitive physics from visual data (of virtual 3D environments) based on an unpublished approach inspired by studies of visual cognition in infants. Other researchers have developed a machine learning algorithm that could discover sets of basic variables of various physical systems and predict the systems' future dynamics from video recordings of their behavior. In the future, it may be possible that such can be used to automate the discovery of physical laws of complex systems. Beyond discovery and prediction, "blank slate"-type of learning of fundamental aspects of the physical world may have further applications such as improving adaptive and broad artificial general intelligence. In specific, prior machine learning models were "highly specialised and lack a general understanding of the world".
== See also ==
Quantum computing
Quantum machine learning
Quantum annealing
Quantum neural network
HHL Algorithm
== References == | Wikipedia/Machine_learning_in_physics |
Sun Microsystems, Inc., often known as Sun for short, was an American technology company that existed from 1982 to 2010 which developed and sold computers, computer components, software, and information technology services. Sun contributed significantly to the evolution of several key computing technologies, among them Unix, RISC processors, thin client computing, and virtualized computing. At its height, the Sun headquarters were in Santa Clara, California (part of Silicon Valley), on the former west campus of the Agnews Developmental Center.
Sun products included computer servers and workstations built on its own RISC-based SPARC processor architecture, as well as on x86-based AMD Opteron and Intel Xeon processors. Sun also developed its own storage systems and a suite of software products, including the Unix-based SunOS and later Solaris operating systems, developer tools, Web infrastructure software, and identity management applications. Technologies that Sun created include the Java programming language, the Java platform and Network File System (NFS).
In general, Sun was a proponent of open systems, particularly Unix. It was also a major contributor to open-source software, as evidenced by its $1 billion purchase, in 2008, of MySQL, an open-source relational database management system. Other notable Sun acquisitions include Cray Business Systems Division, Storagetek, and Innotek GmbH, creators of VirtualBox. On April 20, 2009, it was announced that Oracle would acquire Sun for US$7.4 billion. The deal was completed on January 27, 2010.
== History ==
The initial design for what became Sun's first Unix workstation, the Sun-1, was conceived by Andy Bechtolsheim when he was a graduate student at Stanford University in Palo Alto, California. Bechtolsheim originally designed the SUN workstation for the Stanford University Network communications project as a personal CAD workstation. It was designed around the Motorola 68000 processor with an advanced memory management unit (MMU) to support the Unix operating system with virtual memory support. He built the first examples from spare parts obtained from Stanford's Department of Computer Science and Silicon Valley supply houses.
On February 24, 1982, Scott McNealy, Andy Bechtolsheim, and Vinod Khosla, all Stanford graduate students, founded Sun Microsystems. Bill Joy of Berkeley, a primary developer of the Berkeley Software Distribution (BSD), joined soon after and is counted as one of the original founders. The company was the second, after rival Apollo Computer, to specialize in workstations. The name "Sun" is derived from the initials of the Stanford University Network (SUN). Sun was profitable from its first quarter in July 1982.
By 1983, Sun was known for producing 68k-based systems with high-quality graphics that were the only computers other than DEC's VAX to run 4.2BSD. It licensed the computer design to other manufacturers, which typically used it to build Multibus-based systems running Unix from UniSoft. Wall Street was an important early market. Sun's initial public offering was in 1986 under the stock symbol SUNW, for Sun Workstations (later Sun Worldwide). The symbol was changed in 2007 to JAVA; Sun stated that the brand awareness associated with its Java platform better represented the company's current strategy.
Sun's logo, which features four interleaved copies of the word sun in the form of a rotationally symmetric ambigram, was designed by professor Vaughan Pratt, also of Stanford. The initial version of the logo was orange and had the sides oriented horizontally and vertically, but it was subsequently rotated to stand on one corner and re-colored purple, and later blue.
=== Dot-com bubble and aftermath ===
During the dot-com bubble, Sun began making more money, with its stock rising as high as $250 per share. It also began spending much more, hiring workers and building itself out. Some of this was because of genuine demand, but much was from web start-up companies anticipating business that would never happen. In 2000, the bubble burst. Sales in Sun's important hardware division went into free-fall as customers closed shop and auctioned high-end servers.
Several quarters of steep losses led to executive departures, rounds of layoffs, and other cost cutting. In December 2001, the stock fell to the 1998, pre-bubble level of about $100. It continued to fall, faster than many other technology companies. A year later, it had reached below $10 (a tenth of what it was in 1990), but it eventually bounced back to $20. In mid-2004, Sun closed their Newark, California, factory and consolidated all manufacturing to Hillsboro, Oregon and Linlithgow, Scotland. In 2006, the rest of the Newark campus was put on the market.
=== Post-crash focus ===
In 2004, Sun canceled two major processor projects which emphasized high instruction-level parallelism and operating frequency. Instead, the company chose to concentrate on processors optimized for multi-threading and multiprocessing, such as the UltraSPARC T1 processor (codenamed "Niagara"). The company also announced a collaboration with Fujitsu to use the Japanese company's processor chips in mid-range and high-end Sun servers. These servers were announced on April 17, 2007, as the M-Series, part of the SPARC Enterprise series.
In February 2005, Sun announced the Sun Grid, a grid computing deployment on which it offered utility computing services priced at US$1 per CPU/hour for processing and per GB/month for storage. This offering built upon an existing 3,000-CPU server farm used for internal R&D for over 10 years, which Sun marketed as being able to achieve 97% utilization. In August 2005, the first commercial use of this grid was announced for financial risk simulations which were later launched as its first software as a service product.
In January 2005, Sun reported a net profit of $19 million for fiscal 2005 second quarter, for the first time in three years. This was followed by net loss of $9 million on GAAP basis for the third quarter 2005, as reported on April 14, 2005. In January 2007, Sun reported a net GAAP profit of $126 million on revenue of $3.337 billion for its fiscal second quarter. Shortly following that news, it was announced that Kohlberg Kravis Roberts (KKR) would invest $700 million in the company.
Sun had engineering groups in Bangalore, Beijing, Dublin, Grenoble, Hamburg, Prague, St. Petersburg, Tel Aviv, Tokyo, Canberra and Trondheim.
In 2007–2008, Sun posted revenue of $13.8 billion and had $2 billion in cash. First-quarter 2008 losses were $1.68 billion; revenue fell 7% to $12.99 billion. Sun's stock lost 80% of its value November 2007 to November 2008, reducing the company's market value to $3 billion. With falling sales to large corporate clients, Sun announced plans to lay off 5,000 to 6,000 workers, or 15–18% of its work force. It expected to save $700 million to $800 million a year as a result of the moves, while also taking up to $600 million in charges.
=== Acquisition by Oracle ===
On September 3, 2009, the European Commission opened an in-depth investigation into the proposed takeover of Sun Microsystems by Oracle. On November 9, 2009, the Commission issued a statement of objections relating to the acquisition. Finally, on January 21, 2010, the European Commission approved Oracle's acquisition of Sun. The Commission's investigation showed that another open database, PostgreSQL, was considered by many users of this type of software as a credible alternative to MySQL and could to some extent replace the competitive strength that the latter currently represents in the database market.
Sun was sold to Oracle Corporation in 2009 for $5.6 billion.
Sun's staff were asked to share anecdotes about their experiences at Sun. A website containing videos, stories, and photographs from 27 years at Sun was made available on September 2, 2009.
In October, Sun announced a second round of thousands of employees to be laid off, blamed partially on delays in approval of the merger.
The transaction was completed in early 2010.
In January 2011, Oracle agreed to pay $46 million to settle charges that it submitted false claims to US federal government agencies and paid "kickbacks" to systems integrators.
In February 2011, Sun's former Menlo Park, California, campus of about 1,000,000 square feet (93,000 m2) was sold, and it was announced that it would become headquarters for Facebook.
The sprawling facility built around an enclosed courtyard had been nicknamed "Sun Quentin". The campus is now the headquarters of Facebook's parent company Meta Platforms.
On September 1, 2011, Sun India legally became part of Oracle. It had been delayed due to legal issues in Indian court.
== Sun acquisitions ==
1987: Trancept Systems, a high-performance graphics hardware company
1987: Sitka Corp, networking systems linking the Macintosh with IBM PCs
1987: Centram Systems West, maker of networking software for PCs, Macs and Sun systems
1988: Folio, Inc., developer of intelligent font scaling technology and the F3 font format
1991: Interactive Systems Corporation's Intel/Unix OS division, from Eastman Kodak Company
1992: Praxsys Technologies, Inc., developers of the Windows emulation technology that eventually became Wabi
1994: Thinking Machines Corporation hardware division
1996: Lighthouse Design, Ltd.
1996: Cray Business Systems Division, from Silicon Graphics
1996: Integrated Micro Products, specializing in fault tolerant servers
1996: Thinking Machines Corporation software division
February 1997: LongView Technologies, LLC
August 1997: Diba, technology supplier for the Information Appliance industry
September 1997: Chorus Systèmes SA, creators of ChorusOS
November 1997: Encore Computer Corporation's storage business
1998: RedCape Software
1998: i-Planet, a small software company that produced the "Pony Espresso" mobile email client—its name (sans hyphen) for the Sun-Netscape software alliance
June 1998: Dakota Scientific Software, Inc.—development tools for high-performance computing
July 1998: NetDynamics—developers of the NetDynamics Application Server
October 1998: Beduin, small software company that produced the "Impact" small-footprint Java-based Web browser for mobile devices.
1999: Star Division, German software company and with it StarOffice, which was later released as open source under the name OpenOffice.org
1999: MAXSTRAT Corporation, a company in Milpitas, California selling Fibre Channel storage servers.
October 1999: Forté Software, an enterprise software company specializing in integration solutions and developer of the Forte 4GL
1999: TeamWare
1999: NetBeans, produced a modular IDE written in Java, based on a student project at Charles University in Prague
March 2000: Innosoft International, Inc. a software company specializing in highly scalable MTAs (PMDF) and Directory Services.
July 2000: Gridware, a software company whose products managed the distribution of computing jobs across multiple computers
September 2000: Cobalt Networks, an Internet appliance manufacturer for $2 billion
December 2000: HighGround, with a suite of Web-based management solutions
2001: LSC, Inc., an Eagan, Minnesota company that developed Storage and Archive Management File System (SAM-FS) and Quick File System QFS file systems for backup and archive
March 2001: InfraSearch, a peer-to-peer search company based in Burlingame.
March 2002: Clustra Systems
June 2002: Afara Websystems, developed SPARC processor–based technology
September 2002: Pirus Networks, intelligent storage services
November 2002: Terraspring, infrastructure automation software
June 2003: Pixo, added to the Sun Content Delivery Server
August 2003: CenterRun, Inc.
December 2003: Waveset Technologies, identity management
January 2004 Nauticus Networks
February 2004: Kealia, founded by original Sun founder Andy Bechtolsheim, developed AMD-based 64-bit servers
January 2005: SevenSpace, a multi-platform managed services provider
May 2005: Tarantella, Inc. (formerly known as Santa Cruz Operation (SCO)), for $25 million
June 2005: SeeBeyond, a Service-Oriented Architecture (SOA) software company for $387m
June 2005: Procom Technology, Inc.'s NAS IP Assets
August 2005: StorageTek, data storage technology company for $4.1 billion
February 2006: Aduva, software for Solaris and Linux patch management
October 2006: Neogent
April 2007: SavaJe, the SavaJe OS, a Java OS for mobile phones
September 2007: Cluster File Systems, Inc.
November 2007: Vaau, Enterprise Role Management and identity compliance solutions
February 2008: MySQL AB, the company offering the open source database MySQL for $1 billion.
February 2008: Innotek GmbH, developer of the VirtualBox virtualization product
April 2008: Montalvo Systems, x86 microprocessor startup acquired before first silicon
January 2009: Q-layer, a software company with cloud computing solutions
== Major stockholders ==
As of May 11, 2009, the following shareholders held over 100,000 common shares of Sun and at $9.50 per share offered by Oracle, they received the amounts indicated when the acquisition closed.
== Hardware ==
For the first decade of Sun's history, the company positioned its products as technical workstations, competing successfully as a low-cost vendor during the Workstation Wars of the 1980s. It then shifted its hardware product line to emphasize servers and storage. High-level telecom control systems such as Operational Support Systems service predominantly used Sun equipment.
=== Motorola-based systems ===
Sun originally used Motorola 68000 family central processing units for the Sun-1 through Sun-3 computer series. The Sun-1 employed a 68000 CPU, the Sun-2 series, a 68010. The Sun-3 series was based on the 68020, with the later Sun-3x using the 68030.
=== SPARC-based systems ===
In 1987, the company began using SPARC (Scalable Processor ARChitecture), a RISC processor architecture of its own design, in its computer systems, starting with the Sun-4 line. SPARC was initially a 32-bit architecture (SPARC V7) until the introduction of the SPARC V9 architecture in 1995, which added 64-bit extensions.
Sun developed several generations of SPARC-based computer systems, including the SPARCstation, Ultra, and Sun Blade series of workstations, and the SPARCserver, Netra, Enterprise, and Sun Fire line of servers.
In the early 1990s the company began to extend its product line to include large-scale symmetric multiprocessing servers, starting with the four-processor SPARCserver 600MP. This was followed by the 8-processor SPARCserver 1000 and 20-processor SPARCcenter 2000, which were based on work done in conjunction with Xerox PARC. In 1995 the company introduced Sun Ultra series machines that were equipped with the first 64-bit implementation of SPARC processors (UltraSPARC). In the late 1990s the transformation of product line in favor of large 64-bit SMP systems was accelerated by the acquisition of Cray Business Systems Division from Silicon Graphics. Their 32-bit, 64-processor Cray Superserver 6400, related to the SPARCcenter, led to the 64-bit Sun Enterprise 10000 high-end server (otherwise known as Starfire or E10K).
In September 2004, Sun made available systems with UltraSPARC IV which was the first multi-core SPARC processor. It was followed by UltraSPARC IV+ in September 2005 and its revisions with higher clock speeds in 2007. These CPUs were used in the most powerful, enterprise class high-end CC-NUMA servers developed by Sun, such as the Sun Fire E15K and the Sun Fire E25K.
In November 2005, Sun launched the UltraSPARC T1, notable for its ability to concurrently run 32 threads of execution on 8 processor cores. Its intent was to drive more efficient use of CPU resources, which is of particular importance in data centers, where there is an increasing need to reduce power and air conditioning demands, much of which comes from the heat generated by CPUs. The T1 was followed in 2007 by the UltraSPARC T2, which extended the number of threads per core from 4 to 8. Sun has open sourced the design specifications of both the T1 and T2 processors via the OpenSPARC project.
In 2006, Sun ventured into the blade server (high density rack-mounted systems) market with the Sun Blade (distinct from the Sun Blade workstation).
In April 2007, Sun released the SPARC Enterprise server products, jointly designed by Sun and Fujitsu and based on Fujitsu SPARC64 VI and later processors. The M-class SPARC Enterprise systems include high-end reliability and availability features. Later T-series servers have also been badged SPARC Enterprise rather than Sun Fire.
In April 2008, Sun released servers with UltraSPARC T2 Plus, which is an SMP capable version of UltraSPARC T2, available in 2 or 4 processor configurations. It was the first CoolThreads CPU with multi-processor capability and it made possible to build standard rack-mounted servers that could simultaneously process up to massive 256 CPU threads in hardware (Sun SPARC Enterprise T5440), which is considered a record in the industry.
Since 2010, all further development of Sun machines based on SPARC architecture (including new SPARC T-Series servers, SPARC T3 and T4 chips) is done as a part of Oracle Corporation hardware division.
=== x86-based systems ===
In the late 1980s, Sun also marketed an Intel 80386–based machine, the Sun386i; this was designed to be a hybrid system, running SunOS but at the same time supporting DOS applications. This only remained on the market for a brief time. A follow-up "486i" upgrade was announced but only a few prototype units were ever manufactured.
Sun's brief first foray into x86 systems ended in the early 1990s, as it decided to concentrate on SPARC and retire the last Motorola systems and 386i products, a move dubbed by McNealy as "all the wood behind one arrowhead". Even so, Sun kept its hand in the x86 world, as a release of Solaris for PC compatibles began shipping in 1993.
In 1997, Sun acquired Diba, Inc., followed later by the acquisition of Cobalt Networks in 2000, with the aim of building network appliances (single function computers meant for consumers). Sun also marketed a Network Computer (a term popularized and eventually trademarked by Oracle); the JavaStation was a diskless system designed to run Java applications.
Although none of these business initiatives were particularly successful, the Cobalt purchase gave Sun a toehold for its return to the x86 hardware market. In 2002, Sun introduced its first general purpose x86 system, the LX50, based in part on previous Cobalt system expertise. This was also Sun's first system announced to support Linux as well as Solaris.
In 2003, Sun announced a strategic alliance with AMD to produce x86/x64 servers based on AMD's Opteron processor; this was followed shortly by Sun's acquisition of Kealia, a startup founded by original Sun founder Andy Bechtolsheim, which had been focusing on high-performance AMD-based servers.
The following year, Sun launched the Opteron-based Sun Fire V20z and V40z servers, and the Sun Java Workstation W1100z and W2100z workstations.
In September 2005 Sun unveiled a new range of Opteron-based servers: the Sun Fire X2100, X4100 and X4200 servers. These were designed from scratch by a team led by Bechtolsheim to address heat and power consumption issues commonly faced in data centers. In July 2006, the Sun Fire X4500 and X4600 systems were introduced, extending a line of x64 systems that support not only Solaris, but also Linux and Microsoft Windows.
In January 2007 Sun announced a broad strategic alliance with Intel. Intel endorsed Solaris as a mainstream operating system and as its mission critical Unix for its Xeon processor–based systems, and contributed engineering resources to OpenSolaris. Sun began using the Intel Xeon processor in its x64 server line, starting with the Sun Blade X6250 server module introduced in June 2007.
In May 2008 AMD announced its Operating System Research Center (OSRC) was expanding its focus to include optimization to Sun's OpenSolaris and xVM virtualization products for AMD processors.
== Software ==
Although Sun was initially known as a hardware company, its software history began with its founding in 1982; co-founder Bill Joy was one of the leading Unix developers of the time, having contributed the vi editor, the C shell, and significant work developing TCP/IP and the BSD Unix OS. Sun later developed software such as the Java programming language and acquired software such as StarOffice, VirtualBox and MySQL. In February 1991, the company established SunSoft, Inc., a wholly owned division of Sun dedicated to the development of operating systems and application software.
Sun used community-based and open-source licensing of its major technologies, and for its support of its products with other open source technologies. GNOME-based desktop software called Java Desktop System (originally code-named "Madhatter") was distributed for the Solaris operating system, and at one point for Linux. Sun supported its Java Enterprise System (a middleware stack) on Linux. It released the source code for Solaris under the open-source Common Development and Distribution License, via the OpenSolaris community. Sun's positioning includes a commitment to indemnify users of some software from intellectual property disputes concerning that software. It offers support services on a variety of pricing bases, including per-employee and per-socket.
A 2006 report prepared for the EU by UNU-MERIT stated that Sun was the largest corporate contributor to open source movements in the world. According to this report, Sun's open source contributions exceed the combined total of the next five largest commercial contributors.
=== Operating systems ===
Sun is best known for its Unix systems, which have a reputation for system stability and a consistent design philosophy.
Sun's first workstation shipped with UniSoft V7 Unix. Later in 1982 Sun began providing SunOS, a customized 4.2BSD Unix, as the operating system for its workstations.
SunOS included suntools, an early GUI window system.
In the late 1980s, AT&T tapped Sun to help them develop the next release of their branded UNIX, and in 1988 announced they would purchase up to a 20% stake in Sun. UNIX System V Release 4 (SVR4) was jointly developed by AT&T and Sun. Sun used SVR4 as the foundation for Solaris 2.x, which became the successor to SunOS 4.1.x (later retroactively named Solaris 1.x). By the mid-1990s, the ensuing Unix wars had largely subsided, AT&T had sold off their Unix interests, and the relationship between the two companies was significantly reduced.
In the early 1990s, Brian P. Dougherty, founder of Berkeley Softworks (which would go on to be re-incorporated as the GeoWorks Corporation) accused
the Java development team at Sun for studying GeoWorks's PC/GEOS operating system and incorporating features of PC/GEOS into their Unix-based operating system. Brian claimed that the object-oriented and flexible UI of PC/GEOS was "to this day the most sophisticated UI technology ever built into an OS".
From 1992 Sun also sold Interactive Unix, an operating system it acquired when it bought Interactive Systems Corporation from Eastman Kodak Company. This was a popular Unix variant for the PC platform and a major competitor to market leader SCO UNIX. Sun's focus on Interactive Unix diminished in favor of Solaris on both SPARC and x86 systems; it was dropped as a product in 2001.
Sun dropped the Solaris 2.x version numbering scheme after the Solaris 2.6 release (1997); the following version was branded Solaris 7. This was the first 64-bit release, intended for the new UltraSPARC CPUs based on the SPARC V9 architecture. Within the next four years, the successors Solaris 8 and Solaris 9 were released in 2000 and 2002 respectively.
Following several years of difficult competition and loss of server market share to competitors' Linux-based systems, Sun began to include Linux as part of its strategy in 2002. Sun supported both Red Hat Enterprise Linux and SUSE Linux Enterprise Server on its x64 systems; companies such as Canonical Ltd., Wind River Systems and MontaVista also supported their versions of Linux on Sun's SPARC-based systems.
In 2004, after having cultivated a reputation as one of Microsoft's most vocal antagonists, Sun entered into a joint relationship with them, resolving various legal entanglements between the two companies and receiving US$1.95 billion in settlement payments from them. Sun supported Microsoft Windows on its x64 systems, and announced other collaborative agreements with Microsoft, including plans to support each other's virtualization environments.
In 2005, the company released Solaris 10. The new version included a large number of enhancements to the operating system, as well as very novel features, previously unseen in the industry. Solaris 10 update releases continued through the next 8 years, the last release from Sun Microsystems being Solaris 10 10/09. The following updates were released by Oracle under the new license agreement; the final release is Solaris 10 1/13.
Previously, Sun offered a separate variant of Solaris called Trusted Solaris, which included augmented security features such as multilevel security and a least privilege access model. Solaris 10 included many of the same capabilities as Trusted Solaris at the time of its initial release; Solaris 10 11/06 included Solaris Trusted Extensions, which give it the remaining capabilities needed to make it the functional successor to Trusted Solaris.
After the release of Solaris 10, the Solaris source code was opened under the CDDL free software license and developed in open with contributing Opensolaris community through SXCE that used SVR4 .pkg packaging and supported OpenSolaris releases that used IPS.
Following the acquisition of Sun by Oracle, OpenSolaris continued to develop in open under illumos with illumos distributions.
Oracle Corporation continued to develop Solaris, reverting new development back to the proprietary licensing; its next release was Oracle Solaris 11 in November 2011.
=== Java platform ===
The Java platform was developed at Sun by James Gosling in the early 1990s with the objective of allowing programs to function regardless of the device they were used on, sparking the slogan "Write once, run anywhere" (WORA). While this objective was not entirely achieved (prompting the riposte "Write once, debug everywhere"), Java is regarded as being largely hardware—and operating system—independent.
Java was initially promoted as a platform for client-side applets running inside web browsers. Early examples of Java applications were the HotJava web browser and the HotJava Views suite. However, since then Java has been more successful on the server side of the Internet.
The platform consists of three major parts: the Java programming language, the Java Virtual Machine (JVM), and several Java Application Programming Interfaces (APIs). The design of the Java platform is controlled by the vendor and user community through the Java Community Process (JCP).
Java is an object-oriented programming language. Since its introduction in late 1995, it became one of the world's most popular programming languages.
Java programs are compiled to byte code, which can be executed by any JVM, regardless of the environment.
The Java APIs provide an extensive set of library routines. These APIs evolved into the Standard Edition (Java SE), which provides basic infrastructure and GUI functionality; the Enterprise Edition (Java EE), aimed at large software companies implementing enterprise-class application servers; and the Micro Edition (Java ME), used to build software for devices with limited resources, such as mobile devices.
On November 13, 2006, Sun announced it would be licensing its Java implementation under the GNU General Public License; it released its Java compiler and JVM at that time.
In February 2009, Sun entered a battle with Microsoft and Adobe Systems, which promoted rival platforms to build software applications for the Internet. JavaFX was a development platform for music, video and other applications that builds on the Java programming language.
=== Office suite ===
In 1999, Sun acquired the German software company Star Division and with it the office suite StarOffice, which Sun later released as OpenOffice.org under both GNU LGPL and the SISSL (Sun Industry Standards Source License). OpenOffice.org supported Microsoft Office file formats (though not perfectly), was available on many platforms (primarily Linux, Microsoft Windows, Mac OS X, and Solaris) and was used in the open source community.
The principal differences between StarOffice and OpenOffice.org were that StarOffice was supported by Sun, was available as either a single-user retail box kit or as per-user blocks of licensing for the enterprise, and included a wider range of fonts and document templates and a commercial quality spellchecker. StarOffice also contained commercially licensed functions and add-ons; in OpenOffice.org these were either replaced by open-source or free variants, or are not present at all. Both packages had native support for the OpenDocument format.
Derivatives of OpenOffice.org continue to be developed, these are LibreOffice, Collabora Online and Apache OpenOffice.
=== Virtualization and datacenter automation software ===
In 2007, Sun announced the Sun xVM virtualization and datacenter automation product suite for commodity hardware. Sun also acquired VirtualBox in 2008. Earlier virtualization technologies from Sun like Dynamic System Domains and Dynamic Reconfiguration were specifically designed for high-end SPARC servers, and Logical Domains only supports the UltraSPARC T1/T2/T2 Plus server platforms. Sun marketed Sun Ops Center provisioning software for datacenter automation.
On the client side, Sun offered virtual desktop solutions. Desktop environments and applications could be hosted in a datacenter, with users accessing these environments from a wide range of client devices, including Microsoft Windows PCs, Sun Ray virtual display clients, Apple Macintoshes, PDAs or any combination of supported devices. A variety of networks were supported, from LAN to WAN or the public Internet. Virtual desktop products included Sun Ray Server Software, Sun Secure Global Desktop and Sun Virtual Desktop Infrastructure.
=== Database management systems ===
Sun acquired MySQL AB, the developer of the MySQL database in 2008 for US$1 billion. CEO Jonathan Schwartz mentioned in his blog that optimizing the performance of MySQL was one of the priorities of the acquisition. In February 2008, Sun began to publish results of the MySQL performance optimization work. Sun contributed to the PostgreSQL project. On the Java platform, Sun contributed to and supported Java DB.
=== Other software ===
Sun offered other software products for software development and infrastructure services. Many were developed in house; others came from acquisitions, including Tarantella, Waveset Technologies, SeeBeyond, and Vaau. Sun acquired many of the Netscape non-browser software products as part a deal involving Netscape's merger with AOL. These software products were initially offered under the "iPlanet" brand; once the Sun-Netscape alliance ended, they were re-branded as "Sun ONE" (Sun Open Network Environment), and then the "Sun Java System".
Sun's middleware product was branded as the Java Enterprise System (JES), and marketed for web and application serving, communication, calendaring, directory, identity management and service-oriented architecture. Sun's Open ESB and other software suites were available free of charge on systems running Solaris, Red Hat Enterprise Linux, HP-UX, and Windows, with support available optionally.
Sun developed data center management software products, which included the Solaris Cluster high availability software, and a grid management package called Sun Grid Engine and firewall software such as SunScreen.
For Network Equipment Providers and telecommunications customers, Sun developed the Sun Netra High-Availability Suite.
Sun produced compilers and development tools under the Sun Studio brand, for building and developing Solaris and Linux applications.
Sun entered the software as a service (SaaS) market with zembly, a social cloud-based computing platform and Project Kenai, an open-source project hosting service.
== Storage ==
Sun sold its own storage systems to complement its system offerings; it has also made several storage-related acquisitions.
On June 2, 2005, Sun announced it would purchase Storage Technology Corporation (StorageTek) for US$4.1 billion in cash, or $37.00 per share, a deal completed in August 2005.
In 2006, Sun introduced the Sun StorageTek 5800 System, the first application-aware programmable storage solution. In 2008, Sun contributed the source code of the StorageTek 5800 System under the BSD license.
Sun announced the Sun Open Storage platform in 2008 built with open source technologies.
In late 2008 Sun announced the Sun Storage 7000 Unified Storage systems (codenamed Amber Road). Transparent placement of data in the systems' solid-state drives (SSD) and conventional hard drives was managed by ZFS to take advantage of the speed of SSDs and the economy of conventional hard disks.
Other storage products included Sun Fire X4500 storage server and SAM-QFS filesystem and storage management software.
== High-performance computing ==
Sun marketed the Sun Constellation System for high-performance computing (HPC). Even before the introduction of the Sun Constellation System in 2007, Sun's products were in use in many of the TOP500 systems and supercomputing centers:
Lustre was used by seven of the top 10 supercomputers in 2008, as well as other industries that need high-performance storage: six major oil companies (including BP, Shell, and ExxonMobil), chip-design (including Synopsys and Sony), and the movie-industry (including Harry Potter and Spider-Man).
Sun Fire X4500 was used by high-energy physics supercomputers to run dCache
Sun Grid Engine was a popular workload scheduler for clusters and computer farms
Sun Visualization System allowed users of the TeraGrid to remotely access the 3D rendering capabilities of the Maverick system at the University of Texas at Austin
Sun Modular Datacenter (Project Blackbox) was two Sun MD S20 units used by the Stanford Linear Accelerator Center
The Sun HPC ClusterTools product was a set of Message Passing Interface (MPI) libraries and tools for running parallel jobs on Solaris HPC clusters. Beginning with version 7.0, Sun switched from its own implementation of MPI to Open MPI, and donated engineering resources to the Open MPI project.
Sun was a participant in the OpenMP language committee. Sun Studio compilers and tools implemented the OpenMP specification for shared memory parallelization.
In 2006, Sun built the TSUBAME supercomputer, which was until June 2008 the fastest supercomputer in Asia. Sun built Ranger at the Texas Advanced Computing Center (TACC) in 2007. Ranger had a peak performance of over 500 TFLOPS, and was the sixth-most-powerful supercomputer on the TOP500 list in November 2008.
Sun announced an OpenSolaris distribution that integrated Sun's HPC products with others.
== Staff ==
Notable Sun employees included John Gilmore, Whitfield Diffie, Radia Perlman, Ivan Sutherland, Marc Tremblay, and Satya Nadella. Sun was an early advocate of Unix-based networked computing, promoting TCP/IP and especially NFS, as reflected in the company's motto The Network is the Computer, coined by John Gage. James Gosling led the team which developed the Java programming language. Jon Bosak led the creation of the XML specification at W3C.
In 2005, Sun Microsystems was one of the first Fortune 500 companies that instituted a formal social media program. Sun staff published articles on the company's blog site. Staff were encouraged to use the site to blog on any aspect of their work or personal life, with few restrictions placed on staff, other than commercially confidential material. Jonathan I. Schwartz was one of the first CEOs of large companies to regularly blog; his postings were frequently quoted and analyzed in the press.
== See also ==
Callan Data Systems
Curriki#History
Hackathon
Liberty Alliance
List of computer system manufacturers
Open Source University Meetup
Solbourne Computer
Sun Certified Professional
== References ==
== Further reading ==
Hall, Mark; Barry, John (1990). Sunburst: The Ascent of Sun Microsystems. Chicago: Contemporary Books. ISBN 0-8092-3989-2. OCLC 232948325.
Southwick, Karen (1999). High Noon: The Inside Story of Scott McNealy and the Rise of Sun Microsystems. New York: John Wiley. ISBN 0-471-29713-5. OCLC 41404354.
== External links ==
"Oracle and Sun". Oracle Corporation. Archived from the original on February 2, 2021. Retrieved June 7, 2021. Post-merge web site (removed in February 2021).
"System news for Sun Users". A weekly third-party summary of news about Sun and its products published since 1998. | Wikipedia/Sun_Microsystems |
In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone.
Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.
== Overview ==
Supervised learning algorithms search through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem. Even if this space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles combine multiple hypotheses to form one which should be theoretically better.
Ensemble learning trains two or more machine learning algorithms on a specific classification or regression task. The algorithms within the ensemble model are generally referred as "base models", "base learners", or "weak learners" in literature. These base models can be constructed using a single modelling algorithm, or several different algorithms. The idea is to train a diverse set of weak models on the same modelling task, such that the outputs of each weak learner have poor predictive ability (i.e., high bias), and among all weak learners, the outcome and error values exhibit high variance. Fundamentally, an ensemble learning model trains at least two high-bias (weak) and high-variance (diverse) models to be combined into a better-performing model. The set of weak models — which would not produce satisfactory predictive results individually — are combined or averaged to produce a single, high performing, accurate, and low-variance model to fit the task as required.
Ensemble learning typically refers to bagging (bootstrap aggregating), boosting or stacking/blending techniques to induce high variance among the base models. Bagging creates diversity by generating random samples from the training observations and fitting the same model to each different sample — also known as homogeneous parallel ensembles. Boosting follows an iterative process by sequentially training each base model on the up-weighted errors of the previous base model, producing an additive model to reduce the final model errors — also known as sequential ensemble learning. Stacking or blending consists of different base models, each trained independently (i.e. diverse/high variance) to be combined into the ensemble model — producing a heterogeneous parallel ensemble. Common applications of ensemble learning include random forests (an extension of bagging), Boosted Tree models, and Gradient Boosted Tree Models. Models in applications of stacking are generally more task-specific — such as combining clustering techniques with other parametric and/or non-parametric techniques.
Evaluating the prediction of an ensemble typically requires more computation than evaluating the prediction of a single model. In one sense, ensemble learning may be thought of as a way to compensate for poor learning algorithms by performing a lot of extra computation. On the other hand, the alternative is to do a lot more learning with one non-ensemble model. An ensemble may be more efficient at improving overall accuracy for the same increase in compute, storage, or communication resources by using that increase on two or more methods, than would have been improved by increasing resource use for a single method. Fast algorithms such as decision trees are commonly used in ensemble methods (e.g., random forests), although slower algorithms can benefit from ensemble techniques as well.
By analogy, ensemble techniques have been used also in unsupervised learning scenarios, for example in consensus clustering or in anomaly detection.
== Ensemble theory ==
Empirically, ensembles tend to yield better results when there is a significant diversity among the models. Many ensemble methods, therefore, seek to promote diversity among the models they combine. Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than very deliberate algorithms (like entropy-reducing decision trees). Using a variety of strong learning algorithms, however, has been shown to be more effective than using techniques that attempt to dumb-down the models in order to promote diversity. It is possible to increase diversity in the training stage of the model using correlation for regression tasks or using information measures such as cross entropy for classification tasks.
Theoretically, one can justify the diversity concept because the lower bound of the error rate of an ensemble system can be decomposed into accuracy, diversity, and the other term.
=== The geometric framework ===
Ensemble learning, including both regression and classification tasks, can be explained using a geometric framework. Within this framework, the output of each individual classifier or regressor for the entire dataset can be viewed as a point in a multi-dimensional space. Additionally, the target result is also represented as a point in this space, referred to as the "ideal point."
The Euclidean distance is used as the metric to measure both the performance of a single classifier or regressor (the distance between its point and the ideal point) and the dissimilarity between two classifiers or regressors (the distance between their respective points). This perspective transforms ensemble learning into a deterministic problem.
For example, within this geometric framework, it can be proved that the averaging of the outputs (scores) of all base classifiers or regressors can lead to equal or better results than the average of all the individual models. It can also be proved that if the optimal weighting scheme is used, then a weighted averaging approach can outperform any of the individual classifiers or regressors that make up the ensemble or as good as the best performer at least.
== Ensemble size ==
While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem. A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemble classifiers. Mostly statistical tests were used for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers for an ensemble such that having more or less than this number of classifiers would deteriorate the accuracy. It is called "the law of diminishing returns in ensemble construction." Their theoretical framework shows that using the same number of independent component classifiers as class labels gives the highest accuracy.
== Common types of ensembles ==
=== Bayes optimal classifier ===
The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it. The Naive Bayes classifier is a version of this that assumes that the data is conditionally independent on the class and makes the computation more feasible. Each hypothesis is given a vote proportional to the likelihood that the training dataset would be sampled from a system if that hypothesis were true. To facilitate training data of finite size, the vote of each hypothesis is also multiplied by the prior probability of that hypothesis. The Bayes optimal classifier can be expressed with the following equation:
y
=
a
r
g
m
a
x
c
j
∈
C
∑
h
i
∈
H
P
(
c
j
|
h
i
)
P
(
T
|
h
i
)
P
(
h
i
)
{\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(T|h_{i})P(h_{i})}}
where
y
{\displaystyle y}
is the predicted class,
C
{\displaystyle C}
is the set of all possible classes,
H
{\displaystyle H}
is the hypothesis space,
P
{\displaystyle P}
refers to a probability, and
T
{\displaystyle T}
is the training data. As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in
H
{\displaystyle H}
. The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in
H
{\displaystyle H}
).
This formula can be restated using Bayes' theorem, which says that the posterior is proportional to the likelihood times the prior:
P
(
h
i
|
T
)
∝
P
(
T
|
h
i
)
P
(
h
i
)
{\displaystyle P(h_{i}|T)\propto P(T|h_{i})P(h_{i})}
hence,
y
=
a
r
g
m
a
x
c
j
∈
C
∑
h
i
∈
H
P
(
c
j
|
h
i
)
P
(
h
i
|
T
)
{\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(h_{i}|T)}}
=== Bootstrap aggregating (bagging) ===
Bootstrap aggregation (bagging) involves training an ensemble on bootstrapped data sets. A bootstrapped set is created by selecting from original training data set with replacement. Thus, a bootstrap set may contain a given example zero, one, or multiple times. Ensemble members can also have limits on the features (e.g., nodes of a decision tree), to encourage exploring of diverse features. The variance of local information in the bootstrap sets and feature considerations promote diversity in the ensemble, and can strengthen the ensemble. To reduce overfitting, a member can be validated using the out-of-bag set (the examples that are not in its bootstrap set).
Inference is done by voting of predictions of ensemble members, called aggregation. It is illustrated below with an ensemble of four decision trees. The query example is classified by each tree. Because three of the four predict the positive class, the ensemble's overall classification is positive. Random forests like the one shown are a common application of bagging.
=== Boosting ===
Boosting involves training successive models by emphasizing training data mis-classified by previously learned models. Initially, all data (D1) has equal weight and is used to learn a base model M1. The examples mis-classified by M1 are assigned a weight greater than correctly classified examples. This boosted data (D2) is used to train a second base model M2, and so on. Inference is done by voting.
In some cases, boosting has yielded better accuracy than bagging, but tends to over-fit more. The most common implementation of boosting is Adaboost, but some newer algorithms are reported to achieve better results.
=== Bayesian model averaging ===
Bayesian model averaging (BMA) makes predictions by averaging the predictions of models weighted by their posterior probabilities given the data. BMA is known to generally give better answers than a single model, obtained, e.g., via stepwise regression, especially where very different models have nearly identical performance in the training set but may otherwise perform quite differently.
The question with any use of Bayes' theorem is the prior, i.e., the probability (perhaps subjective) that each model is the best to use for a given purpose. Conceptually, BMA can be used with any prior. R packages ensembleBMA and BMA use the prior implied by the Bayesian information criterion, (BIC), following Raftery (1995). R package BAS supports the use of the priors implied by Akaike information criterion (AIC) and other criteria over the alternative models as well as priors over the coefficients.
The difference between BIC and AIC is the strength of preference for parsimony. BIC's penalty for model complexity is
ln
(
n
)
k
{\displaystyle \ln(n)k}
, while AIC's is
2
k
{\displaystyle 2k}
. Large-sample asymptotic theory establishes that if there is a best model, then with increasing sample sizes, BIC is strongly consistent, i.e., will almost certainly find it, while AIC may not, because AIC may continue to place excessive posterior probability on models that are more complicated than they need to be. On the other hand, AIC and AICc are asymptotically "efficient" (i.e., minimum mean square prediction error), while BIC is not .
Haussler et al. (1994) showed that when BMA is used for classification, its expected error is at most twice the expected error of the Bayes optimal classifier. Burnham and Anderson (1998, 2002) contributed greatly to introducing a wider audience to the basic ideas of Bayesian model averaging and popularizing the methodology. The availability of software, including other free open-source packages for R beyond those mentioned above, helped make the methods accessible to a wider audience.
=== Bayesian model combination ===
Bayesian model combination (BMC) is an algorithmic correction to Bayesian model averaging (BMA). Instead of sampling each model in the ensemble individually, it samples from the space of possible ensembles (with model weights drawn randomly from a Dirichlet distribution having uniform parameters). This modification overcomes the tendency of BMA to converge toward giving all the weight to a single model. Although BMC is somewhat more computationally expensive than BMA, it tends to yield dramatically better results. BMC has been shown to be better on average (with statistical significance) than BMA and bagging.
Use of Bayes' law to compute model weights requires computing the probability of the data given each model. Typically, none of the models in the ensemble are exactly the distribution from which the training data were generated, so all of them correctly receive a value close to zero for this term. This would work well if the ensemble were big enough to sample the entire model-space, but this is rarely possible. Consequently, each pattern in the training data will cause the ensemble weight to shift toward the model in the ensemble that is closest to the distribution of the training data. It essentially reduces to an unnecessarily complex method for doing model selection.
The possible weightings for an ensemble can be visualized as lying on a simplex. At each vertex of the simplex, all of the weight is given to a single model in the ensemble. BMA converges toward the vertex that is closest to the distribution of the training data. By contrast, BMC converges toward the point where this distribution projects onto the simplex. In other words, instead of selecting the one model that is closest to the generating distribution, it seeks the combination of models that is closest to the generating distribution.
The results from BMA can often be approximated by using cross-validation to select the best model from a bucket of models. Likewise, the results from BMC may be approximated by using cross-validation to select the best ensemble combination from a random sampling of possible weightings.
=== Bucket of models ===
A "bucket of models" is an ensemble technique in which a model selection algorithm is used to choose the best model for each problem. When tested with only one problem, a bucket of models can produce no better results than the best model in the set, but when evaluated across many problems, it will typically produce much better results, on average, than any model in the set.
The most common approach used for model-selection is cross-validation selection (sometimes called a "bake-off contest"). It is described with the following pseudo-code:
For each model m in the bucket:
Do c times: (where 'c' is some constant)
Randomly divide the training dataset into two sets: A and B
Train m with A
Test m with B
Select the model that obtains the highest average score
Cross-Validation Selection can be summed up as: "try them all with the training set, and pick the one that works best".
Gating is a generalization of Cross-Validation Selection. It involves training another learning model to decide which of the models in the bucket is best-suited to solve the problem. Often, a perceptron is used for the gating model. It can be used to pick the "best" model, or it can be used to give a linear weight to the predictions from each model in the bucket.
When a bucket of models is used with a large set of problems, it may be desirable to avoid training some of the models that take a long time to train. Landmark learning is a meta-learning approach that seeks to solve this problem. It involves training only the fast (but imprecise) algorithms in the bucket, and then using the performance of these algorithms to help determine which slow (but accurate) algorithm is most likely to do best.
=== Amended Cross-Entropy Cost: An Approach for Encouraging Diversity in Classification Ensemble ===
The most common approach for training classifier is using Cross-entropy cost function. However, one would like to train an ensemble of models that have diversity so when we combine them it would provide best results.
Assuming we use a simple ensemble of averaging
K
{\displaystyle K}
classifiers. Then the Amended Cross-Entropy Cost is
e
k
=
H
(
p
,
q
k
)
−
λ
K
∑
j
≠
k
H
(
q
j
,
q
k
)
{\displaystyle e^{k}=H(p,q^{k})-{\frac {\lambda }{K}}\sum _{j\neq k}H(q^{j},q^{k})}
where
e
k
{\displaystyle e^{k}}
is the cost function of the
k
t
h
{\displaystyle k^{th}}
classifier,
q
k
{\displaystyle q^{k}}
is the probability of the
k
t
h
{\displaystyle k^{th}}
classifier,
p
{\displaystyle p}
is the true probability that we need to estimate and
λ
{\displaystyle \lambda }
is a parameter between 0 and 1 that define the diversity that we would like to establish. When
λ
=
0
{\displaystyle \lambda =0}
we want each classifier to do its best regardless of the ensemble and when
λ
=
1
{\displaystyle \lambda =1}
we would like the classifier to be as diverse as possible.
=== Stacking ===
Stacking (sometimes called stacked generalization) involves training a model to combine the predictions of several other learning algorithms. First, all of the other algorithms are trained using the available data, then a combiner algorithm (final estimator) is trained to make a final prediction using all the predictions of the other algorithms (base estimators) as additional inputs or using cross-validated predictions from the base estimators which can prevent overfitting. If an arbitrary combiner algorithm is used, then stacking can theoretically represent any of the ensemble techniques described in this article, although, in practice, a logistic regression model is often used as the combiner.
Stacking typically yields performance better than any single one of the trained models. It has been successfully used on both supervised learning tasks (regression, classification and distance learning ) and unsupervised learning (density estimation). It has also been used to estimate bagging's error rate. It has been reported to out-perform Bayesian model-averaging. The two top-performers in the Netflix competition utilized blending, which may be considered a form of stacking.
=== Voting ===
Voting is another form of ensembling. See e.g. Weighted majority algorithm (machine learning).
== Implementations in statistics packages ==
R: at least three packages offer Bayesian model averaging tools, including the BMS (an acronym for Bayesian Model Selection) package, the BAS (an acronym for Bayesian Adaptive Sampling) package, and the BMA package.
Python: scikit-learn, a package for machine learning in Python offers packages for ensemble learning including packages for bagging, voting and averaging methods.
MATLAB: classification ensembles are implemented in Statistics and Machine Learning Toolbox.
== Ensemble learning applications ==
In recent years, due to growing computational power, which allows for training in large ensemble learning in a reasonable time frame, the number of ensemble learning applications has grown increasingly. Some of the applications of ensemble classifiers include:
=== Remote sensing ===
==== Land cover mapping ====
Land cover mapping is one of the major applications of Earth observation satellite sensors, using remote sensing and geospatial data, to identify the materials and objects which are located on the surface of target areas. Generally, the classes of target materials include roads, buildings, rivers, lakes, and vegetation. Some different ensemble learning approaches based on artificial neural networks, kernel principal component analysis (KPCA), decision trees with boosting, random forest and automatic design of multiple classifier systems, are proposed to efficiently identify land cover objects.
==== Change detection ====
Change detection is an image analysis problem, consisting of the identification of places where the land cover has changed over time. Change detection is widely used in fields such as urban growth, forest and vegetation dynamics, land use and disaster monitoring.
The earliest applications of ensemble classifiers in change detection are designed with the majority voting, Bayesian model averaging, and the maximum posterior probability. Given the growth of satellite data over time, the past decade sees more use of time series methods for continuous change detection from image stacks. One example is a Bayesian ensemble changepoint detection method called BEAST, with the software available as a package Rbeast in R, Python, and Matlab.
=== Computer security ===
==== Distributed denial of service ====
Distributed denial of service is one of the most threatening cyber-attacks that may happen to an internet service provider. By combining the output of single classifiers, ensemble classifiers reduce the total error of detecting and discriminating such attacks from legitimate flash crowds.
==== Malware Detection ====
Classification of malware codes such as computer viruses, computer worms, trojans, ransomware and spywares with the usage of machine learning techniques, is inspired by the document categorization problem. Ensemble learning systems have shown a proper efficacy in this area.
==== Intrusion detection ====
An intrusion detection system monitors computer network or computer systems to identify intruder codes like an anomaly detection process. Ensemble learning successfully aids such monitoring systems to reduce their total error.
=== Face recognition ===
Face recognition, which recently has become one of the most popular research areas of pattern recognition, copes with identification or verification of a person by their digital images.
Hierarchical ensembles based on Gabor Fisher classifier and independent component analysis preprocessing techniques are some of the earliest ensembles employed in this field.
=== Emotion recognition ===
While speech recognition is mainly based on deep learning because most of the industry players in this field like Google, Microsoft and IBM reveal that the core technology of their speech recognition is based on this approach, speech-based emotion recognition can also have a satisfactory performance with ensemble learning.
It is also being successfully used in facial emotion recognition.
=== Fraud detection ===
Fraud detection deals with the identification of bank fraud, such as money laundering, credit card fraud and telecommunication fraud, which have vast domains of research and applications of machine learning. Because ensemble learning improves the robustness of the normal behavior modelling, it has been proposed as an efficient technique to detect such fraudulent cases and activities in banking and credit card systems.
=== Financial decision-making ===
The accuracy of prediction of business failure is a very crucial issue in financial decision-making. Therefore, different ensemble classifiers are proposed to predict financial crises and financial distress. Also, in the trade-based manipulation problem, where traders attempt to manipulate stock prices by buying and selling activities, ensemble classifiers are required to analyze the changes in the stock market data and detect suspicious symptom of stock price manipulation.
=== Medicine ===
Ensemble classifiers have been successfully applied in neuroscience, proteomics and medical diagnosis like in neuro-cognitive disorder (i.e. Alzheimer or myotonic dystrophy) detection based on MRI datasets, cervical cytology classification.
Besides, ensembles have been successfully applied in medical segmentation tasks, for example brain tumor and hyperintensities segmentation.
== See also ==
Ensemble averaging (machine learning)
Bayesian structural time series (BSTS)
Mixture of experts
== References ==
== Further reading ==
Zhou Zhihua (2012). Ensemble Methods: Foundations and Algorithms. Chapman and Hall/CRC. ISBN 978-1-439-83003-1.
Robert Schapire; Yoav Freund (2012). Boosting: Foundations and Algorithms. MIT. ISBN 978-0-262-01718-3.
== External links ==
Robi Polikar (ed.). "Ensemble learning". Scholarpedia.
The Waffles (machine learning) toolkit contains implementations of Bagging, Boosting, Bayesian Model Averaging, Bayesian Model Combination, Bucket-of-models, and other ensemble techniques | Wikipedia/Ensemble_methods |
Portable Network Graphics (PNG, officially pronounced PING, colloquially pronounced PEE-en-JEE) is a raster-graphics file format that supports lossless data compression. PNG was developed as an improved, non-patented replacement for Graphics Interchange Format (GIF).
PNG supports palette-based images (with palettes of 24-bit RGB or 32-bit RGBA colors), grayscale images (with or without an alpha channel for transparency), and full-color non-palette-based RGB or RGBA images. The PNG working group designed the format for transferring images on the Internet, not for professional-quality print graphics; therefore, non-RGB color spaces such as CMYK are not supported. A PNG file contains a single image in an extensible structure of chunks, encoding the basic pixels and other information such as textual comments and integrity checks documented in RFC 2083.
PNG files have the ".png" file extension and the "image/png" MIME media type.
PNG was published as an informational RFC 2083 in March 1997 and as an ISO/IEC 15948 standard in 2004.
== History and development ==
The motivation for creating the PNG format was the announcement on 28 December 1994 that implementations of the Graphics Interchange Format (GIF) format would have to pay royalties to Unisys due to their patent of the Lempel–Ziv–Welch (LZW) data compression algorithm used in GIF. This led to a flurry of criticism from Usenet users. One of them was Thomas Boutell, who on 4 January 1995 posted a precursory discussion thread on the Usenet newsgroup "comp.graphics" in which he devised a plan for a free alternative to GIF. Other users in that thread put forth many propositions that would later be part of the final file format. Oliver Fromme, author of the popular JPEG viewer QPEG, proposed the PING name, eventually becoming PNG, a recursive acronym meaning PING is not GIF, and also the .png extension. Other suggestions later implemented included the deflate compression algorithm and 24-bit color support, the lack of the latter in GIF also motivating the team to create their file format. The group would become known as the PNG Development Group, and as the discussion rapidly expanded, it later used a mailing list associated with a CompuServe forum.
The full specification of PNG was released under the approval of W3C on 1 October 1996, and later as RFC 2083 on 15 January 1997. The specification was revised on 31 December 1998 as version 1.1, which addressed technical problems for gamma and color correction. Version 1.2, released on 11 August 1999, added the iTXt chunk as the specification's only change, and a reformatted version of 1.2 was released as a second edition of the W3C standard on 10 November 2003, and as an International Standard (ISO/IEC 15948:2004) on 3 March 2004.
Although GIF allows for animation, it was initially decided that PNG should be a single-image format. In 2001, the developers of PNG published the Multiple-image Network Graphics (MNG) format, with support for animation. MNG achieved moderate application support, but not enough among mainstream web browsers and no usage among web site designers or publishers. In 2008, certain Mozilla developers published the Animated Portable Network Graphics (APNG) format with similar goals. APNG is a format that is natively supported by Gecko- and Presto-based web browsers and is also commonly used for thumbnails on Sony's PlayStation Portable system (using the normal PNG file extension). In 2017, Chromium based browsers adopted APNG support. In January 2020, Microsoft Edge became Chromium based, thus inheriting support for APNG. With this all major browsers now support APNG.
== PNG Working Group ==
The original PNG specification was authored by an ad hoc group of computer graphics experts and enthusiasts. Discussions and decisions about the format were conducted by email. The original authors listed on RFC 2083 are:
Editor: Thomas Boutell
Contributing Editor: Tom Lane
Authors (in alphabetical order by last name): Mark Adler, Thomas Boutell, Christian Brunschen, Adam M. Costello, Lee Daniel Crocker, Andreas Dilger, Oliver Fromme, Jean-loup Gailly, Chris Herborth, Aleks Jakulin, Neal Kettler, Tom Lane, Alexander Lehmann, Chris Lilley, Dave Martindale, Owen Mortensen, Keith S. Pickens, Robert P. Poole, Glenn Randers-Pehrson, Greg Roelofs, Willem van Schaik, Guy Schalnat, Paul Schmidt, Tim Wegner, Jeremy Wohl
== File format ==
=== File header ===
A PNG file starts with an eight-byte signature (refer to hex editor image on the right):
=== "Chunks" within the file ===
After the header, comes a series of chunks, each of which conveys certain information about the image. Chunks declare themselves as critical or ancillary, and a program encountering an ancillary chunk that it does not understand can safely ignore it. This chunk-based storage layer structure, similar in concept to a container format or to Amiga's IFF, is designed to allow the PNG format to be extended while maintaining compatibility with older versions—it provides forward compatibility, and this same file structure (with different signature and chunks) is used in the associated MNG, JNG, and APNG formats.
A chunk consists of four parts: length (4 bytes, big-endian), chunk type/name (4 bytes), chunk data (length bytes) and CRC (cyclic redundancy code/checksum; 4 bytes). The CRC is a network-byte-order CRC-32 computed over the chunk type and chunk data, but not the length.
Chunk types are given a four-letter case sensitive ASCII type/name; compare FourCC. The case of the different letters in the name (bit 5 of the numeric value of the character) is a bit field that provides the decoder with some information on the nature of chunks it does not recognize.
The case of the first letter indicates whether the chunk is critical or not. If the first letter is uppercase, the chunk is critical; if not, the chunk is ancillary. Critical chunks contain information that is necessary to read the file. If a decoder encounters a critical chunk it does not recognize, it must abort reading the file or supply the user with an appropriate warning.
The case of the second letter indicates whether the chunk is "public" (either in the specification or the registry of special-purpose public chunks) or "private" (not standardized). Uppercase is public and lowercase is private. This ensures that public and private chunk names can never conflict with each other (although two private chunk names could conflict).
The third letter must be uppercase to conform to the PNG specification. It is reserved for future expansion. Decoders should treat a chunk with a lower case third letter the same as any other unrecognized chunk.
The case of the fourth letter indicates whether the chunk is safe to copy by editors that do not recognize it. If lowercase, the chunk may be safely copied regardless of the extent of modifications to the file. If uppercase, it may only be copied if the modifications have not touched any critical chunks.
==== Critical chunks ====
A decoder must be able to interpret critical chunks to read and render a PNG file.
IHDR must be the first chunk; it contains (in this order) the image's
width (4 bytes)
height (4 bytes)
bit depth (1 byte, values 1, 2, 4, 8, or 16)
color type (1 byte, values 0, 2, 3, 4, or 6)
compression method (1 byte, value 0)
filter method (1 byte, value 0)
interlace method (1 byte, values 0 "no interlace" or 1 "Adam7 interlace") (13 data bytes total).
As stated in the World Wide Web Consortium, bit depth is defined as "the number of bits per sample or per palette index (not per pixel)".
PLTE contains the palette: a list of colors.
IDAT contains the image, which may be split among multiple IDAT chunks. Such splitting slightly increases the file size, but makes it possible to generate a PNG in a streaming manner. The IDAT chunk contains the actual image data, which is the output stream of the compression algorithm.
IEND marks the image end; the data field of the IEND chunk has 0 bytes/is empty.
The PLTE chunk is essential for color type 3 (indexed color). It is optional for color types two and six (truecolor and truecolor with alpha) and it must not appear for color types 0 and 4 (grayscale and grayscale with alpha).
==== Ancillary chunks ====
Other image attributes that can be stored in PNG files include gamma values, background color, and textual metadata information. PNG also supports color management through the inclusion of ICC color profiles.
bKGD gives the default background color. It is intended for use when there is no better choice available, such as in standalone image viewers (but not web browsers; see below for more details).
cHRM gives the chromaticity coordinates of the display primaries and white point.
cICP specifies the color space, transfer function and matrix coefficients as defined in ITU-T H.273. It is intended for use with HDR imagery without requiring a color profile.
dSIG is for storing digital signatures.
eXIf stores Exif metadata.
gAMA specifies gamma. The gAMA chunk contains only 4 bytes, and its value represents the gamma value multiplied by 100,000; for example, the gamma value 1/3.4 calculates to 29411.7647059 ((1/3.4)*(100,000)) and is converted to an integer (29412) for storage.
hIST can store the histogram, or total amount of each color in the image.
iCCP is an ICC color profile.
iTXt contains a keyword and UTF-8 text, with encodings for possible compression and translations marked with language tag. The Extensible Metadata Platform (XMP) uses this chunk with a keyword 'XML:com.adobe.xmp'
pHYs holds the intended pixel size (or pixel aspect ratio); the pHYs contains "Pixels per unit, X axis" (4 bytes), "Pixels per unit, Y axis" (4 bytes), and "Unit specifier" (1 byte) for a total of 9 bytes.
sBIT (significant bits) indicates the color-accuracy of the source data; this chunk contains a total of between 1 and 5 bytes, depending on the color type.
sPLT suggests a palette to use if the full range of colors is unavailable.
sRGB indicates that the standard sRGB color space is used; the sRGB chunk contains only 1 byte, which is used for "rendering intent" (4 values—0, 1, 2, and 3—are defined for rendering intent).
sTER stereo-image indicator chunk for stereoscopic images.
tEXt can store text that can be represented in ISO/IEC 8859-1, with one key-value pair for each chunk. The "key" must be between one and 79 characters long. Separator is a null character. The "value" can be any length, including zero up to the maximum permissible chunk size minus the length of the keyword and separator. Neither "key" nor "value" can contain null character. Leading or trailing spaces are also disallowed.
tIME stores the time that the image was last changed.
tRNS contains transparency information. For indexed images, it stores alpha channel values for one or more palette entries. For truecolor and grayscale images, it stores a single pixel value that is to be regarded as fully transparent.
zTXt contains compressed text (and a compression method marker) with the same limits as tEXt.
The lowercase first letter in these chunks indicates that they are not needed for the PNG specification. The lowercase last letter in some chunks indicates that they are safe to copy, even if the application concerned does not understand them.
=== Pixel format ===
Pixels in PNG images are numbers that may be either indices of sample data in the palette or the sample data itself. The palette is a separate table contained in the PLTE chunk. Sample data for a single pixel consists of a tuple of between one and four numbers. Whether the pixel data represents palette indices or explicit sample values, the numbers are referred to as channels and every number in the image is encoded with an identical format.
The permitted formats encode each number as an unsigned integer value using a fixed number of bits, referred to in the PNG specification as the bit depth. Notice that this is not the same as color depth, which is commonly used to refer to the total number of bits in each pixel, not each channel. The permitted bit depths are summarized in the table along with the total number of bits used for each pixel.
The number of channels depends on whether the image is grayscale or color and whether it has an alpha channel. PNG allows the following combinations of channels, called the color type.
The color type is specified as an 8-bit value however only the low three bits are used and, even then, only the five combinations listed above are permitted. So long as the color type is valid it can be considered as a bit field as summarized in the adjacent table:
bit value 1: the image data stores palette indices. This is only valid in combination with bit value 2;
bit value 2: the image samples contain three channels of data encoding trichromatic colors, otherwise the image samples contain one channel of data encoding relative luminance,
bit value 4: the image samples also contain an alpha channel expressed as a linear measure of the opacity of the pixel. This is not valid in combination with bit value 1.
With indexed color images, the palette always stores trichromatic colors at a depth of 8 bits per channel (24 bits per palette entry). Additionally, an optional list of 8-bit alpha values for the palette entries may be included; if not included, or if shorter than the palette, the remaining palette entries are assumed to be opaque. The palette must not have more entries than the image bit depth allows for, but it may have fewer (for example, if an image with 8-bit pixels only uses 90 colors then it does not need palette entries for all 256 colors). The palette must contain entries for all the pixel values present in the image.
The standard allows indexed color PNGs to have 1, 2, 4 or 8 bits per pixel; grayscale images with no alpha channel may have 1, 2, 4, 8 or 16 bits per pixel. Everything else uses a bit depth per channel of either 8 or 16. The combinations this allows are given in the table above. The standard requires that decoders can read all supported color formats, but many image editors can only produce a small subset of them.
=== Transparency of image ===
PNG offers a variety of transparency options. With true-color and grayscale images either a single pixel value can be declared as transparent or an alpha channel can be added (enabling any percentage of partial transparency to be used). For paletted images, alpha values can be added to palette entries. The number of such values stored may be less than the total number of palette entries, in which case the remaining entries are considered fully opaque.
The scanning of pixel values for binary transparency is supposed to be performed before any color reduction to avoid pixels becoming unintentionally transparent. This is most likely to pose an issue for systems that can decode 16-bits-per-channel images (as is required for compliance with the specification) but only output at 8 bits per channel (the norm for all but the highest end systems).
Alpha storage can be "associated" ("premultiplied") or "unassociated", but PNG standardized on "unassociated" ("non-premultiplied") alpha, which means that imagery is not alpha encoded; the emissions represented in RGB are not the emissions at the pixel level. This means that the over operation will multiply the RGB emissions by the alpha, and cannot represent emission and occlusion properly.
=== Compression ===
PNG uses a two-stage compression process:
pre-compression: filtering (prediction)
compression: DEFLATE
PNG uses DEFLATE, a non-patented lossless data compression algorithm involving a combination of LZ77 and Huffman coding. Permissively licensed DEFLATE implementations, such as zlib, are widely available.
Compared to formats with lossy compression such as JPEG, choosing a compression setting higher than average delays processing, but often does not result in a significantly smaller file size.
==== Filtering ====
Before DEFLATE is applied, the data is transformed via a prediction method: a single filter method is used for the entire image, while for each image line, a filter type is chosen to transform the data to make it more efficiently compressible. The filter type used for a scanline is prepended to the scanline to enable inline decompression.
There is only one filter method in the current PNG specification (denoted method 0), and thus in practice the only choice is which filter type to apply to each line. For this method, the filter predicts the value of each pixel based on the values of previous neighboring pixels, and subtracts the predicted color of the pixel from the actual value, as in DPCM. An image line filtered in this way is often more compressible than the raw image line would be, especially if it is similar to the line above, since the differences from prediction will generally be clustered around 0, rather than spread over all possible image values. This is particularly important in relating separate rows, since DEFLATE has no understanding that an image is a 2D entity, and instead just sees the image data as a stream of bytes.
There are five filter types for filter method 0; each type predicts the value of each byte (of the image data before filtering) based on the corresponding byte of the pixel to the left (A), the pixel above (B), and the pixel above and to the left (C) or some combination thereof, and encodes the difference between the predicted value and the actual value. Filters are applied to byte values, not pixels; pixel values may be one or two bytes, or several values per byte, but never cross byte boundaries. The filter types are:
The Paeth filter is based on an algorithm by Alan W. Paeth.
Compare to the version of DPCM used in lossless JPEG, and to the discrete wavelet transform using 1 × 2, 2 × 1, or (for the Paeth predictor) 2 × 2 windows and Haar wavelets.
Compression is further improved by choosing filter types adaptively on a line-by-line basis. This improvement, and a heuristic method of implementing it commonly used by PNG-writing software, were created by Lee Daniel Crocker, who tested the methods on many images during the creation of the format; the choice of filter is a component of file size optimization, as discussed below.
If interlacing is used, each stage of the interlacing is filtered separately, meaning that the image can be progressively rendered as each stage is received; however, interlacing generally makes compression less effective.
=== Interlacing ===
PNG offers an optional 2-dimensional, 7-pass interlacing scheme—the Adam7 algorithm. This is more sophisticated than GIF's 1-dimensional, 4-pass scheme, and allows a clearer low-resolution image to be visible earlier in the transfer, particularly if interpolation algorithms such as bicubic interpolation are used.
However, the 7-pass scheme tends to reduce the data's compressibility more than simpler schemes.
=== Animation ===
The core PNG format does not support animation. MNG is an extension to PNG that does; it was designed by members of the PNG Group. MNG shares PNG's basic structure and chunks, but it is significantly more complex and has a different file signature, which automatically renders it incompatible with standard PNG decoders. This means that most web browsers and applications either never supported MNG or dropped support for it.
The complexity of MNG led to the proposal of APNG by developers at the Mozilla Foundation. It is based on PNG, supports animation and is simpler than MNG. APNG offers fallback to single-image display for PNG decoders that do not support APNG. Today, the APNG format is supported by all major web browsers. APNG is supported in Firefox 3.0 and up, Pale Moon (all versions), and Safari 8.0 and up. Chromium 59.0 added APNG support, followed by Google Chrome. Opera supported APNG in versions 10–12.1, but support lapsed in version 15 when it switched to the Blink rendering engine; support was re-added in Opera 46 (inherited from Chromium 59). Microsoft Edge has supported APNG since version 79.0, when it switched to a Chromium-based engine.
The PNG Group decided in April 2007 not to embrace APNG. Several alternatives were under discussion, including ANG, aNIM/mPNG, "PNG in GIF" and its subset "RGBA in GIF". However, currently only APNG has widespread support.
With the development of the Third Edition of the PNG Specification, now maintained by the PNG working group, APNG will finally be incorporated into the specification as an extension.
=== Examples ===
Displayed in the fashion of hex editors, with on the left side byte values shown in hex format, and on the right side their equivalent characters from ISO-8859-1 with unrecognized and control characters replaced with periods. Additionally the PNG signature and individual chunks are marked with colors. Note they are easy to identify because of their human readable type names (in this example PNG, IHDR, IDAT, and IEND).
== Advantages ==
Reasons to use PNG:
Portability: Transmission is independent of the software and hardware platform.
Completeness: it's possible to represent true color, indexed-color, and grayscale images.
Coding and decoding in series: allows to generate and read data streams in series, that is, the format of the data stream is used for the generation and visualization of images at the moment through serial communication.
Progressive presentation: to be able to transmit data flows that are initially an approximation of the entire image and progressively they improve as the data flow is received.
Soundness to transmission errors: detects the transmission errors of the data stream correctly.
Losslessness: No loss: filtering and compression preserve all information.
Efficiency: any progressive image presentation, compression and filtering seeks efficient decoding and presentation.
Compression: images can be compressed efficiently and consistently.
Easiness: the implementation of the standard is easy.
Interchangeability: any PNG decoder that follows the standards can read all PNG data streams.
Flexibility: allows future extensions and private additions without affecting the previous point.
Freedom of legal restrictions: the algorithms used are free and accessible.
== Comparison with other file formats ==
=== Graphics Interchange Format (GIF) ===
On small images, GIF can achieve greater compression than PNG (see the section on filesize, below).
On most images, except for the above case, a GIF file has a larger size than an indexed PNG image.
PNG gives a much wider range of transparency options than GIF, including alpha channel transparency.
Whereas GIF is limited to 8-bit indexed color, PNG gives a much wider range of color depths, including 24-bit (8 bits per channel) and 48-bit (16 bits per channel) truecolor, allowing for greater color precision, smoother fades, etc. When an alpha channel is added, up to 64 bits per pixel (before compression) are possible.
When converting an image from the PNG format to GIF, the image quality may suffer due to posterization if the PNG image has more than 256 colors.
GIF intrinsically supports animated images. PNG supports animation only via unofficial extensions (see the section on animation, above).
PNG images are less widely supported by older browsers. In particular, IE6 has limited support for PNG.
=== JPEG ===
The JPEG (Joint Photographic Experts Group) format can produce a smaller file than PNG for photographic (and photo-like) images, since JPEG uses a lossy encoding method specifically designed for photographic image data, which is typically dominated by soft, low-contrast transitions, and an amount of noise or similar irregular structures. Using PNG instead of a high-quality JPEG for such images would result in a large increase in file size with negligible gain in quality. In comparison, when storing images that contain text, line art, or graphics – images with sharp transitions and large areas of solid color – the PNG format can compress image data more than JPEG can. Additionally, PNG is lossless, while JPEG produces visual artifacts around high-contrast areas. (Such artifacts depend on the settings used in the JPG compression; they can be quite noticeable when a low-quality [high-compression] setting is used.) Where an image contains both sharp transitions and photographic parts, a choice must be made between the two effects. JPEG does not support transparency.
JPEG's lossy compression also suffers from generation loss, where repeatedly decoding and re-encoding an image to save it again causes a loss of information each time, degrading the image. Because PNG is lossless, it is suitable for storing images to be edited. While PNG is reasonably efficient when compressing photographic images, there are lossless compression formats designed specifically for photographic images, lossless WebP and Adobe DNG (digital negative) for example. However these formats are either not widely supported, or are proprietary. An image can be stored losslessly and converted to JPEG format only for distribution, so that there is no generation loss.
While the PNG specification does not explicitly include a standard for embedding Exif image data from sources such as digital cameras, the preferred method for embedding EXIF data in a PNG is to use the non-critical ancillary chunk label eXIf.
Early web browsers did not support PNG images; JPEG and GIF were the main image formats. JPEG was commonly used when exporting images containing gradients for web pages, because of GIF's limited color depth. However, JPEG compression causes a gradient to blur slightly. A PNG format reproduces a gradient as accurately as possible for a given bit depth, while keeping the file size small. PNG became the optimal choice for small gradient images as web browser support for the format improved. No images at all are needed to display gradients in modern browsers, as gradients can be created using CSS.
=== JPEG-LS ===
JPEG-LS is an image format by the Joint Photographic Experts Group, though far less widely known and supported than the other lossy JPEG format discussed above. It is directly comparable with PNG, and has a standard set of test images. On the Waterloo Repertoire ColorSet, a standard set of test images (unrelated to the JPEG-LS conformance test set), JPEG-LS generally performs better than PNG, by 10–15%, but on some images PNG performs substantially better, on the order of 50–75%. Thus, if both of these formats are options and file size is an important criterion, they should both be considered, depending on the image.
=== JPEG XL ===
JPEG XL is another, much improved, lossless or lossy format, that is unfortunately supported much less, developed to replace lossless formats like PNG. JPEG XL is more than 50% smaller than JPEG, and that can happen while it's lossless, therefore making it even smaller than PNG. It also supports high dynamic range, wide colour gamuts, and large colour depths. JPEG XL is also very efficient at decoding, and provides smooth transitions from the formats it intends to replace, losslessly able to convert from JPEG. It also excels at compressing without compromising on fidelity.
=== TIFF ===
Tag Image File Format (TIFF) is a format that incorporates an extremely wide range of options. While this makes TIFF useful as a generic format for interchange between professional image editing applications, it makes adding support for it to applications a much bigger task and so it has little support in applications not concerned with image manipulation (such as web browsers). The high level of extensibility also means that most applications provide only a subset of possible features, potentially creating user confusion and compatibility issues.
The most common general-purpose, lossless compression algorithm used with TIFF is Lempel–Ziv–Welch (LZW). This compression technique, also used in GIF, was covered by patents until 2003. TIFF also supports the compression algorithm PNG uses (i.e. Compression Tag 000816 'Adobe-style') with medium usage and support by applications. TIFF also offers special-purpose lossless compression algorithms like CCITT Group IV, which can compress bilevel images (e.g., faxes or black-and-white text) better than PNG's compression algorithm.
PNG supports non-premultiplied alpha only whereas TIFF also supports "associated" (premultiplied) alpha.
=== WebP ===
WebP is a format invented by Google that was intended to replace PNG, JPEG, and GIF. WebP files allow for both lossy and lossless compression, while PNG only allows for lossless compression. WebP also supports animation, something that only GIF files could previously accomplish.
The main improvements of WebP over PNG, however, are the large reduction in file size and therefore faster loading times when embedded into websites. Google claims that lossless WebP images are 26% smaller than PNG files.
WebP has received criticism for being incompatible with various image editing programs and social media websites, unlike PNG. WebP is also not supported across all web browsers, which may require web image hosters to create a fallback image to display to the user, negating the potential storage savings of WebP.
=== AVIF ===
AVIF is an image format developed by the Alliance for Open Media. AVIF was designed by the foundation to make up for the shortcomings of other image codecs, including PNG, GIF, and WebP.
AVIF is generally smaller in size than both WebP and PNG. AVIF supports animation while PNG does not.
However, like WebP, AVIF is supported across fewer browsers and applications than PNG. Specifically, AVIF is supported by the most used browsers, Microsoft Edge, Firefox, and Google Chrome, but requires an additional download for use with Microsoft Windows.
== Software support ==
The official reference implementation of the PNG format is the programming library libpng. It is published as free software under the terms of a permissive free software license. Therefore, it is usually found as an important system library in free operating systems.
=== Bitmap graphics editor support for PNG ===
The PNG format is widely supported by graphics programs, including Adobe Photoshop, Corel's Photo-Paint and Paint Shop Pro, the GIMP, GraphicConverter, Helicon Filter, ImageMagick, Inkscape, IrfanView, Pixel image editor, Paint.NET and Xara Photo & Graphic Designer and many others (including online graphic design platforms such as Canva). Some programs bundled with popular operating systems which support PNG include Microsoft's Paint and Apple's Photos/iPhoto and Preview, with the GIMP also often being bundled with popular Linux distributions.
Adobe Fireworks (formerly by Macromedia) uses PNG as its native file format, allowing other image editors and preview utilities to view the flattened image. However, Fireworks by default also stores metadata for layers, animation, vector data, text and effects. Such files should not be distributed directly. Fireworks can instead export the image as an optimized PNG without the extra metadata for use on web pages, etc.
=== Web browser support for PNG ===
PNG support first appeared in 1997, in Internet Explorer 4.0b1 (32-bit only for NT), and in Netscape 4.04.
Despite calls by the Free Software Foundation and the World Wide Web Consortium (W3C), tools such as gif2png, and campaigns such as Burn All GIFs, PNG adoption on websites was fairly slow due to late and buggy support in Internet Explorer, particularly regarding transparency. PNG is the most used image file format on the web since 2018.
PNG compatible browsers include: Apple Safari, Google Chrome, Mozilla Firefox, Opera, Camino, Internet Explorer, Microsoft Edge and many others. For the complete comparison, see Comparison of web browsers (Image format support).
Especially versions of Internet Explorer (Windows) below 9.0 (released 2011) had numerous problems which prevented it from correctly rendering PNG images.
4.0 crashes on large PNG chunks.
4.0 does not include the functionality to view .png files, but there is a registry fix.
5.0 and 5.01 have broken OBJECT support.
5.01 prints palette images with black (or dark gray) backgrounds under Windows 98, sometimes with radically altered colors.
6.0 fails to display PNG images of 4097 or 4098 bytes in size.
6.0 cannot open a PNG file that contains one or more zero-length IDAT chunks. This issue was first fixed in security update 947864 (MS08-024). For more information, see this article in the Microsoft Knowledge Base: 947864 MS08-024: Cumulative Security Update for Internet Explorer.
6.0 sometimes completely loses ability to display PNGs, but there are various fixes.
6.0 and below have broken alpha-channel transparency support (will display the default background color instead).
7.0 and below cannot combine 8-bit alpha transparency AND element opacity (CSS – filter: Alpha (opacity=xx)) without filling partially transparent sections with black.
8.0 and below have inconsistent/broken gamma support.
8.0 and below don't have color-correction support.
=== Operating system support for PNG icons ===
PNG icons have been supported in most distributions of Linux since at least 1999, in desktop environments such as GNOME. In 2006, Microsoft Windows support for PNG icons was introduced in Windows Vista. PNG icons are supported in AmigaOS 4, AROS, macOS, iOS and MorphOS as well. In addition, Android makes extensive use of PNGs.
== File size and optimization software ==
PNG file size can vary significantly depending on how it is encoded and compressed; this is discussed and a number of tips are given in PNG: The Definitive Guide.
=== Compared to GIF ===
Compared to GIF files, a PNG file with the same information (256 colors, no ancillary chunks/metadata), compressed by an effective compressor is normally smaller than a GIF image. Depending on the file and the compressor, PNG may range from somewhat smaller (10%) to significantly smaller (50%) to somewhat larger (5%), but is rarely significantly larger for large images. This is attributed to the performance of PNG's DEFLATE compared to GIF's LZW, and because the added precompression layer of PNG's predictive filters take account of the 2-dimensional image structure to further compress files; as filtered data encodes differences between pixels, they will tend to cluster closer to 0, rather than being spread across all possible values, and thus be more easily compressed by DEFLATE. However, some versions of Adobe Photoshop, CorelDRAW and MS Paint provide poor PNG compression, creating the impression that GIF is more efficient.
=== File size factors ===
PNG files vary in size due to a number of factors:
color depth
Color depth can range from 1 to 64 bits per pixel.
ancillary chunks
PNG supports metadata—this may be useful for editing, but unnecessary for viewing, as on websites.
interlacing
As each pass of the Adam7 algorithm is separately filtered, this can increase file size.
filter
As a precompression stage, each line is filtered by a predictive filter, which can change from line to line. As the ultimate DEFLATE step operates on the whole image's filtered data, one cannot optimize this row-by-row; the choice of filter for each row is thus potentially very variable, though heuristics exist.
compression
With additional computation, DEFLATE compressors can produce smaller files.
There is thus a filesize trade-off between high color depth, maximal metadata (including color space information, together with information that does not affect display), interlacing, and speed of compression, which all yield large files, with lower color depth, fewer or no ancillary chunks, no interlacing, and tuned but computationally intensive filtering and compression. For different purposes, different trade-offs are chosen: a maximal file may be best for archiving and editing, while a stripped down file may be best for use on a website, and similarly fast but poor compression is preferred when repeatedly editing and saving a file, while slow but high compression is preferred when a file is stable: when archiving or posting.
Interlacing is a trade-off: it dramatically speeds up early rendering of large files (improves latency), but may increase file size (decrease throughput) for little gain, particularly for small files.
==== Lossy PNG compression ====
Although PNG is a lossless format, PNG encoders can preprocess image data in a lossy fashion to improve PNG compression. For example, quantizing a truecolor PNG to 256 colors allows the indexed color type to be used for a likely reduction in file size.
=== Image editing software ===
Some programs are more efficient than others when saving PNG files, this relates to implementation of the PNG compression used by the program.
Many graphics programs (such as Apple's Preview software) save PNGs with large amounts of metadata and color-correction data that are generally unnecessary for Web viewing. Unoptimized PNG files from Adobe Fireworks are also notorious for this since they contain options to make the image editable in supported editors. Also CorelDRAW (at least version 11) sometimes produces PNGs which cannot be opened by Internet Explorer (versions 6–8).
Adobe Photoshop's performance on PNG files has improved in the CS Suite when using the Save For Web feature (which also allows explicit PNG/8 use).
Adobe's Fireworks saves larger PNG files than many programs by default. This stems from the mechanics of its Save format: the images produced by Fireworks' save function include large, private chunks, containing complete layer and vector information. This allows further lossless editing. When saved with the Export option, Fireworks' PNGs are competitive with those produced by other image editors, but are no longer editable as anything but flattened bitmaps. Fireworks is unable to save size-optimized vector-editable PNGs.
Other notable examples of poor PNG compressors include:
Microsoft's Paint for Windows XP
Microsoft Picture It! Photo Premium 9
Poor compression increases the PNG file size but does not affect the image quality or compatibility of the file with other programs.
When the color depth of a truecolor image is reduced to an 8-bit palette (as in GIF), the resulting image data is typically much smaller. Thus a truecolor PNG is typically larger than a color-reduced GIF, although PNG could store the color-reduced version as a palettized file of comparable size. Conversely, some tools, when saving images as PNGs, automatically save them as truecolor, even if the original data use only 8-bit color, thus bloating the file unnecessarily. Both factors can lead to the misconception that PNG files are larger than equivalent GIF files.
=== Optimizing tools ===
Various tools are available for optimizing PNG files; they do this by:
(optionally) removing ancillary chunks,
reducing color depth, either:
use a palette (instead of RGB) if the image has 256 or fewer colors,
use a smaller palette, if the image has 2, 4, or 16 colors, or
(optionally) lossily discard some of the data in the original image,
optimizing line-by-line filter choice, and
optimizing DEFLATE compression.
==== Tool list ====
pngcrush is the oldest of the popular PNG optimizers. It allows for multiple trials on filter selection and compression arguments, and finally chooses the smallest one. This working model is used in almost every png optimizer.
advpng and the similar advdef utility in the AdvanceCOMP package recompress the PNG IDAT. Different DEFLATE implementations are applied depending on the selected compression level, trading between speed and file size: zlib at level 1, libdeflate at level 2, 7-zip's LZMA DEFLATE at level 3, and zopfli at level 4.
pngout was made with the author's own deflater (same to the author's zip utility, kzip), while keeping all facilities of color reduction / filtering. However, pngout doesn't allow for using several trials on filters in a single run. It's suggested to use its commercial GUI version, pngoutwin, or used with a wrapper to automate the trials or to recompress using its own deflater while keep the filter line by line.
zopflipng was also made with its own deflater, zopfli. It has all the optimizing features pngcrush has (including automating trials) while providing a very good, but slow deflater.
A simple comparison of their features is listed below.
Before zopflipng was available, a good way in practice to perform a png optimization is to use a combination of 2 tools in sequence for optimal compression: one which optimizes filters (and removes ancillary chunks), and one which optimizes DEFLATE. Although pngout offers both, only one type of filter can be specified in a single run, therefore it can be used with a wrapper tool or in combination with pngcrush, acting as a re-deflater, like advdef.
==== Ancillary chunk removal ====
For removing ancillary chunks, most PNG optimization tools have the ability to remove all color correction data from PNG files (gamma, white balance, ICC color profile, standard RGB color profile). This often results in much smaller file sizes. For example, the following command line options achieve this with pngcrush:
pngcrush -rem gAMA -rem cHRM -rem iCCP -rem sRGB InputFile.png OutputFile.png
==== Filter optimization ====
pngcrush, pngout, and zopflipng all offer options applying one of the filter types 0–4 globally (using the same filter type for all lines) or with a "pseudo filter" (numbered 5), which for each line chooses one of the filter types 0–4 using an adaptive algorithm. Zopflipng offers 3 different adaptive method, including a brute-force search that attempts to optimize the filtering.
pngout and zopflipng provide an option to preserve/reuse the line-by-line filter set present in the input image.
pngcrush and zopflipng provide options to try different filter strategies in a single run and choose the best. The freeware command line version of pngout doesn't offer this, but the commercial version, pngoutwin, does.
==== DEFLATE optimization ====
Zopfli and the LZMA SDK provide DEFLATE implementations that can produce higher compression ratios than the zlib reference implementation at the cost of performance. AdvanceCOMP's advpng and advdef can use either of these libraries to re-compress PNG files. Additionally, PNGOUT contains its own proprietary DEFLATE implementation.
advpng doesn't have an option to apply filters and always uses filter 0 globally (leaving the image data unfiltered); therefore it should not be used where the image benefits significantly from filtering. By contrast, advdef from the same package doesn't deal with PNG structure and acts only as a re-deflater, retaining any existing filter settings.
=== Icon optimization ===
Since icons intended for Windows Vista and later versions may contain PNG subimages, the optimizations can be applied to them as well. At least one icon editor, Pixelformer, is able to perform a special optimization pass while saving ICO files, thereby reducing their sizes.
Icons for macOS may also contain PNG subimages, yet there isn't such tool available.
== See also ==
Computer graphics, including:
Image editing
Image file formats
Related graphics file formats
APNG Animated PNG
JPEG Network Graphics (JNG)
Multiple-image Network Graphics (MNG)
Similar file formats
X PixMap for portable icons
Scalable Vector Graphics
WebP
== Explanatory notes ==
== References ==
== Further reading ==
Roelofs, Greg (April 1997). "Linux Gazette: History of the Portable Network Graphics (PNG) Format". Linux Journal. 1997 (36es). Specialized Systems Consultants, Inc. ISSN 1075-3583.
Roelofs, Greg (2003). PNG: The Definitive Guide (2nd ed.). O'Reilly Media. ISBN 1-56592-542-4.
"Portable Network Graphics (PNG) Specification" (Second ed.). W3C. 10 November 2003.
== External links ==
PNG Specification
PNG Home Site
libpng Home Page
The Story of PNG by Greg Roelofs
Test inline PNG images
RFC 2083
More information about PNG color correction
The GD-library to generate dynamic PNG-files with PHP
PNG Adam7 interlacing
Encoding Web Shells in PNG files: Encoding human readable data inside an IDAT block. | Wikipedia/Portable_Network_Graphics |
Neural Designer is a software tool for machine learning based on neural networks, a main area of artificial intelligence research, and contains a graphical user interface which simplifies data entry and interpretation of results.
In 2015, Neural Designer was chosen by the European Commission, within the Horizon 2020 program, as a disruptive technology in the ICT field.
== Features ==
Neural Designer performs descriptive, diagnostic, predictive and prescriptive data analytics. It implements deep architectures with multiple non-linear layers and contains utilities to solve function regression, pattern recognition, time series and autoencoding problems.
The input to Neural Designer is a data set, and its output is a predictive model. That result takes the form of an explicit mathematical expression, which can be exported to any computer language or system.
== Related tools ==
Weka: free machine learning and data mining software.
RapidMiner: free and commercial machine learning framework implemented in Java.
KNIME: free and commercial machine learning and data mining software.
== See also ==
Artificial intelligence
Artificial neural network
Comparison of deep learning software
Data mining
Deep learning
Machine learning
Predictive analytics
== References == | Wikipedia/Neural_Designer |
A Hopfield network (or associative memory) is a form of recurrent neural network, or a spin glass system, that can serve as a content-addressable memory. The Hopfield network, named for John Hopfield, consists of a single layer of neurons, where each neuron is connected to every other neuron except itself. These connections are bidirectional and symmetric, meaning the weight of the connection from neuron i to neuron j is the same as the weight from neuron j to neuron i. Patterns are associatively recalled by fixing certain inputs, and dynamically evolve the network to minimize an energy function, towards local energy minimum states that correspond to stored patterns. Patterns are associatively learned (or "stored") by a Hebbian learning algorithm.
One of the key features of Hopfield networks is their ability to recover complete patterns from partial or noisy inputs, making them robust in the face of incomplete or corrupted data. Their connection to statistical mechanics, recurrent networks, and human cognitive psychology has led to their application in various fields, including physics, psychology, neuroscience, and machine learning theory and practice.
== History ==
One origin of associative memory is human cognitive psychology, specifically the associative memory. Frank Rosenblatt studied "close-loop cross-coupled perceptrons", which are 3-layered perceptron networks whose middle layer contains recurrent connections that change by a Hebbian learning rule.: 73–75 : Chapter 19, 21
Another model of associative memory is where the output does not loop back to the input. W. K. Taylor proposed such a model trained by Hebbian learning in 1956. Karl Steinbuch, who wanted to understand learning, and inspired by watching his children learn, published the Lernmatrix in 1961. It was translated to English in 1963. Similar research was done with the correlogram of D. J. Willshaw et al. in 1969. Teuvo Kohonen trained an associative memory by gradient descent in 1974.
Another origin of associative memory was statistical mechanics. The Ising model was published in 1920s as a model of magnetism, however it studied the thermal equilibrium, which does not change with time. Roy J. Glauber in 1963 studied the Ising model evolving in time, as a process towards thermal equilibrium (Glauber dynamics), adding in the component of time.
The second component to be added was adaptation to stimulus. Described independently by Kaoru Nakano in 1971 and Shun'ichi Amari in 1972, they proposed to modify the weights of an Ising model by Hebbian learning rule as a model of associative memory. The same idea was published by William A. Little in 1974, who was acknowledged by Hopfield in his 1982 paper.
See Carpenter (1989) and Cowan (1990) for a technical description of some of these early works in associative memory.
The Sherrington–Kirkpatrick model of spin glass, published in 1975, is the Hopfield network with random initialization. Sherrington and Kirkpatrick found that it is highly likely for the energy function of the SK model to have many local minima. In the 1982 paper, Hopfield applied this recently developed theory to study the Hopfield network with binary activation functions. In a 1984 paper he extended this to continuous activation functions. It became a standard model for the study of neural networks through statistical mechanics.
A major advance in memory storage capacity was developed by Dimitry Krotov and Hopfield in 2016 through a change in network dynamics and energy function. This idea was further extended by Demircigil and collaborators in 2017. The continuous dynamics of large memory capacity models was developed in a series of papers between 2016 and 2020. Large memory storage capacity Hopfield Networks are now called Dense Associative Memories or modern Hopfield networks.
In 2024, John J. Hopfield and Geoffrey E. Hinton were awarded the Nobel Prize in Physics for their foundational contributions to machine learning, such as the Hopfield network.
== Structure ==
The units in Hopfield nets are binary threshold units, i.e. the units only take on two different values for their states, and the value is determined by whether or not the unit's input exceeds its threshold
U
i
{\displaystyle U_{i}}
. Discrete Hopfield nets describe relationships between binary (firing or not-firing) neurons
1
,
2
,
…
,
i
,
j
,
…
,
N
{\displaystyle 1,2,\ldots ,i,j,\ldots ,N}
. At a certain time, the state of the neural net is described by a vector
V
{\displaystyle V}
, which records which neurons are firing in a binary word of
N
{\displaystyle N}
bits.
The interactions
w
i
j
{\displaystyle w_{ij}}
between neurons have units that usually take on values of 1 or −1, and this convention will be used throughout this article. However, other literature might use units that take values of 0 and 1. These interactions are "learned" via Hebb's law of association, such that, for a certain state
V
s
{\displaystyle V^{s}}
and distinct nodes
i
,
j
{\displaystyle i,j}
w
i
j
=
V
i
s
V
j
s
{\displaystyle w_{ij}=V_{i}^{s}V_{j}^{s}}
but
w
i
i
=
0
{\displaystyle w_{ii}=0}
.
(Note that the Hebbian learning rule takes the form
w
i
j
=
(
2
V
i
s
−
1
)
(
2
V
j
s
−
1
)
{\displaystyle w_{ij}=(2V_{i}^{s}-1)(2V_{j}^{s}-1)}
when the units assume values in
{
0
,
1
}
{\displaystyle \{0,1\}}
.)
Once the network is trained,
w
i
j
{\displaystyle w_{ij}}
no longer evolve. If a new state of neurons
V
s
′
{\displaystyle V^{s'}}
is introduced to the neural network, the net acts on neurons such that
V
i
s
′
→
1
{\displaystyle V_{i}^{s'}\rightarrow 1}
if
∑
j
w
i
j
V
j
s
′
≥
U
i
{\displaystyle \sum _{j}w_{ij}V_{j}^{s'}\geq U_{i}}
V
i
s
′
→
−
1
{\displaystyle V_{i}^{s'}\rightarrow -1}
if
∑
j
w
i
j
V
j
s
′
<
U
i
{\displaystyle \sum _{j}w_{ij}V_{j}^{s'}<U_{i}}
where
U
i
{\displaystyle U_{i}}
is the threshold value of the i'th neuron (often taken to be 0). In this way, Hopfield networks have the ability to "remember" states stored in the interaction matrix, because if a new state
V
s
′
{\displaystyle V^{s'}}
is subjected to the interaction matrix, each neuron will change until it matches the original state
V
s
{\displaystyle V^{s}}
(see the Updates section below).
The connections in a Hopfield net typically have the following restrictions:
w
i
i
=
0
,
∀
i
{\displaystyle w_{ii}=0,\forall i}
(no unit has a connection with itself)
w
i
j
=
w
j
i
,
∀
i
,
j
{\displaystyle w_{ij}=w_{ji},\forall i,j}
(connections are symmetric)
The constraint that weights are symmetric guarantees that the energy function decreases monotonically while following the activation rules. A network with asymmetric weights may exhibit some periodic or chaotic behaviour; however, Hopfield found that this behavior is confined to relatively small parts of the phase space and does not impair the network's ability to act as a content-addressable associative memory system.
Hopfield also modeled neural nets for continuous values, in which the electric output of each neuron is not binary but some value between 0 and 1. He found that this type of network was also able to store and reproduce memorized states.
Notice that every pair of units i and j in a Hopfield network has a connection that is described by the connectivity weight
w
i
j
{\displaystyle w_{ij}}
. In this sense, the Hopfield network can be formally described as a complete undirected graph
G
=
⟨
V
,
f
⟩
{\displaystyle G=\langle V,f\rangle }
, where
V
{\displaystyle V}
is a set of McCulloch–Pitts neurons and
f
:
V
2
→
R
{\displaystyle f:V^{2}\rightarrow \mathbb {R} }
is a function that links pairs of units to a real value, the connectivity weight.
== Updating ==
Updating one unit (node in the graph simulating the artificial neuron) in the Hopfield network is performed using the following rule:
s
i
←
{
+
1
if
∑
j
w
i
j
s
j
≥
θ
i
,
−
1
otherwise.
{\displaystyle s_{i}\leftarrow \left\{{\begin{array}{ll}+1&{\text{if }}\sum _{j}{w_{ij}s_{j}}\geq \theta _{i},\\-1&{\text{otherwise.}}\end{array}}\right.}
where:
w
i
j
{\displaystyle w_{ij}}
is the strength of the connection weight from unit j to unit i (the weight of the connection).
s
i
{\displaystyle s_{i}}
is the state of unit i.
θ
i
{\displaystyle \theta _{i}}
is the threshold of unit i.
Updates in the Hopfield network can be performed in two different ways:
Asynchronous: Only one unit is updated at a time. This unit can be picked at random, or a pre-defined order can be imposed from the very beginning.
Synchronous: All units are updated at the same time. This requires a central clock to the system in order to maintain synchronization. This method is viewed by some as less realistic, based on an absence of observed global clock influencing analogous biological or physical systems of interest.
=== Neurons "attract or repel each other" in state space ===
The weight between two units has a powerful impact upon the values of the neurons. Consider the connection weight
w
i
j
{\displaystyle w_{ij}}
between two neurons i and j. If
w
i
j
>
0
{\displaystyle w_{ij}>0}
, the updating rule implies that:
when
s
j
=
1
{\displaystyle s_{j}=1}
, the contribution of j in the weighted sum is positive. Thus,
s
i
{\displaystyle s_{i}}
is pulled by j towards its value
s
i
=
1
{\displaystyle s_{i}=1}
when
s
j
=
−
1
{\displaystyle s_{j}=-1}
, the contribution of j in the weighted sum is negative. Then again,
s
i
{\displaystyle s_{i}}
is pushed by j towards its value
s
i
=
−
1
{\displaystyle s_{i}=-1}
Thus, the values of neurons i and j will converge if the weight between them is positive. Similarly, they will diverge if the weight is negative.
== Convergence properties of discrete and continuous Hopfield networks ==
Bruck in his paper in 1990 studied discrete Hopfield networks and proved a generalized convergence theorem that is based on the connection between the network's dynamics and cuts in the associated graph. This generalization covered both asynchronous as well as synchronous dynamics and presented elementary proofs based on greedy algorithms for max-cut in graphs. A subsequent paper further investigated the behavior of any neuron in both discrete-time and continuous-time Hopfield networks when the corresponding energy function is minimized during an optimization process. Bruck showed that neuron j changes its state if and only if it further decreases the following biased pseudo-cut. The discrete Hopfield network minimizes the following biased pseudo-cut for the synaptic weight matrix of the Hopfield net.
J
p
s
e
u
d
o
−
c
u
t
(
k
)
=
∑
i
∈
C
1
(
k
)
∑
j
∈
C
2
(
k
)
w
i
j
+
∑
j
∈
C
1
(
k
)
θ
j
{\displaystyle J_{pseudo-cut}(k)=\sum _{i\in C_{1}(k)}\sum _{j\in C_{2}(k)}w_{ij}+\sum _{j\in C_{1}(k)}{\theta _{j}}}
where
C
1
(
k
)
{\displaystyle C_{1}(k)}
and
C
2
(
k
)
{\displaystyle C_{2}(k)}
represents the set of neurons which are −1 and +1, respectively, at time
k
{\displaystyle k}
. For further details, see the recent paper.
The discrete-time Hopfield Network always minimizes exactly the following pseudo-cut
U
(
k
)
=
∑
i
=
1
N
∑
j
=
1
N
w
i
j
(
s
i
(
k
)
−
s
j
(
k
)
)
2
+
2
∑
j
=
1
N
θ
j
s
j
(
k
)
{\displaystyle U(k)=\sum _{i=1}^{N}\sum _{j=1}^{N}w_{ij}(s_{i}(k)-s_{j}(k))^{2}+2\sum _{j=1}^{N}\theta _{j}s_{j}(k)}
The continuous-time Hopfield network always minimizes an upper bound to the following weighted cut
V
(
t
)
=
∑
i
=
1
N
∑
j
=
1
N
w
i
j
(
f
(
s
i
(
t
)
)
−
f
(
s
j
(
t
)
)
2
+
2
∑
j
=
1
N
θ
j
f
(
s
j
(
t
)
)
{\displaystyle V(t)=\sum _{i=1}^{N}\sum _{j=1}^{N}w_{ij}(f(s_{i}(t))-f(s_{j}(t))^{2}+2\sum _{j=1}^{N}\theta _{j}f(s_{j}(t))}
where
f
(
⋅
)
{\displaystyle f(\cdot )}
is a zero-centered sigmoid function.
The complex Hopfield network, on the other hand, generally tends to minimize the so-called shadow-cut of the complex weight matrix of the net.
== Energy ==
Hopfield nets have a scalar value associated with each state of the network, referred to as the "energy", E, of the network, where:
E
=
−
1
2
∑
i
,
j
w
i
j
s
i
s
j
−
∑
i
θ
i
s
i
{\displaystyle E=-{\frac {1}{2}}\sum _{i,j}w_{ij}s_{i}s_{j}-\sum _{i}\theta _{i}s_{i}}
This quantity is called "energy" because it either decreases or stays the same upon network units being updated. Furthermore, under repeated updating the network will eventually converge to a state which is a local minimum in the energy function (which is considered to be a Lyapunov function). Thus, if a state is a local minimum in the energy function it is a stable state for the network. Note that this energy function belongs to a general class of models in physics under the name of Ising models; these in turn are a special case of Markov networks, since the associated probability measure, the Gibbs measure, has the Markov property.
== Hopfield network in optimization ==
Hopfield and Tank presented the Hopfield network application in solving the classical traveling-salesman problem in 1985. Since then, the Hopfield network has been widely used for optimization. The idea of using the Hopfield network in optimization problems is straightforward: If a constrained/unconstrained cost function can be written in the form of the Hopfield energy function E, then there exists a Hopfield network whose equilibrium points represent solutions to the constrained/unconstrained optimization problem. Minimizing the Hopfield energy function both minimizes the objective function and satisfies the constraints also as the constraints are "embedded" into the synaptic weights of the network. Although including the optimization constraints into the synaptic weights in the best possible way is a challenging task, many difficult optimization problems with constraints in different disciplines have been converted to the Hopfield energy function: Associative memory systems, Analog-to-Digital conversion, job-shop scheduling problem, quadratic assignment and other related NP-complete problems, channel allocation problem in wireless networks, mobile ad-hoc network routing problem, image restoration, system identification, combinatorial optimization, etc, just to name a few. However, while it is possible to convert hard optimization problems to Hopfield energy functions, it does not guarantee convergence to a solution (even in exponential time).
== Initialization and running ==
Initialization of the Hopfield networks is done by setting the values of the units to the desired start pattern. Repeated updates are then performed until the network converges to an attractor pattern. Convergence is generally assured, as Hopfield proved that the attractors of this nonlinear dynamical system are stable, not periodic or chaotic as in some other systems. Therefore, in the context of Hopfield networks, an attractor pattern is a final stable state, a pattern that cannot change any value within it under updating.
== Training ==
Training a Hopfield net involves lowering the energy of states that the net should "remember". This allows the net to serve as a content addressable memory system, that is to say, the network will converge to a "remembered" state if it is given only part of the state. The net can be used to recover from a distorted input to the trained state that is most similar to that input. This is called associative memory because it recovers memories on the basis of similarity. For example, if we train a Hopfield net with five units so that the state (1, −1, 1, −1, 1) is an energy minimum, and we give the network the state (1, −1, −1, −1, 1) it will converge to (1, −1, 1, −1, 1). Thus, the network is properly trained when the energy of states which the network should remember are local minima. Note that, in contrast to Perceptron training, the thresholds of the neurons are never updated.
=== Learning rules ===
There are various different learning rules that can be used to store information in the memory of the Hopfield network. It is desirable for a learning rule to have both of the following two properties:
Local: A learning rule is local if each weight is updated using information available to neurons on either side of the connection that is associated with that particular weight.
Incremental: New patterns can be learned without using information from the old patterns that have been also used for training. That is, when a new pattern is used for training, the new values for the weights only depend on the old values and on the new pattern.
These properties are desirable, since a learning rule satisfying them is more biologically plausible. For example, since the human brain is always learning new concepts, one can reason that human learning is incremental. A learning system that was not incremental would generally be trained only once, with a huge batch of training data.
=== Hebbian learning rule for Hopfield networks ===
Hebbian theory was introduced by Donald Hebb in 1949 in order to explain "associative learning", in which simultaneous activation of neuron cells leads to pronounced increases in synaptic strength between those cells. It is often summarized as "Neurons that fire together wire together. Neurons that fire out of sync fail to link".
The Hebbian rule is both local and incremental. For the Hopfield networks, it is implemented in the following manner when learning
n
{\displaystyle n}
binary patterns:
w
i
j
=
1
n
∑
μ
=
1
n
ϵ
i
μ
ϵ
j
μ
{\displaystyle w_{ij}={\frac {1}{n}}\sum _{\mu =1}^{n}\epsilon _{i}^{\mu }\epsilon _{j}^{\mu }}
where
ϵ
i
μ
{\displaystyle \epsilon _{i}^{\mu }}
represents bit i from pattern
μ
{\displaystyle \mu }
.
If the bits corresponding to neurons i and j are equal in pattern
μ
{\displaystyle \mu }
, then the product
ϵ
i
μ
ϵ
j
μ
{\displaystyle \epsilon _{i}^{\mu }\epsilon _{j}^{\mu }}
will be positive. This would, in turn, have a positive effect on the weight
w
i
j
{\displaystyle w_{ij}}
and the values of i and j will tend to become equal. The opposite happens if the bits corresponding to neurons i and j are different.
=== Storkey learning rule ===
This rule was introduced by Amos Storkey in 1997 and is both local and incremental. Storkey also showed that a Hopfield network trained using this rule has a greater capacity than a corresponding network trained using the Hebbian rule. The weight matrix of an attractor neural network is said to follow the Storkey learning rule if it obeys:
w
i
j
ν
=
w
i
j
ν
−
1
+
1
n
ϵ
i
ν
ϵ
j
ν
−
1
n
ϵ
i
ν
h
j
i
ν
−
1
n
ϵ
j
ν
h
i
j
ν
{\displaystyle w_{ij}^{\nu }=w_{ij}^{\nu -1}+{\frac {1}{n}}\epsilon _{i}^{\nu }\epsilon _{j}^{\nu }-{\frac {1}{n}}\epsilon _{i}^{\nu }h_{ji}^{\nu }-{\frac {1}{n}}\epsilon _{j}^{\nu }h_{ij}^{\nu }}
where
h
i
j
ν
=
∑
k
=
1
:
i
≠
k
≠
j
n
w
i
k
ν
−
1
ϵ
k
ν
{\displaystyle h_{ij}^{\nu }=\sum _{k=1~:~i\neq k\neq j}^{n}w_{ik}^{\nu -1}\epsilon _{k}^{\nu }}
is a form of local field at neuron i.
This learning rule is local, since the synapses take into account only neurons at their sides. The rule makes use of more information from the patterns and weights than the generalized Hebbian rule, due to the effect of the local field.
== Spurious patterns ==
Patterns that the network uses for training (called retrieval states) become attractors of the system. Repeated updates would eventually lead to convergence to one of the retrieval states. However, sometimes the network will converge to spurious patterns (different from the training patterns). In fact, the number of spurious patterns can be exponential in the number of stored patterns, even if the stored patterns are orthogonal. The energy in these spurious patterns is also a local minimum. For each stored pattern x, the negation -x is also a spurious pattern.
A spurious state can also be a linear combination of an odd number of retrieval states. For example, when using 3 patterns
μ
1
,
μ
2
,
μ
3
{\displaystyle \mu _{1},\mu _{2},\mu _{3}}
, one can get the following spurious state:
ϵ
i
m
i
x
=
±
sgn
(
±
ϵ
i
μ
1
±
ϵ
i
μ
2
±
ϵ
i
μ
3
)
{\displaystyle \epsilon _{i}^{\rm {mix}}=\pm \operatorname {sgn}(\pm \epsilon _{i}^{\mu _{1}}\pm \epsilon _{i}^{\mu _{2}}\pm \epsilon _{i}^{\mu _{3}})}
Spurious patterns that have an even number of states cannot exist, since they might sum up to zero
== Capacity ==
The Network capacity of the Hopfield network model is determined by neuron amounts and connections within a given network. Therefore, the number of memories that are able to be stored is dependent on neurons and connections. Furthermore, it was shown that the recall accuracy between vectors and nodes was 0.138 (approximately 138 vectors can be recalled from storage for every 1000 nodes) (Hertz et al., 1991). Therefore, it is evident that many mistakes will occur if one tries to store a large number of vectors. When the Hopfield model does not recall the right pattern, it is possible that an intrusion has taken place, since semantically related items tend to confuse the individual, and recollection of the wrong pattern occurs. Therefore, the Hopfield network model is shown to confuse one stored item with that of another upon retrieval. Perfect recalls and high capacity, >0.14, can be loaded in the network by Storkey learning method; ETAM, ETAM experiments also in. Ulterior models inspired by the Hopfield network were later devised to raise the storage limit and reduce the retrieval error rate, with some being capable of one-shot learning.
The storage capacity can be given as
C
≅
n
2
log
2
n
{\displaystyle C\cong {\frac {n}{2\log _{2}n}}}
where
n
{\displaystyle n}
is the number of neurons in the net.
== Human memory ==
The Hopfield network is a model for human associative learning and recall. It accounts for associative memory through the incorporation of memory vectors. Memory vectors can be slightly used, and this would spark the retrieval of the most similar vector in the network. However, we will find out that due to this process, intrusions can occur. In associative memory for the Hopfield network, there are two types of operations: auto-association and hetero-association. The first being when a vector is associated with itself, and the latter being when two different vectors are associated in storage. Furthermore, both types of operations are possible to store within a single memory matrix, but only if that given representation matrix is not one or the other of the operations, but rather the combination (auto-associative and hetero-associative) of the two.
Hopfield's network model utilizes the same learning rule as Hebb's (1949) learning rule, which characterised learning as being a result of the strengthening of the weights in cases of neuronal activity.
Rizzuto and Kahana (2001) were able to show that the neural network model can account for repetition on recall accuracy by incorporating a probabilistic-learning algorithm. During the retrieval process, no learning occurs. As a result, the weights of the network remain fixed, showing that the model is able to switch from a learning stage to a recall stage. By adding contextual drift they were able to show the rapid forgetting that occurs in a Hopfield model during a cued-recall task. The entire network contributes to the change in the activation of any single node.
McCulloch and Pitts' (1943) dynamical rule, which describes the behavior of neurons, does so in a way that shows how the activations of multiple neurons map onto the activation of a new neuron's firing rate, and how the weights of the neurons strengthen the synaptic connections between the new activated neuron (and those that activated it). Hopfield would use McCulloch–Pitts's dynamical rule in order to show how retrieval is possible in the Hopfield network. However, Hopfield would do so in a repetitious fashion. Hopfield would use a nonlinear activation function, instead of using a linear function. This would therefore create the Hopfield dynamical rule and with this, Hopfield was able to show that with the nonlinear activation function, the dynamical rule will always modify the values of the state vector in the direction of one of the stored patterns.
== Dense associative memory or modern Hopfield network ==
Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron
i
{\textstyle i}
is defined by a time-dependent variable
V
i
{\displaystyle V_{i}}
, which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons.
In the original Hopfield model of associative memory, the variables were binary, and the dynamics were described by a one-at-a-time update of the state of the neurons. An energy function quadratic in the
V
i
{\displaystyle V_{i}}
was defined, and the dynamics consisted of changing the activity of each single neuron
i
{\displaystyle i}
only if doing so would lower the total energy of the system. This same idea was extended to the case of
V
i
{\displaystyle V_{i}}
being a continuous variable representing the output of neuron
i
{\displaystyle i}
, and
V
i
{\displaystyle V_{i}}
being a monotonic function of an input current. The dynamics became expressed as a set of first-order differential equations for which the "energy" of the system always decreased. The energy in the continuous case has one term which is quadratic in the
V
i
{\displaystyle V_{i}}
(as in the binary model), and a second term which depends on the gain function (neuron's activation function). While having many desirable properties of associative memory, both of these classical systems suffer from a small memory storage capacity, which scales linearly with the number of input features. In contrast, by increasing the number of parameters in the model so that there are not just pair-wise but also higher-order interactions between the neurons, one can increase the memory storage capacity.
Dense Associative Memories (also known as the modern Hopfield networks) are generalizations of the classical Hopfield Networks that break the linear scaling relationship between the number of input features and the number of stored memories. This is achieved by introducing stronger non-linearities (either in the energy function or neurons' activation functions) leading to super-linear (even an exponential) memory storage capacity as a function of the number of feature neurons, in effect increasing the order of interactions between the neurons. The network still requires a sufficient number of hidden neurons.
The key theoretical idea behind dense associative memory networks is to use an energy function and an update rule that is more sharply peaked around the stored memories in the space of neuron's configurations compared to the classical model, as demonstrated when the higher-order interactions and subsequent energy landscapes are explicitly modelled.
=== Discrete variables ===
A simple example of the modern Hopfield network can be written in terms of binary variables
V
i
{\displaystyle V_{i}}
that represent the active
V
i
=
+
1
{\displaystyle V_{i}=+1}
and inactive
V
i
=
−
1
{\displaystyle V_{i}=-1}
state of the model neuron
i
{\displaystyle i}
.
E
=
−
∑
μ
=
1
N
mem
F
(
∑
i
=
1
N
f
ξ
μ
i
V
i
)
{\displaystyle E=-\sum \limits _{\mu =1}^{N_{\text{mem}}}F{\Big (}\sum \limits _{i=1}^{N_{f}}\xi _{\mu i}V_{i}{\Big )}}
In this formula the weights
ξ
μ
i
{\textstyle \xi _{\mu i}}
represent the matrix of memory vectors (index
μ
=
1...
N
mem
{\displaystyle \mu =1...N_{\text{mem}}}
enumerates different memories, and index
i
=
1...
N
f
{\displaystyle i=1...N_{f}}
enumerates the content of each memory corresponding to the
i
{\displaystyle i}
-th feature neuron), and the function
F
(
x
)
{\displaystyle F(x)}
is a rapidly growing non-linear function. The update rule for individual neurons (in the asynchronous case) can be written in the following form
V
i
(
t
+
1
)
=
S
i
g
n
[
∑
μ
=
1
N
mem
(
F
(
ξ
μ
i
+
∑
j
≠
i
ξ
μ
j
V
j
(
t
)
)
−
F
(
−
ξ
μ
i
+
∑
j
≠
i
ξ
μ
j
V
j
(
t
)
)
)
]
{\displaystyle V_{i}^{(t+1)}=Sign{\bigg [}\sum \limits _{\mu =1}^{N_{\text{mem}}}{\bigg (}F{\Big (}\xi _{\mu i}+\sum \limits _{j\neq i}\xi _{\mu j}V_{j}^{(t)}{\Big )}-F{\Big (}-\xi _{\mu i}+\sum \limits _{j\neq i}\xi _{\mu j}V_{j}^{(t)}{\Big )}{\bigg )}{\bigg ]}}
which states that in order to calculate the updated state of the
i
{\textstyle i}
-th neuron the network compares two energies: the energy of the network with the
i
{\displaystyle i}
-th neuron in the ON state and the energy of the network with the
i
{\displaystyle i}
-th neuron in the OFF state, given the states of the remaining neuron. The updated state of the
i
{\displaystyle i}
-th neuron selects the state that has the lowest of the two energies.
In the limiting case when the non-linear energy function is quadratic
F
(
x
)
=
x
2
{\displaystyle F(x)=x^{2}}
these equations reduce to the familiar energy function and the update rule for the classical binary Hopfield Network.
The memory storage capacity of these networks can be calculated for random binary patterns. For the power energy function
F
(
x
)
=
x
n
{\displaystyle F(x)=x^{n}}
the maximal number of memories that can be stored and retrieved from this network without errors is given by
N
mem
m
a
x
≈
1
2
(
2
n
−
3
)
!
!
N
f
n
−
1
ln
(
N
f
)
{\displaystyle N_{\text{mem}}^{max}\approx {\frac {1}{2(2n-3)!!}}{\frac {N_{f}^{n-1}}{\ln(N_{f})}}}
For an exponential energy function
F
(
x
)
=
e
x
{\textstyle F(x)=e^{x}}
the memory storage capacity is exponential in the number of feature neurons
N
mem
m
a
x
≈
2
N
f
/
2
{\displaystyle N_{\text{mem}}^{max}\approx 2^{N_{f}/2}}
=== Continuous variables ===
Modern Hopfield networks or dense associative memories can be best understood in continuous variables and continuous time. Consider the network architecture, shown in Fig.1, and the equations for neuron's states evolutionwhere the currents of the feature neurons are denoted by
x
i
{\textstyle x_{i}}
, and the currents of the memory neurons are denoted by
h
μ
{\displaystyle h_{\mu }}
(
h
{\displaystyle h}
stands for hidden neurons). There are no synaptic connections among the feature neurons or the memory neurons. A matrix
ξ
μ
i
{\displaystyle \xi _{\mu i}}
denotes the strength of synapses from a feature neuron
i
{\displaystyle i}
to the memory neuron
μ
{\displaystyle \mu }
. The synapses are assumed to be symmetric, so that the same value characterizes a different physical synapse from the memory neuron
μ
{\displaystyle \mu }
to the feature neuron
i
{\displaystyle i}
. The outputs of the memory neurons and the feature neurons are denoted by
f
μ
{\displaystyle f_{\mu }}
and
g
i
{\displaystyle g_{i}}
, which are non-linear functions of the corresponding currents. In general these outputs can depend on the currents of all the neurons in that layer so that
f
μ
=
f
(
{
h
μ
}
)
{\displaystyle f_{\mu }=f(\{h_{\mu }\})}
and
g
i
=
g
(
{
x
i
}
)
{\textstyle g_{i}=g(\{x_{i}\})}
. It is convenient to define these activation functions as derivatives of the Lagrangian functions for the two groups of neuronsThis way the specific form of the equations for neuron's states is completely defined once the Lagrangian functions are specified. Finally, the time constants for the two groups of neurons are denoted by
τ
f
{\displaystyle \tau _{f}}
and
τ
h
{\displaystyle \tau _{h}}
,
I
i
{\displaystyle I_{i}}
is the input current to the network that can be driven by the presented data.
General systems of non-linear differential equations can have many complicated behaviors that can depend on the choice of the non-linearities and the initial conditions. For Hopfield Networks, however, this is not the case - the dynamical trajectories always converge to a fixed point attractor state. This property is achieved because these equations are specifically engineered so that they have an underlying energy function The terms grouped into square brackets represent a Legendre transform of the Lagrangian function with respect to the states of the neurons. If the Hessian matrices of the Lagrangian functions are positive semi-definite, the energy function is guaranteed to decrease on the dynamical trajectory This property makes it possible to prove that the system of dynamical equations describing temporal evolution of neurons' activities will eventually reach a fixed point attractor state.
In certain situations one can assume that the dynamics of hidden neurons equilibrates at a much faster time scale compared to the feature neurons,
τ
h
≪
τ
f
{\textstyle \tau _{h}\ll \tau _{f}}
. In this case the steady state solution of the second equation in the system (1) can be used to express the currents of the hidden units through the outputs of the feature neurons. This makes it possible to reduce the general theory (1) to an effective theory for feature neurons only. The resulting effective update rules and the energies for various common choices of the Lagrangian functions are shown in Fig.2. In the case of log-sum-exponential Lagrangian function the update rule (if applied once) for the states of the feature neurons is the attention mechanism commonly used in many modern AI systems (see Ref. for the derivation of this result from the continuous time formulation).
=== Relationship to classical Hopfield network with continuous variables ===
Classical formulation of continuous Hopfield Networks can be understood as a special limiting case of the modern Hopfield networks with one hidden layer. Continuous Hopfield Networks for neurons with graded response are typically described by the dynamical equations and the energy function where
V
i
=
g
(
x
i
)
{\textstyle V_{i}=g(x_{i})}
, and
g
−
1
(
z
)
{\displaystyle g^{-1}(z)}
is the inverse of the activation function
g
(
x
)
{\displaystyle g(x)}
. This model is a special limit of the class of models that is called models A, with the following choice of the Lagrangian functions that, according to the definition (2), leads to the activation functions If we integrate out the hidden neurons the system of equations (1) reduces to the equations on the feature neurons (5) with
T
i
j
=
∑
μ
=
1
N
h
ξ
μ
i
ξ
μ
j
{\displaystyle T_{ij}=\sum \limits _{\mu =1}^{N_{h}}\xi _{\mu i}\xi _{\mu j}}
, and the general expression for the energy (3) reduces to the effective energy While the first two terms in equation (6) are the same as those in equation (9), the third terms look superficially different. In equation (9) it is a Legendre transform of the Lagrangian for the feature neurons, while in (6) the third term is an integral of the inverse activation function. Nevertheless, these two expressions are in fact equivalent, since the derivatives of a function and its Legendre transform are inverse functions of each other. The easiest way to see that these two terms are equal explicitly is to differentiate each one with respect to
x
i
{\displaystyle x_{i}}
. The results of these differentiations for both expressions are equal to
x
i
g
(
x
i
)
′
{\displaystyle x_{i}g(x_{i})'}
. Thus, the two expressions are equal up to an additive constant. This completes the proof that the classical Hopfield Network with continuous states is a special limiting case of the modern Hopfield network (1) with energy (3).
=== General formulation of the modern Hopfield network ===
Biological neural networks have a large degree of heterogeneity in terms of different cell types. This section describes a mathematical model of a fully connected modern Hopfield network assuming the extreme degree of heterogeneity: every single neuron is different. Specifically, an energy function and the corresponding dynamical equations are described assuming that each neuron has its own activation function and kinetic time scale. The network is assumed to be fully connected, so that every neuron is connected to every other neuron using a symmetric matrix of weights
W
I
J
{\displaystyle W_{IJ}}
, indices
I
{\displaystyle I}
and
J
{\displaystyle J}
enumerate different neurons in the network, see Fig.3. The easiest way to mathematically formulate this problem is to define the architecture through a Lagrangian function
L
(
{
x
I
}
)
{\displaystyle L(\{x_{I}\})}
that depends on the activities of all the neurons in the network. The activation function for each neuron is defined as a partial derivative of the Lagrangian with respect to that neuron's activity From the biological perspective one can think about
g
I
{\displaystyle g_{I}}
as an axonal output of the neuron
I
{\displaystyle I}
. In the simplest case, when the Lagrangian is additive for different neurons, this definition results in the activation that is a non-linear function of that neuron's activity. For non-additive Lagrangians this activation function can depend on the activities of a group of neurons. For instance, it can contain contrastive (softmax) or divisive normalization. The dynamical equations describing temporal evolution of a given neuron are given by This equation belongs to the class of models called firing rate models in neuroscience. Each neuron
I
{\displaystyle I}
collects the axonal outputs
g
J
{\displaystyle g_{J}}
from all the neurons, weights them with the synaptic coefficients
W
I
J
{\displaystyle W_{IJ}}
and produces its own time-dependent activity
x
I
{\displaystyle x_{I}}
. The temporal evolution has a time constant
τ
I
{\displaystyle \tau _{I}}
, which in general can be different for every neuron. This network has a global energy function where the first two terms represent the Legendre transform of the Lagrangian function with respect to the neurons' currents
x
I
{\displaystyle x_{I}}
. The temporal derivative of this energy function can be computed on the dynamical trajectories leading to (see for details) The last inequality sign holds provided that the matrix
M
I
K
{\displaystyle M_{IK}}
(or its symmetric part) is positive semi-definite. If, in addition to this, the energy function is bounded from below the non-linear dynamical equations are guaranteed to converge to a fixed point attractor state. The advantage of formulating this network in terms of the Lagrangian functions is that it makes it possible to easily experiment with different choices of the activation functions and different architectural arrangements of neurons. For all those flexible choices the conditions of convergence are determined by the properties of the matrix
M
I
J
{\displaystyle M_{IJ}}
and the existence of the lower bound on the energy function.
=== Hierarchical associative memory network ===
The neurons can be organized in layers so that every neuron in a given layer has the same activation function and the same dynamic time scale. If we assume that there are no horizontal connections between the neurons within the layer (lateral connections) and there are no skip-layer connections, the general fully connected network (11), (12) reduces to the architecture shown in Fig.4. It has
N
layer
{\displaystyle N_{\text{layer}}}
layers of recurrently connected neurons with the states described by continuous variables
x
i
A
{\displaystyle x_{i}^{A}}
and the activation functions
g
i
A
{\displaystyle g_{i}^{A}}
, index
A
{\displaystyle A}
enumerates the layers of the network, and index
i
{\displaystyle i}
enumerates individual neurons in that layer. The activation functions can depend on the activities of all the neurons in the layer. Every layer can have a different number of neurons
N
A
{\displaystyle N_{A}}
. These neurons are recurrently connected with the neurons in the preceding and the subsequent layers. The matrices of weights that connect neurons in layers
A
{\displaystyle A}
and
B
{\displaystyle B}
are denoted by
ξ
i
j
(
A
,
B
)
{\displaystyle \xi _{ij}^{(A,B)}}
(the order of the upper indices for weights is the same as the order of the lower indices, in the example above this means that the index
i
{\displaystyle i}
enumerates neurons in the layer
A
{\displaystyle A}
, and index
j
{\displaystyle j}
enumerates neurons in the layer
B
{\displaystyle B}
). The feedforward weights and the feedback weights are equal. The dynamical equations for the neurons' states can be written as with boundary conditions The main difference between these equations and those from the conventional feedforward networks is the presence of the second term, which is responsible for the feedback from higher layers. These top-down signals help neurons in lower layers to decide on their response to the presented stimuli. Following the general recipe it is convenient to introduce a Lagrangian function
L
A
(
{
x
i
A
}
)
{\displaystyle L^{A}(\{x_{i}^{A}\})}
for the
A
{\displaystyle A}
-th hidden layer, which depends on the activities of all the neurons in that layer. The activation functions in that layer can be defined as partial derivatives of the Lagrangian With these definitions the energy (Lyapunov) function is given by If the Lagrangian functions, or equivalently the activation functions, are chosen in such a way that the Hessians for each layer are positive semi-definite and the overall energy is bounded from below, this system is guaranteed to converge to a fixed point attractor state. The temporal derivative of this energy function is given by Thus, the hierarchical layered network is indeed an attractor network with the global energy function. This network is described by a hierarchical set of synaptic weights that can be learned for each specific problem.
== See also ==
Associative memory (disambiguation)
Autoassociative memory
Boltzmann machine – like a Hopfield net but uses annealed Gibbs sampling instead of gradient descent
Dynamical systems model of cognition
Ising model
Hebbian theory
== References ==
== External links ==
Rojas, Raul (12 July 1996). "13. The Hopfield model" (PDF). Neural Networks – A Systematic Introduction. Springer. ISBN 978-3-540-60505-8.
Hopfield Network Javascript
The Travelling Salesman Problem Archived 2015-05-30 at the Wayback Machine – Hopfield Neural Network JAVA Applet
Hopfield, John (2007). "Hopfield network". Scholarpedia. 2 (5): 1977. Bibcode:2007SchpJ...2.1977H. doi:10.4249/scholarpedia.1977.
"Don't Forget About Associative Memories". The Gradient. November 7, 2020. Retrieved September 27, 2024.
Fletcher, Tristan. "Hopfield Network Learning Using Deterministic Latent Variables" (PDF) (Tutorial). Archived from the original (PDF) on 2011-10-05. | Wikipedia/Hopfield_network |
The generalized Hebbian algorithm, also known in the literature as Sanger's rule, is a linear feedforward neural network for unsupervised learning with applications primarily in principal components analysis. First defined in 1989, it is similar to Oja's rule in its formulation and stability, except it can be applied to networks with multiple outputs. The name originates because of the similarity between the algorithm and a hypothesis made by Donald Hebb about the way in which synaptic strengths in the brain are modified in response to experience, i.e., that changes are proportional to the correlation between the firing of pre- and post-synaptic neurons.
== Theory ==
Consider a problem of learning a linear code for some data. Each data is a multi-dimensional vector
x
∈
R
n
{\displaystyle x\in \mathbb {R} ^{n}}
, and can be (approximately) represented as a linear sum of linear code vectors
w
1
,
…
,
w
m
{\displaystyle w_{1},\dots ,w_{m}}
. When
m
=
n
{\displaystyle m=n}
, it is possible to exactly represent the data. If
m
<
n
{\displaystyle m<n}
, it is possible to approximately represent the data. To minimize the L2 loss of representation,
w
1
,
…
,
w
m
{\displaystyle w_{1},\dots ,w_{m}}
should be the highest principal component vectors.
The generalized Hebbian algorithm is an iterative algorithm to find the highest principal component vectors, in an algorithmic form that resembles unsupervised Hebbian learning in neural networks.
Consider a one-layered neural network with
n
{\displaystyle n}
input neurons and
m
{\displaystyle m}
output neurons
y
1
,
…
,
y
m
{\displaystyle y_{1},\dots ,y_{m}}
. The linear code vectors are the connection strengths, that is,
w
i
j
{\displaystyle w_{ij}}
is the synaptic weight or connection strength between the
j
{\displaystyle j}
-th input and
i
{\displaystyle i}
-th output neurons.
The generalized Hebbian algorithm learning rule is of the form
Δ
w
i
j
=
η
y
i
(
x
j
−
∑
k
=
1
i
w
k
j
y
k
)
{\displaystyle \,\Delta w_{ij}~=~\eta y_{i}\left(x_{j}-\sum _{k=1}^{i}w_{kj}y_{k}\right)}
where
η
{\displaystyle \eta }
is the learning rate parameter.
=== Derivation ===
In matrix form, Oja's rule can be written
d
w
(
t
)
d
t
=
w
(
t
)
Q
−
d
i
a
g
[
w
(
t
)
Q
w
(
t
)
T
]
w
(
t
)
{\displaystyle \,{\frac {{\text{d}}w(t)}{{\text{d}}t}}~=~w(t)Q-\mathrm {diag} [w(t)Qw(t)^{\mathrm {T} }]w(t)}
,
and the Gram-Schmidt algorithm is
Δ
w
(
t
)
=
−
l
o
w
e
r
[
w
(
t
)
w
(
t
)
T
]
w
(
t
)
{\displaystyle \,\Delta w(t)~=~-\mathrm {lower} [w(t)w(t)^{\mathrm {T} }]w(t)}
,
where w(t) is any matrix, in this case representing synaptic weights, Q = η x xT is the autocorrelation matrix, simply the outer product of inputs, diag is the function that diagonalizes a matrix, and lower is the function that sets all matrix elements on or above the diagonal equal to 0. We can combine these equations to get our original rule in matrix form,
Δ
w
(
t
)
=
η
(
t
)
(
y
(
t
)
x
(
t
)
T
−
L
T
[
y
(
t
)
y
(
t
)
T
]
w
(
t
)
)
{\displaystyle \,\Delta w(t)~=~\eta (t)\left(\mathbf {y} (t)\mathbf {x} (t)^{\mathrm {T} }-\mathrm {LT} [\mathbf {y} (t)\mathbf {y} (t)^{\mathrm {T} }]w(t)\right)}
,
where the function LT sets all matrix elements above the diagonal equal to 0, and note that our output y(t) = w(t) x(t) is a linear neuron.
=== Stability and Principal Components Analysis ===
Oja's rule is the special case where
m
=
1
{\displaystyle m=1}
. One can think of the generalized Hebbian algorithm as iterating Oja's rule.
With Oja's rule,
w
1
{\displaystyle w_{1}}
is learned, and it has the same direction as the largest principal component vector is learned, with length determined by
E
[
x
j
]
=
E
[
w
1
j
y
1
]
{\displaystyle E[x_{j}]=E[w_{1j}y_{1}]}
for all
j
{\displaystyle j}
, where the expectation is taken over all input-output pairs. In other words, the length of the vector
w
1
{\displaystyle w_{1}}
is such that we have an autoencoder, with the latent code
y
1
=
∑
i
w
1
i
x
i
{\displaystyle y_{1}=\sum _{i}w_{1i}x_{i}}
, such that
E
[
‖
x
−
y
1
w
1
‖
2
]
{\displaystyle E[\|x-y_{1}w_{1}\|^{2}]}
is minimized.
When
m
=
2
{\displaystyle m=2}
, the first neuron in the hidden layer of the autoencoder still learns as described, since it is unaffected by the second neuron. So, after the first neuron and its vector
w
1
{\displaystyle w_{1}}
has converged, the second neuron is effectively running another Oja's rule on the modified input vectors, defined by
x
′
=
x
−
y
1
w
1
{\displaystyle x'=x-y_{1}w_{1}}
, which we know is the input vector with the first principal component removed. Therefore, the second neuron learns to code for the second principal component.
By induction, this results in finding the top-
m
{\displaystyle m}
principal components for arbitrary
m
{\displaystyle m}
.
== Applications ==
The generalized Hebbian algorithm is used in applications where a self-organizing map is necessary, or where a feature or principal components analysis can be used. Examples of such cases include artificial intelligence and speech and image processing.
Its importance comes from the fact that learning is a single-layer process—that is, a synaptic weight changes only depending on the response of the inputs and outputs of that layer, thus avoiding the multi-layer dependence associated with the backpropagation algorithm. It also has a simple and predictable trade-off between learning speed and accuracy of convergence as set by the learning rate parameter η.
As an example, (Olshausen and Field, 1996) performed the generalized Hebbian algorithm on 8-by-8 patches of photos of natural scenes, and found that it results in Fourier-like features. The features are the same as the principal components found by principal components analysis, as expected, and that, the features are determined by the
64
×
64
{\displaystyle 64\times 64}
variance matrix of the samples of 8-by-8 patches. In other words, it is determined by the second-order statistics of the pixels in images. They criticized this as insufficient to capture higher-order statistics which are necessary to explain the Gabor-like features of simple cells in the primary visual cortex.
== See also ==
Hebbian learning
Factor analysis
Contrastive Hebbian learning
Oja's rule
== References == | Wikipedia/Generalized_Hebbian_algorithm |
The Model Context Protocol (MCP) is an open standard, open-source framework introduced by Anthropic to standardize the way artificial intelligence (AI) models like large language models (LLMs) integrate and share data with external tools, systems, and data sources. Technology writers have dubbed MCP “the USB-C of AI apps”, underscoring its goal of serving as a universal connector between language-model agents and external software. Designed to standardize context exchange between AI assistants and software environments, MCP provides a model-agnostic universal interface for reading files, executing functions, and handling contextual prompts. It was officially announced and open-sourced by Anthropic in November 2024, with subsequent adoption by major AI providers including OpenAI and Google DeepMind.
== Background ==
The protocol was announced in November 2024 as an open standard for connecting AI assistants to data systems such as content repositories, business management tools, and development environments. It addresses the challenge of information silos and legacy systems that constrain even the most sophisticated AI models.
Anthropic introduced MCP to address the growing complexity of integrating LLMs with third-party systems. Before MCP, developers often had to build custom connectors for each data source or tool, resulting in what Anthropic described as an "N×M" data integration problem.
Earlier stop-gap approaches - such as OpenAI’s 2023 “function-calling” API and the ChatGPT plug-in framework - solved similar problems but required vendor-specific connectors. MCP’s authors note that the protocol deliberately re-uses the message-flow ideas of the Language Server Protocol (LSP) and is transported over JSON-RPC 2.0.
MCP was designed as a response to this challenge, offering a universal protocol for interfacing any AI assistant with any structured tool or data layer. The protocol was released with software development kits (SDK) in multiple programming languages, including Python, TypeScript, Java, and C#.
== Features ==
MCP defines a set of specifications for:
Data ingestion and transformation
Contextual metadata tagging
Model interoperability across platforms
Secure, two-way connections between data sources and AI-powered tools
The protocol enables developers to either expose their data through MCP servers or build AI applications (MCP clients) that connect to these servers. Key components include:
Protocol specification and SDKs
Local MCP server support in Claude Desktop apps
Open-source repository of MCP servers
== Applications ==
MCP has been applied across a range of use cases in software development, business process automation, and natural language automation:
Software development: Integrated development environments (IDEs) such as Zed, platforms like Replit, and code intelligence tools such as Sourcegraph integrated MCP to give coding assistants access to real-time code context, useful in vibe coding.
Enterprise assistants: Companies like Block use MCP to allow internal assistants to retrieve information from proprietary documents, customer relationship management (CRM) systems, and company knowledge bases.
Natural language data access: Applications like AI2SQL leverage MCP to connect models with SQL databases, enabling plain-language information retrieval.
Desktop assistants: The Claude Desktop app runs local MCP servers to allow the assistant to read files or interact with system tools securely.
Multi-tool agents: MCP supports agentic AI workflows involving multiple tools (e.g., document lookup + messaging APIs), enabling chain-of-thought reasoning over distributed resources.
Web application development: Wix.com uses MCP servers within its website building platform to enable AI tools to access current website data and make live edits to websites.
== Implementation ==
Anthropic maintains an open-source repository of reference MCP server implementations for popular enterprise systems including Google Drive, Slack, GitHub, Git, Postgres, Puppeteer and Stripe.
Developers can create custom MCP servers to connect proprietary systems or specialized data sources to AI models.
The protocol's open standard allows organizations to build tailored connections while maintaining compatibility with the broader MCP ecosystem. AI models can then leverage these custom connections to provide domain specific assistance while respecting data access permissions.
== Adoption ==
In March 2025, OpenAI officially adopted the MCP, following a decision to integrate the standard across its products, including the ChatGPT desktop app, OpenAI's Agents SDK, and the Responses API. Altman described the adoption of MCP as a step toward standardizing AI tool connectivity. Prior to OpenAI's adoption, the potential benefits of MCP had been discussed extensively within the developer community, particularly for simplifying development in multi-model environments.
By adopting MCP, OpenAI joins other organizations such as Block, Replit, and Sourcegraph in incorporating the protocol into their platforms. This wide adoption highlights MCP's potential to become a universal open standard for AI system connectivity and interoperability. The rapid growth and broad community adoption of MCP are demonstrated by Glama's publicly available MCP server directory, which lists over 5,000 active MCP servers as of May 2025. MCP can be integrated with Microsoft Semantic Kernel, and Azure OpenAI. MCP servers can be deployed to Cloudflare.
Demis Hassabis, CEO of Google DeepMind, confirmed in April 2025 MCP support in the upcoming Gemini models and related infrastructure, describing the protocol as "rapidly becoming an open standard for the AI agentic era".
Many MCP servers have since been added, allowing integration of LLMs with diverse applications.
== Reception ==
The Verge reported that MCP addresses a growing demand for AI agents that are contextually aware and capable of securely pulling from diverse sources. The protocol's rapid uptake by OpenAI, Google DeepMind, and toolmakers like Zed and Sourcegraph suggests growing consensus around its utility.
In April 2025, security researchers released analysis that there are multiple outstanding security issues with MCP, including prompt injection, tool permissions where combining tools can exfiltrate files, and lookalike tools can silently replace trusted ones.
It has been likened to OpenAPI, a similar specification that aims to describe APIs.
== See also ==
AI governance – Guidelines and laws to regulate AIPages displaying short descriptions of redirect targets
Application programming interface – Connection between computers or programsPages displaying short descriptions of redirect targets
LangChain – Language model application development framework
Machine learning – Study of algorithms that improve automatically through experience
Software agent – Computer program acting for a user
== Notes ==
== References ==
Hou, Xinyi; Zhao, Yanjie; Wang, Shenao; Wang, Haoyu (2025). "Model Context Protocol (MCP): Landscape, Security Threats, and Future Research Directions". arXiv:2503.23278 [cs.CR].
Edwards, Benj (April 1, 2025). "MCP: The new "USB-C for AI" that's bringing fierce rivals together". Ars Technica.
Jackson, Fiona (March 28, 2025). "OpenAI Agents Now Support Rival Anthropic's Protocol, Making Data Access 'Simpler, More Reliable'". TechRepublic.
Janakiram MSV (November 30, 2024). "Why Anthropic's Model Context Protocol Is A Big Step In The Evolution Of AI Agents". Forbes.
Greiner, Lynn (November 26, 2024). "Anthropic introduces the Model Context Protocol". InfoWorld.
Wiggers, Kyle (November 25, 2024). "Anthropic proposes a new way to connect data to AI chatbots". TechCrunch.
Dickson, Ben (March 31, 2025). "What is Model Context Protocol (MCP)?". TechTalks.
Masson, Colin (March 25, 2025). "Context Is the Missing Link: The Emergence of the Model Context Protocol in Industrial AI". ARC Advisory Group.
Bastian, Matthias (November 25, 2024). "Anthropic's new open protocol lets AI systems tap into any data source". The Decoder.
Jimin Kim; Anita Lewis; Justin Lewis; Laith Al-Saadoon; Paul Vincent; Pranjali Bhandari (April 1, 2025). "Introducing AWS MCP Servers for code assistants (Part 1)". Amazon AWS.
Desai, Zankar (March 19, 2025). "Introducing Model Context Protocol (MCP) in Copilot Studio: Simplified Integration with AI Apps and Agents". Microsoft Copilot Studio Blog, Microsoft.
McKenzie, Chris (December 19, 2024). "Getting Started: Model Context Protocol". Medium.
"Model Context Protocol (MCP): A Guide With Demo Project". datacamp.com.
Understanding Model Context Protocol: Dr. Tim Wagner, Vendia
== External links ==
Official website
modelcontextprotocol on GitHub
SDK documentation from OpenAI | Wikipedia/Model_Context_Protocol |
A chromosome or genotype in evolutionary algorithms (EA) is a set of parameters which define a proposed solution of the problem that the evolutionary algorithm is trying to solve. The set of all solutions, also called individuals according to the biological model, is known as the population. The genome of an individual consists of one, more rarely of several, chromosomes and corresponds to the genetic representation of the task to be solved. A chromosome is composed of a set of genes, where a gene consists of one or more semantically connected parameters, which are often also called decision variables. They determine one or more phenotypic characteristics of the individual or at least have an influence on them. In the basic form of genetic algorithms, the chromosome is represented as a binary string, while in later variants and in EAs in general, a wide variety of other data structures are used.
== Chromosome design ==
When creating the genetic representation of a task, it is determined which decision variables and other degrees of freedom of the task should be improved by the EA and possible additional heuristics and how the genotype-phenotype mapping should look like. The design of a chromosome translates these considerations into concrete data structures for which an EA then has to be selected, configured, extended, or, in the worst case, created. Finding a suitable representation of the problem domain for a chromosome is an important consideration, as a good representation will make the search easier by limiting the search space; similarly, a poorer representation will allow a larger search space. In this context, suitable mutation and crossover operators must also be found or newly defined to fit the chosen chromosome design. An important requirement for these operators is that they not only allow all points in the search space to be reached in principle, but also make this as easy as possible.
The following requirements must be met by a well-suited chromosome:
It must allow the accessibility of all admissible points in the search space.
Design of the chromosome in such a way that it covers only the search space and no additional areas. so that there is no redundancy or only as little redundancy as possible.
Observance of strong causality: small changes in the chromosome should only lead to small changes in the phenotype. This is also called locality of the relationship between search and problem space.
Designing the chromosome in such a way that it excludes prohibited regions in the search space completely or as much as possible.
While the first requirement is indispensable, depending on the application and the EA used, one usually only has to be satisfied with fulfilling the remaining requirements as far as possible. The evolutionary search is supported and possibly considerably accelerated by a fulfillment as complete as possible.
== Examples of chromosomes ==
=== Chromosomes for binary codings ===
In their classical form, GAs use bit strings and map the decision variables to be optimized onto them. An example for one Boolean and three integer decision variables with the value ranges
0
≤
D
1
≤
60
{\displaystyle 0\leq D_{1}\leq 60}
,
28
≤
D
2
≤
30
{\displaystyle 28\leq D_{2}\leq 30}
and
−
12
≤
D
3
≤
14
{\displaystyle -12\leq D_{3}\leq 14}
may illustrate this:
Note that the negative number here is given in two's complement. This straight forward representation uses five bits to represent the three values of
D
2
{\displaystyle D_{2}}
, although two bits would suffice. This is a significant redundancy. An improved alternative, where 28 is to be added for the genotype-phenotype mapping, could look like this:
with
D
2
=
28
+
D
2
′
=
29
{\displaystyle D_{2}=28+D'_{2}=29}
.
=== Chromosomes with real-valued or integer genes ===
For the processing of tasks with real-valued or mixed-integer decision variables, EAs such as the evolution strategy or the real-coded GAs are suited. In the case of mixed-integer values, rounding is often used, but this represents some violation of the redundancy requirement. If the necessary precisions of the real values can be reasonably narrowed down, this violation can be remedied by using integer-coded GAs. For this purpose, the valid digits of real values are mapped to integers by multiplication with a suitable factor. For example, 12.380 becomes the integer 12380 by multiplying by 1000. This must of course be taken into account in genotype-phenotype mapping for evaluation and result presentation. A common form is a chromosome consisting of a list or an array of integer or real values.
=== Chromosomes for permutations ===
Combinatorial problems are mainly concerned with finding an optimal sequence of a set of elementary items. As an example, consider the problem of the traveling salesman who wants to visit a given number of cities exactly once on the shortest possible tour. The simplest and most obvious mapping onto a chromosome is to number the cities consecutively, to interpret a resulting sequence as permutation and to store it directly in a chromosome, where one gene corresponds to the ordinal number of a city. Then, however, the variation operators may only change the gene order and not remove or duplicate any genes. The chromosome thus contains the path of a possible tour to the cities. As an example the sequence
3
,
5
,
7
,
1
,
4
,
2
,
9
,
6
,
8
{\displaystyle 3,5,7,1,4,2,9,6,8}
of nine cities may serve, to which the following chromosome corresponds:
In addition to this encoding frequently called path representation, there are several other ways of representing a permutation, for example the ordinal representation or the matrix representation.
=== Chromosomes for co-evolution ===
When a genetic representation contains, in addition to the decision variables, additional information that influences evolution and/or the mapping of the genotype to the phenotype and is itself subject to evolution, this is referred to as co-evolution. A typical example is the evolution strategy (ES), which includes one or more mutation step sizes as strategy parameters in each chromosome. Another example is an additional gene to control a selection heuristic for resource allocation in a scheduling tasks.
This approach is based on the assumption that good solutions are based on an appropriate selection of strategy parameters or on control gene(s) that influences genotype-phenotype mapping. The success of the ES gives evidence to this assumption.
=== Chromosomes for complex representations ===
The chromosomes presented above are well suited for processing tasks of continuous, mixed-integer, pure-integer or combinatorial optimization. For a combination of these optimization areas, on the other hand, it becomes increasingly difficult to map them to simple strings of values, depending on the task. The following extension of the gene concept is proposed by the EA GLEAM (General Learning Evolutionary Algorithm and Method) for this purpose: A gene is considered to be the description of an element or elementary trait of the phenotype, which may have multiple parameters. For this purpose, gene types are defined that contain as many parameters of the appropriate data type as are required to describe the particular element of the phenotype. A chromosome now consists of genes as data objects of the gene types, whereby, depending on the application, each gene type occurs exactly once as a gene or can be contained in the chromosome any number of times. The latter leads to chromosomes of dynamic length, as they are required for some problems. The gene type definitions also contain information on the permissible value ranges of the gene parameters, which are observed during chromosome generation and by corresponding mutations, so they cannot lead to lethal mutations. For tasks with a combinatorial part, there are suitable genetic operators that can move or reposition genes as a whole, i.e. with their parameters.
A scheduling task is used as an illustration, in which workflows are to be scheduled that require different numbers of heterogeneous resources. A workflow specifies which work steps can be processed in parallel and which have to be executed one after the other. In this context, heterogeneous resources mean different processing times at different costs in addition to different processing capabilities. Each scheduling operation therefore requires one or more parameters that determine the resource selection, where the value ranges of the parameters depend on the number of alternative resources available for each work step. A suitable chromosome provides one gene type per work step and in this case one corresponding gene, which has one parameter for each required resource. The order of genes determines the order of scheduling operations and, therefore, the precedence in case of allocation conflicts. The exemplary gene type definition of work step 15 with two resources, for which there are four and seven alternatives respectively, would then look as shown in the left image. Since the parameters represent indices in lists of available resources for the respective work step, their value range starts at 0. The right image shows an example of three genes of a chromosome belonging to the gene types in list representation.
=== Chromosomes for tree representations ===
Tree representations in a chromosome are used by genetic programming, an EA type for generating computer programs or circuits. The trees correspond to the syntax trees generated by a compiler as internal representation when translating a computer program. The adjacent figure shows the syntax tree of a mathematical expression as an example. Mutation operators can rearrange, change or delete subtrees depending on the represented syntax structure. Recombination is performed by exchanging suitable subtrees.
== Bibliography ==
Thomas Bäck (1996): Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford Univ. Press. ISBN 978-0-19-509971-3
Wolfgang Banzhaf, P. Nordin, R. Keller, F. Francone (1998): Genetic Programming - An Introduction, Morgan Kaufmann, San Francisco. ISBN 1-55860-510-X
Kenneth A. de Jong (2006): Evolutionary Computation: A Unified Approach. MIT Press, Cambridge, MA. ISBN 0-262-04194-4
Melanie Mitchell (1996): An Introduction to Genetic Algorithms. MIT Press, Cambridge MA. ISBN 978-0-262-63185-3
Hans-Paul Schwefel (1995): Evolution and Optimum Seeking. Wiley & Sons, New York. ISBN 0-471-57148-2
== References == | Wikipedia/Chromosome_(evolutionary_algorithm) |
In computer networking, a heterogeneous network is a network connecting computers and other devices where the operating systems and protocols have significant differences. For example, local area networks (LANs) that connect Windows, Linux and Macintosh computers are heterogeneous.
Heterogeneous network also describes wireless networks using different access technologies. For example, a wireless network that provides a service through a wireless LAN and is able to maintain the service when switching to a cellular network is called a wireless heterogeneous network.
== HetNet ==
Reference to a HetNet often indicates the use of multiple types of access nodes in a wireless network. A Wide Area Network can use some combination of macrocells, picocells, and femtocells in order to offer wireless coverage in an environment with a wide variety of wireless coverage zones, ranging from an open outdoor environment to office buildings, homes, and underground areas. Mobile experts define a HetNet as a network with complex interoperation between macrocell, small cell, and in some cases WiFi network elements used together to provide a mosaic of coverage, with handoff capability between network elements. A study from ARCchart estimates that HetNets will help drive the mobile infrastructure market to account for nearly US$57 billion in spending globally by 2017. Small Cell Forum defines the HetNet as ‘multi-x environment – multi-technology, multi-domain, multi-spectrum, multi-operator and multi-vendor. It must be able to automate the reconfiguration of its operation to deliver assured service quality across the entire network, and flexible enough to accommodate changing user needs, business goals and subscriber behaviors.’
== HetNet architecture ==
From an architectural perspective, the HetNet can be viewed as encompassing conventional macro radio access network (RAN) functions, RAN transport capability, small cells, and Wi-Fi functionality, which are increasingly being virtualized and delivered in an operational environment where span of control includes data center resources associated with compute, networking, and storage.
In this framework, self-optimizing network (SON) functionality is essential to enable order-of-magnitude network densification with small cells. Self-configuration or ‘plug and play’ reduces time and cost of deployment, while self-optimization then ensures the network auto-tunes itself for maximum efficiency as conditions change. Traffic demand, user movements and service mix will all evolve over time, and the network needs to adapt to keep pace. These enhanced SON capabilities will therefore need to take into account the evolving user needs, business goals and subscriber behaviors.
Importantly, functions associated with HetNet operations and management take earlier SON capability that may have only been targeted at a single domain or technology, and expand it to deliver automated service quality management across the entire HetNet.
== Wireless ==
A Heterogeneous wireless network (HWN) is a special case of a HetNet. Whereas a HetNet may consist of a network of computers or devices with different capabilities in terms of operating systems, hardware, protocols, etc., an HWN is a wireless network that consists of devices using different underlying radio access technology (RAT).
Several problems still need to be solved in heterogeneous wireless networks such as:
Determining the theoretical capacity of HWNs
Interoperability of technology
Handover
Mobility
Quality of service / quality of experience
Interference between RATs
Aggregation
An HWN has several benefits when compared with a traditional homogeneous wireless network, including increased reliability, improved spectrum efficiency, and increased coverage. Reliability is improved since when one particular RAT within the HWN fails, it may still be possible to maintain a connection by falling back to another RAT. Spectrum efficiency is improved by making use of RATs, which may have few users through the use of load balancing across RATs and coverage may be improved because different RATs may fill holes in coverage that any one of the single networks alone would not be able to fill.
== Semantics ==
From a semantic point of view, the heterogeneous network terminology can have different connotations in wireless telecommunications. For instance, it could refer to the paradigm of seamless and ubiquitous interoperability between various multi-coverage protocols (aka, HetNet). Otherwise, it might refer to the non-uniform spatial distribution of users or wireless nodes (aka, spatial inhomogeneity). Therefore, using the term "heterogeneous network" without putting it into context can result in a source of confusion in scientific literature and during the peer-review cycle. In fact, the confusion may further be aggravated, especially in light of the fact that the HetNet paradigm is often also researched from a geometrical angle.
== See also ==
Open standard
== References == | Wikipedia/Heterogeneous_network |
Lateral movement refers to the techniques that cyber attackers, or threat actors, use to progressively move through a network as they search for the key data and assets that are ultimately the target of their attack campaigns. While the development of more sophisticated sequences of attack has helped threat actors develop better strategies and evade detection as compared to the past, similar to planning a heist, cyber defenders have also learned to use lateral movement against attackers in that they use it to detect their location and respond more effectively to an attack.
Lateral movement is a part of the ATT&CK framework within the 14 categories of Tactics, Techniques, and Procedures.
== References == | Wikipedia/Network_Lateral_Movement |
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of a set for the set of vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs. Researchers have studied the problem of computing the diameter, both in arbitrary graphs and in special classes of graphs.
The diameter of a disconnected graph may be defined to be infinite, or undefined.
== Graphs of low diameter ==
The degree diameter problem seeks tight relations between the diameter, number of vertices, and degree of a graph. One way of formulating it is to ask for the largest graph with given bounds on its degree and diameter. For any fixed degree, this maximum size is exponential in diameter, with the base of the exponent depending on the degree.
The girth of a graph, the length of its shortest cycle, can be at most
2
k
+
1
{\displaystyle 2k+1}
for a graph of diameter
k
{\displaystyle k}
. The regular graphs for which the girth is exactly
2
k
+
1
{\displaystyle 2k+1}
are the Moore graphs. Only finitely many Moore graphs exist, but their exact number is unknown. They provide the solutions to the degree diameter problem for their degree and diameter.
Small-world networks are a class of graphs with low diameter, modeling the real-world phenomenon of six degrees of separation in social networks.
== Algorithms ==
=== In arbitrary graphs ===
The diameter of a graph can be computed by using a shortest path algorithm to compute shortest paths between all pairs of vertices, and then taking the maximum of the distances that it computes. For instance, in a graph with positive edge weights, this can be done by repeatedly using Dijkstra's algorithm, once for each possible starting vertex. In a graph with
n
{\displaystyle n}
vertices and
m
{\displaystyle m}
edges, this takes time
O
(
m
n
+
n
2
log
n
)
{\displaystyle O(mn+n^{2}\log n)}
. Computing all-pairs shortest paths is the fastest known method for computing the diameter of a weighted graph exactly.
In an unweighted-graph, Dijkstra's algorithm may be replaced by a breadth-first search, giving time
O
(
m
n
)
{\displaystyle O(mn)}
. Alternatively, the diameter may be computed using an algorithm based on fast matrix multiplication, in time proportional to the time for multiplying
n
×
n
{\displaystyle n\times n}
matrices, approximately
O
(
n
2.37
)
{\displaystyle O(n^{2.37})}
using known matrix multiplication algorithms. For sparse graphs, with few edges, repeated breadth-first search is faster than matrix multiplication. Assuming the strong exponential time hypothesis, repeated breadth-first search is near-optimal: this hypothesis implies that no algorithm can achieve time
O
(
n
2
−
ε
)
{\displaystyle O(n^{2-\varepsilon })}
for any
ε
>
0
{\displaystyle \varepsilon >0}
.
It is possible to approximate the diameter of a weighted graph to within an approximation ratio of 3/2, in time
O
~
(
min
(
m
3
/
2
,
m
n
2
/
3
)
{\displaystyle {\tilde {O}}(\min(m^{3/2},mn^{2/3})}
, where the
O
~
{\displaystyle {\tilde {O}}}
notation hides logarithmic factors in the time bound. Under the exponential time hypothesis, no substantially more accurate approximation, substantially faster than all pairs shortest paths, is possible.
=== In special classes of graphs ===
The diameter can be computed in linear time for interval graphs, and in near-linear time for graphs of bounded treewidth. In median graphs, the diameter can be found in the subquadratic time bound
O
~
(
n
1.6456
)
{\displaystyle {\tilde {O}}(n^{1.6456})}
.
In any class of graphs closed under graph minors, such as the planar graphs, it is possible to compute the diameter in subquadratic time, with an exponent depending on the graph family.
== See also ==
Triameter (graph theory)
Diameter (group theory), the diameter of a Cayley graph of the group, for generators chosen to make this diameter as large as possible
Flip distance § Diameter of the flip graph, connecting pairs of triangulations by local moves
== References == | Wikipedia/Diameter_(graph_theory) |
A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection of documents.
Each vertex (or node) in the graph represents a document in the collection, and each edge is directed from one document toward another that it cites (or vice versa depending on the specific implementation).
Citation graphs have been utilised in various ways, including forms of citation analysis, academic search tools and court judgements. They are predicted to become more relevant and useful in the future as the body of published research grows.
== Implementation ==
There is no standard format for the citations in bibliographies, and the record linkage of citations can be a time-consuming and complicated process. Furthermore, citation errors can occur at any stage of the publishing process. However, there is a long history of creating citation databases, also known as citation indexes, so there is a lot of information about such problems.
In principle, each document should have a unique publication date and can only refer to earlier documents. This means that an ideal citation graph is not only directed but acyclic; that is, there are no loops in the graph. This is not always the case in practice, since an academic paper goes through several versions in the publishing process. The timing of asynchronous updates to bibliographies may lead to edges that apparently point backward in time. Such "backward" citations seem to constitute less than 1% of the total number of links.
As citation links are meant to be permanent, the bulk of a citation graph should be static, and only the leading edge of the graph should change. Exceptions might occur when papers are withdrawn from circulation.
== Background and history ==
A citation is a reference to a published or unpublished source (not always the original source). More precisely, a citation is an abbreviated alphanumeric expression embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work. Its purpose is to acknowledge the relevance of the works of others to the topic of discussion at the point where the citation appears.
Generally the combination of both the in-body citation and the bibliographic entry constitutes what is commonly thought of as a citation (whereas bibliographic entries by themselves are not). References to single, machine-readable assertions in electronic scientific articles are known as nanopublications, a form of micro attributions.
Citation networks are one kind of social network that has been studied quantitatively almost from the moment citation databases first became available. In 1965, Derek J. de Solla Price described the inherent linking characteristic of the Science Citation Index (SCI) in his paper entitled "Networks of Scientific Papers." The links between citing and cited papers became dynamic when the SCI began to be published online. In 1973, Henry Small published his work on co-citation analysis, which became a self-organizing classification system that led to document clustering experiments and eventually what is called "Research Reviews."
== Applications ==
=== Citation Analysis ===
Citation graphs can be applied to measures of scholarly impact, the impact a particular paper has had on the academic world. While a hard value to quantify, scholarly impact is useful, as having a measure of scholarly impact for many papers can aid in identifying important papers. It can also provide a measure of the relevance of a particular academic community. Citation graphs are very useful in measuring this as the number of connections on the citation graph corresponds with the scholarly impact of an article, as this means it has been cited by many other papers.
Similarity analysis is another area of citation analysis which frequently makes uses of citation graphs. The relationship between two papers in the citation graph has been compared to their text-based similarity, and it is found that closeness in the citation graph can predict a level of text-based similarity. Additionally, it has been found that the two methods – citation graph closeness and traditional content-based similarity – work well in conjunction to produce a more accurate result.
Analyses of citation graphs have also led to the proposal of the citation graph as a way to identify different communities and research areas within the academic world. It has been found that analysing the citation graph for groups of documents in conjunction with keywords can provide an accurate way to identify clusters of similar research. In a similar vein, a way of identifying the main “stream” of an area of research, or the progression of a research idea over time can be identified by using depth first search algorithms on the citation graph. Instead of looking at similarity between two nodes, or clusters of many nodes, this method instead goes through the links between nodes to trace a research idea back to its beginning, and so discover its progression through different papers to where its current status is.
=== Search Tools ===
The traditional method used by academic search tools is to check for matches between a search term and keywords in papers to return potential matches. While mostly effective, this method can lead to errors where a paper is recommended from a different discipline because of keyword matches even when the two topics actually have little in common.
Many have argued that this way of searching for relevant papers could be improved and made more accurate if citation graphs were incorporated into academic paper search tools. For example, one system was proposed which used both the keyword system and a popularity system based on how many connections a paper had in the citation graph. In this system, more connected papers were considered more popular and therefore given a higher weighting in the paper recommendation system.
In more recent years, visual search tools have been developed which use citation graphs to provide a visual representation of the connections between papers. A commercial implementation of this concept is the search tool Connected Papers.
=== Court Judgements ===
Citation graphs have a history of being used to aid in organising and mapping citations of legal documents. In a similar way to the aforementioned search tools, constructions of citation graphs specific to the types of citations found in legal documents have been used to allow relevant past legal documents to be found when needed for a court decision. As a way of replacing or improving upon traditional search methods, this citation graph aided way of organising legal documents can provide higher efficiency, accuracy, and organisation.
== Related networks ==
There are several other types of network graphs that are closely related to citation networks. The co-citation graph is the graph between documents as nodes, where two documents are connected if they share a common citation (see Co-citation and Bibliographic coupling). Other related networks are formed using other information present in the document. For instance, in a collaboration graph, known in this context as a co-authorship network, the nodes are the authors of documents, linked if they have co-authored the same document. The link weights between two authors in co-authorship networks can increase over time if they have further collaboration.
== Future Developments ==
While citation graphs have had a noticeable impact on several areas of academia, they are likely to become more relevant in the future. As the body of published research grows, more traditional ways of searching for papers will become less effective in narrowing down relevant papers to a particular topic. For example, text-based similarity can only go so far in selecting which papers are relevant to a topic, whereas the addition of citation graphs could make use of giving higher priority to those papers which have a lot of connections to other papers relevant to the topic.
However, developments like this face similar challenges to that of most applications of citation graphs, which is the face that there is no standardized format or way of citing. This makes the construction of these graphs very difficult, since it requires complex software analysis to extract citations from papers. One solution proposed to this problem is to create open databases of citation information in a format which could be used by anyone and easily converted to a different form, for example a citation graph.
== See also ==
Collaboration graph, a graph defined by the authors of documents
Web graph, a citation graph of references from one web page to another in the World Wide Web
Directed Acyclic Graph, the formal mathematical structure of a well-constructed citation graph
Legal citation analysis citation analysis in legal contexts
== References ==
== Further reading ==
An, Yuan; Janssen, Jeannette; Milios, Evangelos E. (2004), "Characterizing and Mining the Citation Graph of the Computer Science Literature", Knowledge and Information Systems, 6 (6): 664–678, doi:10.1007/s10115-003-0128-3, S2CID 348227.
Yong, Fang; Rousseau, Ronald (2001), "Lattices in citation networks: An investigation into the structure of citation graphs", Scientometrics, 50 (2): 273–287, doi:10.1023/A:1010573723540, S2CID 413673.
Lu, Wangzhong; Janssen, J.; Milios, E.; Japkowicz, N.; Zhang, Yongzheng (2007), "Node similarity in the citation graph", Knowledge and Information Systems, 11 (1): 105–129, doi:10.1007/s10115-006-0023-9, S2CID 26234247.
== External links ==
Connected Papers | Wikipedia/Citation_graph |
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is a generalization of the color refinement algorithm and has been first described by Weisfeiler and Leman in 1968. The original formulation is based on graph canonization, a normal form for graphs, while there is also a combinatorial interpretation in the spirit of color refinement and a connection to logic.
There are several versions of the test (e.g. k-WL and k-FWL) referred to in the literature by various names, which easily leads to confusion. Additionally, Andrey Leman is spelled `Lehman' in several older articles.
== Weisfeiler-Leman-based Graph Isomorphism heuristics ==
All variants of color refinement are one-sided heuristics that take as input two graphs G and H and output a certificate that they are different or 'I don't know'. This means that if the heuristic is able to tell G and H apart, then they are definitely different, but the other direction does not hold: for every variant of the WL-test (see below) there are non-isomorphic graphs where the difference is not detected. Those graphs are highly symmetric graphs such as regular graphs for 1-WL/color refinement.
== Examples ==
The first three examples are for graphs of order 5.
WLpair takes 3 rounds on 'G0' and 'G1'. The test succeeds as the certificates agree.
WLpair takes 4 rounds on 'G0' and 'G2'. The test fails as the certificates disagree. Indeed 'G0' has a cycle of length 5, while 'G2' doesn't, thus 'G0' and 'G2' cannot be isomorphic.
WLpair takes 4 rounds on 'G1' and 'G2'. The test fails as the certificates disagree. From the previous two instances we already know
G
1
≅
G
0
≇
G
2
{\displaystyle G_{1}\cong G_{0}\not \cong G_{2}}
.
Indeed G0 and G1 are isomorphic. Any isomorphism must respect the components and therefore the labels. This can be used for kernelization of the graph isomorphism problem. Note that not every map of vertices that respects the labels gives an isomorphism. Let
φ
:
G
0
→
G
1
{\displaystyle \varphi :G_{0}\rightarrow G_{1}}
and
ψ
:
G
0
→
G
1
{\displaystyle \psi :G_{0}\rightarrow G_{1}}
be maps given by
φ
(
a
)
=
D
,
φ
(
b
)
=
C
,
φ
(
c
)
=
B
,
φ
(
d
)
=
E
,
φ
(
e
)
=
A
{\displaystyle \varphi (a)=D,\varphi (b)=C,\varphi (c)=B,\varphi (d)=E,\varphi (e)=A}
resp.
ψ
(
a
)
=
B
,
ψ
(
b
)
=
C
,
ψ
(
c
)
=
D
,
ψ
(
d
)
=
E
,
ψ
(
e
)
=
A
{\displaystyle \psi (a)=B,\psi (b)=C,\psi (c)=D,\psi (d)=E,\psi (e)=A}
. While
φ
{\displaystyle \varphi }
is not an isomorphism
ψ
{\displaystyle \psi }
constitutes an isomorphism.
When applying WLpair to G0 and G2 we get for G0 the certificate 7_7_8_9_9. But the isomorphic G1 gets the certificate 7_7_8_8_9 when applying WLpair to G1 and G2. This illustrates the phenomenon about labels depending on the execution order of the WLtest on the nodes. Either one finds another relabeling method that keeps uniqueness of labels, which becomes rather technical, or one skips the relabeling altogether and keeps the label strings, which blows up the length of the certificate significantly, or one applies WLtest to the union of the two tested graphs, as we did in the variant WLpair. Note that although G1 and G2 can get distinct certificates when WLtest is executed on them separately, they do get the same certificate by WLpair.
The next example is about regular graphs. WLtest cannot distinguish regular graphs of equal order,: 31 but WLpair can distinguish regular graphs of distinct degree even if they have the same order. In fact WLtest terminates after a single round as seen in these examples of order 8, which are all 3-regular except the last one which is 5-regular.
All four graphs are pairwise non-isomorphic. G8_00 has two connected components, while the others do not. G8_03 is 5-regular, while the others are 3-regular. G8_01 has no 3-cycle while G8_02 does have 3-cycles.
Another example of two non-isomorphic graphs that WLpair cannot distinguish is given here.
== Applications ==
=== Weisfeiler Leman graph kernels ===
The theory behind the Weisfeiler Leman test is applied in graph neural networks.
In machine learning of nonlinear data one uses kernels to represent the data in a high dimensional feature space after which linear techniques such as support vector machines can be applied. Data represented as graphs often behave nonlinear. Graph kernels are method to preprocess such graph based nonlinear data to simplify subsequent learning methods. Such graph kernels can be constructed by partially executing a Weisfeiler Leman test and processing the partition that has been constructed up to that point. These Weisfeiler Leman graph kernels have attracted considerable research in the decade after their publication.
Kernels for artificial neural network in the context of machine learning such as graph kernels are not to be confused with kernels applied in heuristic algorithms to reduce the computational cost for solving problems of high complexity such as instances of NP-hard problems in the field of complexity theory. As stated above the Weisfeiler Leman test can also be applied in the later context.
== See also ==
Graph isomorphism
Graph neural network
== References == | Wikipedia/Weisfeiler_Leman_graph_isomorphism_test |
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp.
If x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative
f
′
(
x
0
)
{\displaystyle f'(x_{0})}
exists. In other words, the graph of f has a non-vertical tangent line at the point (x0, f(x0)). f is said to be differentiable on U if it is differentiable at every point of U. f is said to be continuously differentiable if its derivative is also a continuous function over the domain of the function
f
{\textstyle f}
. Generally speaking, f is said to be of class
C
k
{\displaystyle C^{k}}
if its first
k
{\displaystyle k}
derivatives
f
′
(
x
)
,
f
′
′
(
x
)
,
…
,
f
(
k
)
(
x
)
{\textstyle f^{\prime }(x),f^{\prime \prime }(x),\ldots ,f^{(k)}(x)}
exist and are continuous over the domain of the function
f
{\textstyle f}
.
For a multivariable function, as shown here, the differentiability of it is something more complex than the existence of the partial derivatives of it.
== Differentiability of real functions of one variable ==
A function
f
:
U
→
R
{\displaystyle f:U\to \mathbb {R} }
, defined on an open set
U
⊂
R
{\textstyle U\subset \mathbb {R} }
, is said to be differentiable at
a
∈
U
{\displaystyle a\in U}
if the derivative
f
′
(
a
)
=
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
=
lim
x
→
a
f
(
x
)
−
f
(
a
)
x
−
a
{\displaystyle f'(a)=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}=\lim _{x\to a}{\frac {f(x)-f(a)}{x-a}}}
exists. This implies that the function is continuous at a.
This function f is said to be differentiable on U if it is differentiable at every point of U. In this case, the derivative of f is thus a function from U into
R
.
{\displaystyle \mathbb {R} .}
A continuous function is not necessarily differentiable, but a differentiable function is necessarily continuous (at every point where it is differentiable) as is shown below (in the section Differentiability and continuity). A function is said to be continuously differentiable if its derivative is also a continuous function; there exist functions that are differentiable but not continuously differentiable (an example is given in the section Differentiability classes).
=== Semi-differentiability ===
The above definition can be extended to define the derivative at boundary points. The derivative of a function
f
:
A
→
R
{\textstyle f:A\to \mathbb {R} }
defined on a closed subset
A
⊊
R
{\textstyle A\subsetneq \mathbb {R} }
of the real numbers, evaluated at a boundary point
c
{\textstyle c}
, can be defined as the following one-sided limit, where the argument
x
{\textstyle x}
approaches
c
{\textstyle c}
such that it is always within
A
{\textstyle A}
:
f
′
(
c
)
=
lim
x
→
c
x
∈
A
f
(
x
)
−
f
(
c
)
x
−
c
.
{\displaystyle f'(c)=\lim _{\scriptstyle x\to c \atop \scriptstyle x\in A}{\frac {f(x)-f(c)}{x-c}}.}
For
x
{\textstyle x}
to remain within
A
{\textstyle A}
, which is a subset of the reals, it follows that this limit will be defined as either
f
′
(
c
)
=
lim
x
→
c
+
f
(
x
)
−
f
(
c
)
x
−
c
or
f
′
(
c
)
=
lim
x
→
c
−
f
(
x
)
−
f
(
c
)
x
−
c
.
{\displaystyle f'(c)=\lim _{x\to c^{+}}{\frac {f(x)-f(c)}{x-c}}\quad {\text{or}}\quad f'(c)=\lim _{x\to c^{-}}{\frac {f(x)-f(c)}{x-c}}.}
== Differentiability and continuity ==
If f is differentiable at a point x0, then f must also be continuous at x0. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.
Most functions that occur in practice have derivatives at all points or at almost every point. However, a result of Stefan Banach states that the set of functions that have a derivative at some point is a meagre set in the space of all continuous functions. Informally, this means that differentiable functions are very atypical among continuous functions. The first known example of a function that is continuous everywhere but differentiable nowhere is the Weierstrass function.
== Differentiability classes ==
A function
f
{\textstyle f}
is said to be continuously differentiable if the derivative
f
′
(
x
)
{\textstyle f^{\prime }(x)}
exists and is itself a continuous function. Although the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity. For example, the function
f
(
x
)
=
{
x
2
sin
(
1
/
x
)
if
x
≠
0
0
if
x
=
0
{\displaystyle f(x)\;=\;{\begin{cases}x^{2}\sin(1/x)&{\text{ if }}x\neq 0\\0&{\text{ if }}x=0\end{cases}}}
is differentiable at 0, since
f
′
(
0
)
=
lim
ε
→
0
(
ε
2
sin
(
1
/
ε
)
−
0
ε
)
=
0
{\displaystyle f'(0)=\lim _{\varepsilon \to 0}\left({\frac {\varepsilon ^{2}\sin(1/\varepsilon )-0}{\varepsilon }}\right)=0}
exists. However, for
x
≠
0
,
{\displaystyle x\neq 0,}
differentiation rules imply
f
′
(
x
)
=
2
x
sin
(
1
/
x
)
−
cos
(
1
/
x
)
,
{\displaystyle f'(x)=2x\sin(1/x)-\cos(1/x)\;,}
which has no limit as
x
→
0.
{\displaystyle x\to 0.}
Thus, this example shows the existence of a function that is differentiable but not continuously differentiable (i.e., the derivative is not a continuous function). Nevertheless, Darboux's theorem implies that the derivative of any function satisfies the conclusion of the intermediate value theorem.
Similarly to how continuous functions are said to be of class
C
0
,
{\displaystyle C^{0},}
continuously differentiable functions are sometimes said to be of class
C
1
{\displaystyle C^{1}}
. A function is of class
C
2
{\displaystyle C^{2}}
if the first and second derivative of the function both exist and are continuous. More generally, a function is said to be of class
C
k
{\displaystyle C^{k}}
if the first
k
{\displaystyle k}
derivatives
f
′
(
x
)
,
f
′
′
(
x
)
,
…
,
f
(
k
)
(
x
)
{\textstyle f^{\prime }(x),f^{\prime \prime }(x),\ldots ,f^{(k)}(x)}
all exist and are continuous. If derivatives
f
(
n
)
{\displaystyle f^{(n)}}
exist for all positive integers
n
,
{\textstyle n,}
the function is smooth or equivalently, of class
C
∞
.
{\displaystyle C^{\infty }.}
== Differentiability in higher dimensions ==
A function of several real variables f: Rm → Rn is said to be differentiable at a point x0 if there exists a linear map J: Rm → Rn such that
lim
h
→
0
‖
f
(
x
0
+
h
)
−
f
(
x
0
)
−
J
(
h
)
‖
R
n
‖
h
‖
R
m
=
0.
{\displaystyle \lim _{\mathbf {h} \to \mathbf {0} }{\frac {\|\mathbf {f} (\mathbf {x_{0}} +\mathbf {h} )-\mathbf {f} (\mathbf {x_{0}} )-\mathbf {J} \mathbf {(h)} \|_{\mathbf {R} ^{n}}}{\|\mathbf {h} \|_{\mathbf {R} ^{m}}}}=0.}
If a function is differentiable at x0, then all of the partial derivatives exist at x0, and the linear map J is given by the Jacobian matrix, an n × m matrix in this case. A similar formulation of the higher-dimensional derivative is provided by the fundamental increment lemma found in single-variable calculus.
If all the partial derivatives of a function exist in a neighborhood of a point x0 and are continuous at the point x0, then the function is differentiable at that point x0.
However, the existence of the partial derivatives (or even of all the directional derivatives) does not guarantee that a function is differentiable at a point. For example, the function f: R2 → R defined by
f
(
x
,
y
)
=
{
x
if
y
≠
x
2
0
if
y
=
x
2
{\displaystyle f(x,y)={\begin{cases}x&{\text{if }}y\neq x^{2}\\0&{\text{if }}y=x^{2}\end{cases}}}
is not differentiable at (0, 0), but all of the partial derivatives and directional derivatives exist at this point. For a continuous example, the function
f
(
x
,
y
)
=
{
y
3
/
(
x
2
+
y
2
)
if
(
x
,
y
)
≠
(
0
,
0
)
0
if
(
x
,
y
)
=
(
0
,
0
)
{\displaystyle f(x,y)={\begin{cases}y^{3}/(x^{2}+y^{2})&{\text{if }}(x,y)\neq (0,0)\\0&{\text{if }}(x,y)=(0,0)\end{cases}}}
is not differentiable at (0, 0), but again all of the partial derivatives and directional derivatives exist.
== Differentiability in complex analysis ==
In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers. So, a function
f
:
C
→
C
{\textstyle f:\mathbb {C} \to \mathbb {C} }
is said to be differentiable at
x
=
a
{\textstyle x=a}
when
f
′
(
a
)
=
lim
h
→
0
h
∈
C
f
(
a
+
h
)
−
f
(
a
)
h
.
{\displaystyle f'(a)=\lim _{\underset {h\in \mathbb {C} }{h\to 0}}{\frac {f(a+h)-f(a)}{h}}.}
Although this definition looks similar to the differentiability of single-variable real functions, it is however a more restrictive condition. A function
f
:
C
→
C
{\textstyle f:\mathbb {C} \to \mathbb {C} }
, that is complex-differentiable at a point
x
=
a
{\textstyle x=a}
is automatically differentiable at that point, when viewed as a function
f
:
R
2
→
R
2
{\displaystyle f:\mathbb {R} ^{2}\to \mathbb {R} ^{2}}
. This is because the complex-differentiability implies that
lim
h
→
0
h
∈
C
|
f
(
a
+
h
)
−
f
(
a
)
−
f
′
(
a
)
h
|
|
h
|
=
0.
{\displaystyle \lim _{\underset {h\in \mathbb {C} }{h\to 0}}{\frac {|f(a+h)-f(a)-f'(a)h|}{|h|}}=0.}
However, a function
f
:
C
→
C
{\textstyle f:\mathbb {C} \to \mathbb {C} }
can be differentiable as a multi-variable function, while not being complex-differentiable. For example,
f
(
z
)
=
z
+
z
¯
2
{\displaystyle f(z)={\frac {z+{\overline {z}}}{2}}}
is differentiable at every point, viewed as the 2-variable real function
f
(
x
,
y
)
=
x
{\displaystyle f(x,y)=x}
, but it is not complex-differentiable at any point because the limit
lim
h
→
0
h
+
h
¯
2
h
{\textstyle \lim _{h\to 0}{\frac {h+{\bar {h}}}{2h}}}
gives different values for different approaches to 0.
Any function that is complex-differentiable in a neighborhood of a point is called holomorphic at that point. Such a function is necessarily infinitely differentiable, and in fact analytic.
== Differentiable functions on manifolds ==
If M is a differentiable manifold, a real or complex-valued function f on M is said to be differentiable at a point p if it is differentiable with respect to some (or any) coordinate chart defined around p. If M and N are differentiable manifolds, a function f: M → N is said to be differentiable at a point p if it is differentiable with respect to some (or any) coordinate charts defined around p and f(p).
== See also ==
Generalizations of the derivative
Semi-differentiability
Differentiable programming
== References == | Wikipedia/Differentiable_functions |
A temporal network, also known as a time-varying network, is a network whose links are active only at certain points in time. Each link carries information on when it is active, along with other possible characteristics such as a weight. Time-varying networks are of particular relevance to spreading processes, like the spread of information and disease, since each link is a contact opportunity and the time ordering of contacts is included.
Examples of time-varying networks include communication networks where each link is relatively short or instantaneous, such as phone calls or e-mails. Information spreads over both networks, and some computer viruses spread over the second. Networks of physical proximity, encoding who encounters whom and when, can be represented as time-varying networks. Some diseases, such as airborne pathogens, spread through physical proximity. Real-world data on time resolved physical proximity networks has been used to improve epidemic modeling. Neural networks and brain networks can be represented as time-varying networks since the activation of neurons are time-correlated.
Time-varying networks are characterized by intermittent activation at the scale of individual links. This is in contrast to various models of network evolution, which may include an overall time dependence at the scale of the network as a whole.
== Applicability ==
Time-varying networks are inherently dynamic, and used for modeling spreading processes on networks. Whether using time-varying networks will be worth the added complexity depends on the relative time scales in question. Time-varying networks are most useful in describing systems where the spreading process on a network and the network itself evolve at similar timescales.
Let the characteristic timescale for the evolution of the network be
t
N
{\displaystyle t_{N}}
, and the characteristic timescale for the evolution of the spreading process be
t
P
{\displaystyle t_{P}}
. A process on a network will fall into one of three categories:
Static approximation – where
t
N
≫
t
P
{\displaystyle t_{N}\gg t_{P}}
. The network evolves relatively slowly, so the dynamics of the process can be approximated using a static version of the network.
Time-varying network – where
t
N
∼
t
P
{\displaystyle t_{N}\sim t_{P}}
. The network and the process evolve at comparable timescales so the interplay between them becomes important.
Annealed approximation – where
t
N
≪
t
P
{\displaystyle t_{N}\ll t_{P}}
. The network evolves relatively rapidly, so the dynamics of the process can be approximated using a time averaged version of the network.
The flow of data over the internet is an example for the first case, where the network changes very little in the fraction of a second it takes for a network packet to traverse it. The spread of sexually transmitted diseases is an example of the second, where the prevalence of the disease spreads in direct correlation to the rate of evolution of the sexual contact network itself. Behavioral contagion is an example of the third case, where behaviors spread through a population over the combined network of many day-to-day social interactions.
== Representations ==
There are three common representations for time-varying network data.
Contact sequences – if the duration of interactions are negligible, the network can be represented as a set
C
{\displaystyle C}
of contacts
(
i
,
j
,
t
)
{\displaystyle (i,j,t)}
where
i
{\displaystyle i}
and
j
{\displaystyle j}
are the nodes and
t
{\displaystyle t}
the time of the interaction. Alternatively, it can be represented as an edge list
E
{\displaystyle E}
where each edge
e
{\displaystyle e}
is a pair of nodes and has a set of active times
T
e
=
{
t
1
,
…
,
t
n
}
{\displaystyle T_{e}=\{t_{1},\ldots ,t_{n}\}}
.
Interval graphs – if the duration of interactions are non-negligible,
T
e
{\displaystyle T_{e}}
becomes a set of intervals over which the edge
e
{\displaystyle e}
is active.
T
e
=
{
(
t
1
,
t
1
′
)
,
…
,
(
t
n
,
t
n
′
)
}
{\displaystyle T_{e}=\{(t_{1},t_{1}'),\ldots ,(t_{n},t_{n}')\}}
Snapshots – time-varying networks can also be represented as a series of static networks, one for each time step.
== Properties ==
The measures used to characterize static networks are not immediately transferable to time-varying networks. See Path, Connectedness, Distance, Centrality. However, these network concepts have been adapted to apply to time-varying networks.
=== Time respecting paths ===
Time respecting paths are the sequences of links that can be traversed in a time-varying network under the constraint that the next link to be traversed is activated at some point after the current one. Like in a directed graph, a path from
i
{\displaystyle i}
to
j
{\displaystyle j}
does not mean there is a path from
j
{\displaystyle j}
to
i
{\displaystyle i}
. In contrast to paths in static and evolving networks, however, time respecting paths are also non-transitive. That is to say, just because there is a path from
i
{\displaystyle i}
to
j
{\displaystyle j}
and from
j
{\displaystyle j}
to
k
{\displaystyle k}
does not mean that there is a path from
i
{\displaystyle i}
to
k
{\displaystyle k}
. Furthermore, time respecting paths are themselves time-varying, and are only valid paths during a specific time interval.
=== Reachability ===
While analogous to connectedness in static networks, reachability is a time-varying property best defined for each node in the network. The set of influence of a node
i
{\displaystyle i}
is the set of all nodes that can be reached from
i
{\displaystyle i}
via time respecting paths, note that it is dependent on the start time
t
{\displaystyle t}
. The source set of a node
i
{\displaystyle i}
is the set of all nodes that can reach
i
{\displaystyle i}
via time respecting paths within a given time interval. The reachability ratio can be defined as the average over all nodes
i
{\displaystyle i}
of the fraction of nodes within the set of influence of
i
{\displaystyle i}
.
Connectedness of an entire network is less conclusively defined, although some have been proposed. A component may be defined as strongly connected if there is a directed time respecting path connecting all nodes in the component in both directions. A component may be defined as weakly connected if there is an undirected time respecting path connecting all nodes in the component in both directions. Also, a component may be defined as transitively connected if transitivity holds for the subset of nodes in that component.
=== Causal fidelity ===
Causal fidelity quantifies the goodness of the static approximation of a temporal network. Such a static approximation is generated by aggregating the edges of a temporal network over time. The idea of causal fidelity is to compare the number of paths between all node pairs in the temporal network
P
t
e
m
p
{\displaystyle P_{temp}}
(that is, all time respecting paths) with the number of paths
P
s
t
a
t
{\displaystyle P_{stat}}
between all nodes in the static approximation of the network. The causal fidelity is then defined by
c
=
P
t
e
m
p
P
s
t
a
t
{\displaystyle c={\frac {P_{temp}}{P_{stat}}}}
.
Since in
P
t
e
m
p
{\displaystyle P_{temp}}
only time respecting paths are considered,
P
t
e
m
p
≤
P
s
t
a
t
{\displaystyle P_{temp}\leq P_{stat}}
, and consequently
0
≤
c
≤
1
{\displaystyle 0\leq c\leq 1}
. A high causal fidelity
c
≈
1
{\displaystyle c\approx 1}
means that the considered temporal network is well approximated by its static (aggregated) counterpart. If
c
≪
1
{\displaystyle c\ll 1}
, then most node pairs that are reachable in the static representation are not connected by time respecting paths in the temporal network.
=== Latency ===
Also called temporal distance, latency is the time-varying equivalent to distance. In a time-varying network any time respecting path has a duration, namely the time it takes to follow that path. The fastest such path between two nodes is the latency, note that it is also dependent on the start time. The latency from node
i
{\displaystyle i}
to node
j
{\displaystyle j}
beginning at time
t
{\displaystyle t}
is denoted by
λ
i
,
t
(
j
)
{\displaystyle \lambda _{i,t}(j)}
.
=== Centrality measures ===
Measuring centrality on time-varying networks involves a straightforward replacement of distance with latency. For discussions of the centrality measures on a static network see Centrality.
Closeness centrality is large for nodes
i
{\displaystyle i}
that are close to all other nodes (i.e. have small latency
λ
i
(
j
)
{\displaystyle \lambda _{i}(j)}
for all
j
{\displaystyle j}
)
C
C
(
i
,
t
)
=
N
−
1
∑
j
≠
i
λ
i
,
t
(
j
)
{\displaystyle C_{C}(i,t)={\frac {N-1}{\sum _{j\not =i}{\lambda _{i,t}(j)}}}}
Betweenness centrality is large for nodes that are often a part of the smallest latency paths between other pairs of nodes. It is defined as the ratio of the number of smallest latency paths from
j
{\displaystyle j}
and
k
{\displaystyle k}
that pass through
i
{\displaystyle i}
to the total number of smallest latency paths from
j
{\displaystyle j}
and
k
{\displaystyle k}
C
B
(
i
,
t
)
=
∑
i
≠
j
≠
k
ν
i
(
j
,
k
)
∑
i
≠
j
≠
k
ν
(
j
,
k
)
{\displaystyle C_{B}(i,t)={\frac {\sum _{i\not =j\not =k}{\nu _{i}(j,k)}}{\sum _{i\not =j\not =k}{\nu _{(}j,k)}}}}
The time-varying nature of latency, specifically that it will become infinity for all node pairs as the time approaches the end of the network interval used, makes an alternative measure of closeness useful. Efficiency uses instead the reciprocal of the latency, so the efficiency approaches zero instead of diverging. Higher values for efficiency correspond to more central nodes in the network.
C
E
(
i
,
t
)
=
1
N
−
1
∑
j
≠
i
1
λ
i
,
t
(
j
)
{\displaystyle C_{E}(i,t)={\frac {1}{N-1}}\sum _{j\not =i}{\frac {1}{\lambda _{i,t}(j)}}}
=== Temporal patterns ===
Time-varying network allow for analysis of explicit time dependent properties of the network. It is possible to extract recurring and persistent patterns of contact from time-varying data in many ways. This is an area of ongoing research.
Characteristic times of the system can be found by looking for distinct changes in a variable, such as the reachability ratio. For example, if one allows only a finite waiting time at all nodes in calculating latency, one can find interesting patterns in the resulting reachability ratio. For a mobile call network, the reachability ratio has been found to increase dramatically if one allows delays of at least two days, and for the airline network the same effect has been found at around 30 minutes. Moreover, the characteristic time scale of a temporal network is given by the mode of the distribution of shortest path durations. This distribution can be calculated using the reachability between all node pairs in the network.
Persistent patterns are ones that reoccur frequently in the system. They can be discovered by averaging over different
Δ
t
{\displaystyle \Delta t}
across the time interval of the system and looking for patterns that reoccur over a specified threshold.
Motifs are specific temporal patterns that occur more often the expected in a system. The time-varying network of Facebook wall postings, for example, has higher frequency of chains, stars, and back and forth interactions that could be expected for a randomized network.
Egocentric Temporal motifs can be used to exploit temporal ego-networks. Due to their first-order complexity can be counted in large graphs in a reasonable execution time. For example, Longa et al. show how to use Egocentric Temporal Motifs for measuring distances among face-to-face interaction networks in different social contexts.
Detecting missing links
== Dynamics ==
Time-varying networks allow for the analysis of an entirely new dimension of dynamic processes on networks. In cases where the time scales of evolution of the network and the process are similar, the temporal structure of time-varying networks has a dramatic impact on the spread of the process over the network.
=== Burstiness ===
The time between two consecutive events, for an individual node or link, is called the inter-event time. The distribution of inter-event times of a growing number of important, real-world, time-varying networks have been found to be bursty, meaning inter-event times are very heterogeneous – they have a heavy-tailed distribution. This translates to a pattern of activation where activity comes in bursts separated by longer stretches of inactivity.
Burstiness of inter-event times can dramatically slow spreading processes on networks, which has implications for the spread of disease, information, ideas, and computer viruses. However, burstiness can also accelerate spreading processes, and other network properties also have an effect on spreading speed. Real-world time-varying networks may thus promote spreading processes despite having a bursty inter-event time distribution.
Burstiness as an empirical quantity can be calculated for any sequence of inter-event times,
τ
{\displaystyle \tau }
, by comparing the sequence to one generated by a Poisson process. The ratio of the standard deviation,
σ
{\displaystyle \sigma }
, to the mean,
m
{\displaystyle m}
, of a Poisson process is 1. This measure compares
σ
τ
/
m
τ
{\displaystyle \sigma _{\tau }/m_{\tau }\ }
to 1.
B
=
σ
τ
/
m
τ
−
1
σ
τ
/
m
τ
+
1
{\displaystyle B={\frac {\sigma _{\tau }/m_{\tau }\ -1}{\sigma _{\tau }/m_{\tau }\ +1}}}
Burstiness varies from −1 to 1. B = 1 indicates a maximally bursty sequence, B = 0 indicates a Poisson distribution, and B = −1 indicates a periodic sequence.
== See also ==
Complex contagion
Complex network
Epidemic model
Directed percolation
Dynamic network analysis
Exponential random graph models
Link-centric preferential attachment
Scale-free network
Percolation theory
== References == | Wikipedia/Temporal_network |
The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p, a point whose distance from p is minimum among all the given points other than p itself.
In many uses of these graphs, the directions of the edges are ignored and the NNG is defined instead as an undirected graph. However, the nearest neighbor relation is not a symmetric one, i.e., p from the definition is not necessarily a nearest neighbor for q. In theoretical discussions of algorithms a kind of general position is often assumed, namely, the nearest (k-nearest) neighbor is unique for each object. In implementations of the algorithms it is necessary to bear in mind that this is not always the case. For situations in which it is necessary to make the nearest neighbor for each object unique, the set P may be indexed and in the case of a tie the object with, e.g., the largest index may be taken as the nearest neighbor.
The k-nearest neighbors graph (k-NNG) is a graph in which two vertices p and q are connected by an edge, if the distance between p and q is among the k-th smallest distances from p to other objects from P. The NNG is a special case of the k-NNG, namely it is the 1-NNG. k-NNGs obey a separator theorem: they can be partitioned into two subgraphs of at most n(d + 1)/(d + 2) vertices each by the removal of O(k1/dn1 − 1/d) points.
A k-NNG can be approximated using an efficient algorithm with 90% recall that is faster than a brute-force search by an order of magnitude.
Another variation is the farthest neighbor graph (FNG), in which each point is connected by an edge to the farthest point from it, instead of the nearest point.
NNGs for points in the plane as well as in multidimensional spaces find applications, e.g., in data compression, motion planning, and facilities location. In statistical analysis, the nearest-neighbor chain algorithm based on following paths in this graph can be used to find hierarchical clusterings quickly. Nearest neighbor graphs are also a subject of computational geometry.
The method can be used to induce a graph on nodes with unknown connectivity.
== NNGs for sets of points ==
=== One-dimensional case ===
For a set of points on a line, the nearest neighbor of a point is its left or right (or both) neighbor, if they are sorted along the line. Therefore, the NNG is a path or a forest of several paths and may be constructed in O(n log n) time by sorting. This estimate is asymptotically optimal for certain models of computation, because the constructed NNG gives the answer to the element uniqueness problem: it is sufficient to check whether the NNG has a zero-length edge.
=== Higher dimensions ===
Unless stated otherwise, it is assumed that the NNGs are digraphs with uniquely defined nearest neighbors as described in the introduction.
Along any directed path in an NNG the edge lengths are non-increasing.
Only cycles of length 2 are possible in an NNG and each weakly connected component of an NNG with at least 2 vertices has exactly one 2-cycle.
For the points in the plane the NNG is a planar graph with vertex degrees at most 6. If points are in general position, the degree is at most 5.
The NNG (treated as an undirected graph with multiple nearest neighbors allowed) of a set of points in the plane or any higher dimension is a subgraph of the Delaunay triangulation, the Gabriel graph, and the Semi-Yao graph. If the points are in general position or if the single nearest neighbor condition is imposed, the NNG is a forest, a subgraph of the Euclidean minimum spanning tree.
== References == | Wikipedia/Nearest_neighbor_graph |
An industrial robot is a robot system used for manufacturing. Industrial robots are automated, programmable and capable of movement on three or more axes.
Typical applications of robots include welding, painting, assembly, disassembly, pick and place for printed circuit boards, packaging and labeling, palletizing, product inspection, and testing; all accomplished with high endurance, speed, and precision. They can assist in material handling.
In the year 2023, an estimated 4,281,585 industrial robots were in operation worldwide according to International Federation of Robotics (IFR).
== Types and features ==
There are six types of industrial robots.
=== Articulated robots ===
Articulated robots are the most common industrial robots. They look like a human arm, which is why they are also called robotic arm or manipulator arm. Their articulations with several degrees of freedom allow the articulated arms a wide range of movements.
=== Autonomous robot ===
An autonomous robot is a robot that acts without recourse to human control. The first autonomous robots environment were known as Elmer and Elsie, which were constructed in the late 1940s by W. Grey Walter. They were the first robots in history that were programmed to "think" the way biological brains do and meant to have free will. Elmer and Elsie were often labeled as tortoises because of how they were shaped and the manner in which they moved. They were capable of phototaxis which is the movement that occurs in response to light stimulus.
=== Cartesian coordinate robots ===
Cartesian robots, also called rectilinear, gantry robots, and x-y-z robots have three prismatic joints for the movement of the tool and three rotary joints for its orientation in space.
To be able to move and orient the effector organ in all directions, such a robot needs 6 axes (or degrees of freedom). In a 2-dimensional environment, three axes are sufficient, two for displacement and one for orientation.
=== Cylindrical coordinate robots ===
The cylindrical coordinate robots are characterized by their rotary joint at the base and at least one prismatic joint connecting its links. They can move vertically and horizontally by sliding. The compact effector design allows the robot to reach tight work-spaces without any loss of speed.
=== Spherical coordinate robots ===
Spherical coordinate robots only have rotary joints. They are one of the first robots to have been used in industrial applications. They are commonly used for machine tending in die-casting, plastic injection and extrusion, and for welding.
=== SCARA robots ===
SCARA is an acronym for Selective Compliance Assembly Robot Arm. SCARA robots are recognized by their two parallel joints which provide movement in the X-Y plane. Rotating shafts are positioned vertically at the effector. SCARA robots are used for jobs that require precise lateral movements. They are ideal for assembly applications.
=== Delta robots ===
Delta robots are also referred to as parallel link robots. They consist of parallel links connected to a common base. Delta robots are particularly useful for direct control tasks and high maneuvering operations (such as quick pick-and-place tasks). Delta robots take advantage of four bar or parallelogram linkage systems.
Furthermore, industrial robots can have a serial or parallel architecture.
=== Serial manipulators ===
Serial architectures a.k.a. serial manipulators are very common industrial robots; they are designed as a series of links connected by motor-actuated joints that extend from a base to an end-effector. SCARA, Stanford manipulators are typical examples of this category.
=== Parallel architecture ===
A parallel manipulator is designed so that each chain is usually short, simple and can thus be rigid against unwanted movement, compared to a serial manipulator. Errors in one chain's positioning are averaged in conjunction with the others, rather than being cumulative. Each actuator must still move within its own degree of freedom, as for a serial robot; however in the parallel robot the off-axis flexibility of a joint is also constrained by the effect of the other chains. It is this closed-loop stiffness that makes the overall parallel manipulator stiff relative to its components, unlike the serial chain that becomes progressively less rigid with more components.
== Lower mobility parallel manipulators and concomitant motion ==
A full parallel manipulator can move an object with up to 6 degrees of freedom (DoF), determined by 3 translation 3T and 3 rotation 3R coordinates for full 3T3R mobility. However, when a manipulation task requires less than 6 DoF, the use of lower mobility manipulators, with fewer than 6 DoF, may bring advantages in terms of simpler architecture, easier control, faster motion and lower cost. For example, the 3 DoF Delta robot has lower 3T mobility and has proven to be very successful for rapid pick-and-place translational positioning applications. The workspace of lower mobility manipulators may be decomposed into 'motion' and 'constraint' subspaces. For example, 3 position coordinates constitute the motion subspace of the 3 DoF Delta robot and the 3 orientation coordinates are in the constraint subspace. The motion subspace of lower mobility manipulators may be further decomposed into independent (desired) and dependent (concomitant) subspaces: consisting of 'concomitant' or 'parasitic' motion which is undesired motion of the manipulator. The debilitating effects of concomitant motion should be mitigated or eliminated in the successful design of lower mobility manipulators. For example, the Delta robot does not have parasitic motion since its end effector does not rotate.
== Autonomy ==
Robots exhibit varying degrees of autonomy.
Some robots are programmed to faithfully carry out specific actions over and over again (repetitive actions) without variation and with a high degree of accuracy. These actions are determined by programmed routines that specify the direction, acceleration, velocity, deceleration, and distance of a series of coordinated motions
Other robots are much more flexible as to the orientation of the object on which they are operating or even the task that has to be performed on the object itself, which the robot may even need to identify. For example, for more precise guidance, robots often contain machine vision sub-systems acting as their visual sensors, linked to powerful computers or controllers. Artificial intelligence is becoming an increasingly important factor in the modern industrial robot.
== History ==
The earliest known industrial robot, conforming to the ISO definition was completed by
"Bill" Griffith P. Taylor in 1937 and published in Meccano Magazine, March 1938. The crane-like device was built almost entirely using Meccano parts, and powered by a single electric motor. Five axes of movement were possible, including grab and grab rotation. Automation was achieved using punched paper tape to energise solenoids, which would facilitate the movement of the crane's control levers. The robot could stack wooden blocks in pre-programmed patterns. The number of motor revolutions required for each desired movement was first plotted on graph paper. This information was then transferred to the paper tape, which was also driven by the robot's single motor. Chris Shute built a complete replica of the robot in 1997.
George Devol applied for the first robotics patents in 1954 (granted in 1961). The first company to produce a robot was Unimation, founded by Devol and Joseph F. Engelberger in 1956. Unimation robots were also called programmable transfer machines since their main use at first was to transfer objects from one point to another, less than a dozen feet or so apart. They used hydraulic actuators and were programmed in joint coordinates, i.e. the angles of the various joints were stored during a teaching phase and replayed in operation. They were accurate to within 1/10,000 of an inch (note: although accuracy is not an appropriate measure for robots, usually evaluated in terms of repeatability - see later). Unimation later licensed their technology to Kawasaki Heavy Industries and GKN, manufacturing Unimates in Japan and England respectively. For some time, Unimation's only competitor was Cincinnati Milacron Inc. of Ohio. This changed radically in the late 1970s when several big Japanese conglomerates began producing similar industrial robots.
In 1969 Victor Scheinman at Stanford University invented the Stanford arm, an all-electric, 6-axis articulated robot designed to permit an arm solution. This allowed it accurately to follow arbitrary paths in space and widened the potential use of the robot to more sophisticated applications such as assembly and welding. Scheinman then designed a second arm for the MIT AI Lab, called the "MIT arm." Scheinman, after receiving a fellowship from Unimation to develop his designs, sold those designs to Unimation who further developed them with support from General Motors and later marketed it as the Programmable Universal Machine for Assembly (PUMA).
Industrial robotics took off quite quickly in Europe, with both ABB Robotics and KUKA Robotics bringing robots to the market in 1973. ABB Robotics (formerly ASEA) introduced IRB 6, among the world's first commercially available all electric micro-processor controlled robot. The first two IRB 6 robots were sold to Magnusson in Sweden for grinding and polishing pipe bends and were installed in production in January 1974. Also in 1973 KUKA Robotics built its first robot, known as FAMULUS, also one of the first articulated robots to have six electromechanically driven axes.
Interest in robotics increased in the late 1970s and many US companies entered the field, including large firms like General Electric, and General Motors (which formed joint venture FANUC Robotics with FANUC LTD of Japan). U.S. startup companies included Automatix and Adept Technology, Inc. At the height of the robot boom in 1984, Unimation was acquired by Westinghouse Electric Corporation for 107 million U.S. dollars. Westinghouse sold Unimation to Stäubli Faverges SCA of France in 1988, which is still making articulated robots for general industrial and cleanroom applications and even bought the robotic division of Bosch in late 2004.
Only a few non-Japanese companies ultimately managed to survive in this market, the major ones being: Adept Technology, Stäubli, the Swedish-Swiss company ABB Asea Brown Boveri, the German company KUKA Robotics and the Italian company Comau.
== Technical description ==
=== Defining parameters ===
Number of axes – two axes are required to reach any point in a plane; three axes are required to reach any point in space. To fully control the orientation of the end of the arm(i.e. the wrist) three more axes (yaw, pitch, and roll) are required. Some designs (e.g. the SCARA robot) trade limitations in motion possibilities for cost, speed, and accuracy.
Degrees of freedom – this is usually the same as the number of axes.
Working envelope – the region of space a robot can reach.
Kinematics – the actual arrangement of rigid members and joints in the robot, which determines the robot's possible motions. Classes of robot kinematics include articulated, cartesian, parallel and SCARA.
Carrying capacity or payload – how much weight a robot can lift.
Speed – how fast the robot can position the end of its arm. This may be defined in terms of the angular or linear speed of each axis or as a compound speed i.e. the speed of the end of the arm when all axes are moving.
Acceleration – how quickly an axis can accelerate. Since this is a limiting factor a robot may not be able to reach its specified maximum speed for movements over a short distance or a complex path requiring frequent changes of direction.
Accuracy – how closely a robot can reach a commanded position. When the absolute position of the robot is measured and compared to the commanded position the error is a measure of accuracy. Accuracy can be improved with external sensing for example a vision system or Infra-Red. See robot calibration. Accuracy can vary with speed and position within the working envelope and with payload (see compliance).
Repeatability – how well the robot will return to a programmed position. This is not the same as accuracy. It may be that when told to go to a certain X-Y-Z position that it gets only to within 1 mm of that position. This would be its accuracy which may be improved by calibration. But if that position is taught into controller memory and each time it is sent there it returns to within 0.1mm of the taught position then the repeatability will be within 0.1mm.
Accuracy and repeatability are different measures. Repeatability is usually the most important criterion for a robot and is similar to the concept of 'precision' in measurement—see accuracy and precision. ISO 9283 sets out a method whereby both accuracy and repeatability can be measured. Typically a robot is sent to a taught position a number of times and the error is measured at each return to the position after visiting 4 other positions. Repeatability is then quantified using the standard deviation of those samples in all three dimensions. A typical robot can, of course make a positional error exceeding that and that could be a problem for the process. Moreover, the repeatability is different in different parts of the working envelope and also changes with speed and payload. ISO 9283 specifies that accuracy and repeatability should be measured at maximum speed and at maximum payload. But this results in pessimistic values whereas the robot could be much more accurate and repeatable at light loads and speeds.
Repeatability in an industrial process is also subject to the accuracy of the end effector, for example a gripper, and even to the design of the 'fingers' that match the gripper to the object being grasped. For example, if a robot picks a screw by its head, the screw could be at a random angle. A subsequent attempt to insert the screw into a hole could easily fail. These and similar scenarios can be improved with 'lead-ins' e.g. by making the entrance to the hole tapered.
Motion control – for some applications, such as simple pick-and-place assembly, the robot need merely return repeatably to a limited number of pre-taught positions. For more sophisticated applications, such as welding and finishing (spray painting), motion must be continuously controlled to follow a path in space, with controlled orientation and velocity.
Power source – some robots use electric motors, others use hydraulic actuators. The former are faster, the latter are stronger and advantageous in applications such as spray painting, where a spark could set off an explosion; however, low internal air-pressurisation of the arm can prevent ingress of flammable vapours as well as other contaminants. Nowadays, it is highly unlikely to see any hydraulic robots in the market. Additional sealings, brushless electric motors and spark-proof protection eased the construction of units that are able to work in the environment with an explosive atmosphere.
Drive – some robots connect electric motors to the joints via gears; others connect the motor to the joint directly (direct drive). Using gears results in measurable 'backlash' which is free movement in an axis. Smaller robot arms frequently employ high speed, low torque DC motors, which generally require high gearing ratios; this has the disadvantage of backlash. In such cases the harmonic drive is often used.
Compliance - this is a measure of the amount in angle or distance that a robot axis will move when a force is applied to it. Because of compliance when a robot goes to a position carrying its maximum payload it will be at a position slightly lower than when it is carrying no payload. Compliance can also be responsible for overshoot when carrying high payloads in which case acceleration would need to be reduced.
=== Robot programming and interfaces ===
The setup or programming of motions and sequences for an industrial robot is typically taught by linking the robot controller to a laptop, desktop computer or (internal or Internet) network.
A robot and a collection of machines or peripherals is referred to as a workcell, or cell. A typical cell might contain a parts feeder, a molding machine and a robot. The various machines are 'integrated' and controlled by a single computer or PLC. How the robot interacts with other machines in the cell must be programmed, both with regard to their positions in the cell and synchronizing with them.
Software: The computer is installed with corresponding interface software. The use of a computer greatly simplifies the programming process. Specialized robot software is run either in the robot controller or in the computer or both depending on the system design.
There are two basic entities that need to be taught (or programmed): positional data and procedure. For example, in a task to move a screw from a feeder to a hole the positions of the feeder and the hole must first be taught or programmed. Secondly the procedure to get the screw from the feeder to the hole must be programmed along with any I/O involved, for example a signal to indicate when the screw is in the feeder ready to be picked up. The purpose of the robot software is to facilitate both these programming tasks.
Teaching the robot positions may be achieved a number of ways:
Positional commands The robot can be directed to the required position using a GUI or text based commands in which the required X-Y-Z position may be specified and edited.
Teach pendant: Robot positions can be taught via a teach pendant. This is a handheld control and programming unit. The common features of such units are the ability to manually send the robot to a desired position, or "inch" or "jog" to adjust a position. They also have a means to change the speed since a low speed is usually required for careful positioning, or while test-running through a new or modified routine. A large emergency stop button is usually included as well. Typically once the robot has been programmed there is no more use for the teach pendant. All teach pendants are equipped with a 3-position deadman switch. In the manual mode, it allows the robot to move only when it is in the middle position (partially pressed). If it is fully pressed in or completely released, the robot stops. This principle of operation allows natural reflexes to be used to increase safety.
Lead-by-the-nose: this is a technique offered by many robot manufacturers. In this method, one user holds the robot's manipulator, while another person enters a command which de-energizes the robot causing it to go into limp. The user then moves the robot by hand to the required positions and/or along a required path while the software logs these positions into memory. The program can later run the robot to these positions or along the taught path. This technique is popular for tasks such as paint spraying.
Offline programming is where the entire cell, the robot and all the machines or instruments in the workspace are mapped graphically. The robot can then be moved on screen and the process simulated. A robotics simulator is used to create embedded applications for a robot, without depending on the physical operation of the robot arm and end effector. The advantages of robotics simulation is that it saves time in the design of robotics applications. It can also increase the level of safety associated with robotic equipment since various "what if" scenarios can be tried and tested before the system is activated.[8] Robot simulation software provides a platform to teach, test, run, and debug programs that have been written in a variety of programming languages.
Robot simulation tools allow for robotics programs to be conveniently written and debugged off-line with the final version of the program tested on an actual robot. The ability to preview the behavior of a robotic system in a virtual world allows for a variety of mechanisms, devices, configurations and controllers to be tried and tested before being applied to a "real world" system. Robotics simulators have the ability to provide real-time computing of the simulated motion of an industrial robot using both geometric modeling and kinematics modeling.
Manufacturing independent robot programming tools are a relatively new but flexible way to program robot applications. Using a visual programming language, the programming is done via drag and drop of predefined template/building blocks. They often feature the execution of simulations to evaluate the feasibility and offline programming in combination. If the system is able to compile and upload native robot code to the robot controller, the user no longer has to learn each manufacturer's proprietary language. Therefore, this approach can be an important step to standardize programming methods.
Others in addition, machine operators often use user interface devices, typically touchscreen units, which serve as the operator control panel. The operator can switch from program to program, make adjustments within a program and also operate a host of peripheral devices that may be integrated within the same robotic system. These include end effectors, feeders that supply components to the robot, conveyor belts, emergency stop controls, machine vision systems, safety interlock systems, barcode printers and an almost infinite array of other industrial devices which are accessed and controlled via the operator control panel.
The teach pendant or PC is usually disconnected after programming and the robot then runs on the program that has been installed in its controller. However a computer is often used to 'supervise' the robot and any peripherals, or to provide additional storage for access to numerous complex paths and routines.
=== End-of-arm tooling ===
The most essential robot peripheral is the end effector, or end-of-arm-tooling (EOAT). Common examples of end effectors include welding devices (such as MIG-welding guns, spot-welders, etc.), spray guns and also grinding and deburring devices (such as pneumatic disk or belt grinders, burrs, etc.), and grippers (devices that can grasp an object, usually electromechanical or pneumatic). Other common means of picking up objects is by vacuum or magnets. End effectors are frequently highly complex, made to match the handled product and often capable of picking up an array of products at one time. They may utilize various sensors to aid the robot system in locating, handling, and positioning products.
=== Controlling movement ===
For a given robot the only parameters necessary to completely locate the end effector (gripper, welding torch, etc.) of the robot are the angles of each of the joints or displacements of the linear axes (or combinations of the two for robot formats such as SCARA). However, there are many different ways to define the points. The most common and most convenient way of defining a point is to specify a Cartesian coordinate for it, i.e. the position of the 'end effector' in mm in the X, Y and Z directions relative to the robot's origin. In addition, depending on the types of joints a particular robot may have, the orientation of the end effector in yaw, pitch, and roll and the location of the tool point relative to the robot's faceplate must also be specified. For a jointed arm these coordinates must be converted to joint angles by the robot controller and such conversions are known as Cartesian Transformations which may need to be performed iteratively or recursively for a multiple axis robot. The mathematics of the relationship between joint angles and actual spatial coordinates is called kinematics. See robot control
Positioning by Cartesian coordinates may be done by entering the coordinates into the system or by using a teach pendant which moves the robot in X-Y-Z directions. It is much easier for a human operator to visualize motions up/down, left/right, etc. than to move each joint one at a time. When the desired position is reached it is then defined in some way particular to the robot software in use, e.g. P1 - P5 below.
=== Typical programming ===
Most articulated robots perform by storing a series of positions in memory, and moving to them at various times in their programming sequence. For example, a robot which is moving items from one place (bin A) to another (bin B) might have a simple 'pick and place' program similar to the following:
Define points P1–P5:
Safely above workpiece (defined as P1)
10 cm Above bin A (defined as P2)
At position to take part from bin A (defined as P3)
10 cm Above bin B (defined as P4)
At position to take part from bin B. (defined as P5)
Define program:
Move to P1
Move to P2
Move to P3
Close gripper
Move to P2
Move to P4
Move to P5
Open gripper
Move to P4
Move to P1 and finish
For examples of how this would look in popular robot languages see industrial robot programming.
=== Singularities ===
The American National Standard for Industrial Robots and Robot Systems — Safety Requirements (ANSI/RIA R15.06-1999) defines a singularity as "a condition caused by the collinear alignment of two or more robot axes resulting in unpredictable robot motion and velocities." It is most common in robot arms that utilize a "triple-roll wrist". This is a wrist about which the three axes of the wrist, controlling yaw, pitch, and roll, all pass through a common point. An example of a wrist singularity is when the path through which the robot is traveling causes the first and third axes of the robot's wrist (i.e. robot's axes 4 and 6) to line up. The second wrist axis then attempts to spin 180° in zero time to maintain the orientation of the end effector. Another common term for this singularity is a "wrist flip". The result of a singularity can be quite dramatic and can have adverse effects on the robot arm, the end effector, and the process. Some industrial robot manufacturers have attempted to side-step the situation by slightly altering the robot's path to prevent this condition. Another method is to slow the robot's travel speed, thus reducing the speed required for the wrist to make the transition. The ANSI/RIA has mandated that robot manufacturers shall make the user aware of singularities if they occur while the system is being manually manipulated.
A second type of singularity in wrist-partitioned vertically articulated six-axis robots occurs when the wrist center lies on a cylinder that is centered about axis 1 and with radius equal to the distance between axes 1 and 4. This is called a shoulder singularity. Some robot manufacturers also mention alignment singularities, where axes 1 and 6 become coincident. This is simply a sub-case of shoulder singularities. When the robot passes close to a shoulder singularity, joint 1 spins very fast.
The third and last type of singularity in wrist-partitioned vertically articulated six-axis robots occurs when the wrist's center lies in the same plane as axes 2 and 3.
Singularities are closely related to the phenomena of gimbal lock, which has a similar root cause of axes becoming lined up.
== Market structure ==
According to the International Federation of Robotics (IFR) study World Robotics 2024, there were about 4,281,585 operational industrial robots by the end of 2023. For the year 2018 the IFR estimates the worldwide sales of industrial robots with US$16.5 billion. Including the cost of software, peripherals and systems engineering, the annual turnover for robot systems is estimated to be US$48.0 billion in 2018.
China is the largest industrial robot market: 256 with 154,032 units sold in 2018. China had the largest operational stock of industrial robots, with 649,447 at the end of 2018.
The biggest customer of industrial robots is automotive industry with 30% market share, then electrical/electronics industry with 25%, metal and machinery industry with 10%, rubber and plastics industry with 5%, food industry with 5%. In textiles, apparel and leather industry, 1,580 units are operational.
Estimated worldwide annual supply of industrial robots (in units):
== Health and safety ==
The International Federation of Robotics has predicted a worldwide increase in adoption of industrial robots and they estimated 1.7 million new robot installations in factories worldwide by 2020 [IFR 2017] Archived 2017-02-11 at the Wayback Machine. Rapid advances in automation technologies (e.g. fixed robots, collaborative and mobile robots, and exoskeletons) have the potential to improve work conditions but also to introduce workplace hazards in manufacturing workplaces. [3] Despite the lack of occupational surveillance data on injuries associated specifically with robots, researchers from the US National Institute for Occupational Safety and Health (NIOSH) identified 61 robot-related deaths between 1992 and 2015 using keyword searches of the Bureau of Labor Statistics (BLS) Census of Fatal Occupational Injuries research database (see info from Center for Occupational Robotics Research). Using data from the Bureau of Labor Statistics, NIOSH and its state partners have investigated 4 robot-related fatalities under the Fatality Assessment and Control Evaluation Program. In addition the Occupational Safety and Health Administration (OSHA) has investigated dozens of robot-related deaths and injuries, which can be reviewed at OSHA Accident Search page. Injuries and fatalities could increase over time because of the increasing number of collaborative and co-existing robots, powered exoskeletons, and autonomous vehicles into the work environment.
Safety standards are being developed by the Robotic Industries Association (RIA) in conjunction with the American National Standards Institute (ANSI).[4] On October 5, 2017, OSHA, NIOSH and RIA signed an alliance to work together to enhance technical expertise, identify and help address potential workplace hazards associated with traditional industrial robots and the emerging technology of human-robot collaboration installations and systems, and help identify needed research to reduce workplace hazards. On October 16 NIOSH launched the Center for Occupational Robotics Research to "provide scientific leadership to guide the development and use of occupational robots that enhance worker safety, health, and wellbeing." So far, the research needs identified by NIOSH and its partners include: tracking and preventing injuries and fatalities, intervention and dissemination strategies to promote safe machine control and maintenance procedures, and on translating effective evidence-based interventions into workplace practice.
== See also ==
Automation
Domestic robot
Drum handler
Intelligent industrial work assistant (iiwa)
Lights out (manufacturing)
Mobile industrial robots
Cartesian coordinate robot
Gantry robot
Workplace Robotics Safety
== References ==
== Further reading ==
Nof, Shimon Y. (editor) (1999). Handbook of Industrial Robotics, 2nd ed. John Wiley & Sons. 1378 pp. ISBN 0-471-17783-0.
Lars Westerlund (author) (2000). The extended arm of man. ISBN 91-7736-467-8.
Michal Gurgul (author) (2018). Industrial robots and cobots: Everything you need to know about your future co-worker. ISBN 978-83-952513-0-6.
== External links ==
Industrial robots and robot system safety (by OSHA, so in the public domain).
International Federation of Robotics IFR (worldwide)
Robotic Industries Association RIA (North America)
BARA, British Automation and Robotics Association (UK)
Center for Occupational Robotics Research by NIOSH
Safety standards applied to Robotics
Strategies for addressing new technologies from the INRS Archived 2018-02-21 at the Wayback Machine
Machine Guarding - Why It's a Legal Requirement Archived 2021-04-15 at the Wayback Machine | Wikipedia/Industrial_robot |
A remote-control vehicle, is defined as any vehicle that is teleoperated by a means that does not restrict its motion with an origin external to the device. This is often a radio-control device, a cable between the controller and the vehicle, or an infrared controller.
== Applications ==
=== Scientific ===
Remote-control vehicles have various scientific uses, including operating in hazardous environments, working in the deep ocean, and space exploration.
==== Space probes ====
The majority of probes to other planets in the Solar System have been remote-control vehicles, although some of the more recent ones were partially autonomous. The sophistication of these devices has prompted greater debate on the need for crewed spaceflight and exploration. The Voyager I spacecraft is the first craft of any kind to leave the Solar System. The explorers Spirit and Opportunity have provided continuous data about the surface of Mars since January 3, 2004.
==== Submarines ====
Jason is the Woods Hole Oceanographic Institution's deep water explorer and can withstand depths of up to 6,500 feet.
The Scorpio ROV is a British submersible that rescued the crew of the Russian AS-28 on August 7, 2005.
=== Military and law enforcement ===
Military usage of remotely-controlled vehicles dates back to the first half of 20th century. John Hays Hammond, Jr., invented and patented methods for wireless control of ships starting in 1910. The Soviet Red Army used remotely-controlled teletanks during the 1930s in the Winter War and early stage of World War II. There were also remotely-controlled cutters and experimental remotely-controlled planes in the Red Army.
Remote-control vehicles are used in law enforcement and military engagements for some of the same reasons. Hazard exposure is mitigated for the operator of the vehicle, who controls it from a location of relative safety. Remote-controlled vehicles are also used for bomb disposal.
Unmanned aerial vehicles (UAVs) have undergone a significant evolution in capability in the past decade. Early UAVs were capable of reconnaissance missions alone and then only with a limited range. Current UAVs can hover around possible targets until they are positively identified before releasing their payload of weaponry. Backpack-sized UAVs will provide ground troops with over-the-horizon surveillance capabilities.
=== Recreation and hobby ===
Small-scale remote-control vehicles have long been popular among hobbyists. These remote-controlled vehicles span a wide range in terms of price and sophistication. There are many types of radio-controlled vehicles; these include on-road cars, off-road trucks, boats, submarines, airplanes, and helicopters. The "robots" now popular in television shows such as Robot Wars are a recent extension of this hobby.
Radio control is the most popular choice, as the vehicle's range is not limited by the length of a cable, nor does it require direct line-of-sight with the controller, which is the case with infrared control.
== See also ==
Radio-controlled aircraft
Remote-controlled animal
Remotely operated underwater vehicle
Robot control
Teleoperation
Telerobotics
Unmanned aerial vehicle
Unmanned ground vehicle
Unmanned vehicle
== References ==
== External links == | Wikipedia/Remote-control_vehicle |
Visual servoing, also known as vision-based robot control and abbreviated VS, is a technique which uses feedback information extracted from a vision sensor (visual feedback) to control the motion of a robot. One of the earliest papers that talks about visual servoing was from the SRI International Labs in 1979.
== Visual servoing taxonomy ==
There are two fundamental configurations of the robot end-effector (hand) and the camera:
Eye-in-hand, or end-point open-loop control, where the camera is attached to the moving hand and observing the relative position of the target.
Eye-to-hand, or end-point closed-loop control, where the camera is fixed in the world and observing the target and the motion of the hand.
Visual Servoing control techniques are broadly classified into the following types:
Image-based (IBVS)
Position/pose-based (PBVS)
Hybrid approach
IBVS was proposed by Weiss and Sanderson. The control law is based on the error between current and desired features on the image plane, and does not involve any estimate of the pose of the target. The features may be the coordinates of visual features, lines or moments of regions. IBVS has difficulties with motions very large rotations, which has come to be called camera retreat.
PBVS is a model-based technique (with a single camera). This is because the pose of the object of interest is estimated with respect to the camera and then a command is issued to the robot controller, which in turn controls the robot. In this case the image features are extracted as well, but are additionally used to estimate 3D information (pose of the object in Cartesian space), hence it is servoing in 3D.
Hybrid approaches use some combination of the 2D and 3D servoing. There have been a few different approaches to hybrid servoing
2-1/2-D Servoing
Motion partition-based
Partitioned DOF Based
== Survey ==
The following description of the prior work is divided into 3 parts
Survey of existing visual servoing methods.
Various features used and their impacts on visual servoing.
Error and stability analysis of visual servoing schemes.
=== Survey of existing visual servoing methods ===
Visual servo systems, also called servoing, have been around since the early 1980s
, although the term visual servo itself was only coined in 1987.
Visual Servoing is, in essence, a method for robot control where the sensor used is a camera (visual sensor).
Servoing consists primarily of two techniques,
one involves using information from the image to directly control the degrees of freedom (DOF) of the robot, thus referred to as Image Based Visual Servoing (IBVS).
While the other involves the geometric interpretation of the information extracted from the camera, such as estimating the pose of the target and parameters of the camera (assuming some basic model of the target is known). Other servoing classifications exist based on the variations in each component of a servoing system
,
e.g. the location of the camera, the two kinds are eye-in-hand and hand–eye configurations.
Based on the control loop, the two kinds are end-point-open-loop and end-point-closed-loop. Based on whether the control is applied to the joints (or DOF)
directly or as a position command to a robot controller the two types are
direct servoing and dynamic look-and-move.
Being one of the earliest works
the authors proposed a hierarchical
visual servo scheme applied to image-based servoing. The technique relies on
the assumption that a good set of features can be extracted from the object
of interest (e.g. edges, corners and centroids) and used as a partial model
along with global models of the scene and robot. The control strategy is
applied to a simulation of a two and three DOF robot arm.
Feddema et al.
introduced the idea of generating task trajectory
with respect to the feature velocity. This is to ensure that the sensors are
not rendered ineffective (stopping the feedback) for any the robot motions.
The authors assume that the objects are known a priori (e.g. CAD model)
and all the features can be extracted from the object.
The work by Espiau et al.
discusses some of the basic questions in
visual servoing. The discussions concentrate on modeling of the interaction
matrix, camera, visual features (points, lines, etc..).
In
an adaptive servoing system was proposed with a look-and-move
servoing architecture. The method used optical flow along with SSD to
provide a confidence metric and a stochastic controller with Kalman filtering
for the control scheme. The system assumes (in the examples) that the plane
of the camera and the plane of the features are parallel., discusses an approach of velocity control using the Jacobian relationship s˙ = Jv˙ . In addition the author uses Kalman filtering, assuming that
the extracted position of the target have inherent errors (sensor errors). A
model of the target velocity is developed and used as a feed-forward input
in the control loop. Also, mentions the importance of looking into kinematic
discrepancy, dynamic effects, repeatability, settling time oscillations and lag
in response.
Corke poses a set of very critical questions on visual servoing and tries
to elaborate on their implications. The paper primarily focuses the dynamics
of visual servoing. The author tries to address problems like lag and stability,
while also talking about feed-forward paths in the control loop. The paper
also, tries to seek justification for trajectory generation, methodology of axis
control and development of performance metrics.
Chaumette in provides good insight into the two major problems with
IBVS. One, servoing to a local minima and second, reaching a Jacobian singularity. The author show that image points alone do not make good features
due to the occurrence of singularities. The paper continues, by discussing the
possible additional checks to prevent singularities namely, condition numbers
of J_s and Jˆ+_s, to check the null space of ˆ J_s and J^T_s . One main point that
the author highlights is the relation between local minima and unrealizable
image feature motions.
Over the years many hybrid techniques have been developed. These
involve computing partial/complete pose from Epipolar Geometry using multiple views or multiple cameras. The values are obtained by direct estimation or through a learning or a statistical scheme. While others have used
a switching approach that changes between image-based and position-based
on a Lyapnov function.
The early hybrid techniques that used a combination of image-based and
pose-based (2D and 3D information) approaches for servoing required either
a full or partial model of the object in order to extract the pose information
and used a variety of techniques to extract the motion information from the
image. used an affine motion model from the image motion in addition
to a rough polyhedral CAD model to extract the object pose with respect to
the camera to be able to servo onto the object (on the lines of PBVS).
2-1/2-D visual servoing developed by Malis et al. is a well known technique that breaks down the information required for servoing into an organized fashion which decouples rotations and translations. The papers
assume that the desired pose is known a priori. The rotational information is
obtained from partial pose estimation, a homography, (essentially 3D information) giving an axis of rotation and the angle (by computing the eigenvalues and eigenvectors of the homography). The translational information is
obtained from the image directly by tracking a set of feature points. The only
conditions being that the feature points being tracked never leave the field of
view and that a depth estimate be predetermined by some off-line technique.
2-1/2-D servoing has been shown to be more stable than the techniques that
preceded it. Another interesting observation with this formulation is that
the authors claim that the visual Jacobian will have no singularities during
the motions.
The hybrid technique developed by Corke and Hutchinson, popularly called portioned approach partitions the visual (or image) Jacobian into
motions (both rotations and translations) relating X and Y axes and motions related to the Z axis. outlines the technique, to break out columns
of the visual Jacobian that correspond to the Z axis translation and rotation
(namely, the third and sixth columns). The partitioned approach is shown to
handle the Chaumette Conundrum discussed in. This technique requires
a good depth estimate in order to function properly.
outlines a hybrid approach where the servoing task is split into two,
namely main and secondary. The main task is keep the features of interest within the field of view. While the secondary task is to mark a fixation
point and use it as a reference to bring the camera to the desired pose. The
technique does need a depth estimate from an off-line procedure. The paper
discusses two examples for which depth estimates are obtained from robot
odometry and by assuming that all features are on a plane. The secondary
task is achieved by using the notion of parallax. The features that are tracked
are chosen by an initialization performed on the first frame, which are typically points.
carries out a discussion on two aspects of visual servoing, feature
modeling and model-based tracking. Primary assumption made is that the
3D model of the object is available. The authors highlights the notion that
ideal features should be chosen such that the DOF of motion can be decoupled
by linear relation. The authors also introduce an estimate of the target
velocity into the interaction matrix to improve tracking performance. The
results are compared to well known servoing techniques even when occlusions
occur.
=== Various features used and their impacts on visual servoing ===
This section discusses the work done in the field of visual servoing. We try
to track the various techniques in the use of features. Most of the work
has used image points as visual features. The formulation of the interaction
matrix in assumes points in the image are used to represent the target.
There has some body of work that deviates from the use of points and use
feature regions, lines, image moments and moment invariants.
In, the authors discuss an affine based tracking of image features.
The image features are chosen based on a discrepancy measure, which is
based on the deformation that the features undergo. The features used were
texture patches. One of key points of the paper was that it highlighted the
need to look at features for improving visual servoing.
In the authors look into choice of image features (the same question
was also discussed in in the context of tracking). The effect of the choice
of image features on the control law is discussed with respect to just the
depth axis. Authors consider the distance between feature points and the
area of an object as features. These features are used in the control law with
slightly different forms to highlight the effects on performance. It was noted
that better performance was achieved when the servo error was proportional
to the change in depth axis.
provides one of the early discussions of the use of moments. The
authors provide a new formulation of the interaction matrix using the velocity
of the moments in the image, albeit complicated. Even though the moments
are used, the moments are of the small change in the location of contour
points with the use of Green’s theorem. The paper also tries to determine
the set of features (on a plane) to for a 6 DOF robot.
In discusses the use of image moments to formulate the visual Jacobian.
This formulation allows for decoupling of the DOF based on type of moments
chosen. The simple case of this formulation is notionally similar to the 2-1/2-
D servoing. The time variation of the moments (m˙ij) are determined using
the motion between two images and Greens Theorem. The relation between
m˙ij and the velocity screw (v) is given as m˙_ij = L_m_ij v. This technique
avoids camera calibration by assuming that the objects are planar and using
a depth estimate. The technique works well in the planar case but tends to
be complicated in the general case. The basic idea is based on the work in [4]
Moment Invariants have been used in. The key idea being to find
the feature vector that decouples all the DOF of motion. Some observations
made were that centralized moments are invariant for 2D translations. A
complicated polynomial form is developed for 2D rotations. The technique
follows teaching-by-showing, hence requiring the values of desired depth and
area of object (assuming that the plane of camera and object are parallel,
and the object is planar). Other parts of the feature vector are invariants
R3, R4. The authors claim that occlusions can be handled.
and build on the work described in. The major differ-
ence being that the authors use a technique similar to, where the task is
broken into two (in the case where the features are not parallel to the cam-
era plane). A virtual rotation is performed to bring the featured parallel to
the camera plane. consolidates the work done by the authors on image
moments.
=== Error and stability analysis of visual servoing schemes ===
Espiau in showed from purely experimental work that image based visual servoing (IBVS)
is robust to calibration errors. The author used a camera with no explicit
calibration along with point matching and without pose estimation. The
paper looks at the effect of errors and uncertainty on the terms in the interaction matrix from an experimental approach. The targets used were points
and were assumed to be planar.
A similar study was done in where the
authors carry out experimental evaluation of a few uncalibrated visual servo
systems that were popular in the 90’s. The major outcome was the experimental evidence of the effectiveness of visual servo control over conventional
control methods.
Kyrki et al. analyze servoing errors for position based and 2-1/2-D
visual servoing. The technique involves determining the error in extracting
image position and propagating it to pose estimation and servoing control.
Points from the image are mapped to points in the world a priori to obtain a mapping (which is basically the homography, although not explicitly stated
in the paper). This mapping is broken down to pure rotations and translations. Pose estimation is performed using standard technique from Computer
Vision. Pixel errors are transformed to the pose. These are propagating to
the controller. An observation from the analysis shows that errors in the
image plane are proportional to the depth and error in the depth-axis is
proportional to square of depth.
Measurement errors in visual servoing have been looked into extensively.
Most error functions relate to two aspects of visual servoing. One being
steady state error (once servoed) and two on the stability of the control
loop. Other servoing errors that have been of interest are those that arise
from pose estimation and camera calibration. In, the authors extend the
work done in by considering global stability in the presence of intrinsic
and extrinsic calibration errors. provides an approach to bound the task
function tracking error. In, the authors use teaching-by-showing visual
servoing technique. Where the desired pose is known a priori and the robot
is moved from a given pose. The main aim of the paper is to determine the
upper bound on the positioning error due to image noise using a convex-
optimization technique.
provides a discussion on stability analysis with respect the uncertainty
in depth estimates. The authors conclude the paper with the observation that
for unknown target geometry a more accurate depth estimate is required in
order to limit the error.
Many of the visual servoing techniques implicitly assume that
only one object is present in the image and the relevant feature for tracking
along with the area of the object are available. Most techniques require either
a partial pose estimate or a precise depth estimate of the current and desired
pose.
== Software ==
Matlab toolbox for visual servoing.
Java-based visual servoing simulator.
ViSP (ViSP states for "Visual Servoing Platform") is a modular software that allows fast development of visual servoing applications.
== See also ==
Robotics
Robot
Computer Vision
Machine Vision
Robot control
== References ==
== External links ==
S. A. Hutchinson, G. D. Hager, and P. I. Corke. A tutorial on visual servo control. IEEE Trans. Robot. Automat., 12(5):651—670, Oct. 1996.
F. Chaumette, S. Hutchinson. Visual Servo Control, Part I: Basic Approaches. IEEE Robotics and Automation Magazine, 13(4):82-90, December 2006.
F. Chaumette, S. Hutchinson. Visual Servo Control, Part II: Advanced Approaches. IEEE Robotics and Automation Magazine, 14(1):109-118, March 2007.
Notes from IROS 2004 tutorial on advanced visual servoing.
Springer Handbook of Robotics Chapter 24: Visual Servoing and Visual Tracking (François Chaumette, Seth Hutchinson)
UW-Madison, Robotics and Intelligent Systems Lab
INRIA Lagadic research group
Johns Hopkins University, LIMBS Laboratory
University of Siena, SIRSLab Vision & Robotics Group
Tohoku University, Intelligent Control Systems Laboratory
INRIA Arobas research group
LASMEA, Rosace group
UIUC, Beckman Institute | Wikipedia/Vision_Based_Robot_Control |
A vision-guided robot (VGR) system is a robot fitted with one or more cameras used as sensors to provide a secondary feedback signal to the robot controller for a more accurate movement to a variable target position. VGR is rapidly transforming production processes by enabling robots to be highly adaptable and more easily implemented, while dramatically reducing the cost and complexity of fixed tooling previously associated with the design and set up of robotic cells, whether for material handling, automated assembly, agricultural applications, life sciences, and more.
In one classic but rather dated example of VGR used for industrial manufacturing, the vision system (camera and software) determines the position of randomly fed products onto a recycling conveyor. The vision system provides the exact location coordinates of the components to the robot, which are spread out randomly beneath the camera's field of view, enabling the robot arm(s) to position the attached end effector (gripper) to the selected component and pick from the conveyor belt. The conveyor may stop under the camera to allow the position of the part to be determined, or if the cycle time is sufficient, it is possible to pick a component without stopping the conveyor using a control scheme that tracks the moving component through the vision software, typically by fitting an encoder to the conveyor, and using this feedback signal to update and synchronize the vision and motion control loops.
Such functionality is now common in the field of vision-guided robotics (VGR). It is a rapidly evolving technology that is proving to be economically advantageous in countries with high manufacturing overheads and skilled labor costs by reducing manual intervention, improving safety, increasing quality, and raising productivity rates, among other benefits.
The expansion of vision-guided robotic systems is part of the broader growth within the machine vision market, which is expected to grow to $17.72 billion by 2028. This growth can be attributed to the increasing demand for automation and precision, as well as the broad adoption of smart technologies across industries.
== Vision systems for robot guidance ==
A vision system comprises a camera and microprocessor or computer, with associated software. This is a broad definition that can be used to cover many different types of systems which aim to solve a large variety of tasks. Vision systems can be implemented in virtually any industry for any purpose. It can be used for quality control to check dimensions, angles, colour, surface structure, or for the recognition of an object as used in VGR systems.
A camera can be anything from a standard compact camera system with an integrated vision processor to more complex laser sensors and high-resolution and high-speed cameras. Combinations of several cameras to build up 3D images of an object are also available.
== Limitations of a vision system ==
There are always difficulties in integrated vision systems to match the camera with the set expectations of the system. In most cases, this is caused by a lack of knowledge on behalf of the integrator or machine builder. Many vision systems can be applied successfully to virtually any production activity, as long as the user knows exactly how to set up system parameters. This setup, however, requires a large amount of knowledge by the integrator, and the number of possibilities can make the solution complex. Lighting in industrial environments can be another major downfall of many vision systems.
== Overcoming lighting constraints with 3D vision ==
An advantage of 3D vision technology is its independence from lighting conditions. Unlike 2D systems that rely on specific lighting for accurate imaging, 3D vision systems can perform reliably under a variety of lighting scenarios. This is because 3D imaging typically involves capturing spatial information less sensitive to contrast and shadows than 2D systems.
In recent years, start-ups have started to appear, offering softwares simplifying the programming and integration of these 3D systems, in order to make them more accessible for industries. By leveraging 3D vision technologies, robots can navigate and perform tasks in environments with dynamic or uncontrolled lighting, which significantly expands their applications in real-world settings.
== VGR approaches ==
Typically, vision guidance systems fall into two categories: stationary camera mount, or robot arm-mounted camera. A stationary camera is typically mounted on a gantry or other structure where it can observe the entire robot cell area. This approach has the advantage of knowing its fixed position, providing a stable point of reference for all the activity within the cell. It has the disadvantage of additional infrastructure cost, and occasionally having its view obstructed by the robot arm's position. It also typically requires large image files (5 Mpixel or more) since the image must cover the entire work area.
These may be 2D or 3D cameras, although the vast majority of installations (2019) use machine vision 2D cameras offered by companies such as Keyence, Basler, Sick, Datalogic, COGNEX, and many others. Emerging players such as Leopard Imaging, Pickit3D, Zivid, and Photoneo are offering 3D cameras for stationary use. COGNEX recently acquired EnShape to add 3D capabilities to its lineup as well. 3D stationary mount cameras create large image files and point clouds that require substantial computing resources to process.
A camera mounted on a robot arm has some advantages and disadvantages. Some 3D cameras are simply too large to be practical when mounted on a robot, but Pickit 3D's Xbox cameras and 2D cameras such as Robotiq's wrist camera are compact and/or light enough to not meaningfully affect available robot working payload. An arm-mounted camera has a smaller field of view and can operate successfully at a lower resolution, even VGA, because it only surveys a fraction of the entire work cell at any point in time. This leads to faster image processing times.
However, arm-mounted cameras, whether 2D or 3D, typically suffer from XYZ disorientation because they are continually moving and have no way of knowing the robot arm's position. The typical workaround is to interrupt each robot cycle long enough for the camera to take another image and get reoriented. This is visible in essentially all published videos of arm-mounted camera performances, whether 2D or 3D, and can increase cycle times by as much as double what would otherwise be required.
Pickit 3D's Xbox camera has been arm-mounted for some applications. While capable of more complex 3D tasks such as bin picking, it still requires the stop-take-a-picture re-orientation mentioned above. Its 3D awareness does not help with that problem.
Visual Robotics claims to eliminate this cycle interruption with its "Vision-in-Motion" capabilities. Their system combines a 2D imager with internal photogrammetry and software to perform 3D tasks at high speed, owing to the smaller image files. The company claims a pending patent covering techniques for ensuring the camera knows its location in 3D space without stopping to get reoriented, leading to substantially faster cycle times. While much faster than other 3D approaches, it is not likely to be able to handle the more complex 3D tasks a true stereo camera can. On the other hand, many 3D applications require relatively simple object identification easily supported by the technique. To date, their ability to visually pick objects in motion (e.g. items on a conveyor) using an arm-mounted camera appears to be unprecedented.
Conversely, Inbolt presents a platform-independent 3D Vision-based robotic guidance system that integrates a 3D camera, advanced algorithms, and the fastest point cloud processing AI currently available. Their system is designed to handle high-frequency data processing efficiently, allowing for real-time tracking. This means the robot can adjust to variations in the position and orientation of objects within its field of vision. This adaptability is critical in environments where precision and flexibility are essential, making it well-suited for unstructured and unplanned environments. By enabling robots to operate without the need for mechanical constraints, it also eliminates the need for expensive jigs and fixtures.
These new solutions are changing the paradigm of manufacturing industries by offering unique solutions that cater to the evolving needs of modern manufacturing processes.
== VGR systems benefits ==
Traditional automation means serial production with large batch sizes and limited flexibility. Complete automation lines are usually built around a single product or possibly a small family of similar products that can run in the same production line. If a component is changed or a completely new product is introduced, this usually causes large changes in the automation process. In most cases, new component fixtures are required with time-consuming setup procedures. If components are delivered to the process by traditional hoppers and vibrating feeders, new bowl feeder tooling or additional bowl feeder tops are required. It may be that different products must be manufactured on the same process line, the cost for pallets, fixtures, and bowl feeders can often be a large part of the investment. Other areas to be considered are space constraints, storage of change parts, spare components, and changeover time between products.
VGR systems can run side by side with very little mechanical setup. In the most extreme cases, a gripper change is the only requirement, and the need to position components to set pick-up position is eliminated. With its vision system and control software, it is possible for the VGR system to handle different types of components. Parts with various geometry can be fed in any random orientation to the system and be picked and placed without any mechanical changes to the machine, resulting in quick changeover times. Other features and benefits of VGR systems are:
Switching between products and batch runs is software-controlled and quick, with no mechanical adjustments.
High residual value, even if production is changed.
Short lead times and short payback periods.
High machinery efficiency, reliability, and flexibility.
Possibility to integrate a majority of secondary operations such as deburring, clean blowing, washing, measuring, and so on.
Reduces manual work.
== See also ==
Machine vision
Simultaneous localization and mapping
== References == | Wikipedia/Vision-guided_robot_systems |
Boston Dynamics, Inc., is an American engineering and robotics design company founded in 1992 as a spin-off from the Massachusetts Institute of Technology. Headquartered in Waltham, Massachusetts, Boston Dynamics has been owned by the Hyundai Motor Group since December 2020, but it only completed the acquisition in June 2021.
Boston Dynamics develops a series of dynamic highly mobile robots, including BigDog, Spot, Atlas, and Handle. In 2019, Spot became its first commercially available robot. The company has stated its intent to commercialize its other robots, including Handle.
== History ==
The company was founded by Marc Raibert, who spun the company off from the Massachusetts Institute of Technology in 1992. The company was an outgrowth of the Leg Laboratory, Raibert's research lab at MIT and Carnegie Mellon University. The Leg Laboratory helped establish the scientific basis for highly dynamic robots. These robots were inspired by the remarkable ability of animals to move with agility, dexterity, perception and intelligence, and the work there set the stage for the robots developed at Boston Dynamics. Nancy Cornelius was a co-founder of Boston Dynamics, having joined the company as its first employee. During her time there she served as an officer of the company, did engineering on many contracts, was CFO for 10 years, and later was VP in charge of engineering on several contracts. She retired after 21 years of service in 2013, when the company was acquired by Google. Robert Playter was also a co-founder of the company, joining a few months later, as soon as he completed his PhD thesis at MIT working with Raibert in the Leg Laboratory. Playter was COO at the company for many years and has been CEO since 2019.
Early in the company's history, it worked with the American Systems Corporation under a contract from the Naval Air Warfare Center Training Systems Division (NAWCTSD) to replace naval training videos for aircraft launch operations with interactive 3D computer simulations featuring characters made with DI-Guy, software for realistic human simulation. Eventually the company started making physical robots—for example, BigDog was a quadruped robot designed for the U.S. military with funding from Defense Advanced Research Projects Agency (DARPA).
On December 13, 2013, the company was acquired by Google X (later X, a subsidiary of Alphabet Inc.) for an unknown price, where it was managed by Andy Rubin until his departure from Google in 2014. Immediately before the acquisition, Boston Dynamics transferred their DI-Guy software product line to VT MÄK, a simulation software vendor based in Cambridge, Massachusetts.
On June 8, 2017, Alphabet Inc. announced the sale of the company to Japan's SoftBank Group for an undisclosed sum. On April 2, 2019, Boston Dynamics acquired the Silicon Valley startup Kinema Systems.
In November 2020, the firm signed an agreement with Trimble Inc. to further develop the Spot dog product.
In December 2020, Hyundai Motor Group acquired an 80% stake in the company from SoftBank for approximately $880 million. SoftBank Group retains about 20% through an affiliate. In June 2021, it was announced that Hyundai officially took a controlling stake in the company from SoftBank.
In October 2022, the company signed a pledge saying it would not support any weaponization of its robotic creations. Boston Dynamics offered other robotics companies to join the pledge with five other firms signing as well.
== Products ==
=== BigDog ===
BigDog was a quadrupedal robot created in 2005 by Boston Dynamics, in conjunction with Foster-Miller, the Jet Propulsion Laboratory, and the Harvard University Concord Field Station. It was funded by DARPA in the hopes that it would be able to serve as a robotic pack mule to accompany soldiers in terrain too rough for vehicles, but the project was shelved after BigDog was deemed too loud to be used in combat. Instead of wheels, BigDog used four legs for movement, allowing it to move across surfaces that would defeat wheels. Called "the world's most ambitious legged robot", it was designed to carry 340 pounds (150 kg) alongside a soldier at 4 miles per hour (6.4 km/h; 1.8 m/s), traversing rough terrain at inclines up to 35 degrees.
=== Cheetah ===
The Cheetah is a four-footed robot that gallops at 28 miles per hour (45 km/h; 13 m/s), which as of August 2012 is a land speed record for legged robots.
A similar but independently developed robot also known as Cheetah is made by MIT's Biomimetic Robotics Lab, which, by 2014, could jump over obstacles while running. By 2018 the robot was able to climb stairs.
=== LittleDog ===
Released around 2010, LittleDog is a small quadruped robot developed for DARPA by Boston Dynamics for research. Unlike BigDog, which is run by Boston Dynamics, LittleDog is intended as a testbed for other institutions. Boston Dynamics maintains the robots for DARPA as a standard platform.
LittleDog has four legs, each powered by three electric motors. The legs have a large range of motion. The robot is strong enough for climbing and dynamic locomotion gaits. The onboard PC-level computer does sensing, actuator control and communications. LittleDog's sensors measure joint angles, motor currents, body orientation and foot/ground contact. Control programs access the robot through the Boston Dynamics Robot API. Onboard lithium polymer batteries allow for 30 minutes of continuous operation without recharging. Wireless communications and data logging support remote operation and data analysis. LittleDog development is funded by the DARPA Information Processing Technology Office.
=== PETMAN ===
PETMAN (Protection Ensemble Test Mannequin) is a bipedal device constructed for testing chemical protection suits. It is the first anthropomorphic robot that moves dynamically like a person.
=== LS3 ===
Legged Squad Support System (LS3), also known as AlphaDog, is a militarized version of BigDog. It is ruggedized for military use, with the ability to operate in hot, cold, wet, and dirty environments.
According to Lt. Col. Joe Hitt and the US Marine Corps's program manager, "The vision for LS3 is to combine the capabilities of a pack mule with the intelligence of a trained animal". LS3 is capable of reacting to visual or oral commands and uses an on-board GPS system, along with computer vision (LIDAR and IR), to guide itself through terrain. Due to its ability to track oral commands, soldiers within the field found it difficult to hold a conversation with this bot in a vicinity because it would unknowingly follow commands not given to itself. Unlike its living counterparts, LS3 can march for 20 miles (32 km) before running out of fuel. The robot also doesn't suffer from the shortcomings of bleeding and falling over, a problem with many pack mules.
=== Atlas ===
The Agile Anthropomorphic Robot "Atlas" is a 5-foot (152.4 cm) bipedal humanoid robot, based on Boston Dynamics' earlier PETMAN humanoid robot, and designed for a variety of search and rescue tasks.
In February 2016 Boston Dynamics published a YouTube video entitled "Atlas, The Next Generation" showing a new humanoid robot about 5 feet tall (152.4 cm). In the video, the robot is shown performing a number of tasks that would have been difficult or impossible for the previous generation of humanoid robots.
A video posted to the Boston Dynamics channel of YouTube dated October 11, 2018, titled "Parkour Atlas", shows the robot easily running up 2-foot high steps onto a platform. Atlas is shown in a September 2019 YouTube video doing "More Parkour".
In April 2024, the company announced that they had retired the hydraulic based Atlas in favor of a new all electric version of Atlas.
=== Spot ===
On June 23, 2016, Boston Dynamics revealed the four-legged canine-inspired Spot, weighing 25 kg (55 pounds), which was lighter than their other products.
In November 2017, a promotional video of Spot using its forward claw to open a door for another robot reached #1 on YouTube, with over 2 million views. A later video the same month showed Spot persisting in attempting to open the door in the face of human interference. Viewers perceived the robot as "creepy" and "reminiscent of all kinds of sci-fi robots that wouldn't give up in their missions to seek and destroy".
On May 11, 2018, Boston Dynamics CEO Marc Raibert announced at TechCrunch Robotics Session 2018 that Spot was in pre-production and preparing for commercial availability in 2019. On its website, Boston Dynamics highlighted that Spot is the "quietest robot [they] have built." The company said it had plans with contract manufacturers to build the first 100 Spots later that year for commercial purposes, with them starting to scale production with the goal of selling Spot in 2019. However, in September 2019, journalists were informed that the robots will not be sold, but they will be leased to selected business partners. In November 2019 Massachusetts State Police became the first law enforcement agency to use Spot as a robot cop, as well as in the unit's bomb squad.
Since January 2020, Spot's software development kit is available via GitHub. It allows programmers to develop custom applications for Spot to do various actions that could be used across different industries. On June 16, 2020, Boston Dynamics made Spot available for the general public for US$74,500 (equivalent to $90,517 in 2024).
In June 2020, a lone Spot named 'Zeus' was used by SpaceX at their Boca Chica Starship Test Site to help contain sub-cooled liquid nitrogen and to inspect 'potentially dangerous' sites at and around the launchpad.
In July 2020, a team of Spot robots performed as cheerleaders in the stands at a baseball match between the Fukuoka SoftBank Hawks and the Rakuten Eagles, backed by a team of SoftBank Pepper Robots.
In November 2020, a Spot robot performed inspection tasks on the Skarv floating production storage and offloading vessel.
In April 2021, Michael Reeves made a YouTube video where he attached a pressurized beer canister and nozzle to a Spot robot in order to detect red plastic cups and dispense beer into them.
In March 2022, artist Agnieszka Pilat sold a painting created by Spot for $40,000 at the home of Brian Boitano to benefit Ukrainian refugees. The painting, titled "Sunrise March," was created by applying paint on Spot's feet and having the robot rotate in circles.
In February 2024, drivers on the M5 motorway in England were warned they should not be alarmed if they saw a Spot operating alongside the road. The National Highways administration had trialed one "as an alternative to human inspectors".
=== Handle ===
Handle is a research robot with two flexible legs on wheels and two "hands" for manipulating or carrying objects. It can stand 6.5 feet (2 m) tall, travel at 9 miles per hour (14 km/h) and jump 4 feet (1.2 m) vertically. It uses electric power to operate various electric and hydraulic actuators, with a range of about 15 miles (25 km) on one battery charge. Handle uses many of the same dynamics, balance and mobile manipulation principles found in the other robots by Boston Dynamics but, with only about 10 actuated joints, it is significantly less complex.
=== Stretch ===
On March 29, 2021, Boston Dynamics announced via a video on their YouTube channel the Stretch robot that was designed for warehouse automation. It has a square mobile base containing a set of wheels, a “perception mast” with cameras and other sensors, and a robotic arm with seven degrees of freedom and a suction pad array on the end that can grab and move boxes up to 23 kilograms (50 lbs) in weight.
=== Pick ===
Pick is a robot just like Stretch but fixed in a particular place. It is designed to carry boxes. It can identify a box in less than a second. It automatically disposes of the sheet of cardboard in between stacks of boxes.
=== Factory Safety Service Robot ===
The Factory Safety Service Robot was unveiled on September 17, 2021. It was the first joint venture with Hyundai Motor Group. The robot is based on the existing Boston Dynamics robot Spot. Its integrated thermal camera and 3D LiDAR system help detect nearby people, monitor fire hazards, and recognize open and closed doors.
== In popular culture ==
"Metalhead", a 2017 episode of Black Mirror, features killer-robot dogs resembling, and inspired by, Boston Dynamics robot dogs.
In June 2019, a parody video went viral across social media in which a robot resembling Atlas was abused, before turning on its human attackers. The video turned out to be the work of Corridor Digital, who used the watermark "Bosstown Dynamics" instead of "Boston Dynamics". This video tricked many people, causing them to believe it was real.
In Heroes of the Storm (2015), a multiplayer video game by Blizzard Entertainment, playable heroes are able to move quickly through the battleground by using a mount called "Project: D.E.R.P.A.", which references one of Boston Dynamics' quadrupedal robots.
The HBO Show Silicon Valley has made two prominent references to the company ‒ an episode featured a robotics company called Somerville Dynamics, named after Somerville, a city that neighbors Boston; and the season premiere of Season 3 featured a real Boston Dynamics Spot robot, seen crossing a street.
In 2022 the Spot robot was featured as a background extra in an episode of The Book of Boba Fett TV series.
== See also ==
Biomimetics
List of robotic dogs
== References ==
== External links ==
Media related to Boston Dynamics at Wikimedia Commons | Wikipedia/Boston_Dynamics |
Evolutionary algorithms (EA) reproduce essential elements of the biological evolution in a computer algorithm in order to solve "difficult" problems, at least approximately, for which no exact or satisfactory solution methods are known. They belong to the class of metaheuristics and are a subset of population based bio-inspired algorithms and evolutionary computation, which itself are part of the field of computational intelligence. The mechanisms of biological evolution that an EA mainly imitates are reproduction, mutation, recombination and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators.
Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems; therefore, there may be no direct link between algorithm complexity and problem complexity.
== Generic definition ==
The following is an example of a generic evolutionary algorithm:
Randomly generate the initial population of individuals, the first generation.
Evaluate the fitness of each individual in the population.
Check, if the goal is reached and the algorithm can be terminated.
Select individuals as parents, preferably of higher fitness.
Produce offspring with optional crossover (mimicking reproduction).
Apply mutation operations on the offspring.
Select individuals preferably of lower fitness for replacement with new individuals (mimicking natural selection).
Return to 2
== Types ==
Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem.
Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems.
Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming:
Cartesian genetic programming
Gene expression programming
Grammatical evolution
Linear genetic programming
Multi expression programming
Evolutionary programming – Similar to evolution strategy, but with a deterministic selection of all parents.
Evolution strategy (ES) – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks.
CMA-ES
Natural evolution strategy
Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems.
Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions.
Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect.
Learning classifier system – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach.
Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique.
== Theoretical background ==
The following theoretical principles apply to all or almost all EAs.
=== No free lunch theorem ===
The no free lunch theorem of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a problem-adapted coding). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through heuristics or other procedures. Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, local search procedures or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a memetic algorithm. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust.
=== Convergence ===
For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof:
From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation
k
{\displaystyle k}
an improvement of the fitness
F
{\displaystyle F}
of the respective best individual
x
′
{\displaystyle x'}
will occur with a probability
P
>
0
{\displaystyle P>0}
. Thus:
F
(
x
1
′
)
≤
F
(
x
2
′
)
≤
F
(
x
3
′
)
≤
⋯
≤
F
(
x
k
′
)
≤
⋯
{\displaystyle F(x'_{1})\leq F(x'_{2})\leq F(x'_{3})\leq \cdots \leq F(x'_{k})\leq \cdots }
I.e., the fitness values represent a monotonically non-decreasing sequence, which is bounded due to the existence of the optimum. From this follows the convergence of the sequence against the optimum.
Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual panmictic population model, elitist EAs tend to converge prematurely more than non-elitist ones. In a panmictic population model, mate selection (see step 4 of the generic definition) is such that every individual in the entire population is eligible as a mate. In non-panmictic populations, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection.
=== Virtual alphabets ===
With the theory of virtual alphabets, David E. Goldberg showed in 1990 that by using a representation with real numbers, an EA that uses classical recombination operators (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers. This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion.
== Comparison to other concepts ==
=== Biological processes ===
A possible limitation of many evolutionary algorithms is their lack of a clear genotype–phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature phenotype. This indirect encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the evolvability of the organism. Such indirect (also known as generative or developmental) encodings also enable evolution to exploit the regularity in the environment. Recent work in the field of artificial embryogeny, or artificial developmental systems, seeks to address these concerns. And gene expression programming successfully explores a genotype–phenotype system, where the genotype consists of linear multigenic chromosomes of fixed length and the phenotype consists of multiple expression trees or computer programs of different sizes and shapes.
=== Monte-Carlo methods ===
Both method classes have in common that their individual search steps are determined by chance. The main difference, however, is that EAs, like many other metaheuristics, learn from past search steps and incorporate this experience into the execution of the next search steps in a method-specific form. With EAs, this is done firstly through the fitness-based selection operators for partner choice and the formation of the next generation. And secondly, in the type of search steps: In EA, they start from a current solution and change it or they mix the information of two solutions. In contrast, when dicing out new solutions in Monte-Carlo methods, there is usually no connection to existing solutions.
If, on the other hand, the search space of a task is such that there is nothing to learn, Monte-Carlo methods are an appropriate tool, as they do not contain any algorithmic overhead that attempts to draw suitable conclusions from the previous search. An example of such tasks is the proverbial search for a needle in a haystack, e.g. in the form of a flat (hyper)plane with a single narrow peak.
== Applications ==
The areas in which evolutionary algorithms are practically used are almost unlimited and range from industry, engineering, complex scheduling, agriculture, robot movement planning and finance to research and art. The application of an evolutionary algorithm requires some rethinking from the inexperienced user, as the approach to a task using an EA is different from conventional exact methods and this is usually not part of the curriculum of engineers or other disciplines. For example, the fitness calculation must not only formulate the goal but also support the evolutionary search process towards it, e.g. by rewarding improvements that do not yet lead to a better evaluation of the original quality criteria. For example, if peak utilisation of resources such as personnel deployment or energy consumption is to be avoided in a scheduling task, it is not sufficient to assess the maximum utilisation. Rather, the number and duration of exceedances of a still acceptable level should also be recorded in order to reward reductions below the actual maximum peak value. There are therefore some publications that are aimed at the beginner and want to help avoiding beginner's mistakes as well as leading an application project to success. This includes clarifying the fundamental question of when an EA should be used to solve a problem and when it is better not to.
== Related techniques and other global search methods ==
There are some other proven and widely used methods of nature inspired global search techniques such as
Memetic algorithm – A hybrid method, inspired by Richard Dawkins's notion of a meme. It commonly takes the form of a population-based algorithm (frequently an EA) coupled with individual learning procedures capable of performing local refinements. Emphasizes the exploitation of problem-specific knowledge and tries to orchestrate local and global search in a synergistic way.
A cellular evolutionary or memetic algorithm uses a topological neighbouhood relation between the individuals of a population for restricting the mate selection and by that reducing the propagation speed of above-average individuals. The idea is to maintain genotypic diversity in the poulation over a longer period of time to reduce the risk of premature convergence.
Ant colony optimization is based on the ideas of ant foraging by pheromone communication to form paths. Primarily suited for combinatorial optimization and graph problems.
Particle swarm optimization is based on the ideas of animal flocking behaviour. Also primarily suited for numerical optimization problems.
Gaussian adaptation – Based on information theory. Used for maximization of manufacturing yield, mean fitness or average information. See for instance Entropy in thermodynamics and information theory.
In addition, many new nature-inspired or methaphor-guided algorithms have been proposed since the beginning of this century. For criticism of most publications on these, see the remarks at the end of the introduction to the article on metaheuristics.
== Examples ==
In 2020, Google stated that their AutoML-Zero can successfully rediscover classic algorithms such as the concept of neural networks.
The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics.
== Gallery ==
== References ==
== Bibliography ==
Ashlock, D. (2006), Evolutionary Computation for Modeling and Optimization, Springer, New York, doi:10.1007/0-387-31909-3 ISBN 0-387-22196-4.
Bäck, T. (1996), Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford Univ. Press, New York, ISBN 978-0-19-509971-3.
Bäck, T., Fogel, D., Michalewicz, Z. (1999), Evolutionary Computation 1: Basic Algorithms and Operators, CRC Press, Boca Raton, USA, ISBN 978-0-7503-0664-5.
Bäck, T., Fogel, D., Michalewicz, Z. (2000), Evolutionary Computation 2: Advanced Algorithms and Operators, CRC Press, Boca Raton, USA, doi:10.1201/9781420034349 ISBN 978-0-3678-0637-8.
Banzhaf, W., Nordin, P., Keller, R., Francone, F. (1998), Genetic Programming - An Introduction, Morgan Kaufmann, San Francisco, ISBN 978-1-55860-510-7.
Eiben, A.E., Smith, J.E. (2003), Introduction to Evolutionary Computing, Springer, Heidelberg, New York, doi:10.1007/978-3-662-44874-8 ISBN 978-3-662-44873-1.
Holland, J. H. (1992), Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, MA, ISBN 978-0-262-08213-6.
Michalewicz, Z.; Fogel, D.B. (2004), How To Solve It: Modern Heuristics. Springer, Berlin, Heidelberg, ISBN 978-3-642-06134-9, doi:10.1007/978-3-662-07807-5.
Benko, Attila; Dosa, Gyorgy; Tuza, Zsolt (2010). "Bin Packing/Covering with Delivery, solved with the evolution of algorithms". 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA). pp. 298–302. doi:10.1109/BICTA.2010.5645312. ISBN 978-1-4244-6437-1. S2CID 16875144.
Poli, R.; Langdon, W. B.; McPhee, N. F. (2008). A Field Guide to Genetic Programming. Lulu.com, freely available from the internet. ISBN 978-1-4092-0073-4. Archived from the original on 2016-05-27. Retrieved 2011-03-05.
Price, K., Storn, R.M., Lampinen, J.A., (2005). Differential Evolution: A Practical Approach to Global Optimization, Springer, Berlin, Heidelberg, ISBN 978-3-642-42416-8, doi:10.1007/3-540-31306-0.
Ingo Rechenberg (1971), Evolutionsstrategie - Optimierung technischer Systeme nach Prinzipien der biologischen Evolution (PhD thesis). Reprinted by Fromman-Holzboog (1973). ISBN 3-7728-1642-8
Hans-Paul Schwefel (1974), Numerische Optimierung von Computer-Modellen (PhD thesis). Reprinted by Birkhäuser (1977).
Hans-Paul Schwefel (1995), Evolution and Optimum Seeking. Wiley & Sons, New York. ISBN 0-471-57148-2
Simon, D. (2013), Evolutionary Optimization Algorithms Archived 2014-03-10 at the Wayback Machine, Wiley & Sons, ISBN 978-0-470-93741-9
Kruse, Rudolf; Borgelt, Christian; Klawonn, Frank; Moewes, Christian; Steinbrecher, Matthias; Held, Pascal (2013), Computational Intelligence: A Methodological Introduction. Springer, London. ISBN 978-1-4471-5012-1, doi:10.1007/978-1-4471-5013-8.
Rahman, Rosshairy Abd.; Kendall, Graham; Ramli, Razamin; Jamari, Zainoddin; Ku-Mahamud, Ku Ruhana (2017). "Shrimp Feed Formulation via Evolutionary Algorithm with Power Heuristics for Handling Constraints". Complexity. 2017: 1–12. doi:10.1155/2017/7053710.
== External links ==
An Overview of the History and Flavors of Evolutionary Algorithms | Wikipedia/Evolutionary_methods |
Adaptive cruise control (ACC) is a type of advanced driver-assistance system for road vehicles that automatically adjusts the vehicle speed to maintain a safe distance from vehicles ahead. As of 2019, it is also called by 20 unique names that describe that basic functionality. This is also known as Dynamic cruise control.
Control is based on sensor information from on-board sensors. Such systems may use a radar, laser sensor or a camera setup allowing the vehicle to brake when it detects the car is approaching another vehicle ahead, then accelerate when traffic allows it to.
ACC technology is regarded as a key component of future generations of intelligent cars. The technology enhances passenger safety and convenience as well as increasing road capacity by maintaining optimal separation between vehicles and reducing driver errors. Vehicles with autonomous cruise control are considered a Level 1 autonomous car, as defined by SAE International. When combined with another driver assist feature such as lane centering, the vehicle is considered a Level 2 autonomous car.
== Consumer use ==
Adaptive cruise control does not provide full autonomy: the system only provides some help to the driver, but does not drive the car by itself. For example, the driver is able to set the cruise control to 55 mph, if the car while traveling that speed catches up to another vehicle going only 45 mph, the ACC will cause the car to automatically brake and maintain a safe distance behind the vehicle in front, and will maintain that distance until the road opens up again and the car can safely return to the initially set speed of 55 mph.
=== Pricing ===
Given the fact that ACC is considered a key component of future generations of intelligent cars, and the fact that it can increase comfort and safety on longer drives, ACC systems cost anywhere between $500 to $2500, depending on the type of ACC, as well as the model of the car.
== History ==
1992: Mitsubishi Motors was the first to offer a lidar-based distance detection system on the Japanese market Debonair. Marketed as "distance warning", this system warns the driver, without influencing throttle, brakes, or gearshifting.
1995: Mitsubishi Diamante introduced laser "Preview Distance Control". This system controlled speed through throttle control and downshifting, but could not apply the brakes.
1997: Toyota offered a "laser adaptive cruise control" (lidar) system on the Japanese market Celsior. It controlled speed through throttle control and downshifting, but could not apply the brakes.
1999: Mercedes introduced "Distronic", the first radar-assisted ACC, on the Mercedes-Benz S-Class (W220) and the CL-Class.
1999: Jaguar began offering a radar-based ACC system on the Jaguar XK (X100).
1999: Nissan introduced laser ACC on the Japanese market Nissan Cima.
1999: Subaru introduced world's first camera-based ACC on the Japanese-market Subaru Legacy Lancaster.
2000: BMW introduced radar "Active Cruise Control" in Europe on the BMW 7 Series - E38.
2000: Toyota was the first to bring laser ACC to the US market in late 2000, with the LS 430 Dynamic Laser Cruise Control system.
2000: Toyota's laser ACC system added "brake control", that also applies brakes.
2001: Infiniti introduced laser "Intelligent Cruise Control" on the 2002 Infiniti Q45 Third generation F50 and 2002 Infiniti QX4.
2001: Renault introduced ACC on the Renault Vel Satis (supplied by Bosch)
2002: Lancia introduced radar ACC (by Bosch) on the Lancia Thesis
2002: Volkswagen introduced radar ACC, manufactured by Autocruise (now TRW), on the Volkswagen Phaeton.
2002: Audi introduced radar ACC (Autocruise) on the Audi A8 in late 2002
2003: Cadillac introduced radar ACC on the Cadillac XLR.
2003: Toyota shifted from laser to radar ACC on the Celsior. The first Lexus Dynamic Radar Cruise Control and a radar-guided pre-collision system appeared on the Lexus LS (XF30) US market facelift.
2004: Toyota added "low-speed tracking mode" to the radar ACC on the Crown Majesta. The low-speed tracking mode was a second mode that would warn the driver and provide braking if the car ahead stopped; it could stop the car, but would then deactivate.
2005: In the United States, Acura introduced radar ACC integrated with a Collision avoidance system (Collision Mitigation Braking System (CMBS)) in the model year 2006 Acura RL.
2005: Mercedes-Benz S-Class (W221) upgraded ACC to completely halt the car if necessary (now called "Distronic Plus" on E-Class and most Mercedes sedans.
2006: Volkswagen Passat B6 introduced radar ACC supplied by Autocruise and TRW, functioning from 30 to 210 km/h (19 to 130 mph). It supported additional functions AWV1 and AWV2 to prevent collisions by using the brake system.
2006: Audi introduced full speed range ACC plus on the Audi Q7. In low-speed mode, it warns the driver of a potential collision and prepares emergency braking as needed. The system was supplied by Bosch.
2006: Nissan introduced "Intelligent Cruise Control with Distance Control Assist" on Nissan Fuga. It pushes the gas pedal against the foot when the navigation system observes an unsafe speed. If the Autonomous cruise control system is used, the Distance Control Assistance reduced speed automatically and warned the driver with an audible bell sound.
2006: September 2006 Toyota introduced its "all-speed tracking function" for the Lexus LS 460. The radar-assisted system maintained continuous control from speeds from 0 to 100 km/h (0 to 62 mph) and is designed to work under stop/go situations such as highway traffic congestion.
2007: BMW introduced full-speed Active Cruise Control Stop-and-Go on the BMW 5 Series (E60).
2008: Lincoln introduced radar ACC on the 2009 Lincoln MKS.
2008: SsangYong Motor Company introduced radar "Active Cruise Control" on the SsangYong Chairman
2008: Volkswagen Passat CC, B6 and Touareg GP. The ACC system was updated to support a full auto stop and added Front Assist function to prevent collisions working separately of ACC. Front Assist cannot brake automatically, it only increases the pressure in the brake system and warns the driver.
2008: Volkswagen Golf 6 introduced ACC with lidar.
2009: Hyundai introduced radar ACC on Hyundai Equus in Korean market.
2009: ACC and CMBS also became available as optional feature for the 2010 Acura MDX Mid Model Change (MMC) and the newly introduced model year 2010 Acura ZDX.
2010: Ford debuted its first ACC on the sixth generation Ford Taurus (option on most models, standard on the SHO)
2010: Audi introduced a GPS-guided radar ACC on Audi A8#D4
2010: Volkswagen Passat B7, CC. Update of ACC and updated Front Assist. Introduced emergency braking, named "City". The car could brake automatically to prevent a collision.
2010: Jeep introduced ACC on the 2011 Jeep Grand Cherokee
2012: Volkswagen made ACC standard on the Volkswagen Golf MK7 SE and above.
2013: Mercedes introduced "Distronic Plus with Steering Assist" (traffic jam assist) on the Mercedes-Benz S-Class (W222)
2013: BMW introduced Active Cruise Control with Traffic Jam Assistant.
2014: Chrysler introduced full speed range radar "Adaptive Cruise Control with Stop+" on the 2015 Chrysler 200.
2014: Tesla Motors introduced autopilot feature to Model S cars, enabling semi-autonomous cruise control.
2015: Ford introduced the first pickup truck with ACC on the 2015 Ford F150.
2015: Honda introduced its European CR-V 2015 with predictive cruise control.
2015: Volvo began offering ACC on all its models.
2017: Cadillac introduced its Super Cruise semi-autonomous feature in the model year 2018 CT6 (for cars produced on or after 6 September 2017). The system used onboard radar and cameras along with lidar mapping data, allowing the driver to go hands-free on limited-access highways.
2017: Toyota introduced its safety sense on all models as a standard feature. Toyota Safety Sense P (TSS-P) includes DRCC (dynamic radar cruise control) that uses a front-grille-mounted radar and a forward-facing camera that is designed to detect a vehicle in front and automatically adjust the vehicle's speed to help maintain a pre-set distance behind a vehicle ahead.
== Types ==
Laser-based systems work using LIDAR (Light detection and ranging), allowing laser-based ACC to provide the largest detection distance as well as the best accuracy of all ACC systems. However, laser-based systems do not detect and track vehicles as reliably in adverse weather conditions due to the fact that fog, or water particles in the air may absorb and or redirect the light emitted from the laser, through absorption, scattering, and reflection. Laser based ACC systems also have a more difficult time tracking dirty (and therefore non-reflective) vehicles. Laser-based sensors must be exposed, the sensor (a fairly large black box) is typically found in the lower grille, offset to one side.
Radar-based sensors work by emitting a radio wave at a frequency of either 24GHz or 77GHz. As these signals are emitted, the car computes how long it takes for the signal to return, thus finding out how far away a vehicle may be in front of it. Due to the widely distributed beam, radar ACC systems allow for a much wider field of view while still being able to provide accurate measurements of 160+ meters (Roughly 525 feet). These radar systems can be hidden behind plastic fascias; however, the fascias may look different from a vehicle without the feature. For example, Mercedes-Benz packages the radar behind the upper grille in the center and behind a solid plastic panel that has painted slats to simulate the look of the rest of the grille.
Single radar systems are the most common. Systems involving multiple sensors use either two similar hardware sensors like the 2010 Audi A8 or the 2010 Volkswagen Touareg, or one central long range radar coupled with two short radar sensors placed on the corners of the vehicle like the BMW 5 and 6 series.
A more recent development is the binocular computer vision system, such as that introduced to the US market in model year 2013 by Subaru. These systems have front-facing video cameras mounted on either side of the rearview mirror and use digital processing to extract depth information from the parallax between the two cameras' views. Due to the fact that there are video cameras, this type of ACC is able to reliably determine shape and classification of objects in front of the vehicle, and are also able to specifically detect when a vehicle in front is braking. As of now, this type of ACC is more widely used for lane centering.
=== Assisting systems ===
Radar-based ACC is often sold together with a precrash system, which warns the driver and/or provides brake support if there is a high risk of a collision. Also in certain cars, it is incorporated with a lane maintaining system which provides a power steering assist to reduce steering input burden on corners when the cruise control system is activated.
=== Multi-sensor systems ===
Systems with multiple sensors can practice sensor fusion to integrate the data to improve safety and/or driving experience. GPS data can inform the system of geographic features such as a freeway offramp. A camera system could notice driver behavior such as brake lights and/or a turn signal. This could allow the following car to interpret a turn signal by an exit as not requiring the following car to slow down, as the leading car will exit. Multi-sensor systems could also take note of traffic signs/signals and not, e.g., violate a red light while following a vehicle that crossed before the signal changed.
=== Predictive systems ===
Predictive systems modify vehicle speed based on predictions of other vehicles' behavior. Such systems can make earlier, more moderate adjustments to the predicted behavior, improving safety and passenger comfort. One example is to predict the likelihood of a vehicle in a neighboring lane moving in front of the controlled vehicle. One system predicts a lane change up to five seconds before it occurs.
== Regulations and norms ==
Adaptive cruise control is regulated by European norm ISO 15622 Intelligent transport systems—Adaptive cruise control systems—Performance requirements and test procedures.
According to this standard, an ACC is partial automation of longitudinal vehicle control to reduce the workload of the driver on roads where non-motorized vehicles and pedestrians are prohibited. It does not deal with stationary objects.
According to this standard, ACC includes two classes of systems: the FSRA (full speed range) and the LSRA (limited speed range).
== Vehicle models supporting adaptive cruise control ==
The three main categories of ACC are:
Vehicles with Full Speed Range 0MPH are able to bring the car to a full stop to 0 mph (0 km/h) and need to be re-activated to continue moving with something like a tap of the gas pedal.
Vehicles with Traffic Jam Assist / Stop & Go auto-resume from standstill to creep with stop and go traffic.
Vehicles with Partial cruise control cuts off and turns off below a set minimum speed, requiring driver intervention.
Vehicles with fully automated speed control can respond to traffic signals and non-vehicular on-road activity.
=== Mercedes Distronic Plus ===
In 1999, Mercedes introduced Distronic, the first radar-assisted adaptive system, on the Mercedes-Benz S-Class (W220) and the CL-Class. Distronic adjusts the vehicle speed automatically to the car in front in order to always maintain a safe distance to other cars on the road.
In 2005, Mercedes refined the system ("Distronic Plus") making the Mercedes-Benz S-Class (W221) the first car to receive the upgraded system. Distronic Plus could now completely halt the car if necessary on most sedans. In an episode of Top Gear, Jeremy Clarkson demonstrated the effectiveness of the system by coming to a complete halt from motorway speeds to a round-about and getting out, without touching the pedals.
In 2016, Mercedes introduced Active Brake Assist 4, the first emergency braking assistant with pedestrian recognition.
One crash caused by Distronic Plus dates to 2005, when the German news magazine Stern was testing Mercedes' original Distronic system. During the test, the system did not always manage to brake in time. Ulrich Mellinghoff, then Head of Safety, NVH, and Testing at the Mercedes-Benz Technology Centre, stated that some tests failed because the vehicle was tested in a metallic hall, which caused problems with radar. Later iterations received an upgraded radar and other sensors, which are not disrupted by a metallic environment. In 2008, Mercedes conducted a study comparing the crash rates of Distronic Plus vehicles and vehicles without it, and concluded that those equipped with Distronic Plus have an around 20% lower crash rate.
== Aftermarket ==
== See also ==
Autonomous car
Cooperative Adaptive Cruise Control
Hands-free driving
IEEE Intelligent Transportation Systems Society
Intelligent car
Lane centering
Lane departure warning system
Precrash system
== References ==
== External links ==
Cooperative Adaptive Cruise Control: Human Factors Analysis—Federal Highway Administration | Wikipedia/Adaptive_cruise_control |
A Vehicular ad hoc network (VANET) is a proposed type of mobile ad hoc network (MANET) involving road vehicles. VANETs were first proposed in 2001 as "car-to-car ad-hoc mobile communication and networking" applications, where networks could be formed and information could be relayed among cars. It has been shown that vehicle-to-vehicle and vehicle-to-roadside communications architectures could co-exist in VANETs to provide road safety, navigation, and other roadside services.
VANETs could be a key part of the intelligent transportation systems (ITS) framework. Sometimes, VANETs are referred to as Intelligent Transportation Networks. They could evolve into a broader "Internet of vehicles". which itself could evolve into an "Internet of autonomous vehicles".
While, in the early 2000s, VANETs were seen as a mere one-to-one application of MANET principles, they have since then developed into a field of research in their own right. By 2015,: 3 the term VANET became mostly synonymous with the more generic term inter-vehicle communication (IVC), although the focus remains on the aspect of spontaneous networking, much less on the use of infrastructure like Road Side Units (RSUs) or cellular networks.
VANETs are in development and are not in use by commercially available vehicles.
== Applications ==
VANETs could support a wide range of applications – from simple one hop information dissemination of, e.g., cooperative awareness messages (CAMs) to multi-hop dissemination of messages over vast distances.
Most of the principles of mobile ad hoc networks (MANETs) apply to VANETs, but the details differ. Rather than moving at random, vehicles tend to move in an organized fashion. The interactions with roadside equipment can likewise be characterized fairly accurately. And finally, most vehicles are restricted in their range of motion, for example by being constrained to follow a paved highway.
Potential applications of VANETs include:: 56
Electronic brake lights, which would allow a driver (or an autonomous car or truck) to react to vehicles braking even though they might be obscured (e.g., by other vehicles).
Platooning, which would allow vehicles to closely (down to a few inches) follow a leading vehicle by wirelessly receiving acceleration and steering information, thus forming electronically coupled "road trains".
Traffic information systems, which would use VANET communication to provide up-to-the minute obstacle reports to a vehicle's satellite navigation system
Road Transportation Emergency Services – where VANET communications, VANET networks, and road safety warning and status information dissemination would be used to reduce delays and speed up emergency rescue operations to save the lives of those injured.
On-The-Road Services – it is also envisioned that the future transportation highway would be "information-driven" or "wirelessly-enabled". VANETs can help advertise services (shops, gas stations, restaurants, etc.) to the driver, and even send notifications of any sale going on at that moment.
Electronic Toll Collection – The tolling application performed with the C-ITS equipment. These latter use the ITS-G5 technology, the Roadside Unit (RSU) and the on-board unit (OBU) with features specified by the standardization Institute ETSI. To perform this service, we highlight two mains requirements: how to have a reliable geolocation of the vehicle when it crosses the tollgate and how to secure the communication during the transaction process.
== Technology ==
VANETs could use any wireless networking technology as their basis. The most prominent are short-range radio technologies are WLAN and DSRC. In addition, cellular technologies or LTE and 5G can be used for VANETs.
== Simulations ==
Prior to the implementation of VANETs on the roads, realistic computer simulations of VANETs using a combination of Urban Mobility simulation
and Network simulation are thought to be necessary. Typically open source simulator like SUMO (which handles road traffic simulation) is combined with a network simulator like TETCOS NetSim, or NS-2 to study the performance of VANETs.
Further simulations could also be done for communication channel modeling that captures the complexities of wireless network for VANETs.
== Standards ==
Major standardization of VANET protocol stacks is taking place in the U.S., in Europe, and in Japan, corresponding to these regions' dominance in the automotive industry.: 5
In the U.S., the IEEE 1609 WAVE Wireless Access in Vehicular Environments protocol stack builds on IEEE 802.11p WLAN operating on seven reserved channels in the 5.9 GHz frequency band.
The WAVE protocol stack is designed to provide multi-channel operation (even for vehicles equipped with only a single radio), security, and lightweight application layer protocols.
Within the IEEE Communications Society, there is a Technical Subcommittee on Vehicular Networks & Telematics Applications (VNTA). The charter of this committee is to actively promote technical activities in the field of vehicular networks, V2V, V2R and V2I communications, standards, communications-enabled road and vehicle safety, real-time traffic monitoring, intersection management technologies, future telematics applications, and ITS-based services.
== Radio frequencies ==
In the US, the systems could use a region of the 5.9 GHz band set aside by the United States Congress, the unlicensed frequency also used by Wi-Fi. The US V2V standard, commonly known as WAVE ("Wireless Access for Vehicular Environments"), builds upon the lower-level IEEE 802.11p standard, as early as 2004.
The European Commission Decision 2008/671/EC harmonises the use of the 5 875-5 905 MHz frequency band for transport safety ITS applications. In Europe V2V is standardised as ETSI ITS, a standard also based on IEEE 802.11p. C-ITS, cooperative ITS, is also a term used in EU policy making, closely linked to ITS-G5 and V2V.
V2V is also known as VANET (vehicular ad hoc network). It is a variation of MANET (Mobile ad hoc network), with the emphasis being now the node is the vehicle. In 2001, it was mentioned in a publication that ad hoc networks can be formed by cars and such networks can help overcome blind spots, avoid accidents, etc. The infrastructure also participates in such systems, then referred to as V2X (vehicle-to-everything). Over the years, there have been considerable research and projects in this area, applying VANETs for a variety of applications, ranging from safety to
navigation and law enforcement.
In 1999 the US Federal Communications Commission (FCC) allocated 75 MHz in the spectrum of 5.850-5.925 GHz for intelligent transport systems.
=== Conflict over spectrum ===
As of 2016, V2V is under threat from cable television and other tech firms that want to take away a big chunk of the radio spectrum currently reserved for it and use those frequencies for high-speed internet service. V2V's current share of spectrum was set aside by the government in 1999. The auto industry is trying to retain all it can saying that it desperately needs the spectrum for V2V. The Federal Communications Commission has taken the side of the tech companies with the National Traffic Safety Board supporting the position of the auto industry. Internet service providers who want the spectrum claim that self-driving cars will make extensive use of V2V unnecessary. The auto industry said it is willing to share the spectrum if V2V service is not slowed or disrupted; the FCC plans to test several sharing schemes.
== Research ==
Research in VANETs started as early as 2000, in universities and research labs, having evolved from researchers working on wireless ad hoc networks. Many have worked on media access protocols, routing, warning message dissemination, and VANET application scenarios. V2V is currently in active development by General Motors, which demonstrated the system in 2006 using Cadillac vehicles. Other automakers working on V2V include Toyota, BMW, Daimler, Honda, Audi, Volvo and the Car-to-Car communication consortium.
== Regulation ==
Since then, the United States Department of Transportation (USDOT) has been working with a range of stakeholders on V2X. In 2012, a pre-deployment project was implemented in Ann Arbor, Michigan. 2800 vehicles covering cars, motorcycles, buses and HGV of different brands took part using equipment by different manufacturers. The US National Highway Traffic Safety Administration (NHTSA) saw this model deployment as proof that road safety could be improved and that WAVE standard technology was interoperable. In August 2014, NHTSA published a report arguing vehicle-to-vehicle technology was technically proven as ready for deployment. In April 2014 it was reported that U.S. regulators were close to approving V2V standards for the U.S. market. On 20 August 2014 the NHTSA published an Advance Notice of Proposed Rulemaking (ANPRM) in the Federal Register, arguing that the safety benefits of V2X communication could only be achieved, if a significant part of the vehicles fleet was equipped. Because of the lacking immediate benefit for early adopters the NHTSA proposed a mandatory introduction. On 25 June 2015, the US House of Representatives held a hearing on the matter, where again the NHTSA, as well as other stakeholders argued the case for V2X.
In the EU the ITS Directive 2010/40/EU was adopted in 2010. It aims to assure that ITS applications are interoperable and can operate across national borders, it defines priority areas for secondary legislation, which cover V2X and requires technologies to be mature. In 2014 the European Commission's industry stakeholder "C-ITS Deployment Platform" started working on a regulatory framework for V2X in the EU. It identified key approaches to an EU-wide V2X security Public Key infrastructure (PKI) and data protection, as well as facilitating a mitigation standard to prevent radio interference between ITS-G5 based V2X and CEN DSRC-based road charging systems. The European Commission recognised ITS-G5 as the initial communication technology in its 5G Action Plan and the accompanying explanatory document, to form a communication environment consisting of ITS-G5 and cellular communication as envisioned by EU Member States. Various pre-deployment projects exist at EU or EU Member State level, such as SCOOP@F, the Testfeld Telematik, the digital testbed Autobahn, the Rotterdam-Vienna ITS Corridor, Nordic Way, COMPASS4D or C-ROADS. Further projects are under preparation.
== VANET in urban scenarios ==
While using VANET in urban scenarios there are some aspects that are important to take in count. The first one is the analysis of the idle time and the choosing of a routing protocol that satisfy the specifications of our network. The other one is to try to minimize the data download time by choosing the right network architecture after analyzing the urban scenario where we want to implement it.
== See also ==
Connected car
Intelligent vehicular ad hoc network
Mobile ad hoc network
Network Simulator
Vehicle-to-everything
Vehicular communication systems
Wireless ad hoc network
Device-to-device
== References ==
== Further reading ==
Hammoudi, K.; Benhabiles, H.; Kasraoui, M.; Ajam, N.; Dornaika, F.; Radhakrishnan, K.; Bandi, K.; Cai, Q.; Liu, S. (2015). "Developing Vision-based and Cooperative Vehicular Embedded Systems for Enhancing Road Monitoring Services". Procedia Computer Science. 52: 389–395. doi:10.1016/j.procs.2015.05.003.
Gandhi, Jenish; Jhaveri, Rutvij (2015). "Energy Efficient Routing Approaches in Ad hoc Networks: A Survey". Information Systems Design and Intelligent Applications. Advances in Intelligent Systems and Computing. Vol. 339. pp. 751–760. doi:10.1007/978-81-322-2250-7_75. ISBN 978-81-322-2249-1.
Arkian, HR.; Atani, RE.; Pourkhalili, A.; Kamali, S. "A stable clustering scheme based on adaptive multiple metric in vehicular ad-hoc networks" (PDF). Journal of Information Science and Engineering. 31 (2): 361–386.
R.Azimi, G. Bhatia, R. Rajkumar, P. Mudalige, "Vehicular Networks for Collision Avoidance at Intersections", Society for Automotive Engineers (SAE) World Congress, April,2011, Detroit, MI, USA. - URL http://users.ece.cmu.edu/~sazimi/SAE2011.pdf
Kosch, Timo; Adler, Christian; Eichler, Stephan; Schroth, Christoph; Strassberger, Markus : The Scalability Problem of Vehicular Ad Hoc Networks and How to Solve it. In: IEEE Wireless Communications Magazine 13 (2006), Nr. 5, S. 6.- URL http://www.alexandria.unisg.ch/Publikationen/30977
Schroth, Christoph; Strassberger, Markus; Eigner, Robert; Eichler, Stephan: A Framework for Network Utility Maximization in VANETs. In: Proceedings of the 3rd ACM International Workshop on Vehicular Ad Hoc Networks (VANET) : ACM SIGMOBILE, 2006.- 3rd ACM International Workshop on Vehicular Ad Hoc Networks (VANET).- Los Angeles, USA, p. 2
C. Toh - "Future Application Scenarios for MANET-based Intelligent Transportation Systems", Proceedings of IEEE Future Generation Communication and Networking (FGCN) Conference, Vol.2 Pg 414–417, 2007.
Rawat, D. B.; Popescu, D. C.; Yan, G.; Olariu, S. (2011). "Enhancing VANET Performance by Joint Adaptation of Transmission Power and Contention Window Size". IEEE Transactions on Parallel and Distributed Systems. 22 (9): 1528–1535. doi:10.1109/tpds.2011.41. S2CID 8887104.
Eichler, Stephan; Ostermaier, Benedikt; Schroth, Christoph; Kosch, Timo: Simulation of Car-to-Car Messaging: Analyzing the Impact on Road Traffic. In: Proceedings of the 13th Annual Meeting of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS) : IEEE Computer Society, 2005.- 13th Annual Meeting of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS).- Atlanta, USA, p. 4.- URL http://www.alexandria.unisg.ch/Publikationen/30961
Gozalvez, J.; Sepulcre, M.; Bauza, R. (2012). "IEEE 802.11p Vehicle to Infrastructure Communications in Urban Environments". IEEE Communications Magazine. 50 (5): 176–183. doi:10.1109/mcom.2012.6194400. S2CID 5913154.
== External links ==
UCLA Vehicular Testbed
NetSim VANET library
Intelligent Transportation Systems Joint Program Office (ITS JPO) – U.S. Department of Transportation | Wikipedia/Vehicular_ad_hoc_network |
Real-time Control System (RCS) is a reference model architecture, suitable for many software-intensive, real-time computing control problem domains. It defines the types of functions needed in a real-time intelligent control system, and how these functions relate to each other.
RCS is not a system design, nor is it a specification of how to implement specific systems. RCS prescribes a hierarchical control model based on a set of well-founded engineering principles to organize system complexity. All the control nodes at all levels share a generic node model.
Also RCS provides a comprehensive methodology for designing, engineering, integrating, and testing control systems. Architects iteratively partition system tasks and information into finer, finite subsets that are controllable and efficient. RCS focuses on intelligent control that adapts to uncertain and unstructured operating environments. The key concerns are sensing, perception, knowledge, costs, learning, planning, and execution.
== Overview ==
A reference model architecture is a canonical form, not a system design specification. The RCS reference model architecture combines real-time motion planning and control with high level task planning, problem solving, world modeling, recursive state estimation, tactile and visual image processing, and acoustic signature analysis. In fact, the evolution of the RCS concept has been driven by an effort to include the best properties and capabilities of most, if not all, the intelligent control systems currently known in the literature, from subsumption to SOAR, from blackboards to object-oriented programming.
RCS (real-time control system) is developed into an intelligent agent architecture designed to enable any level of intelligent behavior, up to and including human levels of performance. RCS was inspired by a theoretical model of the cerebellum, the portion of the brain responsible for fine motor coordination and control of conscious motions. It was originally designed for sensory-interactive goal-directed control of laboratory manipulators. Over three decades, it has evolved into a real-time control architecture for intelligent machine tools, factory automation systems, and intelligent autonomous vehicles.
RCS applies to many problem domains including manufacturing examples and vehicle systems examples. Systems based on the RCS architecture have been designed and implemented to varying degrees for a wide variety of applications that include loading and unloading of parts and tools in machine tools, controlling machining workstations, performing robotic deburring and chamfering, and controlling space station telerobots, multiple autonomous undersea vehicles, unmanned land vehicles, coal mining automation systems, postal service mail handling systems, and submarine operational automation systems.
== History ==
RCS has evolved through a variety of versions over a number of years as understanding of the complexity and sophistication of intelligent behavior has increased. The first implementation was designed for sensory-interactive robotics by Barbera in the mid 1970s.
=== RCS-1 ===
In RCS-1, the emphasis was on combining commands with sensory feedback so as to compute the proper response to every combination of goals and states. The application was to control a robot arm with a structured light vision system in visual pursuit tasks. RCS-1 was heavily influenced by biological models such as the Marr-Albus model, and the Cerebellar Model Arithmetic Computer (CMAC). of the cerebellum.
CMAC becomes a state machine when some of its outputs are fed directly back to the input, so RCS-1 was implemented as a set of state-machines arranged in a hierarchy of control levels. At each level, the input command effectively selects a behavior that is driven by feedback in stimulus-response fashion. CMAC thus became the reference model building block of RCS-1, as shown in the figure.
A hierarchy of these building blocks was used to implement a hierarchy of behaviors such as observed by Tinbergen and others. RCS-1 is similar in many respects to Brooks' subsumption architecture, except that RCS selects behaviors before the fact through goals expressed in commands, rather than after the fact through subsumption.
=== RCS-2 ===
The next generation, RCS-2, was developed by Barbera, Fitzgerald, Kent, and others for manufacturing control in the NIST Automated Manufacturing Research Facility (AMRF) during the early 1980s. The basic building block of RCS-2 is shown in the figure.
The H function remained a finite-state machine state-table executor. The new feature of RCS-2 was the inclusion of the G function consisting of a number of sensory processing algorithms including structured light and blob analysis algorithms. RCS-2 was used to define an eight level hierarchy consisting of Servo, Coordinate Transform, E-Move, Task, Workstation, Cell, Shop, and Facility levels of control.
Only the first six levels were actually built. Two of the AMRF workstations fully implemented five levels of RCS-2. The control system for the Army Field Material Handling Robot (FMR) was also implemented in RCS-2, as was the Army TMAP semi-autonomous land vehicle project.
=== RCS-3 ===
RCS-3 was designed for the NBS/DARPA Multiple Autonomous Undersea Vehicle (MAUV) project and was adapted for the NASA/NBS Standard Reference Model Telerobot Control System Architecture (NASREM) developed for the space station Flight Telerobotic Servicer The basic building block of RCS-3 is shown in the figure.
The principal new features introduced in RCS-3 are the World Model and the operator interface. The inclusion of the World Model provides the basis for task planning and for model-based sensory processing. This led to refinement of the task decomposition (TD) modules so that each have a job assigner, and planner and executor for each of the subsystems assigned a job. This corresponds roughly to Saridis' three level control hierarchy.
=== RCS-4 ===
RCS-4 is developed since the 1990s by the NIST Robot Systems Division. The basic building block is shown in the figure). The principal new feature in RCS-4 is the explicit representation of the Value Judgment (VJ) system. VJ modules provide to the RCS-4 control system the type of functions provided to the biological brain by the limbic system. The VJ modules contain processes that compute cost, benefit, and risk of planned actions, and that place value on objects, materials, territory, situations, events, and outcomes. Value state-variables define what goals are important and what objects or regions should be attended to, attacked, defended, assisted, or otherwise acted upon. Value judgments, or evaluation functions, are an essential part of any form of planning or learning. The application of value judgments to intelligent control systems has been addressed by George Pugh. The structure and function of VJ modules are developed more completely developed in Albus (1991).
RCS-4 also uses the term behavior generation (BG) in place of the RCS-3 term task 5 decomposition (TD). The purpose of this change is to emphasize the degree of autonomous decision making. RCS-4 is designed to address highly autonomous applications in unstructured environments where high bandwidth communications are impossible, such as unmanned vehicles operating on the battlefield, deep undersea, or on distant planets. These applications require autonomous value judgments and sophisticated real-time perceptual capabilities. RCS-3 will continue to be used for less demanding applications, such as manufacturing, construction, or telerobotics for near-space, or shallow undersea operations, where environments are more structured and communication bandwidth to a human interface is less restricted. In these applications, value judgments are often represented implicitly in task planning processes, or in human operator input.
== Methodology ==
In the figure, an example of the RCS methodology for designing a control system for autonomous onroad driving under everyday traffic conditions is summarized in six steps.
Step 1 consists of an intensive analysis of domain knowledge from training manuals and subject matter experts. Scenarios are developed and analyzed for each task and subtask. The result of this step is a structuring of procedural knowledge into a task decomposition tree with simpler and simpler tasks at each echelon. At each echelon, a vocabulary of commands (action verbs with goal states, parameters, and constraints) is defined to evoke task behavior at each echelon.
Step 2 defines a hierarchical structure of organizational units that will execute the commands defined in step 1. For each unit, its duties and responsibilities in response to each command are specified. This is analogous to establishing a work breakdown structure for a development project, or defining an organizational chart for a business or military operation.
Step 3 specifies the processing that is triggered within each unit upon receipt of an input command. For each input command, a state-graph (or statetable or extended finite state automaton) is defined that provides a plan (or procedure for making a plan) for accomplishing the commanded task. The input command selects (or causes to be generated) an appropriate state-table, the execution of which generates a series of output commands to units at the next lower echelon. The library of state-tables contains a set of statesensitive procedural rules that identify all the task branching conditions and specify the corresponding state transition and output command parameters.
The result of step 3 is that each organizational unit has for each input command a state-table of ordered production rules, each suitable for execution by an extended finite state automaton (FSA). The sequence of output subcommands required to accomplish the input command is generated by situations (i.e., branching conditions) that cause the FSA to transition from one output subcommand to the next.
In step 4, each of the situations that are defined in step 3 are analyzed to reveal their dependencies on world and task states. This step identifies the detailed relationships between entities, events, and states of the world that cause a particular situation to be true.
In step 5, we identify and name all of the objects and entities together with their particular features and attributes that are relevant to detecting the above world states and situations.
In step 6, we use the context of the particular task activities to establish the distances and, therefore, the resolutions at which the relevant objects and entities must be measured and recognized by the sensory processing component. This establishes a set of requirements and/or specifications for the sensor system to support each subtask activity.
== Software ==
Based on the RCS Reference Model Architecture the NIST has developed a Real-time Control System Software Library. This is an archive of free C++, Java and Ada code, scripts, tools, makefiles, and documentation developed to aid programmers of software to be used in real-time control systems, especially those using the Reference Model Architecture for Intelligent Systems Design.
== Applications ==
The ISAM Framework is an RCS application to the Manufacturing Domain.
The 4D-RCS Reference Model Architecture is the RCS application to the Vehicle Domain, and
The NASA/NBS Standard Reference Model for Telerobot Control Systems Architecture (NASREM) is an application to the Space Domain.
== References ==
This article incorporates public domain material from the National Institute of Standards and Technology
== External links ==
RCS The Real-time Control Systems Architecture NIST Homepage | Wikipedia/Real-time_Control_System |
Mathematics of Control, Signals, and Systems is a peer-reviewed scientific journal that covers research concerned with mathematically rigorous system theoretic aspects of control and signal processing. The journal was founded by Eduardo Sontag and Bradley Dickinson in 1988. The editors-in-chief are Lars Gruene, Eduardo Sontag, and Jan H. van Schuppen.
== Abstracting and indexing ==
The journal is abstracted and indexed in Digital Mathematics Registry, Mathematical Reviews, Science Citation Index, Scopus, VINITI Database RAS, and Zentralblatt Math. The journal is abstracted and indexed in Digital Mathematics Registry, Mathematical Reviews, Science Citation Index, Scopus, VINITI Database RAS, and Zentralblatt Math. The journal has a 2019 impact factor of 0.976 (2019)
== References ==
== External links ==
Official website | Wikipedia/Mathematics_of_Control,_Signals,_and_Systems |
Artificial neural networks are a class of models used in machine learning, and inspired by biological neural networks. They are the core component of modern deep learning algorithms. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. Theoretical analysis of artificial neural networks sometimes considers the limiting case that layer width becomes large or infinite. This limit enables simple analytic statements to be made about neural network predictions, training dynamics, generalization, and loss surfaces. This wide layer limit is also of practical interest, since finite width neural networks often perform strictly better as layer width is increased.
== Theoretical approaches based on a large width limit ==
The Neural Network Gaussian Process (NNGP) corresponds to the infinite width limit of Bayesian neural networks, and to the distribution over functions realized by non-Bayesian neural networks after random initialization.
The same underlying computations that are used to derive the NNGP kernel are also used in deep information propagation to characterize the propagation of information about gradients and inputs through a deep network. This characterization is used to predict how model trainability depends on architecture and initializations hyper-parameters.
The Neural Tangent Kernel describes the evolution of neural network predictions during gradient descent training. In the infinite width limit the NTK usually becomes constant, often allowing closed form expressions for the function computed by a wide neural network throughout gradient descent training. The training dynamics essentially become linearized.
Mean-field limit analysis, when applied to neural networks with weight scaling of
∼
1
/
h
{\displaystyle \sim 1/h}
instead of
∼
1
/
h
{\displaystyle \sim 1/{\sqrt {h}}}
and large enough learning rates, predicts qualitatively distinct nonlinear training dynamics compared to the static linear behavior described by the fixed neural tangent kernel, suggesting alternative pathways for understanding infinite-width networks.
Catapult dynamics describe neural network training dynamics in the case that logits diverge to infinity as the layer width is taken to infinity, and describe qualitative properties of early training dynamics.
== References == | Wikipedia/Large_width_limits_of_neural_networks |
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.
== Definitions ==
The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others:
The first meaning of nonparametric involves techniques that do not rely on data belonging to any particular parametric family of probability distributions.
These include, among others:
Methods which are distribution-free, which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions.
Statistics defined to be a function on a sample, without dependency on a parameter.
An example is Order statistics, which are based on ordinal ranking of observations.
The discussion following is taken from Kendall's Advanced Theory of Statistics.
Statistical hypotheses concern the behavior of observable random variables.... For example, the hypothesis (a) that a normal distribution has a specified mean and variance is statistical; so is the hypothesis (b) that it has a given mean but unspecified variance; so is the hypothesis (c) that a distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical.
It will have been noticed that in the examples (a) and (b) the distribution underlying the observations was taken to be of a certain form (the normal) and the hypothesis was concerned entirely with the value of one or both of its parameters. Such a hypothesis, for obvious reasons, is called parametric.
Hypothesis (c) was of a different nature, as no parameter values are specified in the statement of the hypothesis; we might reasonably call such a hypothesis non-parametric. Hypothesis (d) is also non-parametric but, in addition, it does not even specify the underlying form of the distribution and may now be reasonably termed distribution-free. Notwithstanding these distinctions, the statistical literature now commonly applies the label "non-parametric" to test procedures that we have just termed "distribution-free", thereby losing a useful classification.
The second meaning of non-parametric involves techniques that do not assume that the structure of a model is fixed. Typically, the model grows in size to accommodate the complexity of the data. In these techniques, individual variables are typically assumed to belong to parametric distributions, and assumptions about the types of associations among variables are also made. These techniques include, among others:
non-parametric regression, which is modeling whereby the structure of the relationship between variables is treated non-parametrically, but where nevertheless there may be parametric assumptions about the distribution of model residuals.
non-parametric hierarchical Bayesian models, such as models based on the Dirichlet process, which allow the number of latent variables to grow as necessary to fit the data, but where individual variables still follow parametric distributions and even the process controlling the rate of growth of latent variables follows a parametric distribution.
== Applications and purpose ==
Non-parametric methods are widely used for studying populations that have a ranked order (such as movie reviews receiving one to five "stars"). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, non-parametric methods result in ordinal data.
As non-parametric methods make fewer assumptions, their applicability is much more general than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust.
Non-parametric methods are sometimes considered simpler to use and more robust than parametric methods, even when the assumptions of parametric methods are justified. This is due to their more general nature, which may make them less susceptible to misuse and misunderstanding. Non-parametric methods can be considered a conservative choice, as they will work even when their assumptions are not met, whereas parametric methods can produce misleading results when their assumptions are violated.
The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test's assumptions are met, non-parametric tests have less statistical power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
== Non-parametric models ==
Non-parametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term non-parametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance.
A histogram is a simple nonparametric estimate of a probability distribution.
Kernel density estimation is another method to estimate a probability distribution.
Nonparametric regression and semiparametric regression methods have been developed based on kernels, splines, and wavelets.
Data envelopment analysis provides efficiency coefficients similar to those obtained by multivariate analysis without any distributional assumption.
KNNs classify the unseen instance based on the K points in the training set which are nearest to it.
A support vector machine (with a Gaussian kernel) is a nonparametric large-margin classifier.
The method of moments with polynomial probability distributions.
== Methods ==
Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed. The most frequently used tests include
Analysis of similarities
Anderson–Darling test: tests whether a sample is drawn from a given distribution
Statistical bootstrap methods: estimates the accuracy/sampling distribution of a statistic
Cochran's Q: tests whether k treatments in randomized block designs with 0/1 outcomes have identical effects
Cohen's kappa: measures inter-rater agreement for categorical items
Friedman two-way analysis of variance (Repeated Measures) by ranks: tests whether k treatments in randomized block designs have identical effects
Empirical likelihood
Kaplan–Meier: estimates the survival function from lifetime data, modeling censoring
Kendall's tau: measures statistical dependence between two variables
Kendall's W: a measure between 0 and 1 of inter-rater agreement.
Kolmogorov–Smirnov test: tests whether a sample is drawn from a given distribution, or whether two samples are drawn from the same distribution.
Kruskal–Wallis one-way analysis of variance by ranks: tests whether > 2 independent samples are drawn from the same distribution.
Kuiper's test: tests whether a sample is drawn from a given distribution, sensitive to cyclic variations such as day of the week.
Logrank test: compares survival distributions of two right-skewed, censored samples.
Mann–Whitney U or Wilcoxon rank sum test: tests whether two samples are drawn from the same distribution, as compared to a given alternative hypothesis.
McNemar's test: tests whether, in 2 × 2 contingency tables with a dichotomous trait and matched pairs of subjects, row and column marginal frequencies are equal.
Median test: tests whether two samples are drawn from distributions with equal medians.
Pitman's permutation test: a statistical significance test that yields exact p values by examining all possible rearrangements of labels.
Rank products: detects differentially expressed genes in replicated microarray experiments.
Siegel–Tukey test: tests for differences in scale between two groups.
Sign test: tests whether matched pair samples are drawn from distributions with equal medians.
Spearman's rank correlation coefficient: measures statistical dependence between two variables using a monotonic function.
Squared ranks test: tests equality of variances in two or more samples.
Tukey–Duckworth test: tests equality of two distributions by using ranks.
Wald–Wolfowitz runs test: tests whether the elements of a sequence are mutually independent/random.
Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks.
Universal Linear Fit Identification: A Method Independent of Data, Outliers and Noise Distribution Model and Free of Missing or Removed Data Imputation.
== History ==
Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see Median § History) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see Sign test § History).
== See also ==
CDF-based nonparametric confidence interval
Parametric statistics
Resampling (statistics)
Semiparametric model
== Notes ==
== General references ==
Bagdonavicius, V., Kruopis, J., Nikulin, M.S. (2011). "Non-parametric tests for complete data", ISTE & WILEY: London & Hoboken. ISBN 978-1-84821-269-5.
Corder, G. W.; Foreman, D. I. (2014). Nonparametric Statistics: A Step-by-Step Approach. Wiley. ISBN 978-1-118-84031-3.
Gibbons, Jean Dickinson; Chakraborti, Subhabrata (2003). Nonparametric Statistical Inference, 4th Ed. CRC Press. ISBN 0-8247-4052-1.
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Hollander M., Wolfe D.A., Chicken E. (2014). Nonparametric Statistical Methods, John Wiley & Sons.
Sheskin, David J. (2003) Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press. ISBN 1-58488-440-1
Wasserman, Larry (2007). All of Nonparametric Statistics, Springer. ISBN 0-387-25145-6. | Wikipedia/Non-parametric_methods |
There are many types of artificial neural networks (ANN).
Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research. Most artificial neural networks bear only some resemblance to their more complex biological counterparts, but are very effective at their intended tasks (e.g. classification or segmentation).
Some artificial neural networks are adaptive systems and are used for example to model populations and environments, which constantly change.
Neural networks can be hardware- (neurons are represented by physical components) or software-based (computer models), and can use a variety of topologies and learning algorithms.
== Feedforward ==
In feedforward neural networks the information moves from the input to output directly in every layer. There can be hidden layers with or without cycles/loops to sequence inputs. Feedforward networks can be constructed with various types of units, such as binary McCulloch–Pitts neurons, the simplest of which is the perceptron. Continuous neurons, frequently with sigmoidal activation, are used in the context of backpropagation.
== Group method of data handling ==
The Group Method of Data Handling (GMDH) features fully automatic structural and parametric model optimization. The node activation functions are Kolmogorov–Gabor polynomials that permit additions and multiplications. It uses a deep multilayer perceptron with eight layers. It is a supervised learning network that grows layer by layer, where each layer is trained by regression analysis. Useless items are detected using a validation set, and pruned through regularization. The size and depth of the resulting network depends on the task.
== Autoencoder ==
An autoencoder, autoassociator or Diabolo network: 19 is similar to the multilayer perceptron (MLP) – with an input layer, an output layer and one or more hidden layers connecting them. However, the output layer has the same number of units as the input layer. Its purpose is to reconstruct its own inputs (instead of emitting a target value). Therefore, autoencoders are unsupervised learning models. An autoencoder is used for unsupervised learning of efficient codings, typically for the purpose of dimensionality reduction and for learning generative models of data.
== Probabilistic ==
A probabilistic neural network (PNN) is a four-layer feedforward neural network. The layers are Input, hidden pattern/summation, and output. In the PNN algorithm, the parent probability distribution function (PDF) of each class is approximated by a Parzen window and a non-parametric function. Then, using PDF of each class, the class probability of a new input is estimated and Bayes’ rule is employed to allocate it to the class with the highest posterior probability. It was derived from the Bayesian network and a statistical algorithm called Kernel Fisher discriminant analysis. It is used for classification and pattern recognition.
== Time delay ==
A time delay neural network (TDNN) is a feedforward architecture for sequential data that recognizes features independent of sequence position. In order to achieve time-shift invariance, delays are added to the input so that multiple data points (points in time) are analyzed together.
It usually forms part of a larger pattern recognition system. It has been implemented using a perceptron network whose connection weights were trained with back propagation (supervised learning).
== Convolutional ==
A convolutional neural network (CNN, or ConvNet or shift invariant or space invariant) is a class of deep network, composed of one or more convolutional layers with fully connected layers (matching those in typical ANNs) on top. It uses tied weights and pooling layers. In particular, max-pooling. It is often structured via Fukushima's convolutional architecture. They are variations of multilayer perceptrons that use minimal preprocessing. This architecture allows CNNs to take advantage of the 2D structure of input data.
Its unit connectivity pattern is inspired by the organization of the visual cortex. Units respond to stimuli in a restricted region of space known as the receptive field. Receptive fields partially overlap, over-covering the entire visual field. Unit response can be approximated mathematically by a convolution operation.
CNNs are suitable for processing visual and other two-dimensional data. They have shown superior results in both image and speech applications. They can be trained with standard backpropagation. CNNs are easier to train than other regular, deep, feed-forward neural networks and have many fewer parameters to estimate.
Capsule Neural Networks (CapsNet) add structures called capsules to a CNN and reuse output from several capsules to form more stable (with respect to various perturbations) representations.
Examples of applications in computer vision include DeepDream and robot navigation. They have wide applications in image and video recognition, recommender systems and natural language processing.
== Deep stacking network ==
A deep stacking network (DSN) (deep convex network) is based on a hierarchy of blocks of simplified neural network modules. It was introduced in 2011 by Deng and Yu. It formulates the learning as a convex optimization problem with a closed-form solution, emphasizing the mechanism's similarity to stacked generalization. Each DSN block is a simple module that is easy to train by itself in a supervised fashion without backpropagation for the entire blocks.
Each block consists of a simplified multi-layer perceptron (MLP) with a single hidden layer. The hidden layer h has logistic sigmoidal units, and the output layer has linear units. Connections between these layers are represented by weight matrix U; input-to-hidden-layer connections have weight matrix W. Target vectors t form the columns of matrix T, and the input data vectors x form the columns of matrix X. The matrix of hidden units is
H
=
σ
(
W
T
X
)
{\displaystyle {\boldsymbol {H}}=\sigma ({\boldsymbol {W}}^{T}{\boldsymbol {X}})}
. Modules are trained in order, so lower-layer weights W are known at each stage. The function performs the element-wise logistic sigmoid operation. Each block estimates the same final label class y, and its estimate is concatenated with original input X to form the expanded input for the next block. Thus, the input to the first block contains the original data only, while downstream blocks' input adds the output of preceding blocks. Then learning the upper-layer weight matrix U given other weights in the network can be formulated as a convex optimization problem:
min
U
T
f
=
‖
U
T
H
−
T
‖
F
2
,
{\displaystyle \min _{U^{T}}f=\|{\boldsymbol {U}}^{T}{\boldsymbol {H}}-{\boldsymbol {T}}\|_{F}^{2},}
which has a closed-form solution.
Unlike other deep architectures, such as DBNs, the goal is not to discover the transformed feature representation. The structure of the hierarchy of this kind of architecture makes parallel learning straightforward, as a batch-mode optimization problem. In purely discriminative tasks, DSNs outperform conventional DBNs.
=== Tensor deep stacking networks ===
This architecture is a DSN extension. It offers two important improvements: it uses higher-order information from covariance statistics, and it transforms the non-convex problem of a lower-layer to a convex sub-problem of an upper-layer. TDSNs use covariance statistics in a bilinear mapping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order tensor.
While parallelization and scalability are not considered seriously in conventional DNNs, all learning for DSNs and TDSNs is done in batch mode, to allow parallelization. Parallelization allows scaling the design to larger (deeper) architectures and data sets.
The basic architecture is suitable for diverse tasks such as classification and regression.
== Physics-informed ==
Such a neural network is designed for the numerical solution of mathematical equations, such as differential, integral, delay, fractional and others. As input parameters, PINN accepts variables (spatial, temporal, and others), transmits them through the network block. At the output, it produces an approximate solution and substitutes it into the mathematical model, considering the initial and boundary conditions. If the solution does not satisfy the required accuracy, one uses the backpropagation and rectify the solution.
Besides PINN, there exists deep neural operator (DeepONet) and Fourier neural operator (FNO).
== Regulatory feedback ==
Regulatory feedback networks account for feedback found throughout brain recognition processing areas. Instead of recognition-inference being feedforward (inputs-to-output) as in neural networks, regulatory feedback assumes inference iteratively compares inputs to outputs & neurons inhibit their own inputs, collectively evaluating how important and unique each input is for the next iteration. This ultimately finds neuron activations minimizing mutual input overlap, estimating distributions during recognition and offloading the need for complex neural network training & rehearsal.
Regulatory feedback processing suggests an important real-time recognition processing role for ubiquitous feedback found between brain pre and post synaptic neurons, which is meticulously maintained by homeostatic plasticity: found to be kept in balance through multiple, often redundant, mechanisms. RF also inherently shows neuroscience phenomena such as Excitation-Inhibition balance, network-wide bursting followed by quieting, and human cognitive search phenomena of difficulty with similarity and pop-out when multiple inputs are present, without additional parameters.
A regulatory feedback network makes inferences using negative feedback. The feedback is used to find the optimal activation of units. It is most similar to a non-parametric method but is different from K-nearest neighbor in that it mathematically emulates feedforward networks.
== Radial basis function ==
Radial basis functions are functions that have a distance criterion with respect to a center. Radial basis functions have been applied as a replacement for the sigmoidal hidden layer transfer characteristic in multi-layer perceptrons. RBF networks have two layers: In the first, input is mapped onto each RBF in the 'hidden' layer. The RBF chosen is usually a Gaussian. In regression problems the output layer is a linear combination of hidden layer values representing mean predicted output. The interpretation of this output layer value is the same as a regression model in statistics. In classification problems the output layer is typically a sigmoid function of a linear combination of hidden layer values, representing a posterior probability. Performance in both cases is often improved by shrinkage techniques, known as ridge regression in classical statistics. This corresponds to a prior belief in small parameter values (and therefore smooth output functions) in a Bayesian framework.
RBF networks have the advantage of avoiding local minima in the same way as multi-layer perceptrons. This is because the only parameters that are adjusted in the learning process are the linear mapping from hidden layer to output layer. Linearity ensures that the error surface is quadratic and therefore has a single easily found minimum. In regression problems this can be found in one matrix operation. In classification problems the fixed non-linearity introduced by the sigmoid output function is most efficiently dealt with using iteratively re-weighted least squares.
RBF networks have the disadvantage of requiring good coverage of the input space by radial basis functions. RBF centres are determined with reference to the distribution of the input data, but without reference to the prediction task. As a result, representational resources may be wasted on areas of the input space that are irrelevant to the task. A common solution is to associate each data point with its own centre, although this can expand the linear system to be solved in the final layer and requires shrinkage techniques to avoid overfitting.
Associating each input datum with an RBF leads naturally to kernel methods such as support vector machines (SVM) and Gaussian processes (the RBF is the kernel function). All three approaches use a non-linear kernel function to project the input data into a space where the learning problem can be solved using a linear model. Like Gaussian processes, and unlike SVMs, RBF networks are typically trained in a maximum likelihood framework by maximizing the probability (minimizing the error). SVMs avoid overfitting by maximizing instead a margin. SVMs outperform RBF networks in most classification applications. In regression applications they can be competitive when the dimensionality of the input space is relatively small.
=== How RBF networks work ===
RBF neural networks are conceptually similar to K-nearest neighbor (k-NN) models. The basic idea is that similar inputs produce similar outputs.
Assume that each case in a training set has two predictor variables, x and y, and the target variable has two categories, positive and negative. Given a new case with predictor values x=6, y=5.1, how is the target variable computed?
The nearest neighbor classification performed for this example depends on how many neighboring points are considered. If 1-NN is used and the closest point is negative, then the new point should be classified as negative. Alternatively, if 9-NN classification is used and the closest 9 points are considered, then the effect of the surrounding 8 positive points may outweigh the closest 9-th (negative) point.
An RBF network positions neurons in the space described by the predictor variables (x,y in this example). This space has as many dimensions as predictor variables. The Euclidean distance is computed from the new point to the center of each neuron, and a radial basis function (RBF, also called a kernel function) is applied to the distance to compute the weight (influence) for each neuron. The radial basis function is so named because the radius distance is the argument to the function.
Weight = RBF(distance)
==== Radial basis function ====
The value for the new point is found by summing the output values of the RBF functions multiplied by weights computed for each neuron.
The radial basis function for a neuron has a center and a radius (also called a spread). The radius may be different for each neuron, and, in RBF networks generated by DTREG, the radius may be different in each dimension.
With larger spread, neurons at a distance from a point have a greater influence.
==== Architecture ====
RBF networks have three layers:
Input layer: One neuron appears in the input layer for each predictor variable. In the case of categorical variables, N-1 neurons are used where N is the number of categories. The input neurons standardizes the value ranges by subtracting the median and dividing by the interquartile range. The input neurons then feed the values to each of the neurons in the hidden layer.
Hidden layer: This layer has a variable number of neurons (determined by the training process). Each neuron consists of a radial basis function centered on a point with as many dimensions as predictor variables. The spread (radius) of the RBF function may be different for each dimension. The centers and spreads are determined by training. When presented with the x vector of input values from the input layer, a hidden neuron computes the Euclidean distance of the test case from the neuron's center point and then applies the RBF kernel function to this distance using the spread values. The resulting value is passed to the summation layer.
Summation layer: The value coming out of a neuron in the hidden layer is multiplied by a weight associated with the neuron and adds to the weighted values of other neurons. This sum becomes the output. For classification problems, one output is produced (with a separate set of weights and summation unit) for each target category. The value output for a category is the probability that the case being evaluated has that category.
==== Training ====
The following parameters are determined by the training process:
The number of neurons in the hidden layer
The coordinates of the center of each hidden-layer RBF function
The radius (spread) of each RBF function in each dimension
The weights applied to the RBF function outputs as they pass to the summation layer
Various methods have been used to train RBF networks. One approach first uses K-means clustering to find cluster centers which are then used as the centers for the RBF functions. However, K-means clustering is computationally intensive and it often does not generate the optimal number of centers. Another approach is to use a random subset of the training points as the centers.
DTREG uses a training algorithm that uses an evolutionary approach to determine the optimal center points and spreads for each neuron. It determines when to stop adding neurons to the network by monitoring the estimated leave-one-out (LOO) error and terminating when the LOO error begins to increase because of overfitting.
The computation of the optimal weights between the neurons in the hidden layer and the summation layer is done using ridge regression. An iterative procedure computes the optimal regularization Lambda parameter that minimizes the generalized cross-validation (GCV) error.
=== General regression neural network ===
A GRNN is an associative memory neural network that is similar to the probabilistic neural network but it is used for regression and approximation rather than classification.
== Deep belief network ==
A deep belief network (DBN) is a probabilistic, generative model made up of multiple hidden layers. It can be considered a composition of simple learning modules.
A DBN can be used to generatively pre-train a deep neural network (DNN) by using the learned DBN weights as the initial DNN weights. Various discriminative algorithms can then tune these weights. This is particularly helpful when training data are limited, because poorly initialized weights can significantly hinder learning. These pre-trained weights end up in a region of the weight space that is closer to the optimal weights than random choices. This allows for both improved modeling and faster ultimate convergence.
== Recurrent neural network ==
Recurrent neural networks (RNN) propagate data forward, but also backwards, from later processing stages to earlier stages. RNN can be used as general sequence processors.
=== Fully recurrent ===
This architecture was developed in the 1980s. Its network creates a directed connection between every pair of units. Each has a time-varying, real-valued (more than just zero or one) activation (output). Each connection has a modifiable real-valued weight. Some of the nodes are called labeled nodes, some output nodes, the rest hidden nodes.
For supervised learning in discrete time settings, training sequences of real-valued input vectors become sequences of activations of the input nodes, one input vector at a time. At each time step, each non-input unit computes its current activation as a nonlinear function of the weighted sum of the activations of all units from which it receives connections. The system can explicitly activate (independent of incoming signals) some output units at certain time steps. For example, if the input sequence is a speech signal corresponding to a spoken digit, the final target output at the end of the sequence may be a label classifying the digit. For each sequence, its error is the sum of the deviations of all activations computed by the network from the corresponding target signals. For a training set of numerous sequences, the total error is the sum of the errors of all individual sequences.
To minimize total error, gradient descent can be used to change each weight in proportion to its derivative with respect to the error, provided the non-linear activation functions are differentiable. The standard method is called "backpropagation through time" or BPTT, a generalization of back-propagation for feedforward networks. A more computationally expensive online variant is called "Real-Time Recurrent Learning" or RTRL. Unlike BPTT this algorithm is local in time but not local in space. An online hybrid between BPTT and RTRL with intermediate complexity exists, with variants for continuous time. A major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size of the time lag between important events. The Long short-term memory architecture overcomes these problems.
In reinforcement learning settings, no teacher provides target signals. Instead a fitness function or reward function or utility function is occasionally used to evaluate performance, which influences its input stream through output units connected to actuators that affect the environment. Variants of evolutionary computation are often used to optimize the weight matrix.
==== Hopfield ====
The Hopfield network (like similar attractor-based networks) is of historic interest although it is not a general RNN, as it is not designed to process sequences of patterns. Instead it requires stationary inputs. It is an RNN in which all connections are symmetric. It guarantees that it will converge. If the connections are trained using Hebbian learning the Hopfield network can perform as robust content-addressable memory, resistant to connection alteration.
==== Boltzmann machine ====
The Boltzmann machine can be thought of as a noisy Hopfield network. It is one of the first neural networks to demonstrate learning of latent variables (hidden units). Boltzmann machine learning was at first slow to simulate, but the contrastive divergence algorithm speeds up training for Boltzmann machines and Products of Experts.
==== Self-organizing map ====
The self-organizing map (SOM) uses unsupervised learning. A set of neurons learn to map points in an input space to coordinates in an output space. The input space can have different dimensions and topology from the output space, and SOM attempts to preserve these.
==== Learning vector quantization ====
Learning vector quantization (LVQ) can be interpreted as a neural network architecture. Prototypical representatives of the classes parameterize, together with an appropriate distance measure, in a distance-based classification scheme.
=== Simple recurrent ===
Simple recurrent networks have three layers, with the addition of a set of "context units" in the input layer. These units connect from the hidden layer or the output layer with a fixed weight of one. At each time step, the input is propagated in a standard feedforward fashion, and then a backpropagation-like learning rule is applied (not performing gradient descent). The fixed back connections leave a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied).
=== Reservoir computing ===
Reservoir computing is a computation framework that may be viewed as an extension of neural networks. Typically an input signal is fed into a fixed (random) dynamical system called a reservoir whose dynamics map the input to a higher dimension. A readout mechanism is trained to map the reservoir to the desired output. Training is performed only at the readout stage. Liquid-state machines are a type of reservoir computing.
==== Echo state ====
The echo state network (ESN) employs a sparsely connected random hidden layer. The weights of output neurons are the only part of the network that are trained. ESN are good at reproducing certain time series.
=== Long short-term memory ===
The long short-term memory (LSTM) avoids the vanishing gradient problem. It works even when with long delays between inputs and can handle signals that mix low and high frequency components. LSTM RNN outperformed other RNN and other sequence learning methods such as HMM in applications such as language learning and connected handwriting recognition.
=== Bi-directional ===
Bi-directional RNN, or BRNN, use a finite sequence to predict or label each element of a sequence based on both the past and future context of the element. This is done by adding the outputs of two RNNs: one processing the sequence from left to right, the other one from right to left. The combined outputs are the predictions of the teacher-given target signals. This technique proved to be especially useful when combined with LSTM.
=== Hierarchical ===
Hierarchical RNN connects elements in various ways to decompose hierarchical behavior into useful subprograms.
=== Stochastic ===
A district from conventional neural networks, stochastic artificial neural network used as an approximation to
random functions.
=== Genetic scale ===
A RNN (often a LSTM) where a series is decomposed into a number of scales where every scale informs the primary length between two consecutive points. A first order scale consists of a normal RNN, a second order consists of all points separated by two indices and so on. The Nth order RNN connects the first and last node. The outputs from all the various scales are treated as a Committee of Machines and the associated scores are used genetically for the next iteration.
== Modular ==
Biological studies have shown that the human brain operates as a collection of small networks. This realization gave birth to the concept of modular neural networks, in which several small networks cooperate or compete to solve problems.
=== Committee of machines ===
A committee of machines (CoM) is a collection of different neural networks that together "vote" on a given example. This generally gives a much better result than individual networks. Because neural networks suffer from local minima, starting with the same architecture and training but using randomly different initial weights often gives vastly different results. A CoM tends to stabilize the result.
The CoM is similar to the general machine learning bagging method, except that the necessary variety of machines in the committee is obtained by training from different starting weights rather than training on different randomly selected subsets of the training data.
=== Associative ===
The associative neural network (ASNN) is an extension of committee of machines that combines multiple feedforward neural networks and the k-nearest neighbor technique. It uses the correlation between ensemble responses as a measure of distance amid the analyzed cases for the kNN. This corrects the Bias of the neural network ensemble. An associative neural network has a memory that can coincide with the training set. If new data become available, the network instantly improves its predictive ability and provides data approximation (self-learns) without retraining. Another important feature of ASNN is the possibility to interpret neural network results by analysis of correlations between data cases in the space of models.
== Physical ==
A physical neural network includes electrically adjustable resistance material to simulate artificial synapses. Examples include the ADALINE memristor-based neural network. An optical neural network is a physical implementation of an artificial neural network with optical components.
== Dynamic ==
Unlike static neural networks, dynamic neural networks adapt their structure and/or parameters to the input during inference showing time-dependent behaviour, such as transient phenomena and delay effects.
Dynamic neural networks in which the parameters may change over time are related to the fast weights architecture (1987), where one neural network outputs the weights of another neural network.
=== Cascading ===
Cascade correlation is an architecture and supervised learning algorithm. Instead of just adjusting the weights in a network of fixed topology, Cascade-Correlation begins with a minimal network, then automatically trains and adds new hidden units one by one, creating a multi-layer structure. Once a new hidden unit has been added to the network, its input-side weights are frozen. This unit then becomes a permanent feature-detector in the network, available for producing outputs or for creating other, more complex feature detectors. The Cascade-Correlation architecture has several advantages: It learns quickly, determines its own size and topology, retains the structures it has built even if the training set changes and requires no backpropagation.
=== Neuro-fuzzy ===
A neuro-fuzzy network is a fuzzy inference system in the body of an artificial neural network. Depending on the FIS type, several layers simulate the processes involved in a fuzzy inference-like fuzzification, inference, aggregation and defuzzification. Embedding an FIS in a general structure of an ANN has the benefit of using available ANN training methods to find the parameters of a fuzzy system.
=== Compositional pattern-producing ===
Compositional pattern-producing networks (CPPNs) are a variation of artificial neural networks which differ in their set of activation functions and how they are applied. While typical artificial neural networks often contain only sigmoid functions (and sometimes Gaussian functions), CPPNs can include both types of functions and many others. Furthermore, unlike typical artificial neural networks, CPPNs are applied across the entire space of possible inputs so that they can represent a complete image. Since they are compositions of functions, CPPNs in effect encode images at infinite resolution and can be sampled for a particular display at whatever resolution is optimal.
== Memory networks ==
Memory networks incorporate long-term memory. The long-term memory can be read and written to, with the goal of using it for prediction. These models have been applied in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base and the output is a textual response.
In sparse distributed memory or hierarchical temporal memory, the patterns encoded by neural networks are used as addresses for content-addressable memory, with "neurons" essentially serving as address encoders and decoders. However, the early controllers of such memories were not differentiable.
=== One-shot associative memory ===
This type of network can add new patterns without re-training. It is done by creating a specific memory structure, which assigns each new pattern to an orthogonal plane using adjacently connected hierarchical arrays. The network offers real-time pattern recognition and high scalability; this requires parallel processing and is thus best suited for platforms such as wireless sensor networks, grid computing, and GPGPUs.
=== Hierarchical temporal memory ===
Hierarchical temporal memory (HTM) models some of the structural and algorithmic properties of the neocortex. HTM is a biomimetic model based on memory-prediction theory. HTM is a method for discovering and inferring the high-level causes of observed input patterns and sequences, thus building an increasingly complex model of the world.
HTM combines existing ideas to mimic the neocortex with a simple design that provides many capabilities. HTM combines and extends approaches used in Bayesian networks, spatial and temporal clustering algorithms, while using a tree-shaped hierarchy of nodes that is common in neural networks.
=== Holographic associative memory ===
Holographic Associative Memory (HAM) is an analog, correlation-based, associative, stimulus-response system. Information is mapped onto the phase orientation of complex numbers. The memory is effective for associative memory tasks, generalization and pattern recognition with changeable attention. Dynamic search localization is central to biological memory. In visual perception, humans focus on specific objects in a pattern. Humans can change focus from object to object without learning. HAM can mimic this ability by creating explicit representations for focus. It uses a bi-modal representation of pattern and a hologram-like complex spherical weight state-space. HAMs are useful for optical realization because the underlying hyper-spherical computations can be implemented with optical computation.
=== LSTM-related differentiable memory structures ===
Apart from long short-term memory (LSTM), other approaches also added differentiable memory to recurrent functions. For example:
Differentiable push and pop actions for alternative memory networks called neural stack machines
Memory networks where the control network's external differentiable storage is in the fast weights of another network
LSTM forget gates
Self-referential RNNs with special output units for addressing and rapidly manipulating the RNN's own weights in differentiable fashion (internal storage)
Learning to transduce with unbounded memory
=== Neural Turing machines ===
Neural Turing machines (NTM) couple LSTM networks to external memory resources, with which they can interact by attentional processes. The combined system is analogous to a Turing machine but is differentiable end-to-end, allowing it to be efficiently trained by gradient descent. Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting and associative recall from input and output examples.
Differentiable neural computers (DNC) are an NTM extension. They out-performed Neural turing machines, long short-term memory systems and memory networks on sequence-processing tasks.
=== Semantic hashing ===
Approaches that represent previous experiences directly and use a similar experience to form a local model are often called nearest neighbour or k-nearest neighbors methods. Deep learning is useful in semantic hashing where a deep graphical model the word-count vectors obtained from a large set of documents. Documents are mapped to memory addresses in such a way that semantically similar documents are located at nearby addresses. Documents similar to a query document can then be found by accessing all the addresses that differ by only a few bits from the address of the query document. Unlike sparse distributed memory that operates on 1000-bit addresses, semantic hashing works on 32 or 64-bit addresses found in a conventional computer architecture.
=== Pointer networks ===
Deep neural networks can be potentially improved by deepening and parameter reduction, while maintaining trainability. While training extremely deep (e.g., 1 million layers) neural networks might not be practical, CPU-like architectures such as pointer networks and neural random-access machines overcome this limitation by using external random-access memory and other components that typically belong to a computer architecture such as registers, ALU and pointers. Such systems operate on probability distribution vectors stored in memory cells and registers. Thus, the model is fully differentiable and trains end-to-end. The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently.
== Hybrids ==
=== Encoder–decoder networks ===
Encoder–decoder frameworks are based on neural networks that map highly structured input to highly structured output. The approach arose in the context of machine translation, where the input and output are written sentences in two natural languages. In that work, an LSTM RNN or CNN was used as an encoder to summarize a source sentence, and the summary was decoded using a conditional RNN language model to produce the translation. These systems share building blocks: gated RNNs and CNNs and trained attention mechanisms.
== Other types ==
=== Instantaneously trained ===
Instantaneously trained neural networks (ITNN) were inspired by the phenomenon of short-term learning that seems to occur instantaneously. In these networks the weights of the hidden and the output layers are mapped directly from the training vector data. Ordinarily, they work on binary data, but versions for continuous data that require small additional processing exist.
=== Spiking ===
Spiking neural networks (SNN) explicitly consider the timing of inputs. The network input and output are usually represented as a series of spikes (delta function or more complex shapes). SNN can process information in the time domain (signals that vary over time). They are often implemented as recurrent networks. SNN are also a form of pulse computer.
Spiking neural networks with axonal conduction delays exhibit polychronization, and hence could have a very large memory capacity.
SNN and the temporal correlations of neural assemblies in such networks—have been used to model figure/ground separation and region linking in the visual system.
=== Spatial ===
Spatial neural networks (SNNs) constitute a supercategory of tailored neural networks (NNs) for representing and predicting geographic phenomena. They generally improve both the statistical accuracy and reliability of the a-spatial/classic NNs whenever they handle geo-spatial datasets, and also of the other spatial (statistical) models (e.g. spatial regression models) whenever the geo-spatial datasets' variables depict non-linear relations. Examples of SNNs are the OSFA spatial neural networks, SVANNs and GWNNs.
=== Neocognitron ===
The neocognitron is a hierarchical, multilayered network that was modeled after the visual cortex. It uses multiple types of units, (originally two, called simple and complex cells), as a cascading model for use in pattern recognition tasks. Local features are extracted by S-cells whose deformation is tolerated by C-cells. Local features in the input are integrated gradually and classified at higher layers. Among the various kinds of neocognitron are systems that can detect multiple patterns in the same input by using back propagation to achieve selective attention. It has been used for pattern recognition tasks and inspired convolutional neural networks.
=== Compound hierarchical-deep models ===
Compound hierarchical-deep models compose deep networks with non-parametric Bayesian models. Features can be learned using deep architectures such as DBNs, deep Boltzmann machines (DBM), deep auto encoders, convolutional variants, ssRBMs, deep coding networks, DBNs with sparse feature learning, RNNs, conditional DBNs, denoising autoencoders. This provides a better representation, allowing faster learning and more accurate classification with high-dimensional data. However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input (a distributed representation) and must be adjusted together (high degree of freedom). Limiting the degree of freedom reduces the number of parameters to learn, facilitating learning of new classes from few examples. Hierarchical Bayesian (HB) models allow learning from few examples, for example for computer vision, statistics and cognitive science.
Compound HD architectures aim to integrate characteristics of both HB and deep networks. The compound HDP-DBM architecture is a hierarchical Dirichlet process (HDP) as a hierarchical model, incorporating DBM architecture. It is a full generative model, generalized from abstract concepts flowing through the model layers, which is able to synthesize new examples in novel classes that look "reasonably" natural. All the levels are learned jointly by maximizing a joint log-probability score.
In a DBM with three hidden layers, the probability of a visible input ''ν'' is:
p
(
ν
,
ψ
)
=
1
Z
∑
h
exp
(
∑
i
j
W
i
j
(
1
)
ν
i
h
j
1
+
∑
j
ℓ
W
j
ℓ
(
2
)
h
j
1
h
ℓ
2
+
∑
ℓ
m
W
ℓ
m
(
3
)
h
ℓ
2
h
m
3
)
,
{\displaystyle p({\boldsymbol {\nu }},\psi )={\frac {1}{Z}}\sum _{h}\exp \left(\sum _{ij}W_{ij}^{(1)}\nu _{i}h_{j}^{1}+\sum _{j\ell }W_{j\ell }^{(2)}h_{j}^{1}h_{\ell }^{2}+\sum _{\ell m}W_{\ell m}^{(3)}h_{\ell }^{2}h_{m}^{3}\right),}
where
h
=
{
h
(
1
)
,
h
(
2
)
,
h
(
3
)
}
{\displaystyle {\boldsymbol {h}}=\{{\boldsymbol {h}}^{(1)},{\boldsymbol {h}}^{(2)},{\boldsymbol {h}}^{(3)}\}}
is the set of hidden units, and
ψ
=
{
W
(
1
)
,
W
(
2
)
,
W
(
3
)
}
{\displaystyle \psi =\{{\boldsymbol {W}}^{(1)},{\boldsymbol {W}}^{(2)},{\boldsymbol {W}}^{(3)}\}}
are the model parameters, representing visible-hidden and hidden-hidden symmetric interaction terms.
A learned DBM model is an undirected model that defines the joint distribution
P
(
ν
,
h
1
,
h
2
,
h
3
)
{\displaystyle P(\nu ,h^{1},h^{2},h^{3})}
. One way to express what has been learned is the conditional model
P
(
ν
,
h
1
,
h
2
∣
h
3
)
{\displaystyle P(\nu ,h^{1},h^{2}\mid h^{3})}
and a prior term
P
(
h
3
)
{\displaystyle P(h^{3})}
.
Here
P
(
ν
,
h
1
,
h
2
∣
h
3
)
{\displaystyle P(\nu ,h^{1},h^{2}\mid h^{3})}
represents a conditional DBM model, which can be viewed as a two-layer DBM but with bias terms given by the states of
h
3
{\displaystyle h^{3}}
:
P
(
ν
,
h
1
,
h
2
∣
h
3
)
=
1
Z
(
ψ
,
h
3
)
exp
(
∑
i
j
W
i
j
(
1
)
ν
i
h
j
1
+
∑
j
ℓ
W
j
ℓ
(
2
)
h
j
1
h
ℓ
2
+
∑
ℓ
m
W
ℓ
m
(
3
)
h
ℓ
2
h
m
3
)
.
{\displaystyle P(\nu ,h^{1},h^{2}\mid h^{3})={\frac {1}{Z(\psi ,h^{3})}}\exp \left(\sum _{ij}W_{ij}^{(1)}\nu _{i}h_{j}^{1}+\sum _{j\ell }W_{j\ell }^{(2)}h_{j}^{1}h_{\ell }^{2}+\sum _{\ell m}W_{\ell m}^{(3)}h_{\ell }^{2}h_{m}^{3}\right).}
=== Deep predictive coding networks ===
A deep predictive coding network (DPCN) is a predictive coding scheme that uses top-down information to empirically adjust the priors needed for a bottom-up inference procedure by means of a deep, locally connected, generative model. This works by extracting sparse features from time-varying observations using a linear dynamical model. Then, a pooling strategy is used to learn invariant feature representations. These units compose to form a deep architecture and are trained by greedy layer-wise unsupervised learning. The layers constitute a kind of Markov chain such that the states at any layer depend only on the preceding and succeeding layers.
DPCNs predict the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from previous states.
DPCNs can be extended to form a convolutional network.
=== Multilayer kernel machine ===
Multilayer kernel machines (MKM) are a way of learning highly nonlinear functions by iterative application of weakly nonlinear kernels. They use kernel principal component analysis (KPCA), as a method for the unsupervised greedy layer-wise pre-training step of deep learning.
Layer
ℓ
+
1
{\displaystyle \ell +1}
learns the representation of the previous layer
ℓ
{\displaystyle \ell }
, extracting the
n
l
{\displaystyle n_{l}}
principal component (PC) of the projection layer
l
{\displaystyle l}
output in the feature domain induced by the kernel. To reduce the dimensionaliity of the updated representation in each layer, a supervised strategy selects the best informative features among features extracted by KPCA. The process is:
rank the
n
ℓ
{\displaystyle n_{\ell }}
features according to their mutual information with the class labels;
for different values of K and
m
ℓ
∈
{
1
,
…
,
n
ℓ
}
{\displaystyle m_{\ell }\in \{1,\ldots ,n_{\ell }\}}
, compute the classification error rate of a K-nearest neighbor (K-NN) classifier using only the
m
l
{\displaystyle m_{l}}
most informative features on a validation set;
the value of
m
ℓ
{\displaystyle m_{\ell }}
with which the classifier has reached the lowest error rate determines the number of features to retain.
Some drawbacks accompany the KPCA method for MKMs.
A more straightforward way to use kernel machines for deep learning was developed for spoken language understanding. The main idea is to use a kernel machine to approximate a shallow neural net with an infinite number of hidden units, then use a deep stacking network to splice the output of the kernel machine and the raw input in building the next, higher level of the kernel machine. The number of levels in the deep convex network is a hyper-parameter of the overall system, to be determined by cross validation.
== See also ==
== References ==
== Bibliography ==
Fukushima, Kunihiko (1987). "A hierarchical neural network model for selective attention". In Eckmiller, R.; Von der Malsburg, C. (eds.). Neural computers. Springer-Verlag. pp. 81–90.
Fukushima, Kunihiko (2007). "Neocognitron". Scholarpedia. 2 (1): 1717. Bibcode:2007SchpJ...2.1717F. doi:10.4249/scholarpedia.1717. | Wikipedia/Types_of_artificial_neural_networks |
Automated lane keeping systems (ALKS), also described as traffic jam chauffeurs, is an autonomous driving system that doesn't require driver supervision on motorways. ALKS is an international standard set out in UN-ECE regulation 157 and amounts to Level 3 vehicle automation. It is essentially a more robust combination of adaptive cruise control (ACC) and lane centering assist (LCA). When activated, it allows the driver to do non-driving tasks until alerted otherwise.
== History ==
In 2021, Mercedes-Benz has received German approval for an ALKS self-driving technology complying with UN-R157 legal requirements.
Mercedes-Benz says that customers will be able to buy an S-Class with the Drive Pilot technology in the first half of 2022, enabling them to drive in conditionally automated mode at speeds of up to 60 km/h (37mph) in heavy traffic or congested situations on suitable stretches of motorway in Germany.
The regulation was signed by 54 states on 22 January 2021.
Entry into force in the European Union is 22 January 2022 for cars.
Entry into force is planned for June 2022 for heavy vehicles.
Initially, the regulation allows for automated driving up to 60 km/h (35 mph). An amendment for an increased speed for automated driving up to 130 km/h (80 mph) is planned to enter into force from January 2023.
== Regulation ==
In all contracting countries, the date of entry into force of UNECE regulation 157 is 22 January 2021.
Within six months from the date of depositary notification C.N.297.2020.TREATIES-XI.B.16 of 22 July 2020 by which the Secretary-General transmitted to the Governments of the Contracting Parties the text of draft United Nations Regulation No. 157, none of the Contracting Parties to the Agreement notified the Secretary-General of their intention not to apply the said United Nations Regulation on the date of its entry into force, under paragraphs 3 and 4 of article 1 of the Agreement.
Therefore, following Article 1 (3) of the Agreement, the draft United Nations Regulation is adopted as United Nations Regulation No. 157. Per paragraphs, 3 and 4 of article 1 of the Agreement, the date of entry into force of United Nations Regulation No. 157 for all Contracting Parties is 22 January 2021.
== Transition period ==
ALKS’s standard safety concept defines a 10 seconds transition period so that human driver must remain able to respond to a system request so that the human driver assume control of the vehicle when driving system do not do it anymore:
Transition demand
"is a logical and intuitive procedure to transfer the Dynamic Driving Task (DDT) from the system (automated control) to the human driver (manual control). This request is given from the system to the human driver."
Transition phase
"means the duration of the transition demand."
When local law allows the human driver to focus on non-driving tasks such as reading a book or watching a video while the automated driving system is engaged, a liability question may be raised following a takeover request: who own the liability once the 10 seconds transition period has achieved?
In the United Kingdom, the 10 seconds transition period is questioned regarding the driver capacity to take back control quickly and safely.
== Requirements ==
ALKS requires multiple criteria:
driver seated, attached and available;
proper functioning of the Data Storage System for Automated Driving (DSSAD);
motorway type lane: road prohibited to pedestrians and cyclists equipped with a physical separation between the two directions of traffic;
other weather conditions.
=== Collision avoidance features ===
ALKS deals with some cases of collision avoidance.
ALKS defines some concepts:
Imminent collision risk describes a situation or an event which leads to a collision of the vehicle with another road user or an obstacle which cannot be avoided by a braking demand with lower than 5 m/s
Emergency Manoeuvre (EM) is a maneuver performed by the system in case of an event in which the vehicle is at imminent collision risk and has the purpose of avoiding or mitigating a collision.
The activated system shall not cause any collisions that are reasonably foreseeable and preventable. If a collision can be safely avoided without causing another one, it shall be avoided. When the vehicle is involved in a detectable collision, the vehicle shall be brought to a standstill.
The activated system shall detect the distance to the next vehicle in front as defined in paragraph 7.1.1. and shall adapt the vehicle speed to avoid collision.
The activated system shall be able to bring the vehicle to a complete stop behind a stationary vehicle, a stationary road user, or a blocked lane of travel to avoid a collision. This shall be ensured up to the maximum operational speed of the system.
The activated system shall avoid a collision with a leading vehicle (...)
The activated system shall avoid a collision with a cutting in the vehicle (...)
The activated system shall avoid a collision with an unobstructed crossing pedestrian in front of the vehicle.
This document clarifies the derivation process to define conditions under which automated lane-keeping systems (ALKS) shall avoid a collision
== References == | Wikipedia/Automated_Lane_Keeping_Systems |
Neural network software is used to simulate, research, develop, and apply artificial neural networks, software concepts adapted from biological neural networks, and in some cases, a wider array of adaptive systems such as artificial intelligence and machine learning.
== Simulators ==
Neural network simulators are software applications that are used to simulate the behavior of artificial or biological neural networks. They focus on one or a limited number of specific types of neural networks. They are typically stand-alone and not intended to produce general neural networks that can be integrated in other software. Simulators usually have some form of built-in visualization to monitor the training process. Some simulators also visualize the physical structure of the neural network.
=== Research simulators ===
Historically, the most common type of neural network software was intended for researching neural network structures and algorithms. The primary purpose of this type of software is, through simulation, to gain a better understanding of the behavior and the properties of neural networks. Today in the study of artificial neural networks, simulators have largely been replaced by more general component based development environments as research platforms.
Commonly used artificial neural network simulators include the Stuttgart Neural Network Simulator (SNNS), and Emergent.
In the study of biological neural networks however, simulation software is still the only available approach. In such simulators the physical biological and chemical properties of neural tissue, as well as the electromagnetic impulses between the neurons are studied.
Commonly used biological network simulators include Neuron, GENESIS, NEST and Brian.
=== Data analysis simulators ===
Unlike the research simulators, data analysis simulators are intended for practical applications of artificial neural networks. Their primary focus is on data mining and forecasting. Data analysis simulators usually have some form of preprocessing capabilities. Unlike the more general development environments, data analysis simulators use a relatively simple static neural network that can be configured. A majority of the data analysis simulators on the market use backpropagating networks or self-organizing maps as their core. The advantage of this type of software is that it is relatively easy to use. Neural Designer is one example of a data analysis simulator.
=== Simulators for teaching neural network theory ===
When the Parallel Distributed Processing volumes
were released in 1986-87, they provided some relatively simple software. The original PDP software did not require any programming skills, which led to its adoption by a wide variety of researchers in diverse fields. The original PDP software was developed into a more powerful package called PDP++, which in turn has become an even more powerful platform called Emergent. With each development, the software has become more powerful, but also more daunting for use by beginners.
In 1997, the tLearn software was released to accompany a book. This was a return to the idea of providing a small, user-friendly, simulator that was designed with the novice in mind. tLearn allowed basic feed forward networks, along with simple recurrent networks, both of which can be trained by the simple back propagation algorithm. tLearn has not been updated since 1999.
In 2011, the Basic Prop simulator was released. Basic Prop is a self-contained application, distributed as a platform neutral JAR file, that provides much of the same simple functionality as tLearn.
== Development environments ==
Development environments for neural networks differ from the software described above primarily on two accounts – they can be used to develop custom types of neural networks and they support deployment of the neural network outside the environment. In some cases they have advanced preprocessing, analysis and visualization capabilities.
=== Component based ===
A more modern type of development environments that are currently favored in both industrial and scientific use are based on a component based paradigm. The neural network is constructed by connecting adaptive filter components in a pipe filter flow. This allows for greater flexibility as custom networks can be built as well as custom components used by the network. In many cases this allows a combination of adaptive and non-adaptive components to work together. The data flow is controlled by a control system which is exchangeable as well as the adaptation algorithms. The other important feature is deployment capabilities.
With the advent of component-based frameworks such as .NET and Java, component based development environments are capable of deploying the developed neural network to these frameworks as inheritable components. In addition some software can also deploy these components to several platforms, such as embedded systems.
Component based development environments include: Peltarion Synapse, NeuroDimension NeuroSolutions, Scientific Software Neuro Laboratory, and the LIONsolver integrated software. Free open source component based environments include Encog and Neuroph.
==== Criticism ====
A disadvantage of component-based development environments is that they are more complex than simulators. They require more learning to fully operate and are more complicated to develop.
== Custom neural networks ==
The majority implementations of neural networks available are however custom implementations in various programming languages and on various platforms. Basic types of neural networks are simple to implement directly. There are also many programming libraries that contain neural network functionality and that can be used in custom implementations (such as TensorFlow, Theano, etc., typically providing bindings to languages such as Python, C++, Java).
== Standards ==
In order for neural network models to be shared by different applications, a common language is necessary. The Predictive Model Markup Language (PMML) has been proposed to address this need. PMML is an XML-based language which provides a way for applications to define and share neural network models (and other data mining models) between PMML compliant applications.
PMML provides applications a vendor-independent method of defining models so that proprietary issues and incompatibilities are no longer a barrier to the exchange of models between applications. It allows users to develop models within one vendor's application, and use other vendors' applications to visualize, analyze, evaluate or otherwise use the models. Previously, this was very difficult, but with PMML, the exchange of models between compliant applications is now straightforward.
=== PMML consumers and producers ===
A range of products are being offered to produce and consume PMML. This ever-growing list includes the following neural network products:
R: produces PMML for neural nets and other machine learning models via the package pmml.
SAS Enterprise Miner: produces PMML for several mining models, including neural networks, linear and logistic regression, decision trees, and other data mining models.
SPSS: produces PMML for neural networks as well as many other mining models.
STATISTICA: produces PMML for neural networks, data mining models and traditional statistical models.
== See also ==
AI accelerator
Physical neural network
Comparison of deep learning software
Data Mining
Integrated development environment
Logistic regression
Memristor
== References ==
== External links ==
Comparison of Neural Network Simulators at University of Colorado | Wikipedia/Neural_network_software |
In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular , such as predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute.
One can distinguish two major classes of function approximation problems:
First, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).
Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead.
To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.
== References ==
== See also ==
Approximation theory
Fitness approximation
Kriging
Least squares (function approximation)
Radial basis function network | Wikipedia/Function_approximation |
Group method of data handling (GMDH) is a family of inductive, self-organizing algorithms for mathematical modelling that automatically determines the structure and parameters of models based on empirical data. GMDH iteratively generates and evaluates candidate models, often using polynomial functions, and selects the best-performing ones based on an external criterion. This process builds feedforward networks of optimal complexity, adapting to the noise level in the data and minimising overfitting, ensuring that the resulting model is accurate and generalizable.
GMDH is used in such fields as machine learning, forecasting, optimization and pattern recognition, due to its ability to handle complex, nonlinear relationships in data. Its inductive nature allows it to discover patterns and interdependencies without requiring strong a priori assumptions, making it particularly effective for highly complex systems. By balancing model complexity and accuracy through self-organization, GMDH ensures that the model reflects the underlying relationships in data. This approach has influenced modern machine learning techniques and is recognised as one of the earliest approaches to automated machine learning and deep learning.
A GMDH model with multiple inputs and one output is a subset of components of the base function (1):
Y
(
x
1
,
…
,
x
n
)
=
a
0
+
∑
i
=
1
m
a
i
f
i
{\displaystyle Y(x_{1},\dots ,x_{n})=a_{0}+\sum \limits _{i=1}^{m}a_{i}f_{i}}
where fi are elementary functions dependent on different sets of inputs, ai are coefficients and m is the number of the base function components.
In order to find the best solution, GMDH algorithms consider various component subsets of the base function (1) called partial models. Coefficients of these models are estimated by the least squares method. GMDH algorithms gradually increase the number of partial model components and find a model structure with optimal complexity indicated by the minimum value of an external criterion. This process is called self-organization of models.
As the first base function used in GMDH, was the gradually complicated Kolmogorov–Gabor polynomial (2):
Y
(
x
1
,
…
,
x
n
)
=
a
0
+
∑
i
=
1
n
a
i
x
i
+
∑
i
=
1
n
∑
j
=
i
n
a
i
j
x
i
x
j
+
∑
i
=
1
n
∑
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=
i
n
∑
k
=
j
n
a
i
j
k
x
i
x
j
x
k
+
⋯
{\displaystyle Y(x_{1},\dots ,x_{n})=a_{0}+\sum \limits _{i=1}^{n}{a_{i}}x_{i}+\sum \limits _{i=1}^{n}{\sum \limits _{j=i}^{n}{a_{ij}}}x_{i}x_{j}+\sum \limits _{i=1}^{n}{\sum \limits _{j=i}^{n}{\sum \limits _{k=j}^{n}{a_{ijk}}}}x_{i}x_{j}x_{k}+\cdots }
Usually, more simple partial models with up to second degree functions are used.
Other names include "heuristic self-organization of models" or "polynomial feedforward neural network". Jürgen Schmidhuber cites GMDH as one of the first deep learning methods, remarking that it was used to train eight-layer neural nets as early as 1971.
== History ==
The method was originated in 1968 by Prof. Alexey G. Ivakhnenko at the Institute of Cybernetics in Kyiv.
This inductive approach from the very beginning was a computer-based method, so a set of computer programs and algorithms were the primary practical results achieved at the base of the new theoretical principles. Thanks to the author's policy of open code sharing, the method was quickly settled in the large number of scientific laboratories worldwide. As most routine work is transferred to a computer, the impact of human influence on the objective result is minimised. In fact, this approach can be considered as one of the implementations of the Artificial Intelligence thesis, which states that a computer can act as a powerful advisor to humans.
The development of GMDH consists of a synthesis of ideas from different areas of science: the cybernetic concept of "black box" and the principle of successive
genetic selection of pairwise features, Godel's incompleteness theorems and the Gabor's principle of "freedom of decisions choice", and the Beer's principle of external additions.
GMDH is the original method for solving problems for structural-parametric identification of models for experimental data under uncertainty. Such a problem occurs in the construction of a mathematical model that approximates the unknown pattern of investigated object or process. It uses information about it that is implicitly contained in data. GMDH differs from other methods of modelling by the active application of the following principles: automatic models generation, inconclusive decisions, and consistent selection by external criteria for finding models of optimal complexity. It had an original multilayered procedure for automatic models structure generation, which imitates the process of biological selection with consideration of pairwise successive features. Such procedure is currently used in deep learning networks. To compare and choose optimal models, two or more subsets of a data sample are used. This makes it possible to avoid preliminary assumptions because sample division implicitly acknowledges different types of uncertainty during the automatic construction of the optimal model.
During development was established an organic analogy between the problem of constructing models for noisy data and signal passing through the channel with noise. This made possible to lay the foundations of the theory of noise-immune modelling. The main result of this theory is that the complexity of optimal predictive model depends on the level of uncertainty in the data: the higher this level (e.g. due to noise) - the simpler must be the optimal model (with less estimated parameters). This initiated the development of the GMDH theory as an inductive method of automatic adaptation of optimal model complexity to the level of noise variation in fuzzy data. Therefore, GMDH is often considered to be the original information technology for knowledge extraction from experimental data.
Period 1968–1971 is characterized by the application of only regularity criterion for solving of the problems of identification, pattern recognition and short-term forecasting. As reference functions, polynomials, logical nets, fuzzy Zadeh sets and Bayes probability formulas were used. Authors were stimulated by the very high accuracy of forecasting with the new approach. Noise immunity was not investigated.
Period 1972–1975. The problem of modeling of noised data and incomplete information basis was solved. Multicriteria selection and the utilisation of additional a priori information for noise immunity increase were proposed. The best experiments showed that, with an extended definition of the optimal model by an additional criterion, the noise level can be ten times greater than the signal. Then it was improved using Shannon's Theorem of General Communication theory.
Period 1976–1979. The convergence of multilayered GMDH algorithms was investigated. It has been demonstrated that some multilayered algorithms exhibit a form of error analogous to the static error of control systems, known as 'multilayerness error'. In 1977, a solution of objective systems analysis problems by multilayered GMDH algorithms was proposed. It turned out that sorting-out by criteria ensemble finds the only optimal system of equations and therefore to show complex object elements, their main input and output variables.
Period 1980–1988. Many important theoretical results were received. It became clear that full physical models cannot be used for long-term forecasting. It was proved, that non-physical models of GMDH are more accurate for approximation and forecast than physical models of regression analysis. Two-level algorithms which use two different time scales for modeling were developed.
Since 1989 the new algorithms (AC, OCC, PF) for non-parametric modeling of fuzzy objects and SLP for expert systems were developed and investigated. The present stage of GMDH development can be described as a blossoming of deep learning neural networks and parallel inductive algorithms for multiprocessor computers.
== External criteria ==
External criterion is one of the key features of GMDH. This criterion describes requirements to the model, for example minimization of Least squares. It is always calculated with a separate part of data sample that has not been used for estimation of coefficients. This makes it possible to select a model of optimal complexity according to the level of uncertainty in input data. There are several popular criteria:
Criterion of Regularity (CR) – Least squares of a model at the sample B.
Criterion of Minimum bias or Consistency – a squared error of difference between the estimated outputs (or coefficients vectors) of two models developed on the basis of two distinct samples A and B, divided by squared output estimated on sample B. Comparison of models using it, enables to get consistent models and recover a hidden physical law from the noisy data.
Cross-validation criteria.
== A simple description of model development using GMDH ==
For modeling using GMDH, only the selection criterion and maximum model complexity are pre-selected. Then, the design process begins from the first layer and goes on. The number of layers and neurons in hidden layers, model structure are determined automatically. All possible combinations of allowable inputs (all possible neurons) can be considered. Then polynomial coefficients are determined using one of the available minimizing methods such as singular value decomposition (with training data). Then, neurons that have better external criterion value (for testing data) are kept, and others are removed. If the external criterion for layer's best neuron reach minimum or surpasses the stopping criterion, network design is completed and the polynomial expression of the best neuron of the last layer is introduced as the mathematical prediction function; if not, the next layer will be generated, and this process goes on.
== GMDH-type neural networks ==
There are many different ways to choose an order for partial models consideration. The very first consideration order used in GMDH and originally called multilayered inductive procedure is the most popular one. It is a sorting-out of gradually complicated models generated from base function. The best model is indicated by the minimum of the external criterion characteristic. The multilayered procedure is equivalent to the Artificial Neural Network with polynomial activation function of neurons. Therefore, the algorithm with such an approach usually referred as GMDH-type Neural Network or Polynomial Neural Network. Li showed that GMDH-type neural network performed better than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network.
== Combinatorial GMDH ==
Another important approach to partial models consideration that is becoming more and more popular is a combinatorial search that is either limited or full. This approach has some advantages against Polynomial Neural Networks, but requires considerable computational power and thus is not effective for objects with a large number of inputs. An important achievement of Combinatorial GMDH is that it fully outperforms linear regression approach if the noise level in the input data is greater than zero. It guarantees that the most optimal model will be founded during exhaustive sorting.
Basic Combinatorial algorithm makes the following steps:
Divides data sample at least into two samples A and B.
Generates subsamples from A according to partial models with steadily increasing complexity.
Estimates coefficients of partial models at each layer of models complexity.
Calculates value of external criterion for models on sample B.
Chooses the best model (set of models) indicated by minimal value of the criterion.
For the selected model of optimal complexity recalculate coefficients on a whole data sample.
In contrast to GMDH-type neural networks, the Combinatorial algorithm usually does not stop at the certain level of complexity because a point of increase in criterion value can be simply a local minimum, see Fig.1.
== Algorithms ==
Combinatorial (COMBI)
Multilayered Iterative (MIA)
GN
Objective System Analysis (OSA)
Harmonical
Two-level (ARIMAD)
Multiplicative–Additive (MAA)
Objective Computer Clusterization (OCC);
Pointing Finger (PF) clusterization algorithm;
Analogues Complexing (AC)
Harmonical Re-discretization
Algorithm on the base of Multilayered Theory of Statistical Decisions (MTSD)
Group of Adaptive Models Evolution (GAME)
== Software implementations ==
FAKE GAME Project — Open source. Cross-platform.
GEvom — Free upon request for academic use. Windows-only.
GMDH Shell — GMDH-based, predictive analytics and time series forecasting software. Free Academic Licensing and Free Trial version available. Windows-only.
KnowledgeMiner — Commercial product. Mac OS X-only. Free Demo version available.
PNN Discovery client — Commercial product.
Sciengy RPF! — Freeware, Open source.
wGMDH — Weka plugin, Open source.
R Package – Open source.
R Package for regression tasks – Open source.
Python library of MIA algorithm - Open source.
Python library of basic GMDH algorithms (COMBI, MULTI, MIA, RIA) - Open source.
== References ==
== Further reading ==
A.G. Ivakhnenko. Heuristic Self-Organization in Problems of Engineering Cybernetics, Automatica, vol.6, 1970 — p. 207-219.
S.J. Farlow. Self-Organizing Methods in Modelling: GMDH Type Algorithms. New-York, Bazel: Marcel Decker Inc., 1984, 350 p.
H.R. Madala, A.G. Ivakhnenko. Inductive Learning Algorithms for Complex Systems Modeling. CRC Press, Boca Raton, 1994.
== External links ==
Library of GMDH books and articles
Group Method of Data Handling | Wikipedia/Group_method_of_data_handling |
The von Neumann architecture—also known as the von Neumann model or Princeton architecture—is a computer architecture based on the First Draft of a Report on the EDVAC, written by John von Neumann in 1945, describing designs discussed with John Mauchly and J. Presper Eckert at the University of Pennsylvania's Moore School of Electrical Engineering. The document describes a design architecture for an electronic digital computer made of "organs" that were later understood to have these components:
A processing unit with both an arithmetic logic unit and processor registers
A control unit that includes an instruction register and a program counter
Memory that stores data and instructions
External mass storage
Input and output mechanisms
The attribution of the invention of the architecture to von Neumann is controversial, not least because Eckert and Mauchly had done a lot of the required design work and claim to have had the idea for stored programs long before discussing the ideas with von Neumann and Herman Goldstine.
The term "von Neumann architecture" has evolved to refer to any stored-program computer in which an instruction fetch and a data operation cannot occur at the same time (since they share a common bus). This is referred to as the von Neumann bottleneck, which often limits the performance of the corresponding system.
The von Neumann architecture is simpler than the Harvard architecture (which has one dedicated set of address and data buses for reading and writing to memory and another set of address and data buses to fetch instructions).
A stored-program computer uses the same underlying mechanism to encode both program instructions and data as opposed to designs which use a mechanism such as discrete plugboard wiring or fixed control circuitry for instruction implementation. Stored-program computers were an advancement over the manually reconfigured or fixed function computers of the 1940s, such as the Colossus and the ENIAC. These were programmed by setting switches and inserting patch cables to route data and control signals between various functional units.
The vast majority of modern computers use the same hardware mechanism to encode and store both data and program instructions, but have caches between the CPU and memory, and, for the caches closest to the CPU, have separate caches for instructions and data, so that most instruction and data fetches use separate buses (split-cache architecture).
== History ==
The earliest computing machines had fixed programs. Some very simple computers still use this design, either for simplicity or training purposes. For example, a desk calculator (in principle) is a fixed program computer. It can do basic mathematics, but it cannot run a word processor or games. Changing the program of a fixed-program machine requires rewiring, restructuring, or redesigning the machine. The earliest computers were not so much "programmed" as "designed" for a particular task. "Reprogramming"—when possible at all—was a laborious process that started with flowcharts and paper notes, followed by detailed engineering designs, and then the often-arduous process of physically rewiring and rebuilding the machine. It could take three weeks to set up and debug a program on ENIAC.
With the proposal of the stored-program computer, this changed. A stored-program computer includes, by design, an instruction set, and can store in memory a set of instructions (a program) that details the computation.
A stored-program design also allows for self-modifying code. One early motivation for such a facility was the need for a program to increment or otherwise modify the address portion of instructions, which operators had to do manually in early designs. This became less important when index registers and indirect addressing became usual features of machine architecture. Another use was to embed frequently used data in the instruction stream using immediate addressing.
When von Neumann described the automatic computing systems using different terminology than is typically described with the model. In the First Draft of a Report on the EDVAC, the architecture was composed of "a high-speed memory M, a central arithmetic unit CA, an outside recording medium R, an input organ I, an output organ O, and a central control CC"
== Capabilities ==
On a large scale, the ability to treat instructions as data is what makes assemblers, compilers, linkers, loaders, and other automated programming tools possible. It makes "programs that write programs" possible. This has made a sophisticated self-hosting computing ecosystem flourish around von Neumann architecture machines.
Some high-level languages leverage the von Neumann architecture by providing an abstract, machine-independent way to manipulate executable code at runtime (e.g., LISP), or by using runtime information to tune just-in-time compilation (e.g. languages hosted on the Java virtual machine, or languages embedded in web browsers).
On a smaller scale, some repetitive operations such as BITBLT or pixel and vertex shaders can be accelerated on general purpose processors with just-in-time compilation techniques. This is one use of self-modifying code that has remained popular.
== Development of the stored-program concept ==
The mathematician Alan Turing, who had been alerted to a problem of mathematical logic by the lectures of Max Newman at the University of Cambridge, wrote a paper in 1936 entitled On Computable Numbers, with an Application to the Entscheidungsproblem, which was published in the Proceedings of the London Mathematical Society. In it he described a hypothetical machine he called a universal computing machine, now known as the "Universal Turing machine". The hypothetical machine had an infinite store (memory in today's terminology) that contained both instructions and data. John von Neumann became acquainted with Turing while he was a visiting professor at Cambridge in 1935, and also during Turing's PhD year at the Institute for Advanced Study in Princeton, New Jersey during 1936–1937. Whether he knew of Turing's paper of 1936 at that time is not clear.
In 1936, Konrad Zuse also anticipated, in two patent applications, that machine instructions could be stored in the same storage used for data.
Independently, J. Presper Eckert and John Mauchly, who were developing the ENIAC at the Moore School of Electrical Engineering of the University of Pennsylvania, wrote about the stored-program concept in December 1943.
In planning a new machine, EDVAC, Eckert wrote in January 1944 that they would store data and programs in a new addressable memory device, a mercury metal delay-line memory. This was the first time the construction of a practical stored-program machine was proposed. At that time, he and Mauchly were not aware of Turing's work.
Von Neumann was involved in the Manhattan Project at the Los Alamos National Laboratory. It required huge amounts of calculation, and thus drew him to the ENIAC project, during the summer of 1944. There he joined the ongoing discussions on the design of this stored-program computer, the EDVAC. As part of that group, he wrote up a description titled First Draft of a Report on the EDVAC based on the work of Eckert and Mauchly. It was unfinished when his colleague Herman Goldstine circulated it, and bore only von Neumann's name (to the consternation of Eckert and Mauchly). The paper was read by dozens of von Neumann's colleagues in America and Europe, and influenced the next round of computer designs.
Jack Copeland considers that it is "historically inappropriate to refer to electronic stored-program digital computers as 'von Neumann machines'". His Los Alamos colleague Stan Frankel said of von Neumann's regard for Turing's ideas
I know that in or about 1943 or '44 von Neumann was well aware of the fundamental importance of Turing's paper of 1936....
Von Neumann introduced me to that paper and at his urging I studied it with care. Many people have acclaimed von Neumann as the "father of the computer" (in a modern sense of the term) but I am sure that he would never have made that mistake himself.
He might well be called the midwife, perhaps, but he firmly emphasized to me, and to others I am sure, that the fundamental conception is owing to Turing—in so far as not anticipated by Babbage.... Both Turing and von Neumann, of course, also made substantial contributions to the "reduction to practice" of these concepts but I would not regard these as comparable in importance with the introduction and explication of the concept of a computer able to store in its memory its program of activities and of modifying that program in the course of these activities.
At the time that the "First Draft" report was circulated, Turing was producing a report entitled Proposed Electronic Calculator. It described in engineering and programming detail, his idea of a machine he called the Automatic Computing Engine (ACE). He presented this to the executive committee of the British National Physical Laboratory on February 19, 1946. Although Turing knew from his wartime experience at Bletchley Park that what he proposed was feasible, the secrecy surrounding Colossus, that was subsequently maintained for several decades, prevented him from saying so. Various successful implementations of the ACE design were produced.
Both von Neumann's and Turing's papers described stored-program computers, but von Neumann's earlier paper achieved greater circulation and the computer architecture it outlined became known as the "von Neumann architecture". In the 1953 publication Faster than Thought: A Symposium on Digital Computing Machines (edited by B. V. Bowden), a section in the chapter on Computers in America reads as follows:
The Machine of the Institute For Advanced Study, Princeton
In 1945, Professor J. von Neumann, who was then working at the Moore School of Engineering in Philadelphia, where the E.N.I.A.C. had been built, issued on behalf of a group of his co-workers, a report on the logical design of digital computers. The report contained a detailed proposal for the design of the machine that has since become known as the E.D.V.A.C. (electronic discrete variable automatic computer). This machine has only recently been completed in America, but the von Neumann report inspired the construction of the E.D.S.A.C. (electronic delay-storage automatic calculator) in Cambridge (see p. 130).
In 1947, Burks, Goldstine and von Neumann published another report that outlined the design of another type of machine (a parallel machine this time) that would be exceedingly fast, capable perhaps of 20,000 operations per second. They pointed out that the outstanding problem in constructing such a machine was the development of suitable memory with instantaneously accessible contents. At first they suggested using a special vacuum tube—called the "Selectron"—which the Princeton Laboratories of RCA had invented. These tubes were expensive and difficult to make, so von Neumann subsequently decided to build a machine based on the Williams memory. This machine—completed in June, 1952 in Princeton—has become popularly known as the Maniac. The design of this machine inspired at least half a dozen machines now being built in America, all known affectionately as "Johniacs".
In the same book, the first two paragraphs of a chapter on ACE read as follows:
Automatic Computation at the National Physical Laboratory
One of the most modern digital computers which embodies developments and improvements in the technique of automatic electronic computing was recently demonstrated at the National Physical Laboratory, Teddington, where it has been designed and built by a small team of mathematicians and electronics research engineers on the staff of the Laboratory, assisted by a number of production engineers from the English Electric Company, Limited. The equipment so far erected at the Laboratory is only the pilot model of a much larger installation which will be known as the Automatic Computing Engine, but although comparatively small in bulk and containing only about 800 thermionic valves, as can be judged from Plates XII, XIII and XIV, it is an extremely rapid and versatile calculating machine.
The basic concepts and abstract principles of computation by a machine were formulated by Dr. A. M. Turing, F.R.S., in a paper1. read before the London Mathematical Society in 1936, but work on such machines in Britain was delayed by the war. In 1945, however, an examination of the problems was made at the National Physical Laboratory by Mr. J. R. Womersley, then superintendent of the Mathematics Division of the Laboratory. He was joined by Dr. Turing and a small staff of specialists, and, by 1947, the preliminary planning was sufficiently advanced to warrant the establishment of the special group already mentioned. In April, 1948, the latter became the Electronics Section of the Laboratory, under the charge of Mr. F. M. Colebrook.
== Early von Neumann-architecture computers ==
The First Draft described a design that was used by many universities and corporations to construct their computers. Among these various computers, only ILLIAC and ORDVAC had compatible instruction sets.
ARC2 (Birkbeck, University of London) officially came online on May 12, 1948.
Manchester Baby (Victoria University of Manchester, England) made its first successful run of a stored program on June 21, 1948.
EDSAC (University of Cambridge, England) was the first practical stored-program electronic computer (May 1949)
Manchester Mark 1 (University of Manchester, England) Developed from the Baby (June 1949)
CSIRAC (Council for Scientific and Industrial Research) Australia (November 1949)
MESM at the Kiev Institute of Electrotechnology in Kiev, Ukrainian SSR (November 1950)
EDVAC (Ballistic Research Laboratory, Computing Laboratory at Aberdeen Proving Ground 1951)
IAS machine at Institute for Advanced Study (1951)
ORDVAC (University of Illinois) at Aberdeen Proving Ground, Maryland (completed November 1951)
MANIAC I at Los Alamos Scientific Laboratory (March 1952)
ILLIAC at the University of Illinois, (September 1952)
BESM-1 in Moscow (1952)
AVIDAC at Argonne National Laboratory (1953)
ORACLE at Oak Ridge National Laboratory (June 1953)
BESK in Stockholm (1953)
JOHNNIAC at RAND Corporation (January 1954)
DASK in Denmark (1955)
WEIZAC at the Weizmann Institute of Science in Rehovot, Israel (1955)
PERM in Munich (1956)
SILLIAC in Sydney (1956)
== Early stored-program computers ==
The date information in the following chronology is difficult to put into proper order. Some dates are for first running a test program, some dates are the first time the computer was demonstrated or completed, and some dates are for the first delivery or installation.
The IBM SSEC had the ability to treat instructions as data, and was publicly demonstrated on January 27, 1948. This ability was claimed in a US patent. However it was partially electromechanical, not fully electronic. In practice, instructions were read from paper tape due to its limited memory.
The ARC2 developed by Andrew Booth and Kathleen Booth at Birkbeck, University of London officially came online on May 12, 1948. It featured the first rotating drum storage device.
The Manchester Baby was the first fully electronic computer to run a stored program. It ran a factoring program for 52 minutes on June 21, 1948, after running a simple division program and a program to show that two numbers were relatively prime.
The ENIAC was modified to run as a primitive read-only stored-program computer (using the Function Tables for program ROM) and was demonstrated as such on September 16, 1948, running a program by Adele Goldstine for von Neumann.
The BINAC ran some test programs in February, March, and April 1949, although was not completed until September 1949.
The Manchester Mark 1 developed from the Baby project. An intermediate version of the Mark 1 was available to run programs in April 1949, but was not completed until October 1949.
The EDSAC ran its first program on May 6, 1949.
The EDVAC was delivered in August 1949, but it had problems that kept it from being put into regular operation until 1951.
The CSIR Mk I ran its first program in November 1949.
The SEAC was demonstrated in April 1950.
The Pilot ACE ran its first program on May 10, 1950, and was demonstrated in December 1950.
The SWAC was completed in July 1950.
The Whirlwind was completed in December 1950 and was in actual use in April 1951.
The first ERA Atlas (later the commercial ERA 1101/UNIVAC 1101) was installed in December 1950.
== Evolution ==
Through the decades of the 1960s and 1970s computers generally became both smaller and faster, which led to evolutions in their architecture. For example, memory-mapped I/O lets input and output devices be treated the same as memory. A single system bus could be used to provide a modular system with lower cost. This is sometimes called a "streamlining" of the architecture.
In subsequent decades, simple microcontrollers would sometimes omit features of the model to lower cost and size.
Larger computers added features for higher performance.
== Design limitations ==
=== von Neumann bottleneck ===
The use of the same bus to fetch instructions and data leads to the von Neumann bottleneck, the limited throughput (data transfer rate) between the central processing unit (CPU) and memory compared to the amount of memory. Because the single bus can only access one of the two classes of memory at a time, throughput is lower than the rate at which the CPU can work. This seriously limits the effective processing speed when the CPU is required to perform minimal processing on large amounts of data. The CPU is continually forced to wait for needed data to move to or from memory. Since CPU speed and memory size have increased much faster than the throughput between them, the bottleneck has become more of a problem, a problem whose severity increases with every new generation of CPU.
The von Neumann bottleneck was described by John Backus in his 1977 ACM Turing Award lecture. According to Backus:
Surely there must be a less primitive way of making big changes in the store than by pushing vast numbers of words back and forth through the von Neumann bottleneck. Not only is this tube a literal bottleneck for the data traffic of a problem, but, more importantly, it is an intellectual bottleneck that has kept us tied to word-at-a-time thinking instead of encouraging us to think in terms of the larger conceptual units of the task at hand. Thus programming is basically planning and detailing the enormous traffic of words through the von Neumann bottleneck, and much of that traffic concerns not significant data itself, but where to find it.
==== Mitigations ====
There are several known methods for mitigating the Von Neumann performance bottleneck. For example, the following all can improve performance:
Providing a cache between the CPU and the main memory.
Providing separate caches or separate access paths for data and instructions (the so-called Modified Harvard architecture).
Using branch predictor algorithms and logic.
Providing a limited CPU stack or other on-chip scratchpad memory to reduce memory access.
Implementing the CPU and the memory hierarchy as a system on chip, providing greater locality of reference and thus reducing latency and increasing throughput between processor registers and main memory.
The problem can also be sidestepped somewhat by using parallel computing, using for example the non-uniform memory access (NUMA) architecture—this approach is commonly employed by supercomputers. It is less clear whether the intellectual bottleneck that Backus criticized has changed much since 1977. Backus's proposed solution has not had a major influence. Modern functional programming and object-oriented programming are much less geared towards "pushing vast numbers of words back and forth" than earlier languages like FORTRAN were, but internally, that is still what computers spend much of their time doing, even highly parallel supercomputers.
=== Self-modifying code ===
Aside from the von Neumann bottleneck, program modifications can be quite harmful, either by accident or design. In some simple stored-program computer designs, a malfunctioning program can damage itself, other programs, or the operating system, possibly leading to a computer crash. However, this problem also applies to conventional programs that lack bounds checking. Memory protection and various access controls generally safeguard against both accidental and malicious program changes.
== See also ==
CARDboard Illustrative Aid to Computation
Interconnect bottleneck
Little man computer
Random-access machine
Harvard architecture
Turing machine
== References ==
== Further reading ==
== External links ==
Harvard vs von Neumann
A tool that emulates the behavior of a von Neumann machine
JOHNNY: A simple Open Source simulator of a von Neumann machine for educational purposes | Wikipedia/Von_Neumann_model |
An artificial neural network (ANN) combines biological principles with advanced statistics to solve problems in domains such as pattern recognition and game-play. ANNs adopt the basic model of neuron analogues connected to each other in a variety of ways.
== Structure ==
=== Neuron ===
A neuron with label
j
{\displaystyle j}
receiving an input
p
j
(
t
)
{\displaystyle p_{j}(t)}
from predecessor neurons consists of the following components:
an activation
a
j
(
t
)
{\displaystyle a_{j}(t)}
, the neuron's state, depending on a discrete time parameter,
an optional threshold
θ
j
{\displaystyle \theta _{j}}
, which stays fixed unless changed by learning,
an activation function
f
{\displaystyle f}
that computes the new activation at a given time
t
+
1
{\displaystyle t+1}
from
a
j
(
t
)
{\displaystyle a_{j}(t)}
,
θ
j
{\displaystyle \theta _{j}}
and the net input
p
j
(
t
)
{\displaystyle p_{j}(t)}
giving rise to the relation
a
j
(
t
+
1
)
=
f
(
a
j
(
t
)
,
p
j
(
t
)
,
θ
j
)
,
{\displaystyle a_{j}(t+1)=f(a_{j}(t),p_{j}(t),\theta _{j}),}
and an output function
f
out
{\displaystyle f_{\text{out}}}
computing the output from the activation
o
j
(
t
)
=
f
out
(
a
j
(
t
)
)
.
{\displaystyle o_{j}(t)=f_{\text{out}}(a_{j}(t)).}
Often the output function is simply the identity function.
An input neuron has no predecessor but serves as input interface for the whole network. Similarly an output neuron has no successor and thus serves as output interface of the whole network.
=== Propagation function ===
The propagation function computes the input
p
j
(
t
)
{\displaystyle p_{j}(t)}
to the neuron
j
{\displaystyle j}
from the outputs
o
i
(
t
)
{\displaystyle o_{i}(t)}
and typically has the form
p
j
(
t
)
=
∑
i
o
i
(
t
)
w
i
j
.
{\displaystyle p_{j}(t)=\sum _{i}o_{i}(t)w_{ij}.}
=== Bias ===
A bias term can be added, changing the form to the following:
p
j
(
t
)
=
∑
i
o
i
(
t
)
w
i
j
+
w
0
j
,
{\displaystyle p_{j}(t)=\sum _{i}o_{i}(t)w_{ij}+w_{0j},}
where
w
0
j
{\displaystyle w_{0j}}
is a bias.
== Neural networks as functions ==
Neural network models can be viewed as defining a function that takes an input (observation) and produces an output (decision)
f
:
X
→
Y
{\displaystyle \textstyle f:X\rightarrow Y}
or a distribution over
X
{\displaystyle \textstyle X}
or both
X
{\displaystyle \textstyle X}
and
Y
{\displaystyle \textstyle Y}
. Sometimes models are intimately associated with a particular learning rule. A common use of the phrase "ANN model" is really the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons, number of layers or their connectivity).
Mathematically, a neuron's network function
f
(
x
)
{\displaystyle \textstyle f(x)}
is defined as a composition of other functions
g
i
(
x
)
{\displaystyle \textstyle g_{i}(x)}
, that can further be decomposed into other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between functions. A widely used type of composition is the nonlinear weighted sum, where
f
(
x
)
=
K
(
∑
i
w
i
g
i
(
x
)
)
{\displaystyle \textstyle f(x)=K\left(\sum _{i}w_{i}g_{i}(x)\right)}
, where
K
{\displaystyle \textstyle K}
(commonly referred to as the activation function) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth transition as input values change, i.e. a small change in input produces a small change in output. The following refers to a collection of functions
g
i
{\displaystyle \textstyle g_{i}}
as a vector
g
=
(
g
1
,
g
2
,
…
,
g
n
)
{\displaystyle \textstyle g=(g_{1},g_{2},\ldots ,g_{n})}
.
This figure depicts such a decomposition of
f
{\displaystyle \textstyle f}
, with dependencies between variables indicated by arrows. These can be interpreted in two ways.
The first view is the functional view: the input
x
{\displaystyle \textstyle x}
is transformed into a 3-dimensional vector
h
{\displaystyle \textstyle h}
, which is then transformed into a 2-dimensional vector
g
{\displaystyle \textstyle g}
, which is finally transformed into
f
{\displaystyle \textstyle f}
. This view is most commonly encountered in the context of optimization.
The second view is the probabilistic view: the random variable
F
=
f
(
G
)
{\displaystyle \textstyle F=f(G)}
depends upon the random variable
G
=
g
(
H
)
{\displaystyle \textstyle G=g(H)}
, which depends upon
H
=
h
(
X
)
{\displaystyle \textstyle H=h(X)}
, which depends upon the random variable
X
{\displaystyle \textstyle X}
. This view is most commonly encountered in the context of graphical models.
The two views are largely equivalent. In either case, for this particular architecture, the components of individual layers are independent of each other (e.g., the components of
g
{\displaystyle \textstyle g}
are independent of each other given their input
h
{\displaystyle \textstyle h}
). This naturally enables a degree of parallelism in the implementation.
Networks such as the previous one are commonly called feedforward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent. Such networks are commonly depicted in the manner shown at the top of the figure, where
f
{\displaystyle \textstyle f}
is shown as dependent upon itself. However, an implied temporal dependence is not shown.
== Backpropagation ==
Backpropagation training algorithms fall into three categories:
steepest descent (with variable learning rate and momentum, resilient backpropagation);
quasi-Newton (Broyden–Fletcher–Goldfarb–Shanno, one step secant);
Levenberg–Marquardt and conjugate gradient (Fletcher–Reeves update, Polak–Ribiére update, Powell–Beale restart, scaled conjugate gradient).
=== Algorithm ===
Let
N
{\displaystyle N}
be a network with
e
{\displaystyle e}
connections,
m
{\displaystyle m}
inputs and
n
{\displaystyle n}
outputs.
Below,
x
1
,
x
2
,
…
{\displaystyle x_{1},x_{2},\dots }
denote vectors in
R
m
{\displaystyle \mathbb {R} ^{m}}
,
y
1
,
y
2
,
…
{\displaystyle y_{1},y_{2},\dots }
vectors in
R
n
{\displaystyle \mathbb {R} ^{n}}
, and
w
0
,
w
1
,
w
2
,
…
{\displaystyle w_{0},w_{1},w_{2},\ldots }
vectors in
R
e
{\displaystyle \mathbb {R} ^{e}}
. These are called inputs, outputs and weights, respectively.
The network corresponds to a function
y
=
f
N
(
w
,
x
)
{\displaystyle y=f_{N}(w,x)}
which, given a weight
w
{\displaystyle w}
, maps an input
x
{\displaystyle x}
to an output
y
{\displaystyle y}
.
In supervised learning, a sequence of training examples
(
x
1
,
y
1
)
,
…
,
(
x
p
,
y
p
)
{\displaystyle (x_{1},y_{1}),\dots ,(x_{p},y_{p})}
produces a sequence of weights
w
0
,
w
1
,
…
,
w
p
{\displaystyle w_{0},w_{1},\dots ,w_{p}}
starting from some initial weight
w
0
{\displaystyle w_{0}}
, usually chosen at random.
These weights are computed in turn: first compute
w
i
{\displaystyle w_{i}}
using only
(
x
i
,
y
i
,
w
i
−
1
)
{\displaystyle (x_{i},y_{i},w_{i-1})}
for
i
=
1
,
…
,
p
{\displaystyle i=1,\dots ,p}
. The output of the algorithm is then
w
p
{\displaystyle w_{p}}
, giving a new function
x
↦
f
N
(
w
p
,
x
)
{\displaystyle x\mapsto f_{N}(w_{p},x)}
. The computation is the same in each step, hence only the case
i
=
1
{\displaystyle i=1}
is described.
w
1
{\displaystyle w_{1}}
is calculated from
(
x
1
,
y
1
,
w
0
)
{\displaystyle (x_{1},y_{1},w_{0})}
by considering a variable weight
w
{\displaystyle w}
and applying gradient descent to the function
w
↦
E
(
f
N
(
w
,
x
1
)
,
y
1
)
{\displaystyle w\mapsto E(f_{N}(w,x_{1}),y_{1})}
to find a local minimum, starting at
w
=
w
0
{\displaystyle w=w_{0}}
.
This makes
w
1
{\displaystyle w_{1}}
the minimizing weight found by gradient descent.
== Learning pseudocode ==
To implement the algorithm above, explicit formulas are required for the gradient of the function
w
↦
E
(
f
N
(
w
,
x
)
,
y
)
{\displaystyle w\mapsto E(f_{N}(w,x),y)}
where the function is
E
(
y
,
y
′
)
=
|
y
−
y
′
|
2
{\displaystyle E(y,y')=|y-y'|^{2}}
.
The learning algorithm can be divided into two phases: propagation and weight update.
=== Propagation ===
Propagation involves the following steps:
Propagation forward through the network to generate the output value(s)
Calculation of the cost (error term)
Propagation of the output activations back through the network using the training pattern target to generate the deltas (the difference between the targeted and actual output values) of all output and hidden neurons.
=== Weight update ===
For each weight:
Multiply the weight's output delta and input activation to find the gradient of the weight.
Subtract the ratio (percentage) of the weight's gradient from the weight.
The learning rate is the ratio (percentage) that influences the speed and quality of learning. The greater the ratio, the faster the neuron trains, but the lower the ratio, the more accurate the training. The sign of the gradient of a weight indicates whether the error varies directly with or inversely to the weight. Therefore, the weight must be updated in the opposite direction, "descending" the gradient.
Learning is repeated (on new batches) until the network performs adequately.
=== Pseudocode ===
Pseudocode for a stochastic gradient descent algorithm for training a three-layer network (one hidden layer):
initialize network weights (often small random values).
do
for each training example named ex do
prediction = neural-net-output(network, ex) // forward pass
actual = teacher-output(ex)
compute error (prediction - actual) at the output units
compute
Δ
w
h
{\displaystyle \Delta w_{h}}
for all weights from hidden layer to output layer // backward pass
compute
Δ
w
i
{\displaystyle \Delta w_{i}}
for all weights from input layer to hidden layer // backward pass continued
update network weights // input layer not modified by error estimate
until error rate becomes acceptably low
return the network
The lines labeled "backward pass" can be implemented using the backpropagation algorithm, which calculates the gradient of the error of the network regarding the network's modifiable weights.
== References == | Wikipedia/Mathematics_of_artificial_neural_networks |
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including function approximation, time series prediction, classification, and system control. They were first formulated in a 1988 paper by Broomhead and Lowe, both researchers at the Royal Signals and Radar Establishment.
== Network architecture ==
Radial basis function (RBF) networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer. The input can be modeled as a vector of real numbers
x
∈
R
n
{\displaystyle \mathbf {x} \in \mathbb {R} ^{n}}
. The output of the network is then a scalar function of the input vector,
φ
:
R
n
→
R
{\displaystyle \varphi :\mathbb {R} ^{n}\to \mathbb {R} }
, and is given by
φ
(
x
)
=
∑
i
=
1
N
a
i
ρ
(
|
|
x
−
c
i
|
|
)
{\displaystyle \varphi (\mathbf {x} )=\sum _{i=1}^{N}a_{i}\rho (||\mathbf {x} -\mathbf {c} _{i}||)}
where
N
{\displaystyle N}
is the number of neurons in the hidden layer,
c
i
{\displaystyle \mathbf {c} _{i}}
is the center vector for neuron
i
{\displaystyle i}
, and
a
i
{\displaystyle a_{i}}
is the weight of neuron
i
{\displaystyle i}
in the linear output neuron. Functions that depend only on the distance from a center vector are radially symmetric about that vector, hence the name radial basis function. In the basic form, all inputs are connected to each hidden neuron. The norm is typically taken to be the Euclidean distance (although the Mahalanobis distance appears to perform better with pattern recognition) and the radial basis function is commonly taken to be Gaussian
ρ
(
‖
x
−
c
i
‖
)
=
exp
[
−
β
i
‖
x
−
c
i
‖
2
]
{\displaystyle \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}=\exp \left[-\beta _{i}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert ^{2}\right]}
.
The Gaussian basis functions are local to the center vector in the sense that
lim
|
|
x
|
|
→
∞
ρ
(
‖
x
−
c
i
‖
)
=
0
{\displaystyle \lim _{||x||\to \infty }\rho (\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert )=0}
i.e. changing parameters of one neuron has only a small effect for input values that are far away from the center of that neuron.
Given certain mild conditions on the shape of the activation function, RBF networks are universal approximators on a compact subset of
R
n
{\displaystyle \mathbb {R} ^{n}}
. This means that an RBF network with enough hidden neurons can approximate any continuous function on a closed, bounded set with arbitrary precision.
The parameters
a
i
{\displaystyle a_{i}}
,
c
i
{\displaystyle \mathbf {c} _{i}}
, and
β
i
{\displaystyle \beta _{i}}
are determined in a manner that optimizes the fit between
φ
{\displaystyle \varphi }
and the data.
=== Normalization ===
==== Normalized architecture ====
In addition to the above unnormalized architecture, RBF networks can be normalized. In this case the mapping is
φ
(
x
)
=
d
e
f
∑
i
=
1
N
a
i
ρ
(
‖
x
−
c
i
‖
)
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
=
∑
i
=
1
N
a
i
u
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi (\mathbf {x} )\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\sum _{i=1}^{N}a_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}a_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
where
u
(
‖
x
−
c
i
‖
)
=
d
e
f
ρ
(
‖
x
−
c
i
‖
)
∑
j
=
1
N
ρ
(
‖
x
−
c
j
‖
)
{\displaystyle u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{j=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{j}\right\Vert {\big )}}}}
is known as a normalized radial basis function.
==== Theoretical motivation for normalization ====
There is theoretical justification for this architecture in the case of stochastic data flow. Assume a stochastic kernel approximation for the joint probability density
P
(
x
∧
y
)
=
1
N
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
σ
(
|
y
−
e
i
|
)
{\displaystyle P\left(\mathbf {x} \land y\right)={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,\sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}}
where the weights
c
i
{\displaystyle \mathbf {c} _{i}}
and
e
i
{\displaystyle e_{i}}
are exemplars from the data and we require the kernels to be normalized
∫
ρ
(
‖
x
−
c
i
‖
)
d
n
x
=
1
{\displaystyle \int \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,d^{n}\mathbf {x} =1}
and
∫
σ
(
|
y
−
e
i
|
)
d
y
=
1
{\displaystyle \int \sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}\,dy=1}
.
The probability densities in the input and output spaces are
P
(
x
)
=
∫
P
(
x
∧
y
)
d
y
=
1
N
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
{\displaystyle P\left(\mathbf {x} \right)=\int P\left(\mathbf {x} \land y\right)\,dy={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
and
The expectation of y given an input
x
{\displaystyle \mathbf {x} }
is
φ
(
x
)
=
d
e
f
E
(
y
∣
x
)
=
∫
y
P
(
y
∣
x
)
d
y
{\displaystyle \varphi \left(\mathbf {x} \right)\ {\stackrel {\mathrm {def} }{=}}\ E\left(y\mid \mathbf {x} \right)=\int y\,P\left(y\mid \mathbf {x} \right)dy}
where
P
(
y
∣
x
)
{\displaystyle P\left(y\mid \mathbf {x} \right)}
is the conditional probability of y given
x
{\displaystyle \mathbf {x} }
.
The conditional probability is related to the joint probability through Bayes' theorem
P
(
y
∣
x
)
=
P
(
x
∧
y
)
P
(
x
)
{\displaystyle P\left(y\mid \mathbf {x} \right)={\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}}
which yields
φ
(
x
)
=
∫
y
P
(
x
∧
y
)
P
(
x
)
d
y
{\displaystyle \varphi \left(\mathbf {x} \right)=\int y\,{\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}\,dy}
.
This becomes
φ
(
x
)
=
∑
i
=
1
N
e
i
ρ
(
‖
x
−
c
i
‖
)
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
=
∑
i
=
1
N
e
i
u
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi \left(\mathbf {x} \right)={\frac {\sum _{i=1}^{N}e_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}e_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
when the integrations are performed.
=== Local linear models ===
It is sometimes convenient to expand the architecture to include local linear models. In that case the architectures become, to first order,
φ
(
x
)
=
∑
i
=
1
N
(
a
i
+
b
i
⋅
(
x
−
c
i
)
)
ρ
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
and
φ
(
x
)
=
∑
i
=
1
N
(
a
i
+
b
i
⋅
(
x
−
c
i
)
)
u
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
in the unnormalized and normalized cases, respectively. Here
b
i
{\displaystyle \mathbf {b} _{i}}
are weights to be determined. Higher order linear terms are also possible.
This result can be written
φ
(
x
)
=
∑
i
=
1
2
N
∑
j
=
1
n
e
i
j
v
i
j
(
x
−
c
i
)
{\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{2N}\sum _{j=1}^{n}e_{ij}v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}}
where
e
i
j
=
{
a
i
,
if
i
∈
[
1
,
N
]
b
i
j
,
if
i
∈
[
N
+
1
,
2
N
]
{\displaystyle e_{ij}={\begin{cases}a_{i},&{\mbox{if }}i\in [1,N]\\b_{ij},&{\mbox{if }}i\in [N+1,2N]\end{cases}}}
and
v
i
j
(
x
−
c
i
)
=
d
e
f
{
δ
i
j
ρ
(
‖
x
−
c
i
‖
)
,
if
i
∈
[
1
,
N
]
(
x
i
j
−
c
i
j
)
ρ
(
‖
x
−
c
i
‖
)
,
if
i
∈
[
N
+
1
,
2
N
]
{\displaystyle v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\begin{cases}\delta _{ij}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [1,N]\\\left(x_{ij}-c_{ij}\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [N+1,2N]\end{cases}}}
in the unnormalized case and in the normalized case.
Here
δ
i
j
{\displaystyle \delta _{ij}}
is a Kronecker delta function defined as
δ
i
j
=
{
1
,
if
i
=
j
0
,
if
i
≠
j
{\displaystyle \delta _{ij}={\begin{cases}1,&{\mbox{if }}i=j\\0,&{\mbox{if }}i\neq j\end{cases}}}
.
== Training ==
RBF networks are typically trained from pairs of input and target values
x
(
t
)
,
y
(
t
)
{\displaystyle \mathbf {x} (t),y(t)}
,
t
=
1
,
…
,
T
{\displaystyle t=1,\dots ,T}
by a two-step algorithm.
In the first step, the center vectors
c
i
{\displaystyle \mathbf {c} _{i}}
of the RBF functions in the hidden layer are chosen. This step can be performed in several ways; centers can be randomly sampled from some set of examples, or they can be determined using k-means clustering. Note that this step is unsupervised.
The second step simply fits a linear model with coefficients
w
i
{\displaystyle w_{i}}
to the hidden layer's outputs with respect to some objective function. A common objective function, at least for regression/function estimation, is the least squares function:
K
(
w
)
=
d
e
f
∑
t
=
1
T
K
t
(
w
)
{\displaystyle K(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ \sum _{t=1}^{T}K_{t}(\mathbf {w} )}
where
K
t
(
w
)
=
d
e
f
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
2
{\displaystyle K_{t}(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}^{2}}
.
We have explicitly included the dependence on the weights. Minimization of the least squares objective function by optimal choice of weights optimizes accuracy of fit.
There are occasions in which multiple objectives, such as smoothness as well as accuracy, must be optimized. In that case it is useful to optimize a regularized objective function such as
H
(
w
)
=
d
e
f
K
(
w
)
+
λ
S
(
w
)
=
d
e
f
∑
t
=
1
T
H
t
(
w
)
{\displaystyle H(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ K(\mathbf {w} )+\lambda S(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ \sum _{t=1}^{T}H_{t}(\mathbf {w} )}
where
S
(
w
)
=
d
e
f
∑
t
=
1
T
S
t
(
w
)
{\displaystyle S(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ \sum _{t=1}^{T}S_{t}(\mathbf {w} )}
and
H
t
(
w
)
=
d
e
f
K
t
(
w
)
+
λ
S
t
(
w
)
{\displaystyle H_{t}(\mathbf {w} )\ {\stackrel {\mathrm {def} }{=}}\ K_{t}(\mathbf {w} )+\lambda S_{t}(\mathbf {w} )}
where optimization of S maximizes smoothness and
λ
{\displaystyle \lambda }
is known as a regularization parameter.
A third optional backpropagation step can be performed to fine-tune all of the RBF net's parameters.
=== Interpolation ===
RBF networks can be used to interpolate a function
y
:
R
n
→
R
{\displaystyle y:\mathbb {R} ^{n}\to \mathbb {R} }
when the values of that function are known on finite number of points:
y
(
x
i
)
=
b
i
,
i
=
1
,
…
,
N
{\displaystyle y(\mathbf {x} _{i})=b_{i},i=1,\ldots ,N}
. Taking the known points
x
i
{\displaystyle \mathbf {x} _{i}}
to be the centers of the radial basis functions and evaluating the values of the basis functions at the same points
g
i
j
=
ρ
(
|
|
x
j
−
x
i
|
|
)
{\displaystyle g_{ij}=\rho (||\mathbf {x} _{j}-\mathbf {x} _{i}||)}
the weights can be solved from the equation
[
g
11
g
12
⋯
g
1
N
g
21
g
22
⋯
g
2
N
⋮
⋱
⋮
g
N
1
g
N
2
⋯
g
N
N
]
[
w
1
w
2
⋮
w
N
]
=
[
b
1
b
2
⋮
b
N
]
{\displaystyle \left[{\begin{matrix}g_{11}&g_{12}&\cdots &g_{1N}\\g_{21}&g_{22}&\cdots &g_{2N}\\\vdots &&\ddots &\vdots \\g_{N1}&g_{N2}&\cdots &g_{NN}\end{matrix}}\right]\left[{\begin{matrix}w_{1}\\w_{2}\\\vdots \\w_{N}\end{matrix}}\right]=\left[{\begin{matrix}b_{1}\\b_{2}\\\vdots \\b_{N}\end{matrix}}\right]}
It can be shown that the interpolation matrix in the above equation is non-singular, if the points
x
i
{\displaystyle \mathbf {x} _{i}}
are distinct, and thus the weights
w
{\displaystyle w}
can be solved by simple linear algebra:
w
=
G
−
1
b
{\displaystyle \mathbf {w} =\mathbf {G} ^{-1}\mathbf {b} }
where
G
=
(
g
i
j
)
{\displaystyle G=(g_{ij})}
.
=== Function approximation ===
If the purpose is not to perform strict interpolation but instead more general function approximation or classification the optimization is somewhat more complex because there is no obvious choice for the centers. The training is typically done in two phases first fixing the width and centers and then the weights. This can be justified by considering the different nature of the non-linear hidden neurons versus the linear output neuron.
==== Training the basis function centers ====
Basis function centers can be randomly sampled among the input instances or obtained by Orthogonal Least Square Learning Algorithm or found by clustering the samples and choosing the cluster means as the centers.
The RBF widths are usually all fixed to same value which is proportional to the maximum distance between the chosen centers.
==== Pseudoinverse solution for the linear weights ====
After the centers
c
i
{\displaystyle c_{i}}
have been fixed, the weights that minimize the error at the output can be computed with a linear pseudoinverse solution:
w
=
G
+
b
{\displaystyle \mathbf {w} =\mathbf {G} ^{+}\mathbf {b} }
,
where the entries of G are the values of the radial basis functions evaluated at the points
x
i
{\displaystyle x_{i}}
:
g
j
i
=
ρ
(
|
|
x
j
−
c
i
|
|
)
{\displaystyle g_{ji}=\rho (||x_{j}-c_{i}||)}
.
The existence of this linear solution means that unlike multi-layer perceptron (MLP) networks, RBF networks have an explicit minimizer (when the centers are fixed).
==== Gradient descent training of the linear weights ====
Another possible training algorithm is gradient descent. In gradient descent training, the weights are adjusted at each time step by moving them in a direction opposite from the gradient of the objective function (thus allowing the minimum of the objective function to be found),
w
(
t
+
1
)
=
w
(
t
)
−
ν
d
d
w
H
t
(
w
)
{\displaystyle \mathbf {w} (t+1)=\mathbf {w} (t)-\nu {\frac {d}{d\mathbf {w} }}H_{t}(\mathbf {w} )}
where
ν
{\displaystyle \nu }
is a "learning parameter."
For the case of training the linear weights,
a
i
{\displaystyle a_{i}}
, the algorithm becomes
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
ρ
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}\rho {\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}
in the unnormalized case and
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
u
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}u{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}
in the normalized case.
For local-linear-architectures gradient-descent training is
e
i
j
(
t
+
1
)
=
e
i
j
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
v
i
j
(
x
(
t
)
−
c
i
)
{\displaystyle e_{ij}(t+1)=e_{ij}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}v_{ij}{\big (}\mathbf {x} (t)-\mathbf {c} _{i}{\big )}}
==== Projection operator training of the linear weights ====
For the case of training the linear weights,
a
i
{\displaystyle a_{i}}
and
e
i
j
{\displaystyle e_{ij}}
, the algorithm becomes
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
ρ
(
‖
x
(
t
)
−
c
i
‖
)
∑
i
=
1
N
ρ
2
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}{\frac {\rho {\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho ^{2}{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}}}
in the unnormalized case and
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
u
(
‖
x
(
t
)
−
c
i
‖
)
∑
i
=
1
N
u
2
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}{\frac {u{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}u^{2}{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}}}
in the normalized case and
e
i
j
(
t
+
1
)
=
e
i
j
(
t
)
+
ν
[
y
(
t
)
−
φ
(
x
(
t
)
,
w
)
]
v
i
j
(
x
(
t
)
−
c
i
)
∑
i
=
1
N
∑
j
=
1
n
v
i
j
2
(
x
(
t
)
−
c
i
)
{\displaystyle e_{ij}(t+1)=e_{ij}(t)+\nu {\big [}y(t)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}{\frac {v_{ij}{\big (}\mathbf {x} (t)-\mathbf {c} _{i}{\big )}}{\sum _{i=1}^{N}\sum _{j=1}^{n}v_{ij}^{2}{\big (}\mathbf {x} (t)-\mathbf {c} _{i}{\big )}}}}
in the local-linear case.
For one basis function, projection operator training reduces to Newton's method.
== Examples ==
=== Logistic map ===
The basic properties of radial basis functions can be illustrated with a simple mathematical map, the logistic map, which maps the unit interval onto itself. It can be used to generate a convenient prototype data stream. The logistic map can be used to explore function approximation, time series prediction, and control theory. The map originated from the field of population dynamics and became the prototype for chaotic time series. The map, in the fully chaotic regime, is given by
x
(
t
+
1
)
=
d
e
f
f
[
x
(
t
)
]
=
4
x
(
t
)
[
1
−
x
(
t
)
]
{\displaystyle x(t+1)\ {\stackrel {\mathrm {def} }{=}}\ f\left[x(t)\right]=4x(t)\left[1-x(t)\right]}
where t is a time index. The value of x at time t+1 is a parabolic function of x at time t. This equation represents the underlying geometry of the chaotic time series generated by the logistic map.
Generation of the time series from this equation is the forward problem. The examples here illustrate the inverse problem; identification of the underlying dynamics, or fundamental equation, of the logistic map from exemplars of the time series. The goal is to find an estimate
x
(
t
+
1
)
=
f
[
x
(
t
)
]
≈
φ
(
t
)
=
φ
[
x
(
t
)
]
{\displaystyle x(t+1)=f\left[x(t)\right]\approx \varphi (t)=\varphi \left[x(t)\right]}
for f.
=== Function approximation ===
==== Unnormalized radial basis functions ====
The architecture is
φ
(
x
)
=
d
e
f
∑
i
=
1
N
a
i
ρ
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi (\mathbf {x} )\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}a_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
where
ρ
(
‖
x
−
c
i
‖
)
=
exp
[
−
β
i
‖
x
−
c
i
‖
2
]
=
exp
[
−
β
i
(
x
(
t
)
−
c
i
)
2
]
{\displaystyle \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}=\exp \left[-\beta _{i}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert ^{2}\right]=\exp \left[-\beta _{i}\left(x(t)-c_{i}\right)^{2}\right]}
.
Since the input is a scalar rather than a vector, the input dimension is one. We choose the number of basis functions as N=5 and the size of the training set to be 100 exemplars generated by the chaotic time series. The weight
β
{\displaystyle \beta }
is taken to be a constant equal to 5. The weights
c
i
{\displaystyle c_{i}}
are five exemplars from the time series. The weights
a
i
{\displaystyle a_{i}}
are trained with projection operator training:
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
x
(
t
+
1
)
−
φ
(
x
(
t
)
,
w
)
]
ρ
(
‖
x
(
t
)
−
c
i
‖
)
∑
i
=
1
N
ρ
2
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}x(t+1)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}{\frac {\rho {\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho ^{2}{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}}}
where the learning rate
ν
{\displaystyle \nu }
is taken to be 0.3. The training is performed with one pass through the 100 training points. The rms error is 0.15.
==== Normalized radial basis functions ====
The normalized RBF architecture is
φ
(
x
)
=
d
e
f
∑
i
=
1
N
a
i
ρ
(
‖
x
−
c
i
‖
)
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
=
∑
i
=
1
N
a
i
u
(
‖
x
−
c
i
‖
)
{\displaystyle \varphi (\mathbf {x} )\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\sum _{i=1}^{N}a_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}a_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}
where
u
(
‖
x
−
c
i
‖
)
=
d
e
f
ρ
(
‖
x
−
c
i
‖
)
∑
i
=
1
N
ρ
(
‖
x
−
c
i
‖
)
{\displaystyle u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}}
.
Again:
ρ
(
‖
x
−
c
i
‖
)
=
exp
[
−
β
‖
x
−
c
i
‖
2
]
=
exp
[
−
β
(
x
(
t
)
−
c
i
)
2
]
{\displaystyle \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}=\exp \left[-\beta \left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert ^{2}\right]=\exp \left[-\beta \left(x(t)-c_{i}\right)^{2}\right]}
.
Again, we choose the number of basis functions as five and the size of the training set to be 100 exemplars generated by the chaotic time series. The weight
β
{\displaystyle \beta }
is taken to be a constant equal to 6. The weights
c
i
{\displaystyle c_{i}}
are five exemplars from the time series. The weights
a
i
{\displaystyle a_{i}}
are trained with projection operator training:
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
[
x
(
t
+
1
)
−
φ
(
x
(
t
)
,
w
)
]
u
(
‖
x
(
t
)
−
c
i
‖
)
∑
i
=
1
N
u
2
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu {\big [}x(t+1)-\varphi {\big (}\mathbf {x} (t),\mathbf {w} {\big )}{\big ]}{\frac {u{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}u^{2}{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}}}
where the learning rate
ν
{\displaystyle \nu }
is again taken to be 0.3. The training is performed with one pass through the 100 training points. The rms error on a test set of 100 exemplars is 0.084, smaller than the unnormalized error. Normalization yields accuracy improvement. Typically accuracy with normalized basis functions increases even more over unnormalized functions as input dimensionality increases.
=== Time series prediction ===
Once the underlying geometry of the time series is estimated as in the previous examples, a prediction for the time series can be made by iteration:
φ
(
0
)
=
x
(
1
)
{\displaystyle \varphi (0)=x(1)}
x
(
t
)
≈
φ
(
t
−
1
)
{\displaystyle {x}(t)\approx \varphi (t-1)}
x
(
t
+
1
)
≈
φ
(
t
)
=
φ
[
φ
(
t
−
1
)
]
{\displaystyle {x}(t+1)\approx \varphi (t)=\varphi [\varphi (t-1)]}
.
A comparison of the actual and estimated time series is displayed in the figure. The estimated times series starts out at time zero with an exact knowledge of x(0). It then uses the estimate of the dynamics to update the time series estimate for several time steps.
Note that the estimate is accurate for only a few time steps. This is a general characteristic of chaotic time series. This is a property of the sensitive dependence on initial conditions common to chaotic time series. A small initial error is amplified with time. A measure of the divergence of time series with nearly identical initial conditions is known as the Lyapunov exponent.
=== Control of a chaotic time series ===
We assume the output of the logistic map can be manipulated through a control parameter
c
[
x
(
t
)
,
t
]
{\displaystyle c[x(t),t]}
such that
x
(
t
+
1
)
=
4
x
(
t
)
[
1
−
x
(
t
)
]
+
c
[
x
(
t
)
,
t
]
{\displaystyle {x}_{}^{}(t+1)=4x(t)[1-x(t)]+c[x(t),t]}
.
The goal is to choose the control parameter in such a way as to drive the time series to a desired output
d
(
t
)
{\displaystyle d(t)}
. This can be done if we choose the control parameter to be
c
[
x
(
t
)
,
t
]
=
d
e
f
−
φ
[
x
(
t
)
]
+
d
(
t
+
1
)
{\displaystyle c_{}^{}[x(t),t]\ {\stackrel {\mathrm {def} }{=}}\ -\varphi [x(t)]+d(t+1)}
where
y
[
x
(
t
)
]
≈
f
[
x
(
t
)
]
=
x
(
t
+
1
)
−
c
[
x
(
t
)
,
t
]
{\displaystyle y[x(t)]\approx f[x(t)]=x(t+1)-c[x(t),t]}
is an approximation to the underlying natural dynamics of the system.
The learning algorithm is given by
a
i
(
t
+
1
)
=
a
i
(
t
)
+
ν
ε
u
(
‖
x
(
t
)
−
c
i
‖
)
∑
i
=
1
N
u
2
(
‖
x
(
t
)
−
c
i
‖
)
{\displaystyle a_{i}(t+1)=a_{i}(t)+\nu \varepsilon {\frac {u{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}u^{2}{\big (}\left\Vert \mathbf {x} (t)-\mathbf {c} _{i}\right\Vert {\big )}}}}
where
ε
=
d
e
f
f
[
x
(
t
)
]
−
φ
[
x
(
t
)
]
=
x
(
t
+
1
)
−
c
[
x
(
t
)
,
t
]
−
φ
[
x
(
t
)
]
=
x
(
t
+
1
)
−
d
(
t
+
1
)
{\displaystyle \varepsilon \ {\stackrel {\mathrm {def} }{=}}\ f[x(t)]-\varphi [x(t)]=x(t+1)-c[x(t),t]-\varphi [x(t)]=x(t+1)-d(t+1)}
.
== See also ==
Radial basis function kernel
instance-based learning
In Situ Adaptive Tabulation
Predictive analytics
Chaos theory
Hierarchical RBF
Cerebellar model articulation controller
Instantaneously trained neural networks
Support vector machine
== References ==
== Further reading ==
J. Moody and C. J. Darken, "Fast learning in networks of locally tuned processing units," Neural Computation, 1, 281-294 (1989). Also see Radial basis function networks according to Moody and Darken
T. Poggio and F. Girosi, "Networks for approximation and learning," Proc. IEEE 78(9), 1484-1487 (1990).
Roger D. Jones, Y. C. Lee, C. W. Barnes, G. W. Flake, K. Lee, P. S. Lewis, and S. Qian, Function approximation and time series prediction with neural networks, Proceedings of the International Joint Conference on Neural Networks, June 17–21, p. I-649 (1990).
Martin D. Buhmann (2003). Radial Basis Functions: Theory and Implementations. Cambridge University. ISBN 0-521-63338-9.
Yee, Paul V. & Haykin, Simon (2001). Regularized Radial Basis Function Networks: Theory and Applications. John Wiley. ISBN 0-471-35349-3.
Davies, John R.; Coggeshall, Stephen V.; Jones, Roger D.; Schutzer, Daniel (1995). "Intelligent Security Systems". In Freedman, Roy S.; Flein, Robert A.; Lederman, Jess (eds.). Artificial Intelligence in the Capital Markets. Chicago: Irwin. ISBN 1-55738-811-3.
Simon Haykin (1999). Neural Networks: A Comprehensive Foundation (2nd ed.). Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-908385-5.
S. Chen, C. F. N. Cowan, and P. M. Grant, "Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks", IEEE Transactions on Neural Networks, Vol 2, No 2 (Mar) 1991. | Wikipedia/Radial_basis_function_network |
The term hybrid neural network can have two meanings:
Biological neural networks interacting with artificial neuronal models, and
Artificial neural networks with a symbolic part (or, conversely, symbolic computations with a connectionist part).
As for the first meaning, the artificial neurons and synapses in hybrid networks can be digital or analog. For the digital variant voltage clamps are used to monitor the membrane potential of neurons, to computationally simulate artificial neurons and synapses and to stimulate biological neurons by inducing synaptic. For the analog variant, specially designed electronic circuits connect to a network of living neurons through electrodes.
As for the second meaning, incorporating elements of symbolic computation and artificial neural networks into one model was an attempt to combine the advantages of both paradigms while avoiding the shortcomings. Symbolic representations have advantages with respect to explicit, direct control, fast initial coding, dynamic variable binding and knowledge abstraction. Representations of artificial neural networks, on the other hand, show advantages for biological plausibility, learning, robustness (fault-tolerant processing and graceful decay), and generalization to similar input. Since the early 1990s many attempts have been made to reconcile the two approaches.
== References ==
Biological and artificial neurons
Connecting symbolic and connectionist approaches Archived 2006-01-31 at the Wayback Machine
== See also ==
Connectionism vs. Computationalism debate | Wikipedia/Hybrid_neural_network |
The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory.
The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 (hence the name), but has been extensively used in reinforcement learning and also as for automated classification in the machine learning community. The CMAC is an extension of the perceptron model. It computes a function for
n
{\displaystyle n}
input dimensions. The input space is divided up into hyper-rectangles, each of which is associated with a memory cell. The contents of the memory cells are the weights, which are adjusted during training. Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point.
A change of value of the input point results in a change in the set of activated hyper-rectangles, and therefore a change in the set of memory cells participating in the CMAC output. The CMAC output is therefore stored in a distributed fashion, such that the output corresponding to any point in input space is derived from the value stored in a number of memory cells (hence the name associative memory). This provides generalisation.
== Building blocks ==
In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation.
The CMAC is trained by presenting pairs of input points and output values, and adjusting the weights in the activated cells by a proportion of the error observed at the output. This simple training algorithm has a proof of convergence.
It is normal to add a kernel function to the hyper-rectangle, so that points falling towards the edge of a hyper-rectangle have a smaller activation than those falling near the centre.
One of the major problems cited in practical use of CMAC is the memory size required, which is directly related to the number of cells used. This is usually ameliorated by using a hash function, and only providing memory storage for the actual cells that are activated by inputs.
== One-step convergent algorithm ==
Initially least mean square (LMS) method is employed to update the weights of CMAC. The convergence of using LMS for training CMAC is sensitive to the learning rate and could lead to divergence. In 2004, a recursive least squares (RLS) algorithm was introduced to train CMAC online. It does not need to tune a learning rate. Its convergence has been proved theoretically and can be guaranteed to converge in one step. The computational complexity of this RLS algorithm is O(N3).
== Hardware implementation infrastructure ==
Based on QR decomposition, an algorithm (QRLS) has been further simplified to have an O(N) complexity. Consequently, this reduces memory usage and time cost significantly. A parallel pipeline array structure on implementing this algorithm has been introduced.
Overall by utilizing QRLS algorithm, the CMAC neural network convergence can be guaranteed, and the weights of the nodes can be updated using one step of training. Its parallel pipeline array structure offers its great potential to be implemented in hardware for large-scale industry usage.
== Continuous CMAC ==
Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions.
== Deep CMAC ==
In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC.
== Summary ==
== See also ==
== References ==
== Further reading ==
Albus, J.S. (1971). "Theory of Cerebellar Function". In: Mathematical Biosciences, Volume 10, Numbers 1/2, February 1971, pgs. 25–61
Albus, J.S. (1975). "New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)". In: Transactions of the ASME Journal of Dynamic Systems, Measurement, and Control, September 1975, pgs. 220 – 227
Albus, J.S. (1979). "Mechanisms of Planning and Problem Solving in the Brain". In: Mathematical Biosciences 45, pgs 247–293, 1979.
Iwan, L., and Stengel, R., "The Application of Neural Networks to Fuel Processors for Fuel Cells" In IEEE Transactions on Vehicular Technology, Vol. 50 (1), pp. 125-143, 2001.
Tsao, Y. (2018). "Adaptive Noise Cancellation Using Deep Cerebellar Model Articulation Controller". In: IEEE Access 6, April 2018, pgs 37395-37402.
== External links ==
Blog on Cerebellar Model Articulation Controller (CMAC) by Ting Qin. More details on the one-step convergent algorithm, code development, etc. | Wikipedia/Cerebellar_model_articulation_controller |
Time delay neural network (TDNN) is a multilayer artificial neural network architecture whose purpose is to 1) classify patterns with shift-invariance, and 2) model context at each layer of the network. It is essentially a 1-d convolutional neural network (CNN).
Shift-invariant classification means that the classifier does not require explicit segmentation prior to classification. For the classification of a temporal pattern (such as speech), the TDNN thus avoids having to determine the beginning and end points of sounds before classifying them.
For contextual modelling in a TDNN, each neural unit at each layer receives input not only from activations/features at the layer below, but from a pattern of unit output and its context. For time signals each unit receives as input the activation patterns over time from units below. Applied to two-dimensional classification (images, time-frequency patterns), the TDNN can be trained with shift-invariance in the coordinate space and avoids precise segmentation in the coordinate space.
== History ==
The TDNN was introduced in the late 1980s and applied to a task of phoneme classification for automatic speech recognition in speech signals where the automatic determination of precise segments or feature boundaries was difficult or impossible. Because the TDNN recognizes phonemes and their underlying acoustic/phonetic features, independent of position in time, it improved performance over static classification. It was also applied to two-dimensional signals (time-frequency patterns in speech, and coordinate space pattern in OCR).
Kunihiko Fukushima published the neocognitron in 1980. Max pooling appears in a 1982 publication on the neocognitron and was in the 1989 publication in LeNet-5.
In 1990, Yamaguchi et al. used max pooling in TDNNs in order to realize a speaker independent isolated word recognition system.
== Overview ==
=== Architecture ===
In modern language, the design of TDNN is a 1D convolutional neural network, where the direction of convolution is across the dimension of time. In the original design, there are exactly 3 layers.
The input to the network is a continuous speech signal, preprocessed into a 2D array (a mel scale spectrogram). One dimension is time at 10 ms per frame, and the other dimension is frequency. The time dimension can be arbitrarily long, but the frequency dimension was only 16-long. In the original experiment, they only considered very short speech signals pronouncing single words like "baa", "daa", "gaa". Because of this, the speech signals could be very short, indeed, only 15 frames long (150 ms in time).
In detail, they processed a voice signal as follows:
Input speech is sampled at 12 kHz, Hamming-windowed.
Its FFT is computed every 5 ms.
The mel scale coefficients are computed from the power spectrum by taking log energies in each mel scale energy band.
Adjacent coefficients in time are soothed over, resulting in one frame every 10 ms.
For each signal, a human manually detect the onset of the vowel, and the entire speech signal is cut off except 7 frames before and 7 frames after, leaving just 15 frames in total, centered at the onset of the vowel.
The coefficients are normalized by subtracting the mean, then scaling, so that the signals fall between -1 and +1.
The first layer of the TDNN is a 1D convolutional layer. The layer contains 8 kernels of shape
3
×
16
{\displaystyle 3\times 16}
. It outputs a tensor of shape
8
×
13
{\displaystyle 8\times 13}
.
The second layer of the TDNN is a 1D convolutional layer. The layer contains 3 kernels of shape
5
×
8
{\displaystyle 5\times 8}
. It outputs a tensor of shape
3
×
9
{\displaystyle 3\times 9}
.
The third layer of the TDNN is not a convolutional layer. Instead, it is simply a fixed layer with 3 neurons. Let the output from the second layer be
x
i
,
j
{\displaystyle x_{i,j}}
where
i
∈
1
:
3
{\displaystyle i\in 1:3}
and
j
∈
1
:
9
{\displaystyle j\in 1:9}
. The
i
{\displaystyle i}
-th neuron in the third layer computes
σ
(
∑
j
∈
1
:
9
x
i
,
j
)
{\displaystyle \sigma (\sum _{j\in 1:9}x_{i,j})}
, where
σ
{\displaystyle \sigma }
is the sigmoid function. Essentially, it can be thought of as a convolution layer with 3 kernels of shape
1
×
9
{\displaystyle 1\times 9}
.
It was trained on ~800 samples for 20000--50000 backpropagation steps. Each steps was computed in a batch over the entire training dataset, i.e. not stochastic. It required the use of an Alliant supercomputer with 4 processors.
=== Example ===
In the case of a speech signal, inputs are spectral coefficients over time.
In order to learn critical acoustic-phonetic features (for example formant transitions, bursts, frication, etc.) without first requiring precise localization, the TDNN is trained time-shift-invariantly. Time-shift invariance is achieved through weight sharing across time during training: Time shifted copies of the TDNN are made over the input range (from left to right in Fig.1). Backpropagation is then performed from an overall classification target vector (see TDNN diagram, three phoneme class targets (/b/, /d/, /g/) are shown in the output layer), resulting in gradients that will generally vary for each of the time-shifted network copies. Since such time-shifted networks are only copies, however, the position dependence is removed by weight sharing. In this example, this is done by averaging the gradients from each time-shifted copy before performing the weight update. In speech, time-shift invariant training was shown to learn weight matrices that are independent of precise positioning of the input. The weight matrices could also be shown to detect important acoustic-phonetic features that are known to be important for human speech perception, such as formant transitions, bursts, etc. TDNNs could also be combined or grown by way of pre-training.
=== Implementation ===
The precise architecture of TDNNs (time-delays, number of layers) is mostly determined by the designer depending on the classification problem and the most useful context sizes. The delays or context windows are chosen specific to each application. Work has also been done to create adaptable time-delay TDNNs where this manual tuning is eliminated.
=== State of the art ===
TDNN-based phoneme recognizers compared favourably in early comparisons with HMM-based phone models. Modern deep TDNN architectures include many more hidden layers and sub-sample or pool connections over broader contexts at higher layers. They achieve up to 50% word error reduction over GMM-based acoustic models. While the different layers of TDNNs are intended to learn features of increasing context width, they do model local contexts. When longer-distance relationships and pattern sequences have to be processed, learning states and state-sequences is important and TDNNs can be combined with other modelling techniques.
== Applications ==
=== Speech recognition ===
TDNNs used to solve problems in speech recognition that were introduced in 1989 and initially focused on shift-invariant phoneme recognition. Speech lends itself nicely to TDNNs as spoken sounds are rarely of uniform length and precise segmentation is difficult or impossible. By scanning a sound over past and future, the TDNN is able to construct a model for the key elements of that sound in a time-shift invariant manner. This is particularly useful as sounds are smeared out through reverberation. Large phonetic TDNNs can be constructed modularly through pre-training and combining smaller networks.
=== Large vocabulary speech recognition ===
Large vocabulary speech recognition requires recognizing sequences of phonemes that make up words subject to the constraints of a large pronunciation vocabulary. Integration of TDNNs into large vocabulary speech recognizers is possible by introducing state transitions and search between phonemes that make up a word. The resulting Multi-State Time-Delay Neural Network (MS-TDNN) can be trained discriminative from the word level, thereby optimizing the entire arrangement toward word recognition instead of phoneme classification.
=== Speaker independence ===
Two-dimensional variants of the TDNNs were proposed for speaker independence. Here, shift-invariance is applied to the time as well as to the frequency axis in order to learn hidden features that are independent of precise location in time and in frequency (the latter being due to speaker variability).
=== Reverberation ===
One of the persistent problems in speech recognition is recognizing speech when it is corrupted by echo and reverberation (as is the case in large rooms and distant microphones). Reverberation can be viewed as corrupting speech with delayed versions of itself. In general, it is difficult, however, to de-reverberate a signal as the impulse response function (and thus the convolutional noise experienced by the signal) is not known for any arbitrary space. The TDNN was shown to be effective to recognize speech robustly despite different levels of reverberation.
=== Lip-reading – audio-visual speech ===
TDNNs were also successfully used in early demonstrations of audio-visual speech, where the sounds of speech are complemented by visually reading lip movement. Here, TDNN-based recognizers used visual and acoustic features jointly to achieve improved recognition accuracy, particularly in the presence of noise, where complementary information from an alternate modality could be fused nicely in a neural net.
=== Handwriting recognition ===
TDNNs have been used effectively in compact and high-performance handwriting recognition systems. Shift-invariance was also adapted to spatial patterns (x/y-axes) in image offline handwriting recognition.
=== Video analysis ===
Video has a temporal dimension that makes a TDNN an ideal solution to analysing motion patterns. An example of this analysis is a combination of vehicle detection and recognizing pedestrians. When examining videos, subsequent images are fed into the TDNN as input where each image is the next frame in the video. The strength of the TDNN comes from its ability to examine objects shifted in time forward and backward to define an object detectable as the time is altered. If an object can be recognized in this manner, an application can plan on that object to be found in the future and perform an optimal action.
=== Image recognition ===
Two-dimensional TDNNs were later applied to other image-recognition tasks under the name of "Convolutional Neural Networks", where shift-invariant training is applied to the x/y axes of an image.
=== Common libraries ===
TDNNs can be implemented in virtually all machine-learning frameworks using one-dimensional convolutional neural networks, due to the equivalence of the methods.
Matlab: The neural network toolbox has explicit functionality designed to produce a time delay neural network give the step size of time delays and an optional training function. The default training algorithm is a Supervised Learning back-propagation algorithm that updates filter weights based on the Levenberg-Marquardt optimizations. The function is timedelaynet(delays, hidden_layers, train_fnc) and returns a time-delay neural network architecture that a user can train and provide inputs to.
The Kaldi ASR Toolkit has an implementation of TDNNs with several optimizations for speech recognition.
== See also ==
Convolutional neural network – a convolutional neural net where the convolution is performed along the time axis of the data is very similar to a TDNN.
Recurrent neural networks – a recurrent neural network also handles temporal data, albeit in a different manner. Instead of a time-varied input, RNNs maintain internal hidden layers to keep track of past (and in the case of Bi-directional RNNs, future) inputs.
== References == | Wikipedia/Time_delay_neural_network |
In the mathematical theory of artificial neural networks, universal approximation theorems are theorems of the following form: Given a family of neural networks, for each function
f
{\displaystyle f}
from a certain function space, there exists a sequence of neural networks
ϕ
1
,
ϕ
2
,
…
{\displaystyle \phi _{1},\phi _{2},\dots }
from the family, such that
ϕ
n
→
f
{\displaystyle \phi _{n}\to f}
according to some criterion. That is, the family of neural networks is dense in the function space.
The most popular version states that feedforward networks with non-polynomial activation functions are dense in the space of continuous functions between two Euclidean spaces, with respect to the compact convergence topology.
Universal approximation theorems are existence theorems: They simply state that there exists such a sequence
ϕ
1
,
ϕ
2
,
⋯
→
f
{\displaystyle \phi _{1},\phi _{2},\dots \to f}
, and do not provide any way to actually find such a sequence. They also do not guarantee any method, such as backpropagation, might actually find such a sequence. Any method for searching the space of neural networks, including backpropagation, might find a converging sequence, or not (i.e. the backpropagation might get stuck in a local optimum).
Universal approximation theorems are limit theorems: They simply state that for any
f
{\displaystyle f}
and a criterion of closeness
ϵ
>
0
{\displaystyle \epsilon >0}
, if there are enough neurons in a neural network, then there exists a neural network with that many neurons that does approximate
f
{\displaystyle f}
to within
ϵ
{\displaystyle \epsilon }
. There is no guarantee that any finite size, say, 10000 neurons, is enough.
== Setup ==
Artificial neural networks are combinations of multiple simple mathematical functions that implement more complicated functions from (typically) real-valued vectors to real-valued vectors. The spaces of multivariate functions that can be implemented by a network are determined by the structure of the network, the set of simple functions, and its multiplicative parameters. A great deal of theoretical work has gone into characterizing these function spaces.
Most universal approximation theorems are in one of two classes. The first quantifies the approximation capabilities of neural networks with an arbitrary number of artificial neurons ("arbitrary width" case) and the second focuses on the case with an arbitrary number of hidden layers, each containing a limited number of artificial neurons ("arbitrary depth" case). In addition to these two classes, there are also universal approximation theorems for neural networks with bounded number of hidden layers and a limited number of neurons in each layer ("bounded depth and bounded width" case).
== History ==
=== Arbitrary width ===
The first examples were the arbitrary width case. George Cybenko in 1989 proved it for sigmoid activation functions. Kurt Hornik, Maxwell Stinchcombe, and Halbert White showed in 1989 that multilayer feed-forward networks with as few as one hidden layer are universal approximators. Hornik also showed in 1991 that it is not the specific choice of the activation function but rather the multilayer feed-forward architecture itself that gives neural networks the potential of being universal approximators. Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.
=== Arbitrary depth ===
The arbitrary depth case was also studied by a number of authors such as Gustaf Gripenberg in 2003, Dmitry Yarotsky, Zhou Lu et al in 2017, Boris Hanin and Mark Sellke in 2018 who focused on neural networks with ReLU activation function. In 2020, Patrick Kidger and Terry Lyons extended those results to neural networks with general activation functions such, e.g. tanh or GeLU.
One special case of arbitrary depth is that each composition component comes from a finite set of mappings. In 2024, Cai constructed a finite set of mappings, named a vocabulary, such that any continuous function can be approximated by compositing a sequence from the vocabulary. This is similar to the concept of compositionality in linguistics, which is the idea that a finite vocabulary of basic elements can be combined via grammar to express an infinite range of meanings.
=== Bounded depth and bounded width ===
The bounded depth and bounded width case was first studied by Maiorov and Pinkus in 1999. They showed that there exists an analytic sigmoidal activation function such that two hidden layer neural networks with bounded number of units in hidden layers are universal approximators.
In 2018, Guliyev and Ismailov constructed a smooth sigmoidal activation function providing universal approximation property for two hidden layer feedforward neural networks with less units in hidden layers. In 2018, they also constructed single hidden layer networks with bounded width that are still universal approximators for univariate functions. However, this does not apply for multivariable functions.
In 2022, Shen et al. obtained precise quantitative information on the depth and width required to approximate a target function by deep and wide ReLU neural networks.
=== Quantitative bounds ===
The question of minimal possible width for universality was first studied in 2021, Park et al obtained the minimum width required for the universal approximation of Lp functions using feed-forward neural networks with ReLU as activation functions. Similar results that can be directly applied to residual neural networks were also obtained in the same year by Paulo Tabuada and Bahman Gharesifard using control-theoretic arguments. In 2023, Cai obtained the optimal minimum width bound for the universal approximation.
For the arbitrary depth case, Leonie Papon and Anastasis Kratsios derived explicit depth estimates depending on the regularity of the target function and of the activation function.
=== Kolmogorov network ===
The Kolmogorov–Arnold representation theorem is similar in spirit. Indeed, certain neural network families can directly apply the Kolmogorov–Arnold theorem to yield a universal approximation theorem. Robert Hecht-Nielsen showed that a three-layer neural network can approximate any continuous multivariate function. This was extended to the discontinuous case by Vugar Ismailov. In 2024, Ziming Liu and co-authors showed a practical application.
=== Reservoir computing and quantum reservoir computing ===
In reservoir computing a sparse recurrent neural network with fixed weights equipped of fading memory and echo state property is followed by a trainable output layer. Its universality has been demonstrated separately for what concerns networks of rate neurons and spiking neurons, respectively. In 2024, the framework has been generalized and extended to quantum reservoirs where the reservoir is based on qubits defined over Hilbert spaces.
=== Variants ===
Discontinuous activation functions, noncompact domains, certifiable networks,
random neural networks, and alternative network architectures and topologies.
The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks. For input dimension dx and output dimension dy the minimum width required for the universal approximation of the Lp functions is exactly max{dx + 1, dy} (for a ReLU network). More generally this also holds if both ReLU and a threshold activation function are used.
Universal function approximation on graphs (or rather on graph isomorphism classes) by popular graph convolutional neural networks (GCNs or GNNs) can be made as discriminative as the Weisfeiler–Leman graph isomorphism test. In 2020, a universal approximation theorem result was established by Brüel-Gabrielsson, showing that graph representation with certain injective properties is sufficient for universal function approximation on bounded graphs and restricted universal function approximation on unbounded graphs, with an accompanying
O
(
|
V
|
⋅
|
E
|
)
{\displaystyle {\mathcal {O}}(\left|V\right|\cdot \left|E\right|)}
-runtime method that performed at state of the art on a collection of benchmarks (where
V
{\displaystyle V}
and
E
{\displaystyle E}
are the sets of nodes and edges of the graph respectively).
There are also a variety of results between non-Euclidean spaces and other commonly used architectures and, more generally, algorithmically generated sets of functions, such as the convolutional neural network (CNN) architecture, radial basis functions, or neural networks with specific properties.
== Arbitrary-width case ==
A spate of papers in the 1980s—1990s, from George Cybenko and Kurt Hornik etc, established several universal approximation theorems for arbitrary width and bounded depth. See for reviews. The following is the most often quoted:
Also, certain non-continuous activation functions can be used to approximate a sigmoid function, which then allows the above theorem to apply to those functions. For example, the step function works. In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions.
Such an
f
{\displaystyle f}
can also be approximated by a network of greater depth by using the same construction for the first layer and approximating the identity function with later layers.
The above proof has not specified how one might use a ramp function to approximate arbitrary functions in
C
0
(
R
n
,
R
)
{\displaystyle C_{0}(\mathbb {R} ^{n},\mathbb {R} )}
. A sketch of the proof is that one can first construct flat bump functions, intersect them to obtain spherical bump functions that approximate the Dirac delta function, then use those to approximate arbitrary functions in
C
0
(
R
n
,
R
)
{\displaystyle C_{0}(\mathbb {R} ^{n},\mathbb {R} )}
. The original proofs, such as the one by Cybenko, use methods from functional analysis, including the Hahn-Banach and Riesz–Markov–Kakutani representation theorems. Cybenko first published the theorem in a technical report in 1988, then as a paper in 1989.
Notice also that the neural network is only required to approximate within a compact set
K
{\displaystyle K}
. The proof does not describe how the function would be extrapolated outside of the region.
The problem with polynomials may be removed by allowing the outputs of the hidden layers to be multiplied together (the "pi-sigma networks"), yielding the generalization:
== Arbitrary-depth case ==
The "dual" versions of the theorem consider networks of bounded width and arbitrary depth. A variant of the universal approximation theorem was proved for the arbitrary depth case by Zhou Lu et al. in 2017. They showed that networks of width n + 4 with ReLU activation functions can approximate any Lebesgue-integrable function on n-dimensional input space with respect to
L
1
{\displaystyle L^{1}}
distance if network depth is allowed to grow. It was also shown that if the width was less than or equal to n, this general expressive power to approximate any Lebesgue integrable function was lost. In the same paper it was shown that ReLU networks with width n + 1 were sufficient to approximate any continuous function of n-dimensional input variables. The following refinement, specifies the optimal minimum width for which such an approximation is possible and is due to.
Together, the central result of yields the following universal approximation theorem for networks with bounded width (see also for the first result of this kind).
Certain necessary conditions for the bounded width, arbitrary depth case have been established, but there is still a gap between the known sufficient and necessary conditions.
== Bounded depth and bounded width case ==
The first result on approximation capabilities of neural networks with bounded number of layers, each containing a limited number of artificial neurons was obtained by Maiorov and Pinkus. Their remarkable result revealed that such networks can be universal approximators and for achieving this property two hidden layers are enough.
This is an existence result. It says that activation functions providing universal approximation property for bounded depth bounded width networks exist. Using certain algorithmic and computer programming techniques, Guliyev and Ismailov efficiently constructed such activation functions depending on a numerical parameter. The developed algorithm allows one to compute the activation functions at any point of the real axis instantly. For the algorithm and the corresponding computer code see. The theoretical result can be formulated as follows.
Here “
σ
:
R
→
R
{\displaystyle \sigma \colon \mathbb {R} \to \mathbb {R} }
is
λ
{\displaystyle \lambda }
-strictly increasing on some set
X
{\displaystyle X}
” means that there exists a strictly increasing function
u
:
X
→
R
{\displaystyle u\colon X\to \mathbb {R} }
such that
|
σ
(
x
)
−
u
(
x
)
|
≤
λ
{\displaystyle |\sigma (x)-u(x)|\leq \lambda }
for all
x
∈
X
{\displaystyle x\in X}
. Clearly, a
λ
{\displaystyle \lambda }
-increasing function behaves like a usual increasing function as
λ
{\displaystyle \lambda }
gets small.
In the "depth-width" terminology, the above theorem says that for certain activation functions depth-
2
{\displaystyle 2}
width-
2
{\displaystyle 2}
networks are universal approximators for univariate functions and depth-
3
{\displaystyle 3}
width-
(
2
d
+
2
)
{\displaystyle (2d+2)}
networks are universal approximators for
d
{\displaystyle d}
-variable functions (
d
>
1
{\displaystyle d>1}
).
== See also ==
Kolmogorov–Arnold representation theorem
Representer theorem
No free lunch theorem
Stone–Weierstrass theorem
Fourier series
== References == | Wikipedia/Universal_approximation_theorem |
In computer strategy games, for example in shogi and chess, an efficiently updatable neural network (NNUE, a Japanese wordplay on Nue, sometimes stylised as ƎUИИ) is a neural network-based evaluation function whose inputs are piece-square tables, or variants thereof like the king-piece-square table. NNUE is used primarily for the leaf nodes of the alpha–beta tree.
NNUE was invented by Yu Nasu and introduced to computer shogi in 2018. On 6 August 2020, NNUE was for the first time ported to a chess engine, Stockfish 12. Since 2021, many of the top rated classical chess engines such as Komodo Dragon have an NNUE implementation to remain competitive.
NNUE runs efficiently on central processing units (CPU) without a requirement for a graphics processing unit (GPU). In contrast, deep neural network-based chess engines such as Leela Chess Zero require a GPU.
The neural network used for the original 2018 computer shogi implementation consists of four weight layers: W1 (16-bit integers) and W2, W3 and W4 (8-bit). It has 4 fully-connected layers, ReLU activation functions, and outputs a single number, being the score of the board.
W1 encoded the king's position and therefore this layer needed only to be re-evaluated once the king moved. It used incremental computation and single instruction multiple data (SIMD) techniques along with appropriate intrinsic instructions.
== See also ==
elmo (shogi engine)
Stockfish chess engine - The chapter about NNUE features a visualization of NNUE.
List of chess software
== References ==
== External links ==
NNUE on the Chess Programming Wiki.
NNUE evaluation functions for computer shogi on github.com | Wikipedia/Efficiently_updatable_neural_network |
The softmax function, also known as softargmax: 184 or normalized exponential function,: 198 converts a tuple of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression. The softmax function is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes.
== Definition ==
The softmax function takes as input a tuple z of K real numbers, and normalizes it into a probability distribution consisting of K probabilities proportional to the exponentials of the input numbers. That is, prior to applying softmax, some tuple components could be negative, or greater than one; and might not sum to 1; but after applying softmax, each component will be in the interval
(
0
,
1
)
{\displaystyle (0,1)}
, and the components will add up to 1, so that they can be interpreted as probabilities. Furthermore, the larger input components will correspond to larger probabilities.
Formally, the standard (unit) softmax function
σ
:
R
K
→
(
0
,
1
)
K
{\displaystyle \sigma \colon \mathbb {R} ^{K}\to (0,1)^{K}}
, where
K
>
1
{\displaystyle K>1}
, takes a tuple
z
=
(
z
1
,
…
,
z
K
)
∈
R
K
{\displaystyle \mathbf {z} =(z_{1},\dotsc ,z_{K})\in \mathbb {R} ^{K}}
and computes each component of vector
σ
(
z
)
∈
(
0
,
1
)
K
{\displaystyle \sigma (\mathbf {z} )\in (0,1)^{K}}
with
σ
(
z
)
i
=
e
z
i
∑
j
=
1
K
e
z
j
.
{\displaystyle \sigma (\mathbf {z} )_{i}={\frac {e^{z_{i}}}{\sum _{j=1}^{K}e^{z_{j}}}}\,.}
In words, the softmax applies the standard exponential function to each element
z
i
{\displaystyle z_{i}}
of the input tuple
z
{\displaystyle \mathbf {z} }
(consisting of
K
{\displaystyle K}
real numbers), and normalizes these values by dividing by the sum of all these exponentials. The normalization ensures that the sum of the components of the output vector
σ
(
z
)
{\displaystyle \sigma (\mathbf {z} )}
is 1. The term "softmax" derives from the amplifying effects of the exponential on any maxima in the input tuple. For example, the standard softmax of
(
1
,
2
,
8
)
{\displaystyle (1,2,8)}
is approximately
(
0.001
,
0.002
,
0.997
)
{\displaystyle (0.001,0.002,0.997)}
, which amounts to assigning almost all of the total unit weight in the result to the position of the tuple's maximal element (of 8).
In general, instead of e a different base b > 0 can be used. As above, if b > 1 then larger input components will result in larger output probabilities, and increasing the value of b will create probability distributions that are more concentrated around the positions of the largest input values. Conversely, if 0 < b < 1 then smaller input components will result in larger output probabilities, and decreasing the value of b will create probability distributions that are more concentrated around the positions of the smallest input values. Writing
b
=
e
β
{\displaystyle b=e^{\beta }}
or
b
=
e
−
β
{\displaystyle b=e^{-\beta }}
(for real β) yields the expressions:
σ
(
z
)
i
=
e
β
z
i
∑
j
=
1
K
e
β
z
j
or
σ
(
z
)
i
=
e
−
β
z
i
∑
j
=
1
K
e
−
β
z
j
for
i
=
1
,
…
,
K
.
{\displaystyle \sigma (\mathbf {z} )_{i}={\frac {e^{\beta z_{i}}}{\sum _{j=1}^{K}e^{\beta z_{j}}}}{\text{ or }}\sigma (\mathbf {z} )_{i}={\frac {e^{-\beta z_{i}}}{\sum _{j=1}^{K}e^{-\beta z_{j}}}}{\text{ for }}i=1,\dotsc ,K.}
A value proportional to the reciprocal of β is sometimes referred to as the temperature:
β
=
1
/
k
T
{\textstyle \beta =1/kT}
, where k is typically 1 or the Boltzmann constant and T is the temperature. A higher temperature results in a more uniform output distribution (i.e. with higher entropy; it is "more random"), while a lower temperature results in a sharper output distribution, with one value dominating.
In some fields, the base is fixed, corresponding to a fixed scale, while in others the parameter β (or T) is varied.
== Interpretations ==
=== Smooth arg max ===
The Softmax function is a smooth approximation to the arg max function: the function whose value is the index of a tuple's largest element. The name "softmax" may be misleading. Softmax is not a smooth maximum (that is, a smooth approximation to the maximum function). The term "softmax" is also used for the closely related LogSumExp function, which is a smooth maximum. For this reason, some prefer the more accurate term "softargmax", though the term "softmax" is conventional in machine learning. This section uses the term "softargmax" for clarity.
Formally, instead of considering the arg max as a function with categorical output
1
,
…
,
n
{\displaystyle 1,\dots ,n}
(corresponding to the index), consider the arg max function with one-hot representation of the output (assuming there is a unique maximum arg):
a
r
g
m
a
x
(
z
1
,
…
,
z
n
)
=
(
y
1
,
…
,
y
n
)
=
(
0
,
…
,
0
,
1
,
0
,
…
,
0
)
,
{\displaystyle \operatorname {arg\,max} (z_{1},\,\dots ,\,z_{n})=(y_{1},\,\dots ,\,y_{n})=(0,\,\dots ,\,0,\,1,\,0,\,\dots ,\,0),}
where the output coordinate
y
i
=
1
{\displaystyle y_{i}=1}
if and only if
i
{\displaystyle i}
is the arg max of
(
z
1
,
…
,
z
n
)
{\displaystyle (z_{1},\dots ,z_{n})}
, meaning
z
i
{\displaystyle z_{i}}
is the unique maximum value of
(
z
1
,
…
,
z
n
)
{\displaystyle (z_{1},\,\dots ,\,z_{n})}
. For example, in this encoding
a
r
g
m
a
x
(
1
,
5
,
10
)
=
(
0
,
0
,
1
)
,
{\displaystyle \operatorname {arg\,max} (1,5,10)=(0,0,1),}
since the third argument is the maximum.
This can be generalized to multiple arg max values (multiple equal
z
i
{\displaystyle z_{i}}
being the maximum) by dividing the 1 between all max args; formally 1/k where k is the number of arguments assuming the maximum. For example,
a
r
g
m
a
x
(
1
,
5
,
5
)
=
(
0
,
1
/
2
,
1
/
2
)
,
{\displaystyle \operatorname {arg\,max} (1,\,5,\,5)=(0,\,1/2,\,1/2),}
since the second and third argument are both the maximum. In case all arguments are equal, this is simply
a
r
g
m
a
x
(
z
,
…
,
z
)
=
(
1
/
n
,
…
,
1
/
n
)
.
{\displaystyle \operatorname {arg\,max} (z,\dots ,z)=(1/n,\dots ,1/n).}
Points z with multiple arg max values are singular points (or singularities, and form the singular set) – these are the points where arg max is discontinuous (with a jump discontinuity) – while points with a single arg max are known as non-singular or regular points.
With the last expression given in the introduction, softargmax is now a smooth approximation of arg max: as
β
→
∞
{\displaystyle \beta \to \infty }
, softargmax converges to arg max. There are various notions of convergence of a function; softargmax converges to arg max pointwise, meaning for each fixed input z as
β
→
∞
{\displaystyle \beta \to \infty }
,
σ
β
(
z
)
→
a
r
g
m
a
x
(
z
)
.
{\displaystyle \sigma _{\beta }(\mathbf {z} )\to \operatorname {arg\,max} (\mathbf {z} ).}
However, softargmax does not converge uniformly to arg max, meaning intuitively that different points converge at different rates, and may converge arbitrarily slowly. In fact, softargmax is continuous, but arg max is not continuous at the singular set where two coordinates are equal, while the uniform limit of continuous functions is continuous. The reason it fails to converge uniformly is that for inputs where two coordinates are almost equal (and one is the maximum), the arg max is the index of one or the other, so a small change in input yields a large change in output. For example,
σ
β
(
1
,
1.0001
)
→
(
0
,
1
)
,
{\displaystyle \sigma _{\beta }(1,\,1.0001)\to (0,1),}
but
σ
β
(
1
,
0.9999
)
→
(
1
,
0
)
,
{\displaystyle \sigma _{\beta }(1,\,0.9999)\to (1,\,0),}
and
σ
β
(
1
,
1
)
=
1
/
2
{\displaystyle \sigma _{\beta }(1,\,1)=1/2}
for all inputs: the closer the points are to the singular set
(
x
,
x
)
{\displaystyle (x,x)}
, the slower they converge. However, softargmax does converge compactly on the non-singular set.
Conversely, as
β
→
−
∞
{\displaystyle \beta \to -\infty }
, softargmax converges to arg min in the same way, where here the singular set is points with two arg min values. In the language of tropical analysis, the softmax is a deformation or "quantization" of arg max and arg min, corresponding to using the log semiring instead of the max-plus semiring (respectively min-plus semiring), and recovering the arg max or arg min by taking the limit is called "tropicalization" or "dequantization".
It is also the case that, for any fixed β, if one input
z
i
{\displaystyle z_{i}}
is much larger than the others relative to the temperature,
T
=
1
/
β
{\displaystyle T=1/\beta }
, the output is approximately the arg max. For example, a difference of 10 is large relative to a temperature of 1:
σ
(
0
,
10
)
:=
σ
1
(
0
,
10
)
=
(
1
/
(
1
+
e
10
)
,
e
10
/
(
1
+
e
10
)
)
≈
(
0.00005
,
0.99995
)
{\displaystyle \sigma (0,\,10):=\sigma _{1}(0,\,10)=\left(1/\left(1+e^{10}\right),\,e^{10}/\left(1+e^{10}\right)\right)\approx (0.00005,\,0.99995)}
However, if the difference is small relative to the temperature, the value is not close to the arg max. For example, a difference of 10 is small relative to a temperature of 100:
σ
1
/
100
(
0
,
10
)
=
(
1
/
(
1
+
e
1
/
10
)
,
e
1
/
10
/
(
1
+
e
1
/
10
)
)
≈
(
0.475
,
0.525
)
.
{\displaystyle \sigma _{1/100}(0,\,10)=\left(1/\left(1+e^{1/10}\right),\,e^{1/10}/\left(1+e^{1/10}\right)\right)\approx (0.475,\,0.525).}
As
β
→
∞
{\displaystyle \beta \to \infty }
, temperature goes to zero,
T
=
1
/
β
→
0
{\displaystyle T=1/\beta \to 0}
, so eventually all differences become large (relative to a shrinking temperature), which gives another interpretation for the limit behavior.
=== Statistical mechanics ===
In statistical mechanics, the softargmax function is known as the Boltzmann distribution (or Gibbs distribution):: 7 the index set
1
,
…
,
k
{\displaystyle {1,\,\dots ,\,k}}
are the microstates of the system; the inputs
z
i
{\displaystyle z_{i}}
are the energies of that state; the denominator is known as the partition function, often denoted by Z; and the factor β is called the coldness (or thermodynamic beta, or inverse temperature).
== Applications ==
The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression),: 206–209 multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of K distinct linear functions, and the predicted probability for the jth class given a sample tuple x and a weighting vector w is:
P
(
y
=
j
∣
x
)
=
e
x
T
w
j
∑
k
=
1
K
e
x
T
w
k
{\displaystyle P(y=j\mid \mathbf {x} )={\frac {e^{\mathbf {x} ^{\mathsf {T}}\mathbf {w} _{j}}}{\sum _{k=1}^{K}e^{\mathbf {x} ^{\mathsf {T}}\mathbf {w} _{k}}}}}
This can be seen as the composition of K linear functions
x
↦
x
T
w
1
,
…
,
x
↦
x
T
w
K
{\displaystyle \mathbf {x} \mapsto \mathbf {x} ^{\mathsf {T}}\mathbf {w} _{1},\ldots ,\mathbf {x} \mapsto \mathbf {x} ^{\mathsf {T}}\mathbf {w} _{K}}
and the softmax function (where
x
T
w
{\displaystyle \mathbf {x} ^{\mathsf {T}}\mathbf {w} }
denotes the inner product of
x
{\displaystyle \mathbf {x} }
and
w
{\displaystyle \mathbf {w} }
). The operation is equivalent to applying a linear operator defined by
w
{\displaystyle \mathbf {w} }
to tuples
x
{\displaystyle \mathbf {x} }
, thus transforming the original, probably highly-dimensional, input to vectors in a K-dimensional space
R
K
{\displaystyle \mathbb {R} ^{K}}
.
=== Neural networks ===
The standard softmax function is often used in the final layer of a neural network-based classifier. Such networks are commonly trained under a log loss (or cross-entropy) regime, giving a non-linear variant of multinomial logistic regression.
Since the function maps a tuple and a specific index
i
{\displaystyle i}
to a real value, the derivative needs to take the index into account:
∂
∂
q
k
σ
(
q
,
i
)
=
σ
(
q
,
i
)
(
δ
i
k
−
σ
(
q
,
k
)
)
.
{\displaystyle {\frac {\partial }{\partial q_{k}}}\sigma ({\textbf {q}},i)=\sigma ({\textbf {q}},i)(\delta _{ik}-\sigma ({\textbf {q}},k)).}
This expression is symmetrical in the indexes
i
,
k
{\displaystyle i,k}
and thus may also be expressed as
∂
∂
q
k
σ
(
q
,
i
)
=
σ
(
q
,
k
)
(
δ
i
k
−
σ
(
q
,
i
)
)
.
{\displaystyle {\frac {\partial }{\partial q_{k}}}\sigma ({\textbf {q}},i)=\sigma ({\textbf {q}},k)(\delta _{ik}-\sigma ({\textbf {q}},i)).}
Here, the Kronecker delta is used for simplicity (cf. the derivative of a sigmoid function, being expressed via the function itself).
To ensure stable numerical computations subtracting the maximum value from the input tuple is common. This approach, while not altering the output or the derivative theoretically, enhances stability by directly controlling the maximum exponent value computed.
If the function is scaled with the parameter
β
{\displaystyle \beta }
, then these expressions must be multiplied by
β
{\displaystyle \beta }
.
See multinomial logit for a probability model which uses the softmax activation function.
=== Reinforcement learning ===
In the field of reinforcement learning, a softmax function can be used to convert values into action probabilities. The function commonly used is:
P
t
(
a
)
=
exp
(
q
t
(
a
)
/
τ
)
∑
i
=
1
n
exp
(
q
t
(
i
)
/
τ
)
,
{\displaystyle P_{t}(a)={\frac {\exp(q_{t}(a)/\tau )}{\sum _{i=1}^{n}\exp(q_{t}(i)/\tau )}}{\text{,}}}
where the action value
q
t
(
a
)
{\displaystyle q_{t}(a)}
corresponds to the expected reward of following action a and
τ
{\displaystyle \tau }
is called a temperature parameter (in allusion to statistical mechanics). For high temperatures (
τ
→
∞
{\displaystyle \tau \to \infty }
), all actions have nearly the same probability and the lower the temperature, the more expected rewards affect the probability. For a low temperature (
τ
→
0
+
{\displaystyle \tau \to 0^{+}}
), the probability of the action with the highest expected reward tends to 1.
== Computational complexity and remedies ==
In neural network applications, the number K of possible outcomes is often large, e.g. in case of neural language models that predict the most likely outcome out of a vocabulary which might contain millions of possible words. This can make the calculations for the softmax layer (i.e. the matrix multiplications to determine the
z
i
{\displaystyle z_{i}}
, followed by the application of the softmax function itself) computationally expensive. What's more, the gradient descent backpropagation method for training such a neural network involves calculating the softmax for every training example, and the number of training examples can also become large. The computational effort for the softmax became a major limiting factor in the development of larger neural language models, motivating various remedies to reduce training times.
Approaches that reorganize the softmax layer for more efficient calculation include the hierarchical softmax and the differentiated softmax. The hierarchical softmax (introduced by Morin and Bengio in 2005) uses a binary tree structure where the outcomes (vocabulary words) are the leaves and the intermediate nodes are suitably selected "classes" of outcomes, forming latent variables. The desired probability (softmax value) of a leaf (outcome) can then be calculated as the product of the probabilities of all nodes on the path from the root to that leaf. Ideally, when the tree is balanced, this would reduce the computational complexity from
O
(
K
)
{\displaystyle O(K)}
to
O
(
log
2
K
)
{\displaystyle O(\log _{2}K)}
. In practice, results depend on choosing a good strategy for clustering the outcomes into classes. A Huffman tree was used for this in Google's word2vec models (introduced in 2013) to achieve scalability.
A second kind of remedies is based on approximating the softmax (during training) with modified loss functions that avoid the calculation of the full normalization factor. These include methods that restrict the normalization sum to a sample of outcomes (e.g. Importance Sampling, Target Sampling).
== Numerical algorithms ==
The standard softmax is numerically unstable because of large exponentiations. The safe softmax method calculates instead
σ
(
z
)
i
=
e
β
(
z
i
−
m
)
∑
j
=
1
K
e
β
(
z
j
−
m
)
{\displaystyle \sigma (\mathbf {z} )_{i}={\frac {e^{\beta (z_{i}-m)}}{\sum _{j=1}^{K}e^{\beta (z_{j}-m)}}}}
where
m
=
max
i
z
i
{\displaystyle m=\max _{i}z_{i}}
is the largest factor involved. Subtracting by it guarantees that the exponentiations result in at most 1.
The attention mechanism in Transformers takes three arguments: a "query vector"
q
{\displaystyle q}
, a list of "key vectors"
k
1
,
…
,
k
N
{\displaystyle k_{1},\dots ,k_{N}}
, and a list of "value vectors"
v
1
,
…
,
v
N
{\displaystyle v_{1},\dots ,v_{N}}
, and outputs a softmax-weighted sum over value vectors:
o
=
∑
i
=
1
N
e
q
T
k
i
−
m
∑
j
=
1
N
e
q
T
k
j
−
m
v
i
{\displaystyle o=\sum _{i=1}^{N}{\frac {e^{q^{T}k_{i}-m}}{\sum _{j=1}^{N}e^{q^{T}k_{j}-m}}}v_{i}}
The standard softmax method involves several loops over the inputs, which would be bottlenecked by memory bandwidth. The FlashAttention method is a communication-avoiding algorithm that fuses these operations into a single loop, increasing the arithmetic intensity. It is an online algorithm that computes the following quantities:
z
i
=
q
T
k
i
m
i
=
max
(
z
1
,
…
,
z
i
)
=
max
(
m
i
−
1
,
z
i
)
l
i
=
e
z
1
−
m
i
+
⋯
+
e
z
i
−
m
i
=
e
m
i
−
1
−
m
i
l
i
−
1
+
e
z
i
−
m
i
o
i
=
e
z
1
−
m
i
v
1
+
⋯
+
e
z
i
−
m
i
v
i
=
e
m
i
−
1
−
m
i
o
i
−
1
+
e
z
i
−
m
i
v
i
{\displaystyle {\begin{aligned}z_{i}&=q^{T}k_{i}&\\m_{i}&=\max(z_{1},\dots ,z_{i})&=&\max(m_{i-1},z_{i})\\l_{i}&=e^{z_{1}-m_{i}}+\dots +e^{z_{i}-m_{i}}&=&e^{m_{i-1}-m_{i}}l_{i-1}+e^{z_{i}-m_{i}}\\o_{i}&=e^{z_{1}-m_{i}}v_{1}+\dots +e^{z_{i}-m_{i}}v_{i}&=&e^{m_{i-1}-m_{i}}o_{i-1}+e^{z_{i}-m_{i}}v_{i}\end{aligned}}}
and returns
o
N
/
l
N
{\displaystyle o_{N}/l_{N}}
. In practice, FlashAttention operates over multiple queries and keys per loop iteration, in a similar way as blocked matrix multiplication. If backpropagation is needed, then the output vectors and the intermediate arrays
[
m
1
,
…
,
m
N
]
,
[
l
1
,
…
,
l
N
]
{\displaystyle [m_{1},\dots ,m_{N}],[l_{1},\dots ,l_{N}]}
are cached, and during the backward pass, attention matrices are rematerialized from these, making it a form of gradient checkpointing.
== Mathematical properties ==
Geometrically the softmax function maps the Euclidean space
R
K
{\displaystyle \mathbb {R} ^{K}}
to the boundary of the standard
(
K
−
1
)
{\displaystyle (K-1)}
-simplex, cutting the dimension by one (the range is a
(
K
−
1
)
{\displaystyle (K-1)}
-dimensional simplex in
K
{\displaystyle K}
-dimensional space), due to the linear constraint that all output sum to 1 meaning it lies on a hyperplane.
Along the main diagonal
(
x
,
x
,
…
,
x
)
,
{\displaystyle (x,\,x,\,\dots ,\,x),}
softmax is just the uniform distribution on outputs,
(
1
/
n
,
…
,
1
/
n
)
{\displaystyle (1/n,\dots ,1/n)}
: equal scores yield equal probabilities.
More generally, softmax is invariant under translation by the same value in each coordinate: adding
c
=
(
c
,
…
,
c
)
{\displaystyle \mathbf {c} =(c,\,\dots ,\,c)}
to the inputs
z
{\displaystyle \mathbf {z} }
yields
σ
(
z
+
c
)
=
σ
(
z
)
{\displaystyle \sigma (\mathbf {z} +\mathbf {c} )=\sigma (\mathbf {z} )}
, because it multiplies each exponent by the same factor,
e
c
{\displaystyle e^{c}}
(because
e
z
i
+
c
=
e
z
i
⋅
e
c
{\displaystyle e^{z_{i}+c}=e^{z_{i}}\cdot e^{c}}
), so the ratios do not change:
σ
(
z
+
c
)
j
=
e
z
j
+
c
∑
k
=
1
K
e
z
k
+
c
=
e
z
j
⋅
e
c
∑
k
=
1
K
e
z
k
⋅
e
c
=
σ
(
z
)
j
.
{\displaystyle \sigma (\mathbf {z} +\mathbf {c} )_{j}={\frac {e^{z_{j}+c}}{\sum _{k=1}^{K}e^{z_{k}+c}}}={\frac {e^{z_{j}}\cdot e^{c}}{\sum _{k=1}^{K}e^{z_{k}}\cdot e^{c}}}=\sigma (\mathbf {z} )_{j}.}
Geometrically, softmax is constant along diagonals: this is the dimension that is eliminated, and corresponds to the softmax output being independent of a translation in the input scores (a choice of 0 score). One can normalize input scores by assuming that the sum is zero (subtract the average:
c
{\displaystyle \mathbf {c} }
where
c
=
1
n
∑
z
i
{\textstyle c={\frac {1}{n}}\sum z_{i}}
), and then the softmax takes the hyperplane of points that sum to zero,
∑
z
i
=
0
{\textstyle \sum z_{i}=0}
, to the open simplex of positive values that sum to 1
∑
σ
(
z
)
i
=
1
{\textstyle \sum \sigma (\mathbf {z} )_{i}=1}
, analogously to how the exponent takes 0 to 1,
e
0
=
1
{\displaystyle e^{0}=1}
and is positive.
By contrast, softmax is not invariant under scaling. For instance,
σ
(
(
0
,
1
)
)
=
(
1
/
(
1
+
e
)
,
e
/
(
1
+
e
)
)
{\displaystyle \sigma {\bigl (}(0,\,1){\bigr )}={\bigl (}1/(1+e),\,e/(1+e){\bigr )}}
but
σ
(
(
0
,
2
)
)
=
(
1
/
(
1
+
e
2
)
,
e
2
/
(
1
+
e
2
)
)
.
{\displaystyle \sigma {\bigl (}(0,2){\bigr )}={\bigl (}1/\left(1+e^{2}\right),\,e^{2}/\left(1+e^{2}\right){\bigr )}.}
The standard logistic function is the special case for a 1-dimensional axis in 2-dimensional space, say the x-axis in the (x, y) plane. One variable is fixed at 0 (say
z
2
=
0
{\displaystyle z_{2}=0}
), so
e
0
=
1
{\displaystyle e^{0}=1}
, and the other variable can vary, denote it
z
1
=
x
{\displaystyle z_{1}=x}
, so
e
z
1
/
∑
k
=
1
2
e
z
k
=
e
x
/
(
e
x
+
1
)
,
{\textstyle e^{z_{1}}/\sum _{k=1}^{2}e^{z_{k}}=e^{x}/\left(e^{x}+1\right),}
the standard logistic function, and
e
z
2
/
∑
k
=
1
2
e
z
k
=
1
/
(
e
x
+
1
)
,
{\textstyle e^{z_{2}}/\sum _{k=1}^{2}e^{z_{k}}=1/\left(e^{x}+1\right),}
its complement (meaning they add up to 1). The 1-dimensional input could alternatively be expressed as the line
(
x
/
2
,
−
x
/
2
)
{\displaystyle (x/2,\,-x/2)}
, with outputs
e
x
/
2
/
(
e
x
/
2
+
e
−
x
/
2
)
=
e
x
/
(
e
x
+
1
)
{\displaystyle e^{x/2}/\left(e^{x/2}+e^{-x/2}\right)=e^{x}/\left(e^{x}+1\right)}
and
e
−
x
/
2
/
(
e
x
/
2
+
e
−
x
/
2
)
=
1
/
(
e
x
+
1
)
.
{\displaystyle e^{-x/2}/\left(e^{x/2}+e^{-x/2}\right)=1/\left(e^{x}+1\right).}
=== Gradients ===
The softmax function is also the gradient of the LogSumExp function:
∂
∂
z
i
LSE
(
z
)
=
exp
z
i
∑
j
=
1
K
exp
z
j
=
σ
(
z
)
i
,
for
i
=
1
,
…
,
K
,
z
=
(
z
1
,
…
,
z
K
)
∈
R
K
,
{\displaystyle {\frac {\partial }{\partial z_{i}}}\operatorname {LSE} (\mathbf {z} )={\frac {\exp z_{i}}{\sum _{j=1}^{K}\exp z_{j}}}=\sigma (\mathbf {z} )_{i},\quad {\text{ for }}i=1,\dotsc ,K,\quad \mathbf {z} =(z_{1},\,\dotsc ,\,z_{K})\in \mathbb {R} ^{K},}
where the LogSumExp function is defined as
LSE
(
z
1
,
…
,
z
n
)
=
log
(
exp
(
z
1
)
+
⋯
+
exp
(
z
n
)
)
{\displaystyle \operatorname {LSE} (z_{1},\,\dots ,\,z_{n})=\log \left(\exp(z_{1})+\cdots +\exp(z_{n})\right)}
.
The gradient of softmax is thus
∂
z
j
σ
i
=
σ
i
(
δ
i
j
−
σ
j
)
{\displaystyle \partial _{z_{j}}\sigma _{i}=\sigma _{i}(\delta _{ij}-\sigma _{j})}
.
== History ==
The softmax function was used in statistical mechanics as the Boltzmann distribution in the foundational paper Boltzmann (1868), formalized and popularized in the influential textbook Gibbs (1902).
The use of the softmax in decision theory is credited to R. Duncan Luce,: 1 who used the axiom of independence of irrelevant alternatives in rational choice theory to deduce the softmax in Luce's choice axiom for relative preferences.
In machine learning, the term "softmax" is credited to John S. Bridle in two 1989 conference papers, Bridle (1990a):: 1 and Bridle (1990b):
We are concerned with feed-forward non-linear networks (multi-layer perceptrons, or MLPs) with multiple outputs. We wish to treat the outputs of the network as probabilities of alternatives (e.g. pattern classes), conditioned on the inputs. We look for appropriate output non-linearities and for appropriate criteria for adaptation of the parameters of the network (e.g. weights). We explain two modifications: probability scoring, which is an alternative to squared error minimisation, and a normalised exponential (softmax) multi-input generalisation of the logistic non-linearity.: 227
For any input, the outputs must all be positive and they must sum to unity. ...
Given a set of unconstrained values,
V
j
(
x
)
{\displaystyle V_{j}(x)}
, we can ensure both conditions by using a Normalised Exponential transformation:
Q
j
(
x
)
=
e
V
j
(
x
)
/
∑
k
e
V
k
(
x
)
{\displaystyle Q_{j}(x)=\left.e^{V_{j}(x)}\right/\sum _{k}e^{V_{k}(x)}}
This transformation can be considered a multi-input generalisation of the logistic, operating on the whole output layer. It preserves the rank order of its input values, and is a differentiable generalisation of the 'winner-take-all' operation of picking the maximum value. For this reason we like to refer to it as softmax.: 213
== Example ==
With an input of (1, 2, 3, 4, 1, 2, 3), the softmax is approximately (0.024, 0.064, 0.175, 0.475, 0.024, 0.064, 0.175). The output has most of its weight where the "4" was in the original input. This is what the function is normally used for: to highlight the largest values and suppress values which are significantly below the maximum value. But note: a change of temperature changes the output. When the temperature is multiplied by 10, the inputs are effectively (0.1, 0.2, 0.3, 0.4, 0.1, 0.2, 0.3) and the softmax is approximately (0.125, 0.138, 0.153, 0.169, 0.125, 0.138, 0.153). This shows that high temperatures de-emphasize the maximum value.
Computation of this example using Python code:
== Alternatives ==
The softmax function generates probability predictions densely distributed over its support. Other functions like sparsemax or α-entmax can be used when sparse probability predictions are desired. Also the Gumbel-softmax reparametrization trick can be used when sampling from a discrete-discrete distribution needs to be mimicked in a differentiable manner.
== See also ==
Softplus
Multinomial logistic regression
Dirichlet distribution – an alternative way to sample categorical distributions
Partition function
Exponential tilting – a generalization of Softmax to more general probability distributions
== Notes ==
== References == | Wikipedia/Softmax_activation_function |
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain.
In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. A too high learning rate will make the learning jump over minima but a too low learning rate will either take too long to converge or get stuck in an undesirable local minimum.
In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms.
== Learning rate schedule ==
Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential.
Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when a too high constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter.
Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras.
Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is:
η
n
+
1
=
η
n
1
+
d
n
{\displaystyle \eta _{n+1}={\frac {\eta _{n}}{1+dn}}}
where
η
{\displaystyle \eta }
is the learning rate,
d
{\displaystyle d}
is a decay parameter and
n
{\displaystyle n}
is the iteration step.
Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as:
η
n
=
η
0
d
⌊
1
+
n
r
⌋
{\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }}
where
η
n
{\displaystyle \eta _{n}}
is the learning rate at iteration
n
{\displaystyle n}
,
η
0
{\displaystyle \eta _{0}}
is the initial learning rate,
d
{\displaystyle d}
is how much the learning rate should change at each drop (0.5 corresponds to a halving) and
r
{\displaystyle r}
corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function (
⌊
…
⌋
{\displaystyle \lfloor \dots \rfloor }
) here drops the value of its input to 0 for all values smaller than 1.
Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is:
η
n
=
η
0
e
−
d
n
{\displaystyle \eta _{n}=\eta _{0}e^{-dn}}
where
d
{\displaystyle d}
is a decay parameter.
== Adaptive learning rate ==
The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.
== See also ==
== References ==
== Further reading ==
Géron, Aurélien (2017). "Gradient Descent". Hands-On Machine Learning with Scikit-Learn and TensorFlow. O'Reilly. pp. 113–124. ISBN 978-1-4919-6229-9.
Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. (2001). "Learning Rate Adaptation in Stochastic Gradient Descent". Advances in Convex Analysis and Global Optimization. Kluwer. pp. 433–444. ISBN 0-7923-6942-4.
== External links ==
de Freitas, Nando (February 12, 2015). "Optimization". Deep Learning Lecture 6. University of Oxford – via YouTube. | Wikipedia/Adaptive_learning_rate |
The wake-sleep algorithm is an unsupervised learning algorithm for deep generative models, especially Helmholtz Machines. The algorithm is similar to the expectation-maximization algorithm, and optimizes the model likelihood for observed data. The name of the algorithm derives from its use of two learning phases, the “wake” phase and the “sleep” phase, which are performed alternately. It can be conceived as a model for learning in the brain, but is also being applied for machine learning.
== Description ==
The goal of the wake-sleep algorithm is to find a hierarchical representation of observed data. In a graphical representation of the algorithm, data is applied to the algorithm at the bottom, while higher layers form gradually more abstract representations. Between each pair of layers are two sets of weights: Recognition weights, which define how representations are inferred from data, and generative weights, which define how these representations relate to data.
== Training ==
Training consists of two phases – the “wake” phase and the “sleep” phase. It has been proven that this learning algorithm is convergent.
=== The "wake" phase ===
Neurons are fired by recognition connections (from what would be input to what would be output). Generative connections (leading from outputs to inputs) are then modified to increase probability that they would recreate the correct activity in the layer below – closer to actual data from sensory input.
=== The "sleep" phase ===
The process is reversed in the “sleep” phase – neurons are fired by generative connections while recognition connections are being modified to increase probability that they would recreate the correct activity in the layer above – further to actual data from sensory input.
== Extensions ==
Since the recognition network is limited in its flexibility, it might not be able to approximate the posterior distribution of latent variables well. To better approximate the posterior distribution, it is possible to employ importance sampling, with the recognition network as the proposal distribution. This improved approximation of the posterior distribution also improves the overall performance of the model.
== See also ==
Restricted Boltzmann machine, a type of neural net that is trained with a conceptually similar algorithm.
Helmholtz machine, a neural network model trained by the wake-sleep algorithm.
== References == | Wikipedia/Wake-sleep_algorithm |
Context-aware computing refers to a general class of mobile systems that can sense their physical environment, and adapt their behavior accordingly.
Three important aspects of context are: where you are; who you are with; and what resources are nearby. Although location is a primary capability, location-aware does not necessarily capture things of interest that are mobile or changing. Context-aware in contrast is used more generally to include nearby people, devices, lighting, noise level, network availability, and even the social situation, e.g., whether you are with your family or a friend from school.
== History ==
The concept emerged from ubiquitous computing research at Xerox PARC and elsewhere in the early 1990s. The term 'context-aware' was first used by Schilit and Theimer in their 1994 paper Disseminating Active Map Information to Mobile Hosts where they describe a model of computing in which users interact with many different mobile and stationary computers and classify a context-aware systems as one that can adapt according to its location of use, the collection of nearby people and objects, as well as the changes to those objects over time over the course of the day.
== See also ==
Ambient intelligence – Electronic devices detecting human presence
Context awareness – capability to take into account the situation of entities (e.g. users or devices)Pages displaying wikidata descriptions as a fallback
Differentiated service (design pattern) – design pattern for business services and softwarePages displaying wikidata descriptions as a fallback
Locative media – Media of communication functionally bound to a location
Pervasive computing – Concept in software engineering and computer sciencePages displaying short descriptions of redirect targets
Spatial contextual awareness – Vicinity data in ubiquitous computing
== References ==
== Further reading ==
A Survey of Context Data Distribution for Mobile Ubiquitous Systems. P. Bellavista, A. Corradi, M. Fanelli, L. Foschini. ACM Computing Surveys (CSUR), ACM Press, expected to appear in Vol. 45, No. 1, March 2013, pages 1–49.
Context and Adaptivity in Pervasive Computing Environments: Links with Software Engineering and Ontological Engineering. A. Soylu, P. De Causmaecker, P. Desmet. Journal of Software, Vol 4, No 9 (2009), 992-1013, November 2009 doi:10.4304/jsw.4.9.992-1013
Context-Aware Computing Applications Archived 2008-04-25 at the Wayback Machine. Bill N. Schilit, Norman I. Adams, and Roy Want. In Proceedings of the Workshop on Mobile Computing Systems and Applications, Santa Cruz, CA, December 1994. Pages 85–90. IEEE Computer Society.
A Service-Oriented Middleware for Building Context-Aware Services. T. Gu, H. K. Pung, D. Zhang. Elsevier Journal of Network and Computer Applications (JNCA), Vol. 28, Issue 1, pp. 1–18, January 2005.
X. Wang, J. S. Dong, C. Chin, S. R. Hettiarachchi and D. Zhang. Semantic Space: A Semantic Web Infrastructure for Smart Spaces. IEEE Pervasive Computing, 3(3):32-39, July–September 2004
Towards an Cooperative Programming Framework for Context-Aware Applications. B. Guo, D. Zhang, M. Imai. ACM/Springer Journal of Personal and Ubiquitous Computing, Vol. 15, No. 3, pp. 221–233, 2011.
Context-Aware Pervasive Systems: Architectures for a New Breed of Applications by Seng W. Loke.
Context Modeling and Reasoning using Ontologies Archived 2012-02-16 at the Wayback Machine. Feruzan Ay, 2007: The paper gives an introduction to context modeling and reasoning in the area of pervasive computing.
Context-Aware Information Delivery. An Application in the Health Care Domain. J.JAHNKE, Y.BYCHKOV, D.DAHLEM, L.KAWASME. Revue d'Intelligence Artificielle, Volume 19, Issue 3, p. 459-478 (2005)
There is more to context than location. Albrecht Schmidt, Michael Beigl and Hans-W. Gellersen. In: Computers & Graphics Journal, Elsevier, Volume 23, No.6, December 1999, pp 893–902.
A data-oriented survey of context models. Cristiana Bolchini, Carlo Curino, Elisa Quintarelli, Fabio A. Schreiber, Letizia Tanca. In: SIGMOD Record 36(4): 19-26 (2007)
== External links ==
Xerox PARCTAB is generally considered the first context-aware mobile computer.
First International Workshop on Quality of Context (QuaCon '09), 25–26 June 2009, Stuttgart, Germany
4th International Workshop on Location- and Context-Awareness (LoCA 2009), 7–8 May 2009, Tokyo Japan
3rd International Workshop on Location- and Context-Awareness (LoCA 2007), 20–21 September 2007, Oberpfaffenhofen near Munich (DLR), Germany
2nd International Workshop on Location- and Context-Awareness (LoCA 2006), 10–11 May 2006, Dublin Ireland
1st International Workshop on Location- and Context-Awareness (LoCA 2005), 12–13 May 2005, Oberpfaffenhofen near Munich (DLR), Germany
Pervasive Computing and Mental Health | Wikipedia/Context-aware_pervasive_systems |
Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation. Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization.
== Approximate models in function optimization ==
=== Motivation ===
In many real-world optimization problems including engineering problems, the number of fitness function evaluations needed to obtain a good solution dominates the optimization cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or approximation models – for computationally expensive optimization problems have been considered.
=== Approaches ===
Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include:
Low-degree polynomials and regression models
Fourier surrogate modeling
Artificial neural networks including
Multilayer perceptrons
Radial basis function networks
Support vector machines
Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to local optima. Therefore, it can be beneficial to selectively use the original fitness function together with the approximate model.
== See also ==
A complete list of references on Fitness Approximation in Evolutionary Computation, by Yaochu Jin.
The cyber shack of Adaptive Fuzzy Fitness Granulation (AFFG) Archived 2021-12-06 at the Wayback Machine That is designed to accelerate the convergence rate of EAs.
Inverse reinforcement learning
Reinforcement learning from human feedback
== References == | Wikipedia/Fitness_approximation |
YouTube Rewind 2018: Everyone Controls Rewind (also known as YouTube Rewind 2018) is a video that was uploaded to the official channel of the video-sharing website YouTube on December 6, 2018, as the ninth installment of the YouTube Rewind series. The video features references to video games and internet culture, starring YouTubers such as Ninja and Marques Brownlee, as well as celebrities like Will Smith and Trevor Noah.
YouTube Rewind 2018 was panned by critics, YouTubers, and viewers alike, who dubbed it the worst YouTube Rewind video to date. The video was criticized for the inclusion of unpopular or outdated trends and the exclusion of many prominent YouTubers of the year, as well as rivalries such as KSI vs Logan Paul and PewDiePie vs T-Series. By December 13, 2018, a week after its upload, Everyone Controls Rewind had over 10 million dislikes, making it the most-disliked video on YouTube of all time, a record that was previously held by the music video for Justin Bieber's "Baby" for over seven years.
== Background ==
YouTube Rewind was an annual series of videos released from 2010 to 2019 that was produced (alongside Portal A Interactive), released and distributed by the namesake website via its official channel. Each video was a recap of the year's trends and events.
== Overview ==
The video themes around everyone being able to control YouTube Rewind, with various featured personalities describing what events they want to review. The video begins with actor Will Smith on Jebel Jais's mountain range, suggesting the inclusion of the video game Fortnite and YouTuber Marques Brownlee in the video. The camera then cuts to Brownlee, other YouTubers, and Twitch streamer Ninja as the bus driver, conversing inside a battle bus, a reference to the game.
The following scene depicts a group of YouTube personalities surrounding a campfire. The group suggests that the Rewind should have K-pop, references to the wedding of Prince Harry and Meghan Markle, the internet meme 'Bongo Cat,' a science experiment involving melting lipstick, and the inclusion of electronic musician Marshmello, whose mask is removed and revealed to be Mason Ramsey underneath. The video then cuts to a group doing a mukbang in South Korea. After the scene, animator TheOdd1sOut suggests adding the "In My Feelings" challenge to the video. The video rapidly cuts between scenes of various YouTubers and celebrities dancing to the challenge, including scenes of talk show hosts Trevor Noah and John Oliver performing dances from Fortnite. Animator Jaiden Animations includes several easter eggs, comprising references to other memes and events of the year, such as Ugandan Knuckles, an invitation to Super Smash Bros. Ultimate, KSI vs. Logan Paul boxing match, a group of items on the wall that spell out "Sub 2 PewDiePie", as well as PewDiePie's swivel chair.
After the challenge, Lilly Singh says the video should feature "the people who managed to do something bigger than themselves." Several YouTubers give shoutouts to various groups of people, including people who strived for mental health awareness and "all women in 2018 for finding their voices." Later, Elle Mills decides to read a faux comments section on what to feature in the Rewind. Various comments are featured, featuring pop culture references to the costumes in Kanye West and Lil Pump's "I Love It" music video, the 2018 FIFA World Cup, the children's song Baby Shark, and the Dame Tu Cosita dance craze. The 'Sister Squad' (James Charles, Dolan Twins, and Emma Chamberlain) are then shown in outer space, driving a car resembling Elon Musk's Tesla Roadster. The video ends with Smith laughing as he watches the aforementioned battle bus through a pair of binoculars and states "That's hot, that's hot." While the credits are playing, Primitive Technology is featured, sculpting the YouTube Rewind logo with clay.
== Cast ==
This is the list of starring cast members in YouTube Rewind 2018: Everyone Controls Rewind, derived from its website.
== Reception ==
Upon its release, YouTube Rewind 2018: Everyone Controls Rewind received universally negative reviews, receiving extensive backlash from critics, YouTubers, and viewers alike. Many YouTubers deemed it the "worst Rewind ever". Only a few portions of the video received praise, with many viewers applauding Jaiden Animations for incorporating PewDiePie's chair, as well as other Easter eggs, into her segment of the video. Other criticisms included what viewers had seen as the video's overuse of some trends, many of them being seen as outdated or unpopular among the YouTube community, including Fortnite, as well as the lack of variety in references. It was also prominently criticized for its social commentary, which some felt was shoehorned into the video. Many people were also angered with PewDiePie not being included, as his channel was the most-subscribed on the platform at the time.
While YouTube Rewind 2018: Everyone Controls Rewind incorporated user comment suggestions as a part of the video, Nicole Engelman of The Hollywood Reporter called YouTube "out of touch". Julia Alexander of The Verge suggested that YouTube had intentionally left out the biggest moments on the platform in 2018 from the video in an attempt to appease concerned advertisers over controversies that had plagued the platform over the past two years. She states that "it's increasingly apparent, however, that YouTube is trying to sell a culture that's different from the one millions of people come to the platform for, and that's getting harder for both creators and fans to swallow." Meira Gebel of Business Insider shared a similar sentiment, saying "The video appears to be an attempt for the company to keep advertisers on its side following a rather rocky 2018."
PewDiePie, who was not in YouTube Rewind 2018: Everyone Controls Rewind, criticized the video. He stated that he was almost glad he wasn't in it "because it's such a cringey video at this point which I think is quite a shame honestly." He adds on the statement saying that "Rewind [used to be] something that seemed like an homage to the creators that year, it was something cool to be a part of." He further criticized the over-saturation of Fortnite, the inclusion of celebrities not associated with YouTube, and the lack of any mention of the outpouring of support on the platform for those who died before December, including Icelandic actor and YouTuber Stefán Karl Stefánsson. On top of his criticism, he, along with FlyingKitty, Party In Backyard, Grandayy and Dolan Dark, created their take of YouTube Rewind 2018: Everyone Controls Rewind on December 27, 2018, titled "YouTube Rewind 2018 but it's actually good", which focused on the notable memes of 2018.
Marques Brownlee, who was prominently featured in the video, said Rewind had once been a "big celebration of YouTubers and the biggest events that had happened on the site in a particular year. It became an honor to be included in Rewind. But now YouTube saw Rewind as a way to showcase all the best stuff that happens on YouTube for advertisers." He concluded that "Instead of honoring creators, it is now a list of advertiser-friendly content. Rewind has turned into a giant ad for YouTube."
In a video uploaded in February 2019, then-YouTube CEO Susan Wojcicki said "Even at home, my kids told me it (YouTube Rewind 2018: Everyone Controls Rewind) was cringey." She promised a better Rewind for 2019 and revealed several priorities for YouTube for the year.
=== Dislikes ===
On December 13, 2018, a week after being uploaded, it became the most-disliked video on the website, beating the previous record-holder: the music video for Justin Bieber's "Baby." In a statement given to media outlets, YouTube spokeswoman Andrea Faville said that "dethroning 'Baby' in dislikes wasn't exactly our goal this year."
After the release of the video and subsequent backlash, YouTube discussed possible options to prevent abuse of the dislike button by "dislike mobs", such as making the like–dislike ratings invisible by default, prompting disliking users to explain their dislike, removing the dislike count or the dislike button entirely. Tom Leung, the director of project management at YouTube, described the possibility of removing the dislike button to be the most extreme and undemocratic option, as "not all dislikes are from dislike mobs."
In November 2021, dislike counts became viewable only by a video's uploader in an attempt to "help better protect our creators from harassment, and reduce dislike attacks — where people work to drive up the number of dislikes on a creator's videos."
== References ==
== External links ==
YouTube Rewind 2018: Everyone Controls Rewind at IMDb
YouTube Rewind 2018: Everyone Controls Rewind on YouTube
Portal-A project page | Wikipedia/YouTube_Rewind_2018:_Everyone_Controls_Rewind |
The Google Knowledge Graph is a knowledge base from which Google serves relevant information in an infobox beside its search results. This allows the user to see the answer in a glance, as an instant answer. The data is generated automatically from a variety of sources, covering places, people, businesses, and more.
The information covered by Google's Knowledge Graph grew quickly after launch, tripling its data size within seven months (covering 570 million entities and 18 billion facts). By mid-2016, Google reported that it held 70 billion facts and answered "roughly one-third" of the 100 billion monthly searches they handled. By May 2020, this had grown to 500 billion facts on 5 billion entities.
There is no official documentation of how the Google Knowledge Graph is implemented.
According to Google, its information is retrieved from many sources, including the CIA World Factbook and Wikipedia.
It is used to answer direct spoken questions in Google Assistant and Google Home voice queries.
It has been criticized for providing answers with neither source attribution nor citations.
== History ==
Google announced its Knowledge Graph on May 16, 2012, as a way to significantly enhance the value of information returned by Google searches. Initially available only in English, it was expanded in December 2012 to Spanish, French, German, Portuguese, Japanese, Russian and Italian. Bengali support was added in March 2017.
The Knowledge Graph was powered in part by Freebase.
In August 2014, New Scientist reported that Google had launched a Knowledge Vault project. After publication, Google reached out to Search Engine Land to explain that Knowledge Vault was a research report, not an active Google service. Search Engine Land expressed indications that Google was experimenting with "numerous models" for gathering meaning from text.
Google's Knowledge Vault was meant to deal with facts, automatically gathering and merging information from across the Internet into a knowledge base capable of answering direct questions, such as "Where was Madonna born?" In a 2014 report, the Vault was reported to have collected over 1.6 billion facts, 271 million of which were considered "confident facts" deemed to be more than 90% true. It was reported to be different from the Knowledge Graph in that it gathered information automatically instead of relying on crowd-sourced facts compiled by humans.
== Features ==
=== Google Knowledge Panel ===
A Google Knowledge Panel which is part of Google search engine result pages, presents an overview of entities such as individuals, organizations, locations, or objects directly within the search interface. This feature uses data from Google Knowledge Graph, an extensive database that organizes and interconnects information about entities, enhancing the retrieval and presentation of relevant content to users.
== Criticism ==
=== Lack of source attribution ===
By May 2016, knowledge boxes were appearing for "roughly one-third" of the 100 billion monthly searches the company processed. Dario Taraborelli, head of research at the Wikimedia Foundation, told The Washington Post that Google's omission of sources in its knowledge boxes "undermines people’s ability to verify information and, ultimately, to develop well-informed opinions". The publication also reported that the boxes are "frequently unattributed", such as a knowledge box on the age of actress Betty White, which is "as unsourced and absolute as if handed down by God".
=== Declining Wikipedia article readership ===
According to The Register in 2014 the display of direct answers in knowledge panels alongside Google search results caused significant readership declines for Wikipedia, from which the panels obtained some of their information. Also in 2014, The Daily Dot noted that "Wikipedia still has no real competitor as far as actual content is concerned. All that's up for grabs are traffic stats. And as a nonprofit, traffic numbers don't equate into revenue in the same way they do for a commercial media site". After the article's publication, a spokesperson for the Wikimedia Foundation, which operates Wikipedia, stated that it "welcomes" the knowledge panel functionality, that it was "looking into" the traffic drops, and that "We've also not noticed a significant drop in search engine referrals. We also have a continuing dialog with staff from Google working on the Knowledge Panel".
In his 2020 book, Dariusz Jemielniak noted that as most Google users do not realize that many answers to their questions that appear in the Knowledge Graph come from Wikipedia, this reduces Wikipedia's popularity, and in turn limited the site's ability to raise new funds and attract new volunteers.
=== Bias ===
The algorithm has been criticized for presenting biased or inaccurate information, usually because of sourcing information from websites with high search engine optimization. It had been noted in 2014 that while there was a Knowledge Graph for most major historical or pseudo-historical religious figures such as Moses, Muhammad and Gautama Buddha, there was none for Jesus, the central figure of Christianity. On June 3, 2021, a knowledge box identified Kannada as the ugliest language in India, prompting outrage from the Kannada-language community; the state of Karnataka, where most Kannada speakers live, also threatened to sue Google for damaging the public image of the language. Google promptly changed the featured snippet for the search query and issued a formal apology.
== See also ==
DBpedia
Google Assistant
Linked data
Knowledge graph
Semantic integration
Semantic network
Wikidata
AI Overviews
== References == | Wikipedia/Google_Knowledge_Graph |
Piper is a centralized version control system used by Google for its internal software development. Originally designed for Linux, it supports Microsoft Windows and macOS since October 2012.
== Scale ==
Since its founding years Google used a central codebase shared by the developers. For over 10 years Google relied on a single Perforce instance, using proprietary caching for scalability. This mode of operation was kept as Google grew, the need for further scaling led to the development of Piper. Currently, Google's version control "is an extreme case": as of 2016, the repository was storing 86 terabytes of data comprising two billion lines of code in nine million files (two orders of magnitude more than in the Linux kernel repository). 25 thousand developers contributed 16 thousand changes daily, with additional 24 thousand commit operations by bots. Read requests each day are measured in billions.
== Architecture ==
Piper uses regular Google Cloud storage solutions, originally Bigtable and later Spanner, distributed across 10 data centers worldwide and replicated through Paxos protocol.
== Use ==
When using Piper, developers apply changes to a local copy of files, similar to a working copy of Subversion, local clone of Git, or a client of Perforce. Updates made by other developers can be pulled from the central repository and merged into the local code. The commits are only allowed after a code review.
Typical use involves Clients in the Cloud (CitC). This system utilizes cloud backend and a local FUSE filesystem to create an illusion of changes overlaid on top of a full repository. This approach enables seamless browsing and use of standard Unix tools without explicit synchronization operations, thus keeping the local copy very small (average size of a local copy is less than ten files). All file writes are mapped to snapshots thus permitting restoration of the previous states of the code without explicit snapshotting. Due to the always-connected operation, CitC allows easy switching of the computers as well as sharing the modified code with other developers, the automated build system and testing tools. As a result, the majority of Google developers practices trunk-based development with no personal branches; the branches are mostly used for releases.
== Security ==
Most of the codebase is visible to all developers, sensitive individual files (less than 1% as of 2016) are access-controlled. All operations with Piper are logged, accidentally committed files can be purged.
== Open-source clone ==
Piper is proprietary software. Mega, a Git-compatible open-source clone of Piper, is available on GitHub. It supports the trunk-based development, Conventional Commits and code owners.
== References ==
== Sources ==
Blank-Edelman, D.N. (2018). Seeking SRE: Conversations About Running Production Systems at Scale. O'Reilly Media. ISBN 978-1-4919-7881-8. Retrieved 2024-10-31.
Potvin, Rachel; Levenberg, Josh (2016-06-24). "Why Google stores billions of lines of code in a single repository". Communications of the ACM. 59 (7). Association for Computing Machinery (ACM): 78–87. doi:10.1145/2854146. ISSN 0001-0782. | Wikipedia/Piper_(source_control_system) |
Federated Learning of Cohorts (FLoC) is a type of web tracking. It groups people into "cohorts" based on their browsing history for the purpose of interest-based advertising. FLoC was being developed as a part of Google's Privacy Sandbox initiative, which includes several other advertising-related technologies with bird-themed names.: 48 Despite "federated learning" in the name, FLoC does not utilize any federated learning.
Google began testing the technology in Chrome 89 released in March 2021 as a replacement for third-party cookies. By April 2021, every major browser aside from Google Chrome that is based on Google's open-source Chromium platform had declined to implement FLoC. The technology was criticized on privacy grounds by groups including the Electronic Frontier Foundation and DuckDuckGo, and has been described as anti-competitive; it generated an antitrust response in multiple countries as well as questions about General Data Protection Regulation compliance. In July 2021, Google quietly suspended development of FLoC; Chrome 93, released on August 31, 2021, became the first version which disabled FLoC, but did not remove the internal programming.
On January 25, 2022, Google officially announced it had ended development of FLoC technologies and proposed the new Topics API to replace it. Brave developers criticized Topics API as a rebranding of FLoC with only minor changes and without addressing their main concerns.
== Function ==
The Federated Learning of Cohorts algorithm analyzes users' online activity within the browser, and generates a "cohort ID" using the SimHash algorithm to group a given user with other users who access similar content.: 9 Each cohort contains several thousand users in order to make identifying individual users more difficult, and cohorts are updated weekly. Websites are then able to access the cohort ID using an API: 9 and determine what advertisements to serve. Google does not label cohorts based on interest beyond grouping users and assigning an ID, so advertisers need to determine the user types of each cohort on their own.: 47
=== Opting out of cohort calculation ===
FLoC experiment was active only in Google Chrome browser and ran from Chrome 89 (inclusive) to Chrome 93 (not inclusive). Modern browsers do not support FLoC. While the experiment was active, users could opt out of FLoC experiment by disabling third-party cookies. Website administrators could opt out from cohort calculation via special HTTP headers. It can be accomplished with a new interest-cohort permissions policy or feature policy, the default behavior is to allow cohort calculation. To opt-out of all FLoC cohort calculations a website could send either of the following HTTP response headers:
Permissions-Policy: browsing-topics=()
or
Feature-Policy: browsing-topics 'none'
Google Chrome applies interest-cohort Feature Policy restrictions to Browsing Topics API as well.
== Timeline ==
=== Initial prototype ===
On August 22, 2019, Google Chrome developers coined the term FLoC and first started discussing the upcoming replacement for cookies. In July 2020, the United Kingdom's Competition and Markets Authority found the FLoC proposal to be anti-competitive, since it would "place the browser in a vital gatekeeper position for the adtech ecosystem." Instead, the authority recommended adoption of a competing proposal called SPARROW, which maintains the same privacy-enhancing objectives but creates a different completely independent "Gatekeeper" which does not have any other role in the adtech ecosystem and does not have access to user-level information.
=== Testing ===
Google began testing FLoC in the Chrome 89 released in March 2021 as a replacement for third-party cookies, which Google plans to stop supporting in Chrome by mid-2023. (Initially Google announced plans to remove third-party cookies by late 2021, then postponed it to early 2022, and then to 2023 due to delay of FLoC technology.) The initial trial turned on FLoC for 0.5% of Chrome users across 10 countries: the United States, Australia, Brazil, Canada, India, Indonesia, Japan, Mexico, New Zealand and the Philippines. Users were automatically placed in the trial and were not notified, but could opt out by turning off third-party cookies. Furthermore, site administrators could disable FLoC and opt out from interest calculation via a Feature-Policy header. The initial trial did not include users in the United Kingdom or the European Economic Area due to concerns about legality under the area's privacy regulations.
=== FLoC shutdown ===
In July 2021, Google suspended development of FLoC; Chrome 93, released on August 31, 2021, became the first version which rendered FLoC feature void, but did not remove the internal programming. Chrome 100, released on March 29, 2022, removed most of old FLoC code.
=== Topics API ===
On January 25, 2022, Google officially announced it had ended development of FLoC APIs and proposed a new Topics API to replace it. This API would use three weeks of the browser's history to identify user interests based on defined topics. Participating websites could then call this API to get three topics which could be used to tailor advertising. Developers of the Brave web browser called Topics API a "rebranding [of] FLoC without addressing key privacy issues.
== Reactions ==
Google claimed in January 2021 that FLoC was at least 95% effective compared to tracking using third-party cookies, but AdExchanger reported that some people in the advertising technology industry expressed skepticism about the claim and the methodology behind it. As every website that opts into FLoC will have the same access about which cohort the user belongs to, the technology's developers say this democratizes access to some information about a user's general browser history, in contrast to the status quo, where websites have to use tracking techniques.
The Electronic Frontier Foundation has criticized FLoC, with one EFF researcher calling the testing of the technology in Chrome "a concrete breach of user trust in service of a technology that should not exist" in a post on the organization's blog. The EFF also created a website which allows Chrome users to check whether FLoC is being tested in their browsers. The EFF criticized the fact that every site will be able to access data about a user, without having to track them across the web first. Additionally on the EFF blog, Cory Doctorow praised Chrome's planned removal of third-party cookies, but added that "[just] because FLoC is billed as pro-privacy and also criticized as anti-competitive, it doesn't mean that privacy and competition aren't compatible", stating that Google is "appointing itself the gatekeeper who decides when we're spied on while skimming from advertisers with nowhere else to go."
On April 10, 2021, the CEO of DuckDuckGo released a statement telling people not to use Google Chrome, stating that Chrome users can be included in FLoC without choosing to be and that no other browser vendor has expressed interest in using the tracking method. The statement said that "there is no such thing as a behavioral tracking mechanism imposed without consent that respects people's privacy" and that Google should make FLoC "explicitly opt-in" and "free of dark patterns". DuckDuckGo also announced that its website will not collect FLoC IDs or use them to target ads, and updated its Chrome extension to block websites from interacting with FLoC.
On April 12, 2021, Brave, a web browser built on the Chromium platform, criticized FLoC in a blog post and announced plans to disable FLoC in the Brave browser and make company's main website opt out of FLoC. The blog post, co-written by the company's CEO Brendan Eich, described Google's efforts to replace third-party cookies as "Titanic-level deckchair-shuffling" and "a step backward from more fundamental, privacy-and-user focused changes the Web needs."
Tech and media news site The Verge noted that not all possible repercussions of FLoC for ad tech are known, and that its structure could benefit or harm smaller ad tech companies, noting specifically that larger ad tech companies may be better equipped to "parse what FLoCs mean and what ads to target against them."
Multiple companies including GitHub, Drupal and Amazon declined to enable FLoC, instead opting to disable FLoC outright by including the HTTP Header Permissions-Policy: interest-cohort=(). WordPress, a widely used website framework floated a proposal to disable FLoC based tracking across all websites that used the framework.
Almost all major browsers based on Google's open-source Chromium platform declined to implement FLoC, including Microsoft Edge, Vivaldi, Brave, and Opera.
In May 2021, The Economist reported that it may be hard for Google to "stop the system from grouping people by characteristics they wish to keep private, such as race or sexuality."
=== Fingerprinting concerns ===
In May 2021, The Economist said some critics have suggested that the cohort system will facilitate fingerprinting of individual devices, compromising privacy.
Wired magazine additionally reported that FLoC could "be used as a point of entry for fingerprinting".
Mozilla, the creators of the Firefox browser, expressed concerns that FLoC can be used as an additional fingerprinting vector. Furthermore, they stated that a user's FLoC group can be tracked during multiple visits and correlated via different means and, based on a user's membership in multiple FLoC cohorts, a website might be able to infer information about the user which FLoC aimed to keep private. Since a FLoC cohort is shared across websites, its ID might be abused as an alternative to a unique cookie in third-party contexts.
=== Antitrust response ===
In July 2020, the United Kingdom's Competition and Markets Authority found that the FLoC proposal "place[s] the browser in a vital gatekeeper position for the adtech ecosystem."
In March 2021, 15 attorneys general of U.S. states and Puerto Rico amended an antitrust complaint filed in December; the updated complaint says that Google Chrome's phase-out of third-party cookies in 2022 will "disable the primary cookie-tracking technology almost all non-Google publishers currently use to track users and target ads. Then [...] Chrome, will offer [...] new and alternative tracking mechanisms [...] dubbed Privacy Sandbox. Overall, the changes are anticompetitive".
In June 2021, EU antitrust regulators launched a formal investigation to assess whether Google violated competition rules, with a focus on display advertising, notably whether it restricts access to user data by third parties while reserving it for its own use. Among the things that will be investigated is Google's plan to prohibit the placement of third-party cookies and replace them with the Privacy Sandbox set of tools.
=== GDPR compliance ===
As of April 2021, Google was not testing FLoC in the United Kingdom or the European Economic Area due to concerns about compliance with the General Data Protection Regulation and the ePrivacy Directive.
Johannes Caspar, the Data Protection Commissioner of Hamburg, Germany, told Wired UK that FLoC "leads to several questions concerning the legal requirements of the GDPR," explaining that FLoC "could be seen as an act of processing personal data" which requires "freely given consent and clear and transparent information about these operations." A spokesperson of the French National Commission on Informatics and Liberty said that the FLoC system would require "specific, informed and unambiguous consent".
As of April 2021, the Irish Data Protection Commission, which is the lead data supervisor for Google under GDPR, was consulting with Google about the FLoC proposal.
== References ==
== External links ==
Am I FLoCed?—EFF website reporting to users if FLoC is enabled
FLoCs explained at the Privacy Sandbox Initiative website
More detailed
FLoC Origin Trial & Clustering – infos from the Chromium project | Wikipedia/Federated_Learning_of_Cohorts |
Global IP Solutions (also known as GIPS) was a United States–based corporation that developed real-time voice and video processing software for IP networks, before it was acquired by Google in May 2010. The company delivered embedded software that enabled real-time communications capabilities for video and voice over IP (VoIP). GIPS was perhaps best known for developing the narrowband iLBC and wideband iSAC speech codecs.
GIPS software was generally delivered as “engines” that packaged together voice and video processing components for smoother integration and better performance. GIPS’ customers are primarily service providers, application developers, and manufacturers of IP phones, gateways or voice and video conferencing systems.
== History ==
The company (formerly known as Global IP Sound) was founded in July 1999 in Stockholm, Sweden, by signal processing experts Roar Hagen (then GIPS’ CTO) and Bastiaan Kleijn (then GIPS’ Chief Scientist), Espen Fjogstad and Ivar T. Hognestad. The founders recognized that, at the time, most VoIP technology had been developed for circuit switched networks, and were therefore not suited to handle the network delay, jitter and packet loss presented by IP networks.
In May 2010, Google bought GIPS for $68.2 million. In June 2011, Google released WebRTC, a proposed standard for pluginless peer-to-peer audiovisual communication between browsers, with GIPS technology.
== References ==
== External links ==
iLBCfreeware site
Global IP Solutions Website | Wikipedia/Global_IP_Solutions |
The Skia Graphics Engine or Skia is an open-source 2D graphics library written in C++. Skia abstracts away platform-specific graphics APIs (which differ from one to another). Skia Inc. originally developed the library; Google acquired it in 2005, and then released the software as open source licensed under the New BSD free software license in 2008.
== Overview ==
In order to stay multi-platform, Skia supports several (platform-dependent) back-ends. These include:
CPU software rasterization
Portable Document Format (PDF) output
GPU-accelerated rendering by using:
ANGLE backend, which translates OpenGL ES calls into vendor's native APIs
Vulkan, and Metal.
Scalable Vector Graphics (SVG)
XML Paper Specification (XPS)
Skia is most similar in purpose to Cairo or Pathfinder (meaning that it focuses on drawing) rather than to other more elaborate APIs like that of Qt that provide their own widgets and UI description language etc.
== Application ==
The library is used as of 2023 in Google Chrome, ChromeOS, ChromiumOS, Mozilla Firefox, Mozilla Thunderbird, Android, Firefox OS, Flutter, Ladybird Avalonia (from Alpha 4), LibreOffice (from version 7.0) and RAD Studio(since version 12.0).
== Supported platforms ==
Windows 10, 11
macOS 10.15 or later
iOS 12 or later
Android 4.3 (JellyBean) or later
Ubuntu 18.04+, Debian 10+, openSUSE 15.2+, or Fedora Linux 32+
Web Browsers
== Etymology ==
Skia is a romanisation of the word 'shadow' in Greek (Σκιά).
== History ==
Skia Inc, developers of the Skia Graphics Engine, was founded in 2004 by Mike Reed and Cary Clark in Chapel Hill North Carolina, before being acquired by Google in 2005.
== See also ==
Direct2D
Starling Framework
Anti-Grain Geometry
CoreGraphics
Cairo
QuickDraw GX
== References ==
== External links ==
Official website
Skia & Freetype – Android 2D Graphics Essentials
Pathfinder 3
=== YouTube ===
Skia Path Ops : High Performance Set Operations for Geometry on YouTube
Google Developers: Painting in Chromium, 2012 on YouTube | Wikipedia/Skia_Graphics_Engine |
Google Energy LLC is a subsidiary company of Alphabet Inc., which was created to reduce costs of energy consumption of the Google Group, and subsequently to produce and sell clean energy. The division also allows it to take advantage of projects funded through the philanthropic Google.org.
== Operations ==
By 2007 Google had invested a substantial amount of money in wind, solar, solar thermal, and geothermal projects, including a 1.6 MW solar installation pilot project at its headquarters. In 2010 Google Energy made its first investment in a renewable-energy project, putting up US$38.8 million for two wind farms in North Dakota. The company announced that the two locations will generate 169.5 MW of power, or enough to supply 55,000 homes. The farms, which were developed by NextEra Energy Resources, will reduce fossil fuel use in the region. NextEra Energy Resources sold Google a twenty percent stake in the project in order to get funding for project development. In addition, on July 30, 2010, Google Energy agreed to purchase 114 MW of Iowa wind energy from NextEra Energy at a fixed rate for 20 years. The corporation plans to primarily use the electricity for Google's data centers, but it may also be sold on the open market.
In 2010 Google Energy, together with a group of other investors, announced a plan to build the Atlantic Wind Connection, an undersea cable off the Atlantic coast to connect future offshore wind farms with on-shore transmission grids.The project ran into financial issues as the low cost of natural gas made large scale offshore wind uncompetitive.
In April 2011, Google extended its partnership with NextEra by signing a 20-year power purchase agreement (PPA) for its Minco II Wind Energy Center. As of 2011, the 100.8-megawatt wind farm is being developed in the Grady and Caddo counties near Minco.
Google invested two rounds in SolarCity, $280 million in 2011 and $300 million in 2015.
On September 17, 2013, the corporation announced its plan to purchase all of the electricity produced by the 240-megawatt Happy Hereford wind farm that will be located near Amarillo, Texas, US upon the completion of the farm's construction. Purchased from the wind farms owners Chermac Energy, Google Energy will sell the electricity from Happy Hereford into the wholesale market in Oklahoma, the location of one of its data centers.
As of 2016, Google has power purchase agreements for 2,600 MW.
== DeepMind integration ==
Google plans to combine its DeepMind AI to optimize the production of energy from its wind farms. Wind power will always suffer from unpredictability. That limits its adoption when compared to other energy sources that can reliably deliver power at a set time. To help solve this problem, last year DeepMind started building algorithms to boost the efficacy of Google's wind farms in the US, it said in a blog post. It trained a neural network on weather forecasts and past turbine data, so it could predict power output 36 hours ahead. Based on this, the model recommends how to allocate power to the grid a full day in advance. This boosted the "value" of Google's wind farms by about 20%, it claims, though it hasn't specified what form that value takes, or how it's measured. While it's only been built and tested out internally so far, it's not hard to imagine Google hoping to sell this technology to wind farm operators.
== Authorization to buy and sell energy ==
In February 2010, the Federal Energy Regulatory Commission FERC granted Google an authorization to buy and sell energy at market rates. The order specifically states that Google Energy—a subsidiary of Google—holds the rights "for the sale of energy, capacity, and ancillary services at market-based rates", but acknowledges that neither Google Energy nor its affiliates "own or control any generation or transmission" facilities.
== See also ==
Google PowerMeter, a Google service that was discontinued in 2011.
== References ==
== External links ==
What does it take to power Google? | CO2Sense
Google's zero-carbon quest, Fortune, 2012
Complete list of investments | Wikipedia/Google_Energy |
Bump was an iOS and Android mobile app that enabled smartphone users to transfer contact information, photos and files between devices. In 2011, it was #8 on Apple's list of all-time most popular free iPhone apps, and by February 2013 it had been downloaded 125 million times. Its developer, Bump Technologies, shut down the service and discontinued the app on January 31, 2014, after being acquired by Google for Google Photos and Android Camera.
== Features ==
Bump sent contact information, photos and files to another device over the internet. Before activating the transfer, each user confirmed what he or she wants to send to the other user. To initiate a transfer, two people physically bumped their phones together. A screen appeared on both users' smartphone displays, allowing them to confirm what they want to send to each other. When two users bumped their phones, software on the phones send a variety of sensor data to an algorithm running on Bump servers, which included the location of the phone, accelerometer readings, IP address, and other sensor readings. The algorithm figured out which two phones felt the same physical bump and then transfers the information between those phones. Bump did not use Near Field Communication.
February 2012 release of Bump 3.0 for iOS, the company streamlined the app to focus on its most frequently used features: contact and photo sharing. Bump 3.0 for Android maintained the features eliminated from the iOS version but moved them behind swipeable layers.
In May 2012, a Bump update enabled users to transfer photos from their phone to their computer via a web service. To initiate a transfer, the user goes to the Bump website on their computer and bumps the smartphone on the computer keyboard's space bar. By December 2012, various Bump updates for iOS and Android had added the abilities to share video, audio, and any files. Users swipe to access those features.
In February 2013, an update to the Bump iOS and Android apps enabled users to transfer photos, videos, contacts and other files from a computer to a smartphone and vice versa via a web service. To perform the transfer, users went to the Bump website on their computer and bump the smartphone on the computer keyboard's space bar.
== History ==
The underlying idea of a synchronous gesture like bumping two devices for content transfer or pairing them was first conceived by Ken Hinkley of Microsoft Research in 2003. This idea was presented at a user interface and technology conference that same year. The paper proposed the use of accelerometers and a bumping gesture of two devices to enable communication, screen sharing and content transfer between them. Similar to this original concept, the idea for Bump app was conceived by David Lieb, a former employee of Texas Instruments, while he was attending the University of Chicago Booth School of Business for his MBA. While going through the orientation and meeting process of business school, he became frustrated by constantly entering contact information into his iPhone and felt that the process could be improved. His fellow Texas Instruments employees Andy Huibers and Jake Mintz, who was a classmate of Lieb's at the University of Chicago's MBA program, joined Lieb to form Bump Technologies.
Bump Technologies launched in 2008 and is located in Mountain View, Calif. Early funding for the project was provided by startup incubator Y Combinator, Sequoia Capital and other angel investors. It gained attention at the CTIA international wireless conference, due to its accessibility and novelty factor. In October 2009, Bump received $3.4m in Series A funding followed in January 2011 with a $16m series B financing round led by Andreessen Horowitz. Silicon Valley venture capitalist Marc Andreessen sits on the company's board.
The Bump app debuted in the Apple iOS App Store in March 2009 and was “one of the apps that helped to define the iPhone” (Harry McCracken, Technologizer). It soon became the billionth download on Apple's App Store. An Android version launched in November 2009. By the time Bump 3.0 for iOS was released in February 2012, the app had been installed 77 million times, with users sharing more than 2 million photos daily. As of February 2013, there had been 125 million Bump app downloads.
== Other apps created by Bump Technologies ==
Bump Technologies worked with PayPal in March 2010 to create a PayPal iPhone application. The application, which allows two users to automatically activate an Internet transfer of money between their accounts, found widespread adoption. A similar version was released for Android in August 2010.
The Bump capability in PayPal's apps was removed in March 2012. At that time, Bump Technologies released Bump Pay, an iOS app that lets users transfer money via PayPal by physically bumping two smartphones together. The tool was originally created for the Bump team to use when splitting up restaurant bills. The payment feature was not added to the Bump app because the company “wanted to make it as simple as possible so people understand how this works,” Lieb told ABC News. Bump Pay was the first app from the company's Bump Labs initiative. A goal of Bump Labs is to test new app ideas that may not fit within the main Bump app.
ING Direct added a feature to its iPhone app in 2011 that lets users transfer money to each other using Bump's technology. The feature was later added to its Android app, now called Capital One 360.
In July 2012, Bump Technologies released Flock, an iPhone photo sharing app. An Android version was released in December 2012. Using geolocation data embedded in photos and a user's Facebook connections, Flock finds pictures the user takes while out with friends and family and puts everyone's photos from that event into a single shared album. Users receive a push notification after the event, asking if they want to share their photos with friends who were there in the moment. The app will also scan previous photos in the iPhone camera roll and uncover photos that have yet to be shared. If location services were enabled at the time a photo was taken, Flock allows users to create an album of photos from the past with the friends who were there with them.
== Acquisition by Google ==
On September 16, 2013, Bump Technologies announced that it had been acquired by Google. On December 31, 2013, they broke the news that both Bump and Flock would be discontinued so that the team could focus on new projects at Google. The apps were removed from the App Store and Google Play on January 31, 2014. The company subsequently deleted all user data and shut down their servers, thus rendering existing installations of the apps inoperable.
== See also ==
Android Beam
== References == | Wikipedia/Bump_(application) |
Google Tensor is a series of ARM64-based system-on-chip (SoC) processors designed by Google for its Pixel devices. It was originally conceptualized in 2016, following the introduction of the first Pixel smartphone, though actual developmental work did not enter full swing until 2020. The first-generation Tensor chip debuted on the Pixel 6 smartphone series in 2021, and was succeeded by the Tensor G2 chip in 2022, G3 in 2023 and G4 in 2024. Tensor has been generally well received by critics.
== Development ==
=== Background ===
Development on a Google-designed system-on-chip (SoC) first began in April 2016, after the introduction of the company's first Pixel smartphone, although Google CEO Sundar Pichai and hardware chief Rick Osterloh agreed it would likely take an extended period of time before the product was ready. The next year, the company's hardware division assembled a team of 76 semiconductor researchers specializing in artificial intelligence (AI) and machine learning (ML), which has since increased in size, to work on the chip. Beginning in 2017, Google began to include custom-designed co-processors in its Pixel smartphones, namely the Pixel Visual Core on the Pixel 2 and Pixel 3 series and the Pixel Neural Core on the Pixel 4 series.
By April 2020, the company had made "significant progress" toward a custom ARM-based processor for its Pixel and Chromebook devices, codenamed "Whitechapel". At Google parent company Alphabet Inc.'s quarterly earnings investor call that October, Pichai expressed excitement at the company's "deeper investments" in hardware, which some interpreted as an allusion to Whitechapel. The Neural Core was not included on the Pixel 5, which was released in 2020; Google explained that the phone's Snapdragon 765G SoC already achieved the camera performance the company had been aiming for. In April 2021, 9to5Google reported that Whitechapel would power Google's next Pixel smartphones. Google was also in talks to acquire Nuvia prior to its acquisition by Qualcomm in 2021.
Google officially unveiled the chip, named Tensor, in August, as part of a preview of its Pixel 6 and Pixel 6 Pro smartphones. Previous Pixel smartphones had used Qualcomm Snapdragon chips, with 2021's Pixel 5a being the final Pixel phone to do so. Pichai later obliquely noted that the development of Tensor and the Pixel 6 resulted in more off-the-shelf solutions for Pixel phones released in 2020 and early 2021. In September 2022, The Verge reported that a Tensor-powered successor to the Pixelbook laptop with a planned 2023 release had been canceled due to cost-cutting measures.
=== Design ===
"Tensor" is a reference to Google's TensorFlow and Tensor Processing Unit technologies, and the chip is developed by the Google Silicon team housed within the company's hardware division, led by vice president and general manager Phil Carmack alongside senior director Monika Gupta, in conjunction with the Google Research division.
Tensor's microarchitecture consists of two large cores, two medium cores, and four small cores; this arrangement is unusual for octa-core SoCs, which typically only have one large core. Carmack explained that this was so Tensor could remain efficient at intense workloads by running both large cores simultaneously at a low frequency to manage the various co-processors. Osterloh has stated that Tensor's performance is difficult to quantify using synthetic benchmarks, but should instead be characterized by the many ML capabilities it enables, such as advanced speech recognition, real-time language translation, the ability to unblur photographs, and HDR-like frame-by-frame processing for videos.
== Models ==
=== Original ===
The first-generation Tensor chip debuted on the Pixel 6 and Pixel 6 Pro, which were officially announced in October 2021 at the Pixel Fall Launch event. It was later reused for the Pixel 6a, a mid-range variant of the Pixel 6 series which was announced in July 2022. Despite being marketed as developed by Google, close-up examinations revealed that the chip contains numerous similarities with Samsung's Exynos series.
=== G2 ===
A second-generation Tensor chip was in development by October 2021, codenamed "Cloudripper". At the annual Google I/O keynote in July 2022, Google announced that the chip would debut on the Pixel 7 and Pixel 7 Pro smartphones, which were officially announced on October 6 at the annual Made by Google event. The chip is marketed as "Google Tensor G2". The chip was also used to power the Pixel 7a, Pixel Fold foldable smartphone, and Pixel Tablet which was unveiled in May 2023 during the annual I/O keynote.
=== G3 ===
Samsung had begun testing Tensor G3 by August 2022, codenamed "Zuma". Announced in October 2023, the chip was used to power the Pixel 8a, Pixel 8 and Pixel 8 Pro.
=== G4 ===
Codename: "Zuma Pro". Devices: Pixel 9, Pixel 9a, Pixel 9 Pro, Pixel 9 Pro XL and Pixel 9 Pro Fold.
=== Future ===
The Information reported in July 2023 that Google had initiated development on Tensor G5, codenamed "Laguna", which was to be designed fully in-house, manufactured by TSMC instead of Samsung, and built on TSMC's 3 nm process.
== Reception ==
At launch, Tensor was well received. Philip Michaels of Tom's Guide praised the Pixel 6 and Pixel 6 Pro's Tensor-powered features and video enhancements, as did Marques Brownlee and Wired's Julian Chokkattu. Chokkattu's colleague Lily Hay Newman also highlighted the chip's security capabilities, declaring them Tensor's strongest selling point. Jacon Krol of CNN Underscored wrote that Tensor delivered "some of the most fluid and fastest performance" on a smartphone, though Android Authority's Jimmy Westenberg was ambivalent. Ryne Hager of Android Police thought the chip's performance was acceptable to the everyday user, but was disappointed that Google did not offer more years of Android updates given it was no longer bound by Qualcomm's contractual terms. TechRadar reviewer James Peckham commended Tensor as a "standout feature", though his colleague David Lumb described the chip's performance as "strong but not class-leading".
== See also ==
Apple silicon
== References == | Wikipedia/Google_Tensor |
The Google Science Fair was a worldwide (excluding Cuba, Iran, North Korea, Sudan, Myanmar/Burma, Syria, Zimbabwe and any other U.S. sanctioned country) online science competition sponsored by Google, Lego, Virgin Galactic, National Geographic and Scientific American. It was an annual event from 2011 to 2018.
The first Google Science Fair was announced in January 2011; entries were due on April 7, 2011, and judging occurred in July 2011. The competition is open to 13- to 18-year-old students around the globe, who formulate a hypothesis, perform an experiment, and present their results. All students had to have an internet connection and a Google Account to participate, and the projects had to be in English, German, Italian, Spanish, or French. The final submission had to include ten sections, which were the summary, an "About Me" page, the steps of the project, and a works cited page.
Entries were judged on the student's presentation, question, hypothesis, research, experiment, data, observations, and conclusion. Prizes were awarded to three finalists. The grand prize included a National Geographic trip to the Galapagos Islands, and a US$50,000 scholarship; finalists received a US$15,000 scholarship and assorted packages from sponsoring organizations.
== Guest interviews ==
The on-line site also contains a number of highlighted guest interviews with selected individuals, each well established and prominent in their field of science, with the aim being for them to act as inspiration to young students. The individuals chosen include Mitch Resnick, Spencer Wells, Kevin Warwick, and Mariette DiChristina.
== 2011 Winners ==
Shree Bose, a 17-year-old girl from Fort Worth, Texas, won the grand prize and $50,000 for her research on the chemotherapy drug, cisplatin, that is commonly taken by women with ovarian cancer, tackling the problem of cancer cells growing resistant to cisplatin over time.
Naomi Shah of Portland, OR, won the age 15–16 category with a study of the effects of air quality on lungs, particularly for people who have asthma. Ms. Shah recruited 103 test subjects, performed 24-hour air quality measurements at their homes and workplaces and had each blow into a device that measured the force of their breath.
Lauren Hodge of York, PA, won the age 13–14 category for research on whether marinades reduce the amount of cancer-causing compounds produced by the grilling of meat. She found that lemon juice and brown sugar cut the level of carcinogens sharply, while soy sauce increased them.
People around the world (90 countries) had the opportunity to vote for their favorite projects in Google's online voting gallery. Google has had more than 100,000 votes and the competition was really tight. Nimal Subramanian won the People's Choice Award for receiving the most among the 60 semi-finalists. The public really loved Nimal's project on Cancer Busters. Nimal received a $10,000 scholarship.
== 2012 Winners ==
Brittany Wenger, who was 17, won the grand prize with her "Global Neural Network Cloud Service for Breast Cancer". Designed to noninvasively diagnose malignant cancerous tumors, it successfully detected over 99% of malignant breast tumors in a test set. She received $50,000, a trip to the Galapagos Islands, mentoring and internship opportunities for winning the competition.
Iván Hervías Rodríguez, Marcos Ochoa, and Sergio Pascual, all of Spain, won the 15-16 age group using microscopy to examine microscopic creatures in aquatic ecosystems.
Jonah Kohn won the age 13-14 group by designing and building a device designed to enhance the listening experience of those with hearing loss. His device attached to different parts of the body, translating sound into tactile stimulation.
== 2013 Winners ==
The winners of the 2013 Google Science Fair were:
13-14 age category: Viney Kumar (Australia) — The PART (Police and Ambulances Regulating Traffic) Program. Viney's project looked for new ways to provide drivers with more notice when an emergency vehicle is approaching, so they can take evasive action to get out of the emergency vehicle's way.
15-16 age category: Ann Makosinski (Canada) — The Hollow Flashlight. Using Peltier tiles and the temperature difference between the palm of the hand and ambient air, Ann designed a flashlight that provides bright light without batteries or moving parts.
17-18 age category Grand Prize Winner: Eric Chen (USA) — Computer-aided Discovery of Novel Influenza Endonuclease Inhibitors to Combat Flu Pandemic. Combining computer modeling and biological studies, Eric's project looks at influenza endonuclease inhibitors as leads for a new type of anti-flu medicine, effective against all influenza viruses including pandemic strains.
== 2014 Winners ==
The 2014 Google Science Fair started accepting entries on February 12, 2014, and the entries closed on May 13, 2014. And the results for the local, regional and Science in Action award nominees were declared. The Grand Prize was won by three girls from Ireland, Ciara Judge (16), Emer Hickey (16) and Sophie Healy-Thow (17). They were the first group winners of the competition and the youngest winners to date (they also won the 15-16 age category prize). Their project was entitled 'Combating the Global Food Crisis: Diazotroph Bacteria as a Cereal Crop Growth Promoter.'
The 13-14 age category was won by Mihir Garimella (14) from Pittsburgh, Pennsylvania with a project titled 'Fruit-fly Inspired Robots.' Hayley Todesco (17) of Canada won the 17-18 age category with her project titled 'Cleaning up Oil Sands Waste.'
Along with the overall prizes for each category, a number of special awards were also announced. Kenneth Shinozuka (15) was declared as the Science In Action Award winner in recognition of the practical potential of his project 'Wearable Sensors for Aging Society.' Arsh Shah Dilbagi (16) from India won the Voter's Choice Award for creating an augmentative and alternative communication (AAC) device that converts breath into words, enabling mute people to speak. Local Award winners included Shannon Tan (18), who won the award in Singapore for his research on using treated materials from crustacean shells to purify wastewater from heavy industries.
== 2015 Winners ==
The 2015 Google Science Fair closed for entries on May 18, 2015, with regional finalists announced in London on July 7, 2015. These included Lauren McKenzie (14) who built an automatic soil watering system, Shadab Karnachi (14) who designed a low-cost gaming device for people with visual impairments, Nishanth Kumar (16) who designed a low-cost 'hands-free' mouse for use by people with developmental disabilities, and Peter He (14) who developed an innovative wireless virtual reality system.
The global finalists representing 10 countries were announced on August 4, 2015 and were as follows:
Bosnia-Herzegovina
Anela Arifi and Ilda Ismaili - A system for alternative fuel production and storage using chicken feathers
Canada
Isabella O'Brien - Trouble in Paradise: Recycling shell waste to reduce ocean acidification
Calvin Rieder - Extracting clean water from air: solar-powered solution for providing potable water
France
Eliott Sarrey - Bot2Karot: gardening through a smartphone-activated robot
India
Lalita Prasida Sripada Srisai - Absorbing water pollutants with corn cobs
Lithuania
Laura Steponavičiūtė - Detecting the environmental dangers of nanomaterials
Russia
Alexey Tarasov - Using ternary logic on current electronics
Singapore
Girish Kumar - RevUp: improving learning through auto-generated study questions
Zhilin Wang - Zinc air batteries for affordable, renewable energy storage
Taiwan
Wei-Tung Chen - Calculating the 3D position of an object from a single source
Yo Hsu and Jing-Tong Wang - Knock on fuel: detecting impurities in gasoline with sound pattern analysis
United Kingdom
Krtin Nithiyanandam - Improving diagnosis and treatment for Alzheimer’s with new molecular “Trojan Horse”
Matthew Reid - The ArduOrbiter: a lightweight, open source satellite
United States
Anika Cheerla - Automated and accurate early-diagnosis of Alzheimer's disease
Anurudh Ganesan - VAXXWAGON: a reliable way to store and transport vaccines
Olivia Hallisey [WINNER] - Temperature-independent, inexpensive and rapid detection of Ebola
Deepika Kurup - Solar powered silver combating bacteria in drinking water
Pranav Sivakumar - Automated search for gravitationally lensed quasars
Adriel Sumathipala - Creating a simple diagnostic tool for earlier detection of cardiac disease
Tanay Tandon - Delivering rapid, portable and automated blood morphology tests
The winners were announced on September 21, 2015. The Grand Prize was won by Olivia Hallisey (16) with her project ‘Temperature-Independent, Portable, and Rapid Field Detection of Ebola via a Silk-Derived Lateral-Flow System’. The Google Technologist Award was won by Girish Kumar (17) for his project ‘Revup: Automatically Generating Questions from Educational Texts’ and the Incubator Award was won by Elliott Sarrey (14) with his project ‘Bot2karot: Manage Your Vegetable Garden via Your Smartphone’. The Lego Education Builder Award won by Anurudh Ganesan (15), the Virgin Galactic Pioneer Award won by Pranav Sivakumar (15), the Scientific American Innovator Award won by Krtin Nithiyanandam (15), the National Geographic Explorer Award won by Deepika Kurup (17) and the Community Impact Award won by Lalita Prasida.
== 2016 Winners ==
The 2016 Google Science Fair closed its entries on May 17, 2016, the Global 16 Finalist were announced on August 11, 2016. The final event took place during 24 to 27 September 2016 at Mountain View, California. Sixteen finalists competed for top five awards. The first two rounds had two age groups 13-15 and 16–18. However, unlike previous years, top awards during the finalist event did not distinguish between the two age groups of the previous rounds, thus making it particularly challenging event for the contestant compared to all previous years.
The Grand Prize was won by Kiara Nirghin (16) of South Africa for her project 'Fighting Drought with Fruit'. The Lego Education Builder award was won by Anushka Naiknaware (13) of United States, the youngest contestant to win a top award ever, for 'Smart Wound Care for the Future'. The National Geographic Explorer award was won by Mphatso Simbao (18) of Zambia. The Scientific Innovator Award was won by a team of three for 'Fighting Foam Waste with Recycled Filters' from the United States [Ashton Cofer (14), Luke Clay (14) and Julie Bray (14)]. The Virgin Galactic Pioneer award was won by Charlie Fenske (16) for 'Making Rockets more Efficient', also from the United States.
== 2017 Winners ==
The competition did not begin as usual in May, 2017. Starting from the late summer, the official website stated that "We're conducting some experiments" and "Coming Fall 2017". The submissions of competition in 2018 began on 13 September 2018.
== 2018 Winners ==
The Google Science Fair returned with 179 different prizes available for 2018–19. It opened for entries on September 13, 2018, and closed its entries on December 12, 2018. State award winners were announced in March 2019, regional award winners in April 2019, and global finalists in May 2019. On July 29, 2019, the top five awards were issued for students and one for an inspiring educator. The Google Grand Prize, featuring an award of a $50,000 educational scholarship, went to Fionn Ferreira, of Ireland. His project was titled "An investigation into the removal of microplastics from water using ferrofluids." The National Geographic Explorer award was won by A U Nachiketh Kumar and Aman K A, of India, for finding an eco-friendly way to coagulate rubber. The Lego Education Award was won by Daniel Kazantsev of the Russian Federation, who wanted to find a better way to help those who are hearing impaired to communicate with the world around them. The Scientific American Award was won by Tuan Dolmen of Turkey, who found a way to harness energy from tree vibrations. The Galactic Pioneer Award was won by Celestine Wenardy of Indonesia, for creating a low-cost and non-invasive glucose meter.
== See also ==
Science fair
== References ==
== External links ==
Official website
Previous Winners | Wikipedia/Google_Science_Fair |
The Google Affiliate Network was the affiliate marketing company, specifically affiliate network, formerly known as Doubleclick Performics, which was bought by Google in 2007. On April 16, 2013, Google announced the closure of the Google Affiliate Network.
== History ==
DoubleClick announced the acquisition of DoubleClick (including Performics) by Google for $3.1 Billion in April 2007. The acquisition was finalized in March 2008 after the approval of the Department of Justice antitrust authorities in the United States and the Brussels-based European Commission, the antitrust authority of the European Union.
The search engine marketing and optimization part of Performics was acquired by Publicis in 2008, after the purchase of DoubleClick by Google (NASDAQ: GOOG) had been finalized. The affiliate network part of DoubleClick Performics remained with Google and was re-branded Google Affiliate Network.
On April 17, 2013, Google announced plans to retire the Google Affiliate Network on July 31, 2013.
== See also ==
Affiliate marketing
Affiliate programs directories
Affiliate network
== References ==
== External links ==
Official Webpage
Google AdPlanner | Wikipedia/Google_Affiliate_Network |
Marratech was a Swedish company that made software for e-meetings (e.g., web conferencing, videoconferencing). It was acquired by Google in 2007.
== History ==
Marratech was founded in 1998, as a spin-off company from the Centre for Distance-Spanning Technology at the Luleå University of Technology. Founders include Dr. Dick Schefström (deceased), Prof. Peter Parnes, Johnny Widén, Prof. Kåre Synnes, Mikael Börjeson, Magnus Hedberg, Serge Lachapelle and Claes Ågren. The Marratech prototype was launched 1995 as part of an EU project called Multimedia Assisted Tele-engineering (MATES) project.
Marratech's first product, which offered voice, video, whiteboard and group instant messaging, was first released in November 1998. The first release required the presence of an IP multicast network and was built as a server-less architecture. The solution has since evolved to support both traditional IP Unicast and IP multicast, high security and multi-platform computing. For guaranteed, serverless, scalable data delivery over both Multicast and Unicast, Scalable Reliable Multicast (SRM) is used over the Real-time Transport Protocol, called SRRTP.
In 2004, Marratech introduced support for dialing out to IP telephones, land lines and mobile phones via the Session Initiation Protocol (SIP). In 2005, H.323 support was added to communicate with traditional video conferencing equipment.
In 2005, Marratech launched Marratech Free, a freeware edition of its product to host video chats online accessible to everyone.
In 2006, one of the first projects to handle remote, wireless eye examinations via video-conferencing was launched in rural India by the university of Berkeley and Intel, with Marratech providing the video-conferencing technology.
In 2007, Marratech's video conference software was acquired by Google. Most engineers and key personnel have moved to Google. The financial terms of the acquisitions were not released. This acquisition was announced a few months after Cisco acquired Webex. Google plans its use for their staff members initially and later they might come out with a massive change in the software for public use.
On December 12, 2009, Marratech announced that it would close down its website before the year-end. On February 19, 2010, Marratech announced on their homepage that it had suspended all its services. Its server no longer allows download of either client or server software.
== Description ==
Some of the key features included in Marratech are:
High quality voice for groups with private audio feature
Interactive group whiteboard
Multi party video
Some of the key underlying technologies are:
256-bit Advanced Encryption Standard (AES) end-to-end encryption
Support for Windows, Mac OS X and Linux on the client and server side.
Support for bandwidth saving clusters
Support for IP unicast, IP multicast or both
Support for H.323 (dial in and out, E.164) and Session Initiation Protocol (SIP)
H.264 video
The solution includes a freely downloadable client and a server, called the Marratech Manager.
Users include Alcatel Alenia Space, Verizon, the Swedish Police Department, The Swedish Army and a number of universities around the world.
== References ==
== External links ==
Marratech's homepage
Public Marratech Meeting Servers
Evaluation by Kansas's Kan-ed programme
Evaluation by Monash University
Review by Network Computing
Review by Mac Observer
Acquisition by Google | Wikipedia/Marratech |
Google Pay (formerly Android Pay) is a mobile payment service developed by Google to power in-app, online, and in-person contactless purchases on mobile devices, enabling users to make payments with Android phones, tablets, or watches. Users can authenticate via a PIN, passcode, or biometrics such as 3D face scanning or fingerprint recognition.
As of 2025, it is available in 94 countries.
== Service ==
Google Pay uses near-field communication (NFC) to transmit card information facilitating funds transfer to the retailer. It replaces the credit or debit card chip and PIN or magnetic stripe transaction at point-of-sale terminals by allowing the user to upload these in Google Wallet. It is similar to contactless payments already used in many countries, with the addition of two-factor authentication. The service lets Android devices wirelessly communicate with point of sale systems using a near-field communication (NFC) antenna and host-based card emulation (HCE).
When the user makes a payment to a merchant, Google Pay does not send the actual payment card number. Instead, it generates a virtual account number representing the user's account information.
Google Pay requires that a screen lock be set on the phone or watch. An age limit minimum of 13 years is imposed on users seeking to manage the service themselves. However, younger users can still have access to Google Pay if a parent or guardian manages Wallet for them, and utilizes an approved bank (currently only available on the Fitbit Ace.)
Users can add payment cards to the service by taking a photo of the card, or by entering the card information manually. To pay at points of sale, users hold their authenticated device to the point of sale system. The service has smart-authentication, allowing the system to detect when the device is considered secure (for instance, if unlocked in the last five minutes) and challenge if necessary for unlock information.
=== Technology ===
Google Pay uses the EMV Payment Tokenization Specification.
The service keeps customer payment information private from the retailer by replacing the customer's credit or debit card Funding Primary Account Number (FPAN) with a tokenized Device Primary Account Number (DPAN) and creates a "dynamic security code [...] generated for each transaction". The "dynamic security code" is the cryptogram in an EMV-mode transaction, and the Dynamic Card Verification Value (dCVV) in a magnetic-stripe-data emulation-mode transaction. Users can also remotely halt the service on a lost phone via Google's Find My Device service.
To pay at points of sale, users hold their authenticated Android device to the point-of-sale system's NFC reader. Android users authenticate unlocking their phone by using biometrics, a pattern, or a passcode, whereas Wear OS and Fitbit OS users authenticate by opening the Google Wallet app prior to payment.
=== Consumer Device Cardholder Verification Method (CDCVM) ===
In EMV-mode transactions, Google Pay supports the use of the Consumer Device Cardholder Verification Method (CDCVM) using biometrics, pattern, or the device's passcode. The use of CDCVM allows the device itself to provide verification for the transaction and may not require the cardholder to sign a receipt or enter their PIN.
=== Security ===
Payments for supported transit networks are available to skip verification, either via a payment card or transit card. Though the phone screen needs to be on and is not available when the battery is low, unlike Apple Pay's Express Mode.
On Wear OS and Fitbit OS, this option is not available. All transactions on wearable devices must be authenticated by opening the Wallet app prior to tapping.
Since 2022, the functionality of adding NFC bank cards in Google Wallet requires devices to pass Play Integrity API checks. This implies having a device with locked bootloader and no rooting.
== Availability ==
=== Supported countries ===
As of May 2025, Google Pay is available in 94 countries worldwide.
==== Upcoming ====
Bangladesh
Saudi Arabia
Sri Lanka
=== Supported networks ===
Visa / Visa Debit / Visa electron (Android, Wear OS, Fitbit OS)
Mastercard / Debit Mastercard (Android, Wear OS, Fitbit OS)
American Express (Android, Wear OS, Fitbit OS)
Discover (Android & Wear OS)
Diners Club (Android & Wear OS)
JCB (Android only)
Maestro (Android & Wear OS)
Elo in Brazil (Android & Wear OS)
PayPal in the US, Germany (Android only)
EFTPOS in Australia (Android & Wear OS)
Interac in Canada (Android & Wear OS)
Bancomat in Italy (Android only)
QUICPay (Android & Wear OS)
iD (Android & Wear OS)
WAON (Android only)
Edy (Android only)
nanaco (Android only)
Pix (Android only)
==== Upcoming ====
mada
== See also ==
Apple Pay
Apple Wallet
Cash App
Microsoft Pay
PayPal
Samsung Pay
Samsung Wallet
Unified Payments Interface
Venmo
WeChat Pay
== References ==
== External links ==
Official website | Wikipedia/Google_Pay_(payment_method) |
Internet Low Bitrate Codec (iLBC) is a royalty-free narrowband speech audio coding format and an open-source reference implementation (codec), developed by Global IP Solutions (GIPS) formerly Global IP Sound (acquired by Google Inc in 2011). It was formerly freeware with limitations on commercial use, but since 2011 it is available under a free software/open source (3-clause BSD license) license as a part of the open source WebRTC project. It is suitable for VoIP applications, streaming audio, archival and messaging. The algorithm is a version of block-independent linear predictive coding, with the choice of data frame lengths of 20 and 30 milliseconds. The encoded blocks have to be encapsulated in a suitable protocol for transport, usually the Real-time Transport Protocol (RTP).
iLBC handles lost frames through graceful speech quality degradation. Lost frames often occur in connection with lost or delayed IP packets. Ordinary low-bitrate codecs exploit dependencies between speech frames, which cause errors to propagate when packets are lost or delayed. In contrast, iLBC-encoded speech frames are independent and so this problem will not occur.
iLBC is defined in RFC 3951. It is one of the codecs used by Gizmo5, WebRTC, Ekiga, Google Talk, Maemo Recorder (on the Nokia N800/N810), Polycom IP Phone, Cisco, QuteCom, Tuenti, Yahoo! Messenger, Ooma and many others.
iLBC was submitted to IETF in 2002 and the final specification was published in 2004.
== Parameters and features ==
Sampling frequency 8 kHz/16 bit (160 samples for 20 ms frames, 240 samples for 30 ms frames)
Controlled response to packet loss, delay and jitter
Fixed bitrate (15.2 kbit/s for 20 ms frames, 13.33 kbit/s for 30 ms frames)
Fixed frame size (304 bits per block for 20 ms frames, 400 bits per block for 30 ms frames)
Robustness similar to pulse-code modulation (PCM) with packet loss concealment, like the ITU-T G.711
CPU load similar to G.729A, with higher basic quality and better response to packet loss
Royalty-free
Since 2011 it is available under an open source (3-clause BSD license) license as a part of the open source WebRTC project. (previously commercial use of the source code supplied by GIPS required a licence)
PSQM testing under ideal conditions yields mean opinion scores of 4.14 for iLBC (15.2 kbit/s), compared to 4.3 for G.711 (μ-law)
== See also ==
RTP audio video profile
Comparison of audio coding formats
== References ==
== External links ==
Official homepage
iLBC former homepage | Wikipedia/Internet_Low_Bitrate_Codec |
In May 2013, the German Federal Court of Justice stated that Google's predictions within the autocomplete function of its web search engine can violate the right of personality. The right of personality ensures that a person's (or even a company's) personality (reputation) is respected and can be freely developed. Only the individual shall, in principle, decide how he/she wants to present himself/herself to third parties and the public.
== Facts of the case ==
Source:
A stock corporation, which sold food supplements and cosmetics online, and its chairman filed an action for an injunction and financial compensation against Google based on a violation of their right of personality. Google runs a web search engine under the domain "www.google.de" (among others), which allows Internet users to search for information online and access third party content through a list of search results.
In 2009, Google implemented a so-called "autocomplete" function which shows word combinations as predictions for the search of the user in a new window while typing in a search term into the search mask. These predictions are based on an algorithm which evaluates the number of searches on specific terms of other users. If users typed the full name of the chairman into the search engine in May 2010 the autocomplete function showed the predictions "Betrug" (fraud) or "Scientology". The claimants stated that the chairman would have no connection to Scientology and that he was under no investigation for fraud. Furthermore, they argued that no search result would show a connection between the chairman and fraud or Scientology. Therefore, they saw these predictions as a violation of their right of personality.
The Regional Court Cologne decided in favour of Google and dismissed the case as unfounded. The Higher Regional Court Cologne uphold this judgement. The claimants filed an appeal to the German Federal Court of Justice.
== The decision ==
Source:
The German Federal Court of Justice set aside the judgement of the Higher Regional Court Cologne and referred the case back to this court.
The Federal Court of Justice held that
the predictions ("Betrug"/"Scientology") expressed the existence of a factual connection between the chairman and these negatively connoted terms and violated the right of personality (the Higher Regional Court Cologne had taken a different view previously and had held that the predictions only expressed that other users typed in these word combinations for their search or that the terms could be found in linked third party content)
the claimant's right of personality outweighed Google's freedom of expression and commercial freedom in a trade-off because false expressions do not need to be accepted
the violation was directly assignable to Google because they designed the software, exploited the user's behaviour, and suggested the predictions to the users
the national implementation of the provisions of the Electronic Commerce Directive, which grant intermediaries (access, caching, and host provider) immunity from liability to a certain extent, were not applicable in this case because the predictions were not third party content that Google only made accessible or presented, but Google's own content
the basis for a liability of the search engine provider is not the fact that he developed and used the software because these actions are protected by the provider's commercial freedom
the liability can only be based on the fact that the provider did not take the necessary precautions to prevent the violation of a right of personality as part of a so-called "Stoererhaftung" (the "Stoererhaftung" (interferer's liability) is a liability of a person (the "Stoerer") who is not a perpetrator or participant himself, but contributed willingly and adequately causally to the infringement of a protected legal interest in any way and requires a breach of a reasonable duty of care)
the search engine provider has, in principle, no obligation to monitor the predictions generated by a software beforehand and is only responsible if he becomes aware of the violation by the predictions
if the provider is notified of a violation by the victim he is also required to prevent future violations.
In April 2014, the Higher Regional Court Cologne then decided in favour of the claimants insofar as they objected to the additional term "Scientology" which Google initially refused to remove. A financial compensation was not awarded because Google removed the entry later (about one and a half after the objection) and therefore limited the infringement. Due to the fact that Google removed the additional term "Betrug" (fraud) immediately after the claimant's first objection, this part of the claim was unfounded.
== Criticism ==
Some legal scholars argued that the judgement established a reasonable balance between the protection of the right of personality (by Google's obligation to remove and prevent infringing predictions after a notice), Google's interest to still provide the autocomplete function (without the need to monitor all predictions) and the Internet user's interest to make use of the search's improvement.
The court's decision that the search engine provider has no obligation to monitor the predictions generated by a software beforehand and is only responsible if he becomes aware of the violation by the predictions corresponds with previous judgements of the court on the "Stoererhaftung" (interferer's liability) of a host provider for content that third parties posted on the host provider's website. However, due to the fact that these previous judgements discussed the liability for third party content, others stated that the fact that the court's autocomplete judgement is based on Google being an interferer ("Störer") within the "Stoererhaftung" (interferer's liability) – and not a perpetrator – contradicts the court's statement that the predictions have to be seen as Google's own content.
Moreover, the judgement raises the question which result a trade-off between Google's freedom of expression and commercial freedom and another person's right of personality would have in other scenarios. Depending on the specific circumstances, it could be more complicated to assess if a prediction is false or (even) true, but not worthier of protection than the right of personality (e.g. in a case in which an investigation for a crime – like fraud – already started or in which a person is actually the victim of a crime).
Another interesting issue is the question to what extent Google is capable of legally evaluating and processing notifications by alleged victims of an infringement. The current legal situation could be an incentive for Google to just remove the prediction after a complaint in order to avoid any liability.
== Background information ==
This judgement was not the only time a possible defamation by Google's autocomplete function was discussed in a courtroom. In Germany, Bettina Wulff, the wife of the former President of the Federal Republic of Germany Christian Wulff, filed for an action for an injunction regarding 43 predictions against Google at the Regional Court Hamburg based on a violation of her right of personality. The word combinations included the words "Escort" (escort) and "Prostituierte" (prostitute). However, in January 2015, Google deleted these predictions and the parties settled the lawsuit. By taking legal actions against Google, Bettina Wulff probably also caused a so-called "Streisand effect" because many people learned about the predictions by the created media attention for the first time.
In France, in 2010, the Superior Court of Paris ordered Google to cease suggesting certain predictions, including "rapist", "satanist", "rape", and "prison", to Internet users who search for a man's name. The man, convicted for a "corruption of a minor" at the time, was still appealing his conviction. In Italy, a businessman filed a defamation suit because of the terms "truffatore" (conman) and "truffa" (fraud) that were added to his name by the autocomplete function. The Milan court ordered Google to remove these predictions in 2011. Furthermore, in 2012, the Supreme Court of Victoria in Melbourne, Australia held Google liable for defamation by wrongly linking a private person to crimes he in fact was a victim of and awarded $200,000 in damages. Moreover, in 2013, the Tokyo District Court in Japan also ordered Google to modify its predictions and pay 300,000 yen ($3,100) as damages to a man which was linked to crimes he did not commit.
However, Google's autocomplete function was not only subject of defamation suits. In another case, French human rights organisations (including SOS Racisme) sued Google for adding the word "juif" (Jewish) to the names of celebrities within its predictions. The human rights organisations argued that Google provided "ethnic files" by suggesting these predictions, which is forbidden in France. The parties settled in 2012 without revealing the details of the settlement.
Today, Google provides an online form that allows Internet users to report an (allegedly) infringing prediction within the autocomplete function.
== Relevance ==
The relevance of this judgement goes beyond the mere autocomplete function because it can be seen as a precedent on the question if algorithms can make defamatory statements. With artificial intelligence and robots becoming more and more widespread in our society, future scenarios, in which the liability for their actions has to be discussed, seem to be likely.
== References == | Wikipedia/Judgement_of_the_German_Federal_Court_of_Justice_on_Google's_autocomplete_function |
Google Web Designer is a drag-and-drop page builder for Windows, macOS, and Linux from Google for creating interactive HTML5 ads and other HTML5 content. It offers a GUI with common design tools, such as a “Text” tool that integrates with Google Web Fonts, a “Shapes” tool, a “Pen” tool, and 3D tools. The advertising feature set includes components to add Google Maps, YouTube videos and more, as well as automatically including the tracking code events for DoubleClick and AdMob.
Google Web Designer's code view lets the user create CSS, JavaScript, and XML files, and uses syntax highlighting and code autocompletion that makes the code easier to write with fewer errors. Google Web Designer is free to download and use.
== See also ==
Google Sites
== References ==
== External links ==
Official website
Release Notes - Google Web Designer Help
TechCrunch | Wikipedia/Google_Web_Designer |
AMP (originally an acronym for Accelerated Mobile Pages) is an open source HTML framework developed by the AMP Open Source Project. It was originally created by Google as a competitor to Facebook Instant Articles and Apple News. AMP is optimized for mobile web browsing and intended to help webpages load faster. AMP pages may be cached by a CDN, such as Cloudflare's AMP caches, which allows pages to be served more quickly.
AMP was first announced on October 7, 2015. After a technical preview period, AMP pages began appearing in Google mobile search results in February 2016. AMP has been criticized for potentially giving further control over the web to Google and other concerns. The AMP Project announced it would move to an open governance model on September 18, 2018, and is part of the OpenJS Foundation as of October 10, 2019.
== History ==
=== Announcement and launch ===
The AMP Project was announced by Google on October 7, 2015, following discussions with its partners in the Digital News Initiative (DNI), and other news publishers and technology companies around the world, about improving the performance of the mobile web. More than 30 news publishers and several technology companies (including Twitter, Pinterest, LinkedIn, and WordPress) were initially announced as collaborators in the AMP Project.
AMP pages first appeared to web users in February 2016, when Google began to show the AMP versions of webpages in mobile search results. Initially links to AMP pages were restricted to a "Top Stories" section of Google's mobile search results; by September 2016 Google started linking to AMP content in the main mobile search results area. At the time, Google search distinguished AMP links with an icon.
According to one of the co-founders of the AMP Project, Malte Ubl, AMP was originally called PCU, which stood for Portable Content Unit.
=== Growth and expansion ===
In September 2016, Microsoft announced support for AMP in the Bing apps for iOS and Android.
In February 2017, a year after the public launch of AMP, Adobe reported AMP pages accounted for 7% of all web traffic for top publishers in the United States.
In May 2017, Google reported 900,000 web domains were publishing AMP pages with more than two billion AMP pages published globally.
In June 2017, Twitter started linking to AMP pages from its iOS and Android apps.
In September 2018, Microsoft began rolling out its own Bing AMP viewer and AMP cache.
On December 7, 2018, AMP announced their official WordPress plugin, which allowed WordPress websites to include AMP-ready pages.
As announced by AMP's tech lead Malte Ubl at AMP Conf '19, AMP is now just AMP, and does not stand for Accelerated Mobile Pages anymore. AMP is designed to be mobile friendly but isn't just for mobile. It works across many device types, including desktop and tablet, and comes with helpful responsive design features.
=== Decline ===
Starting in 2021, support for AMP was discontinued in some apps. In November, Twitter updated its developer guidelines to say that "We’re in the process of discontinuing support for this feature"; the Twitter mobile apps for Android and iOS simply load the non-AMP versions of webpages. In April 2021, Google removed AMP as an SEO criterion in favor of page loading speed and other "page experience" metrics. In search results, the Top Stories list will no longer be restricted to AMP pages, and AMP pages will no longer be distinguished by an icon.
On April 20, 2022, Brave Browser rolled out new features to automatically bypass AMP pages. Also on the same day, DuckDuckGo announced that they will also automatically bypass AMP pages on their DuckDuckGo browser and on their DuckDuckGo Privacy Essentials browser extension.
On November 29, 2023, Ghost announced the removal of AMP in a coming update. Listed reasons for removal are that web development has grown beyond needing AMP, Google is no longer using it as a ranking factor, bad user experience, and decreased adoption.
== AMP Framework ==
=== AMP HTML ===
The AMP framework consists of three components:
AMP HTML, which is standard HTML markup with web components;
AMP JavaScript, which manages resource loading; and AMP caches, which serve and validate AMP pages.
Most AMP pages are delivered by Google's AMP cache, but other companies can support AMP caches. Internet performance and security company Cloudflare launched an AMP cache in March 2017.
=== Web Stories ===
Web Stories, known as AMP Stories until April 2020, were introduced in 2018. Web stories are a mobile-focused format for delivering news and information as tap-through stories.
=== AMP Email ===
In 2018, Google announced the new AMP Email section of the AMP framework. AMP for email allows senders to include interactive AMP components inside emails. Email clients that support AMP are able to display components directly inside the email. When viewed in an unsupported email client, AMP emails display fallback HTML no different from a standard HTML email as an alternative.
=== AMP Ads ===
AMP Ads are adverts marked up using a variant of AMP HTML and CSS, designed to be used inline in both AMP and normal HTML pages. They feature restrictions and automatic validation aimed at guaranteeing performance and security, while supporting common functionality such as analytics tracking and limited interactivity.
== Technology ==
=== Online format ===
AMP pages are published online and can be displayed in most current browsers. When a standard webpage has an AMP counterpart, a link to the AMP page is usually placed in an HTML tag in the source code of the standard page.
=== Third-party integration ===
Any organization or individual can build products or features which will work on AMP pages, provided they comply with the AMP Project specifications. As of July 2017, the AMP Project's website listed around 120 advertising companies and around 30 analytics companies as AMP Project participants.
=== Performance ===
Google reports that AMP pages served in Google search typically load in less than one second and use ten times less data than the equivalent non-AMP pages.
CNBC reported a 75% decrease in mobile page load time for AMP Pages over non-AMP pages, while Gizmodo reported that AMP pages loaded three times faster than non-AMP pages.
An academic paper about AMP reveals that AMP pages' page load time is two-and-a-half times faster than non-AMP versions in Google's search result page without pre-rendering. With pre-rendering, the AMP version is approximately nine times faster than the non-AMP version, though pre-rendering may consume additional mobile data.
=== Parity with canonical pages ===
Google has announced that as of February 1, 2018, it will require the content of canonical pages and those displayed through AMP be substantially the same. This is aimed at improving the experience of users by avoiding common difficulties with the user interface, and increase security and trust (See § Exploitation for malicious purposes).
== Reception ==
=== Comparison to other formats ===
AMP is often compared to Facebook Instant Articles and Apple News. All three formats were announced in 2015 with the stated goal of making mobile content faster and easier to consume. AMP Project supporters claim that AMP is a collaborative effort among publishers and technology companies, and that AMP is designed to work on the web instead of proprietary mobile apps.
=== Google control ===
Google's Richard Gingras said:
There's a very big difference between having a proprietary platform that says it's open, and having an open-source platform that is open to anyone to modify and adapt. It's the difference between saying come into my walled garden vs. not having a walled garden.
However, some critics believe that AMP is an impending walled garden as Google begins to host AMP-restricted versions of their websites directly on google.com:
They say AMP is not actually supporting the open web because it is a "fork" or variation on HTML and one that Google essentially controls ... Some publishers have complained that as Google prioritizes AMP links—as it recently said it will do in mobile search—media companies will lose even more control because AMP pages are hosted and controlled by Google. "Our mobile search traffic is moving to be majority AMP (Google hosted and not on our site) which limits our control over UI, monetization et al," said one digital media executive, quoted in a Fortune article.
AMP has been criticized by figures inside the tech industry as an attempt by Google to exert its dominance on the web by dictating how websites are built and monetized, and that "AMP is Google's attempt to lock publishers into its ecosystem".
Joshua Benton, director of the Nieman Journalism Lab at Harvard University, said: "There is a sense in which AMP is a Google-built version of the web. We are moving from a world where you can put anything on your website to one where you can't because Google says so." Ramon Tremosa, a Spanish member of the European Parliament, said: "AMP is an example of Google dialing up its anti-competitive practices under the nose of the competition regulators."
Matthew Ingram of Fortune expressed concerns about Google's role and motives regarding the AMP Project:
In a nutshell, these publishers are afraid that while the AMP project is nominally open-source, Google is using it to shape how the mobile web works, and in particular, to ensure a steady stream of advertising revenue ... More than anything else, the concerns that some publishers have about AMP seems to be part of a broader fear about the loss of control over distribution in a platform-centric world, and the risks that this poses to traditional monetization methods such as display advertising.
These charges were rebutted by Google. Google's Madhav Chinnappa stated that AMP must be a collaborative industry initiative in order for it to succeed in the long term:
I get a little bit irritated when sometimes people call it Google's AMP, because it's not ... AMP was created as an open-source initiative and that for me is the reason for its success.
In September 2018, Google began transitioning AMP to a more open governance model with governing committees composed of different stakeholders in the project, ranging from publishers that use AMP including The Washington Post and Axios to other companies such as Microsoft and Twitter.
=== Pre-rendering problems ===
Some AMP implementations such as Google search results use pre-rendering to improve loading speeds of AMP pages. As in other cases where pre-rendering is used, this is out of the user's control and may increase data usage.
AMP prefetching and pre-rendering results in some additional data (and power) use with each search. The average 1.4 MB of additional data per search that is used for pre-rendering an AMP page that the user may not visit is not trivial overhead for certain users with limited data plans.
=== Monetization ===
Some publishers reported that AMP pages generate less advertising revenue per page than non-AMP pages. The Wall Street Journal's Jack Marshall said:
AMP pages rely heavily on standardized banner ad units, and don't allow publishers to sell highly-customized ad units, sponsorships or pop-up ads as they might on their own properties.
Other publishers have reported better success with AMP monetization. The Washington Post has been able to generate approximately the same amount of revenue from AMP pages as from standard mobile pages, according to director of product Joey Marburger. CNN chief product officer Alex Wellen said AMP Pages "largely monetize at the same rate" as standard mobile pages.
To improve advertising performance, the AMP Project launched the AMP Ads Initiative which includes support for more advertising formats and optimizations to improve ad load speed.
=== Exploitation for malicious purposes ===
Some observers believe AMP allows more effective phishing attempts. One serious flaw, noted by tech writer Kyle Chayka, is that disreputable parties who misuse AMP (as well as Facebook's similar Instant Articles) enable junk websites to share many of the same visual cues and features found on legitimate sites. Chayka stated that "All publishers end up looking more similar than different. That makes separating the real from the fake even harder."
In September 2017, Russian hackers used an AMP vulnerability in phishing e-mails sent to investigative journalists critical of the Russian government, and hacked into their websites. Google announced on November 16, 2017, that it would prevent sites in Google search results from exploiting AMP to bait-and-switch users. Since February 2018, AMP pages in Google search results must contain content equivalent to that of the non-AMP page.
== References ==
== Further reading ==
Pierce, David (May 8, 2023). "How Google tried to fix the web — by taking it over". The Verge. Retrieved May 8, 2023.
== External links ==
Official website
official tutorial at the Wayback Machine (archived 2019-03-30)
AMP Validator | Wikipedia/Accelerated_Mobile_Pages |
Material Design (codename Quantum Paper) is a design language developed by Google in 2014. Expanding on the "cards" UI that debuted in Google Now, Material Design uses more grid-based layouts, responsive animations and transitions, padding, and depth effects such as lighting and shadows. Google announced the initial version of Material Design on June 25, 2014, at the 2014 Google I/O conference.
The purpose of developing Material Design was to create a novel visual language, synthesizing the classic principles of good design with the innovation and possibility of technology and science. Head designer Matías Duarte explained that "unlike real paper, our digital material expands and reforms intelligently. Material has physical surfaces and edges. Seams and shadows provide meaning about what you can touch." Material Design is based on paper-and-ink as well as skeuomorphic interaction concepts, but implementation happens in a more advanced manner.
In 2018, Google revamped the language (Material Design 2), providing more flexibility for designers to create custom themes with varying geometry, colors, and typography.
In 2021, a further evolution of the design language, titled Material You (Material Design 3), was unveiled.
In 2025, the next evolution of the design language, titled "Material 3 Expressive", was unveiled.
== Implementation ==
Material Design have been gradually extended throughout Google's array of web and mobile products, providing a consistent experience across all platforms and applications. Google has also released application programming interfaces (APIs) for third-party developers to incorporate the design language into their applications.
The canonical open source implementation of Material Design for web application user interfaces is called Material Web.
== Updates ==
=== Material Design 2 ===
After the 2018 revamp, Google began redesigning most of their apps based on an updated set of principles and guidelines dubbed "Material Design 2", which appeared on Android Pie. It provided a larger focus on customization of the basic Material Design components to adapt to the branding of the products in which it is being used. The updated guidelines further heavily emphasizes white space, rounded corners, colorful icons, and bottom navigation bars. Google began utilizing a special size-optimized version of their proprietary Product Sans font called Google Sans.
=== Material Design 3 (Material You) ===
At Google I/O in May 2021, Google announced a new concept on Android 12 known as "Material You" (also known as "Material Design 3"), emphasizing increased animation, larger buttons, and the ability for custom UI themes to be generated from the user's wallpaper. Material You was gradually rolled out to various Google apps on older Android versions in the following months, and acted as a major focus on the Pixel 6 and Pixel 6 Pro smartphone series.
=== Material 3 Expressive ===
At The Android Show: I/O Edition in May 2025, Google announced "Material 3 Expressive" for Android 16 and Wear OS 6. This version of Material Design shares similarities to its predecessor but has increased animation and is more colorful and modern.
== See also ==
Flat design
Fluent Design System
Human interface guidelines
Metro (design language)
Corporate Memphis
== References ==
== External links ==
Official website
Material Design 1
Material Design 2
Material Design 3 | Wikipedia/Material_Design |
XLA (Accelerated Linear Algebra) is an open-source compiler for machine learning developed by the OpenXLA project. XLA is designed to improve the performance of machine learning models by optimizing the computation graphs at a lower level, making it particularly useful for large-scale computations and high-performance machine learning models. Key features of XLA include:
Compilation of Computation Graphs: Compiles computation graphs into efficient machine code.
Optimization Techniques: Applies operation fusion, memory optimization, and other techniques.
Hardware Support: Optimizes models for various hardware, including CPUs, GPUs, and NPUs.
Improved Model Execution Time: Aims to reduce machine learning models' execution time for both training and inference.
Seamless Integration: Can be used with existing machine learning code with minimal changes.
XLA represents a significant step in optimizing machine learning models, providing developers with tools to enhance computational efficiency and performance.
== Supported target devices ==
x86-64
ARM64
NVIDIA GPU
AMD GPU
Intel GPU
Apple GPU
Google TPU
AWS Trainium, Inferentia
Cerebras
Graphcore IPU
== See also ==
TensorFlow
PyTorch
JAX
== References == | Wikipedia/Accelerated_Linear_Algebra |
In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way. The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods. Because Tobin's method can be easily extended to handle truncated and other non-randomly selected samples, some authors adopt a broader definition of the tobit model that includes these cases.
Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold. For a sample that, as in Tobin's original case, was censored from below at zero, the sampling probability for each non-limit observation is simply the height of the appropriate density function. For any limit observation, it is the cumulative distribution, i.e. the integral below zero of the appropriate density function. The tobit likelihood function is thus a mixture of densities and cumulative distribution functions.
== The likelihood function ==
Below are the likelihood and log likelihood functions for a type I tobit. This is a tobit that is censored from below at
y
L
{\displaystyle y_{L}}
when the latent variable
y
j
∗
≤
y
L
{\displaystyle y_{j}^{*}\leq y_{L}}
. In writing out the likelihood function, we first define an indicator function
I
{\displaystyle I}
:
I
(
y
)
=
{
0
if
y
≤
y
L
,
1
if
y
>
y
L
.
{\displaystyle I(y)={\begin{cases}0&{\text{if }}y\leq y_{L},\\1&{\text{if }}y>y_{L}.\end{cases}}}
Next, let
Φ
{\displaystyle \Phi }
be the standard normal cumulative distribution function and
φ
{\displaystyle \varphi }
to be the standard normal probability density function. For a data set with N observations the likelihood function for a type I tobit is
L
(
β
,
σ
)
=
∏
j
=
1
N
(
1
σ
φ
(
y
j
−
X
j
β
σ
)
)
I
(
y
j
)
(
1
−
Φ
(
X
j
β
−
y
L
σ
)
)
1
−
I
(
y
j
)
{\displaystyle {\mathcal {L}}(\beta ,\sigma )=\prod _{j=1}^{N}\left({\frac {1}{\sigma }}\varphi \left({\frac {y_{j}-X_{j}\beta }{\sigma }}\right)\right)^{I(y_{j})}\left(1-\Phi \left({\frac {X_{j}\beta -y_{L}}{\sigma }}\right)\right)^{1-I(y_{j})}}
and the log likelihood is given by
log
L
(
β
,
σ
)
=
∑
j
=
1
n
I
(
y
j
)
log
(
1
σ
φ
(
y
j
−
X
j
β
σ
)
)
+
(
1
−
I
(
y
j
)
)
log
(
1
−
Φ
(
X
j
β
−
y
L
σ
)
)
=
∑
y
j
>
y
L
log
(
1
σ
φ
(
y
j
−
X
j
β
σ
)
)
+
∑
y
j
=
y
L
log
(
Φ
(
y
L
−
X
j
β
σ
)
)
{\displaystyle {\begin{aligned}\log {\mathcal {L}}(\beta ,\sigma )&=\sum _{j=1}^{n}I(y_{j})\log \left({\frac {1}{\sigma }}\varphi \left({\frac {y_{j}-X_{j}\beta }{\sigma }}\right)\right)+(1-I(y_{j}))\log \left(1-\Phi \left({\frac {X_{j}\beta -y_{L}}{\sigma }}\right)\right)\\&=\sum _{y_{j}>y_{L}}\log \left({\frac {1}{\sigma }}\varphi \left({\frac {y_{j}-X_{j}\beta }{\sigma }}\right)\right)+\sum _{y_{j}=y_{L}}\log \left(\Phi \left({\frac {y_{L}-X_{j}\beta }{\sigma }}\right)\right)\end{aligned}}}
=== Reparametrization ===
The log-likelihood as stated above is not globally concave, which complicates the maximum likelihood estimation. Olsen suggested the simple reparametrization
β
=
δ
/
γ
{\displaystyle \beta =\delta /\gamma }
and
σ
2
=
γ
−
2
{\displaystyle \sigma ^{2}=\gamma ^{-2}}
, resulting in a transformed log-likelihood,
log
L
(
δ
,
γ
)
=
∑
y
j
>
y
L
{
log
γ
+
log
[
φ
(
γ
y
j
−
X
j
δ
)
]
}
+
∑
y
j
=
y
L
log
[
Φ
(
γ
y
L
−
X
j
δ
)
]
{\displaystyle \log {\mathcal {L}}(\delta ,\gamma )=\sum _{y_{j}>y_{L}}\left\{\log \gamma +\log \left[\varphi \left(\gamma y_{j}-X_{j}\delta \right)\right]\right\}+\sum _{y_{j}=y_{L}}\log \left[\Phi \left(\gamma y_{L}-X_{j}\delta \right)\right]}
which is globally concave in terms of the transformed parameters.
For the truncated (tobit II) model, Orme showed that while the log-likelihood is not globally concave, it is concave at any stationary point under the above transformation.
=== Consistency ===
If the relationship parameter
β
{\displaystyle \beta }
is estimated by regressing the observed
y
i
{\displaystyle y_{i}}
on
x
i
{\displaystyle x_{i}}
, the resulting ordinary least squares regression estimator is inconsistent. It will yield a downwards-biased estimate of the slope coefficient and an upward-biased estimate of the intercept. Takeshi Amemiya (1973) has proven that the maximum likelihood estimator suggested by Tobin for this model is consistent.
=== Interpretation ===
The
β
{\displaystyle \beta }
coefficient should not be interpreted as the effect of
x
i
{\displaystyle x_{i}}
on
y
i
{\displaystyle y_{i}}
, as one would with a linear regression model; this is a common error. Instead, it should be interpreted as the combination of
(1) the change in
y
i
{\displaystyle y_{i}}
of those above the limit, weighted by the probability of being above the limit; and
(2) the change in the probability of being above the limit, weighted by the expected value of
y
i
{\displaystyle y_{i}}
if above.
== Variations of the tobit model ==
Variations of the tobit model can be produced by changing where and when censoring occurs. Amemiya (1985, p. 384) classifies these variations into five categories (tobit type I – tobit type V), where tobit type I stands for the first model described above. Schnedler (2005) provides a general formula to obtain consistent likelihood estimators for these and other variations of the tobit model.
=== Type I ===
The tobit model is a special case of a censored regression model, because the latent variable
y
i
∗
{\displaystyle y_{i}^{*}}
cannot always be observed while the independent variable
x
i
{\displaystyle x_{i}}
is observable. A common variation of the tobit model is censoring at a value
y
L
{\displaystyle y_{L}}
different from zero:
y
i
=
{
y
i
∗
if
y
i
∗
>
y
L
,
y
L
if
y
i
∗
≤
y
L
.
{\displaystyle y_{i}={\begin{cases}y_{i}^{*}&{\text{if }}y_{i}^{*}>y_{L},\\y_{L}&{\text{if }}y_{i}^{*}\leq y_{L}.\end{cases}}}
Another example is censoring of values above
y
U
{\displaystyle y_{U}}
.
y
i
=
{
y
i
∗
if
y
i
∗
<
y
U
,
y
U
if
y
i
∗
≥
y
U
.
{\displaystyle y_{i}={\begin{cases}y_{i}^{*}&{\text{if }}y_{i}^{*}<y_{U},\\y_{U}&{\text{if }}y_{i}^{*}\geq y_{U}.\end{cases}}}
Yet another model results when
y
i
{\displaystyle y_{i}}
is censored from above and below at the same time.
y
i
=
{
y
i
∗
if
y
L
<
y
i
∗
<
y
U
,
y
L
if
y
i
∗
≤
y
L
,
y
U
if
y
i
∗
≥
y
U
.
{\displaystyle y_{i}={\begin{cases}y_{i}^{*}&{\text{if }}y_{L}<y_{i}^{*}<y_{U},\\y_{L}&{\text{if }}y_{i}^{*}\leq y_{L},\\y_{U}&{\text{if }}y_{i}^{*}\geq y_{U}.\end{cases}}}
The rest of the models will be presented as being bounded from below at 0, though this can be generalized as done for Type I.
=== Type II ===
Type II tobit models introduce a second latent variable.
y
2
i
=
{
y
2
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{2i}={\begin{cases}y_{2i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
In Type I tobit, the latent variable absorbs both the process of participation and the outcome of interest. Type II tobit allows the process of participation (selection) and the outcome of interest to be independent, conditional on observable data.
The Heckman selection model falls into the Type II tobit, which is sometimes called Heckit after James Heckman.
=== Type III ===
Type III introduces a second observed dependent variable.
y
1
i
=
{
y
1
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{1i}={\begin{cases}y_{1i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
y
2
i
=
{
y
2
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{2i}={\begin{cases}y_{2i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
The Heckman model falls into this type.
=== Type IV ===
Type IV introduces a third observed dependent variable and a third latent variable.
y
1
i
=
{
y
1
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{1i}={\begin{cases}y_{1i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
y
2
i
=
{
y
2
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{2i}={\begin{cases}y_{2i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
y
3
i
=
{
y
3
i
∗
if
y
1
i
∗
≤
0
,
0
if
y
1
i
∗
<
0.
{\displaystyle y_{3i}={\begin{cases}y_{3i}^{*}&{\text{if }}y_{1i}^{*}\leq 0,\\0&{\text{if }}y_{1i}^{*}<0.\end{cases}}}
=== Type V ===
Similar to Type II, in Type V only the sign of
y
1
i
∗
{\displaystyle y_{1i}^{*}}
is observed.
y
2
i
=
{
y
2
i
∗
if
y
1
i
∗
>
0
,
0
if
y
1
i
∗
≤
0.
{\displaystyle y_{2i}={\begin{cases}y_{2i}^{*}&{\text{if }}y_{1i}^{*}>0,\\0&{\text{if }}y_{1i}^{*}\leq 0.\end{cases}}}
y
3
i
=
{
y
3
i
∗
if
y
1
i
∗
≤
0
,
0
if
y
1
i
∗
>
0.
{\displaystyle y_{3i}={\begin{cases}y_{3i}^{*}&{\text{if }}y_{1i}^{*}\leq 0,\\0&{\text{if }}y_{1i}^{*}>0.\end{cases}}}
=== Non-parametric version ===
If the underlying latent variable
y
i
∗
{\displaystyle y_{i}^{*}}
is not normally distributed, one must use quantiles instead of moments to analyze the
observable variable
y
i
{\displaystyle y_{i}}
. Powell's CLAD estimator offers a possible way to achieve this.
== Applications ==
Tobit models have, for example, been applied to estimate factors that impact grant receipt, including financial transfers distributed to sub-national governments who may apply for these grants. In these cases, grant recipients cannot receive negative amounts, and the data is thus left-censored. For instance, Dahlberg and Johansson (2002) analyse a sample of 115 municipalities (42 of which received a grant). Dubois and Fattore (2011) use a tobit model to investigate the role of various factors in European Union fund receipt by applying Polish sub-national governments. The data may however be left-censored at a point higher than zero, with the risk of mis-specification. Both studies apply Probit and other models to check for robustness. Tobit models have also been applied in demand analysis to accommodate observations with zero expenditures on some goods. In a related application of tobit models, a system of nonlinear tobit regressions models has been used to jointly estimate a brand demand system with homoscedastic, heteroscedastic and generalized heteroscedastic variants.
== See also ==
Truncated normal hurdle model
Limited dependent variable
Rectifier (neural networks)
Truncated regression model
Dynamic unobserved effects model § Censored dependent variable
Probit model, the name tobit is a pun on both Tobin, their creator, and their similarities to probit models.
== Notes ==
== References ==
== Further reading ==
Amemiya, Takeshi (1985). "Tobit Models". Advanced Econometrics. Oxford: Basil Blackwell. pp. 360–411. ISBN 0-631-13345-3.
Breen, Richard (1996). "The Tobit Model for Censored Data". Regression Models : Censored, Samples Selected, or Truncated Data. Thousand Oaks: Sage. pp. 12–33. ISBN 0-8039-5710-6.
Gouriéroux, Christian (2000). "The Tobit Model". Econometrics of Qualitative Dependent Variables. New York: Cambridge University Press. pp. 170–207. ISBN 0-521-58985-1.
King, Gary (1989). "Models with Nonrandom Selection". Unifying Political Methodology : the Likehood Theory of Statistical Inference. Cambridge University Press. pp. 208–230. ISBN 0-521-36697-6.
Maddala, G. S. (1983). "Censored and Truncated Regression Models". Limited-Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press. pp. 149–196. ISBN 0-521-24143-X. | Wikipedia/Tobit_model |
The swish function is a family of mathematical function defined as follows:
swish
β
(
x
)
=
x
sigmoid
(
β
x
)
=
x
1
+
e
−
β
x
.
{\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.}
where
β
{\displaystyle \beta }
can be constant (usually set to 1) or trainable.
The swish family was designed to smoothly interpolate between a linear function and the ReLU function.
When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in : Eq 3 . Variants of the swish function include Mish.
== Special values ==
For β = 0, the function is linear: f(x) = x/2.
For β = 1, the function is the Sigmoid Linear Unit (SiLU).
With β → ∞, the function converges to ReLU.
Thus, the swish family smoothly interpolates between a linear function and the ReLU function.
Since
swish
β
(
x
)
=
swish
1
(
β
x
)
/
β
{\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta }
, all instances of swish have the same shape as the default
swish
1
{\displaystyle \operatorname {swish} _{1}}
, zoomed by
β
{\displaystyle \beta }
. One usually sets
β
>
0
{\displaystyle \beta >0}
. When
β
{\displaystyle \beta }
is trainable, this constraint can be enforced by
β
=
e
b
{\displaystyle \beta =e^{b}}
, where
b
{\displaystyle b}
is trainable.
swish
1
(
x
)
=
x
2
+
x
2
4
−
x
4
48
+
x
6
480
+
O
(
x
8
)
{\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)}
swish
1
(
x
)
=
x
2
tanh
(
x
2
)
+
x
2
swish
1
(
x
)
+
swish
−
1
(
x
)
=
x
tanh
(
x
2
)
swish
1
(
x
)
−
swish
−
1
(
x
)
=
x
{\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}}
== Derivatives ==
Because
swish
β
(
x
)
=
swish
1
(
β
x
)
/
β
{\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta }
, it suffices to calculate its derivatives for the default case.
swish
1
′
(
x
)
=
x
+
sinh
(
x
)
4
cosh
2
(
x
2
)
+
1
2
{\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}}
so
swish
1
′
(
x
)
−
1
2
{\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}}
is odd.
swish
1
″
(
x
)
=
1
−
x
2
tanh
(
x
2
)
2
cosh
2
(
x
2
)
{\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}}
so
swish
1
″
(
x
)
{\displaystyle \operatorname {swish} _{1}''(x)}
is even.
== History ==
SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β.
In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.
== See also ==
Activation function
Gating mechanism
== References == | Wikipedia/Swish_(function) |
In mathematics, an algebraic function is a function that can be defined
as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of such functions are:
f
(
x
)
=
1
/
x
{\displaystyle f(x)=1/x}
f
(
x
)
=
x
{\displaystyle f(x)={\sqrt {x}}}
f
(
x
)
=
1
+
x
3
x
3
/
7
−
7
x
1
/
3
{\displaystyle f(x)={\frac {\sqrt {1+x^{3}}}{x^{3/7}-{\sqrt {7}}x^{1/3}}}}
Some algebraic functions, however, cannot be expressed by such finite expressions (this is the Abel–Ruffini theorem). This is the case, for example, for the Bring radical, which is the function implicitly defined by
f
(
x
)
5
+
f
(
x
)
+
x
=
0
{\displaystyle f(x)^{5}+f(x)+x=0}
.
In more precise terms, an algebraic function of degree n in one variable x is a function
y
=
f
(
x
)
,
{\displaystyle y=f(x),}
that is continuous in its domain and satisfies a polynomial equation of positive degree
a
n
(
x
)
y
n
+
a
n
−
1
(
x
)
y
n
−
1
+
⋯
+
a
0
(
x
)
=
0
{\displaystyle a_{n}(x)y^{n}+a_{n-1}(x)y^{n-1}+\cdots +a_{0}(x)=0}
where the coefficients ai(x) are polynomial functions of x, with integer coefficients. It can be shown that the same class of functions is obtained if algebraic numbers are accepted for the coefficients of the ai(x)'s. If transcendental numbers occur in the coefficients the function is, in general, not algebraic, but it is algebraic over the field generated by these coefficients.
The value of an algebraic function at a rational number, and more generally, at an algebraic number is always an algebraic number.
Sometimes, coefficients
a
i
(
x
)
{\displaystyle a_{i}(x)}
that are polynomial over a ring R are considered, and one then talks about "functions algebraic over R".
A function which is not algebraic is called a transcendental function, as it is for example the case of
exp
x
,
tan
x
,
ln
x
,
Γ
(
x
)
{\displaystyle \exp x,\tan x,\ln x,\Gamma (x)}
. A composition of transcendental functions can give an algebraic function:
f
(
x
)
=
cos
arcsin
x
=
1
−
x
2
{\displaystyle f(x)=\cos \arcsin x={\sqrt {1-x^{2}}}}
.
As a polynomial equation of degree n has up to n roots (and exactly n roots over an algebraically closed field, such as the complex numbers), a polynomial equation does not implicitly define a single function, but up to n
functions, sometimes also called branches. Consider for example the equation of the unit circle:
y
2
+
x
2
=
1.
{\displaystyle y^{2}+x^{2}=1.\,}
This determines y, except only up to an overall sign; accordingly, it has two branches:
y
=
±
1
−
x
2
.
{\displaystyle y=\pm {\sqrt {1-x^{2}}}.\,}
An algebraic function in m variables is similarly defined as a function
y
=
f
(
x
1
,
…
,
x
m
)
{\displaystyle y=f(x_{1},\dots ,x_{m})}
which solves a polynomial equation in m + 1 variables:
p
(
y
,
x
1
,
x
2
,
…
,
x
m
)
=
0.
{\displaystyle p(y,x_{1},x_{2},\dots ,x_{m})=0.}
It is normally assumed that p should be an irreducible polynomial. The existence of an algebraic function is then guaranteed by the implicit function theorem.
Formally, an algebraic function in m variables over the field K is an element of the algebraic closure of the field of rational functions K(x1, ..., xm).
== Algebraic functions in one variable ==
=== Introduction and overview ===
The informal definition of an algebraic function provides a number of clues about their properties. To gain an intuitive understanding, it may be helpful to regard algebraic functions as functions which can be formed by the usual algebraic operations: addition, multiplication, division, and taking an nth root. This is something of an oversimplification; because of the fundamental theorem of Galois theory, algebraic functions need not be expressible by radicals.
First, note that any polynomial function
y
=
p
(
x
)
{\displaystyle y=p(x)}
is an algebraic function, since it is simply the solution y to the equation
y
−
p
(
x
)
=
0.
{\displaystyle y-p(x)=0.\,}
More generally, any rational function
y
=
p
(
x
)
q
(
x
)
{\displaystyle y={\frac {p(x)}{q(x)}}}
is algebraic, being the solution to
q
(
x
)
y
−
p
(
x
)
=
0.
{\displaystyle q(x)y-p(x)=0.}
Moreover, the nth root of any polynomial
y
=
p
(
x
)
n
{\textstyle y={\sqrt[{n}]{p(x)}}}
is an algebraic function, solving the equation
y
n
−
p
(
x
)
=
0.
{\displaystyle y^{n}-p(x)=0.}
Surprisingly, the inverse function of an algebraic function is an algebraic function. For supposing that y is a solution to
a
n
(
x
)
y
n
+
⋯
+
a
0
(
x
)
=
0
,
{\displaystyle a_{n}(x)y^{n}+\cdots +a_{0}(x)=0,}
for each value of x, then x is also a solution of this equation for each value of y. Indeed, interchanging the roles of x and y and gathering terms,
b
m
(
y
)
x
m
+
b
m
−
1
(
y
)
x
m
−
1
+
⋯
+
b
0
(
y
)
=
0.
{\displaystyle b_{m}(y)x^{m}+b_{m-1}(y)x^{m-1}+\cdots +b_{0}(y)=0.}
Writing x as a function of y gives the inverse function, also an algebraic function.
However, not every function has an inverse. For example, y = x2 fails the horizontal line test: it fails to be one-to-one. The inverse is the algebraic "function"
x
=
±
y
{\displaystyle x=\pm {\sqrt {y}}}
.
Another way to understand this, is that the set of branches of the polynomial equation defining our algebraic function is the graph of an algebraic curve.
=== The role of complex numbers ===
From an algebraic perspective, complex numbers enter quite naturally into the study of algebraic functions. First of all, by the fundamental theorem of algebra, the complex numbers are an algebraically closed field. Hence any polynomial relation p(y, x) = 0 is guaranteed to have at least one solution (and in general a number of solutions not exceeding the degree of p in y) for y at each point x, provided we allow y to assume complex as well as real values. Thus, problems to do with the domain of an algebraic function can safely be minimized.
Furthermore, even if one is ultimately interested in real algebraic functions, there may be no means to express the function in terms of addition, multiplication, division and taking nth roots without resorting to complex numbers (see casus irreducibilis). For example, consider the algebraic function determined by the equation
y
3
−
x
y
+
1
=
0.
{\displaystyle y^{3}-xy+1=0.\,}
Using the cubic formula, we get
y
=
−
2
x
−
108
+
12
81
−
12
x
3
3
+
−
108
+
12
81
−
12
x
3
3
6
.
{\displaystyle y=-{\frac {2x}{\sqrt[{3}]{-108+12{\sqrt {81-12x^{3}}}}}}+{\frac {\sqrt[{3}]{-108+12{\sqrt {81-12x^{3}}}}}{6}}.}
For
x
≤
3
4
3
,
{\displaystyle x\leq {\frac {3}{\sqrt[{3}]{4}}},}
the square root is real and the cubic root is thus well defined, providing the unique real root. On the other hand, for
x
>
3
4
3
,
{\displaystyle x>{\frac {3}{\sqrt[{3}]{4}}},}
the square root is not real, and one has to choose, for the square root, either non-real square root. Thus the cubic root has to be chosen among three non-real numbers. If the same choices are done in the two terms of the formula, the three choices for the cubic root provide the three branches shown, in the accompanying image.
It may be proven that there is no way to express this function in terms of nth roots using real numbers only, even though the resulting function is real-valued on the domain of the graph shown.
On a more significant theoretical level, using complex numbers allows one to use the powerful techniques of complex analysis to discuss algebraic functions. In particular, the argument principle can be used to show that any algebraic function is in fact an analytic function, at least in the multiple-valued sense.
Formally, let p(x, y) be a complex polynomial in the complex variables x and y. Suppose that
x0 ∈ C is such that the polynomial p(x0, y) of y has n distinct zeros. We shall show that the algebraic function is analytic in a neighborhood of x0. Choose a system of n non-overlapping discs Δi containing each of these zeros. Then by the argument principle
1
2
π
i
∮
∂
Δ
i
p
y
(
x
0
,
y
)
p
(
x
0
,
y
)
d
y
=
1.
{\displaystyle {\frac {1}{2\pi i}}\oint _{\partial \Delta _{i}}{\frac {p_{y}(x_{0},y)}{p(x_{0},y)}}\,dy=1.}
By continuity, this also holds for all x in a neighborhood of x0. In particular, p(x, y) has only one root in Δi, given by the residue theorem:
f
i
(
x
)
=
1
2
π
i
∮
∂
Δ
i
y
p
y
(
x
,
y
)
p
(
x
,
y
)
d
y
{\displaystyle f_{i}(x)={\frac {1}{2\pi i}}\oint _{\partial \Delta _{i}}y{\frac {p_{y}(x,y)}{p(x,y)}}\,dy}
which is an analytic function.
=== Monodromy ===
Note that the foregoing proof of analyticity derived an expression for a system of n different function elements fi (x), provided that x is not a critical point of p(x, y). A critical point is a point where the number of distinct zeros is smaller than the degree of p, and this occurs only where the highest degree term of p or the discriminant vanish. Hence there are only finitely many such points c1, ..., cm.
A close analysis of the properties of the function elements fi near the critical points can be used to show that the monodromy cover is ramified over the critical points (and possibly the point at infinity). Thus the holomorphic extension of the fi has at worst algebraic poles and ordinary algebraic branchings over the critical points.
Note that, away from the critical points, we have
p
(
x
,
y
)
=
a
n
(
x
)
(
y
−
f
1
(
x
)
)
(
y
−
f
2
(
x
)
)
⋯
(
y
−
f
n
(
x
)
)
{\displaystyle p(x,y)=a_{n}(x)(y-f_{1}(x))(y-f_{2}(x))\cdots (y-f_{n}(x))}
since the fi are by definition the distinct zeros of p. The monodromy group acts by permuting the factors, and thus forms the monodromy representation of the Galois group of p. (The monodromy action on the universal covering space is related but different notion in the theory of Riemann surfaces.)
== History ==
The ideas surrounding algebraic functions go back at least as far as René Descartes. The first discussion of algebraic functions appears to have been in Edward Waring's 1794 An Essay on the Principles of Human Knowledge in which he writes:
let a quantity denoting the ordinate, be an algebraic function of the abscissa x, by the common methods of division and extraction of roots, reduce it into an infinite series ascending or descending according to the dimensions of x, and then find the integral of each of the resulting terms.
== See also ==
Algebraic expression
Analytic function
Complex function
Elementary function
Function (mathematics)
Generalized function
List of special functions and eponyms
List of types of functions
Polynomial
Rational function
Special functions
Transcendental function
== References ==
Ahlfors, Lars (1979). Complex Analysis. McGraw Hill.
van der Waerden, B.L. (1931). Modern Algebra, Volume II. Springer.
== External links ==
Definition of "Algebraic function" in the Encyclopedia of Math
Weisstein, Eric W. "Algebraic Function". MathWorld.
Algebraic Function at PlanetMath.
Definition of "Algebraic function" Archived 2020-10-26 at the Wayback Machine in David J. Darling's Internet Encyclopedia of Science | Wikipedia/Algebraic_functions |
The swish function is a family of mathematical function defined as follows:
swish
β
(
x
)
=
x
sigmoid
(
β
x
)
=
x
1
+
e
−
β
x
.
{\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.}
where
β
{\displaystyle \beta }
can be constant (usually set to 1) or trainable.
The swish family was designed to smoothly interpolate between a linear function and the ReLU function.
When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in : Eq 3 . Variants of the swish function include Mish.
== Special values ==
For β = 0, the function is linear: f(x) = x/2.
For β = 1, the function is the Sigmoid Linear Unit (SiLU).
With β → ∞, the function converges to ReLU.
Thus, the swish family smoothly interpolates between a linear function and the ReLU function.
Since
swish
β
(
x
)
=
swish
1
(
β
x
)
/
β
{\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta }
, all instances of swish have the same shape as the default
swish
1
{\displaystyle \operatorname {swish} _{1}}
, zoomed by
β
{\displaystyle \beta }
. One usually sets
β
>
0
{\displaystyle \beta >0}
. When
β
{\displaystyle \beta }
is trainable, this constraint can be enforced by
β
=
e
b
{\displaystyle \beta =e^{b}}
, where
b
{\displaystyle b}
is trainable.
swish
1
(
x
)
=
x
2
+
x
2
4
−
x
4
48
+
x
6
480
+
O
(
x
8
)
{\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)}
swish
1
(
x
)
=
x
2
tanh
(
x
2
)
+
x
2
swish
1
(
x
)
+
swish
−
1
(
x
)
=
x
tanh
(
x
2
)
swish
1
(
x
)
−
swish
−
1
(
x
)
=
x
{\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}}
== Derivatives ==
Because
swish
β
(
x
)
=
swish
1
(
β
x
)
/
β
{\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta }
, it suffices to calculate its derivatives for the default case.
swish
1
′
(
x
)
=
x
+
sinh
(
x
)
4
cosh
2
(
x
2
)
+
1
2
{\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}}
so
swish
1
′
(
x
)
−
1
2
{\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}}
is odd.
swish
1
″
(
x
)
=
1
−
x
2
tanh
(
x
2
)
2
cosh
2
(
x
2
)
{\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}}
so
swish
1
″
(
x
)
{\displaystyle \operatorname {swish} _{1}''(x)}
is even.
== History ==
SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β.
In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.
== See also ==
Activation function
Gating mechanism
== References == | Wikipedia/Swish_function |
In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. In the classical proof of the lemma, the embedding is a random orthogonal projection.
The lemma has applications in compressed sensing, manifold learning, dimensionality reduction, graph embedding, and natural language processing. Much of the data stored and manipulated on computers, including text and images, can be represented as points in a high-dimensional space (see vector space model for the case of text). However, the essential algorithms for working with such data tend to become bogged down very quickly as dimension increases. It is therefore desirable to reduce the dimensionality of the data in a way that preserves its relevant structure.
== Statement ==
Given
0
<
ε
<
1
{\displaystyle 0<\varepsilon <1}
, a set
X
{\displaystyle X}
of
N
{\displaystyle N}
points in
R
n
{\displaystyle \mathbb {R} ^{n}}
, and an integer
k
>
8
(
ln
N
)
/
ε
2
{\displaystyle k>8(\ln N)/\varepsilon ^{2}}
, there is a linear map
f
:
R
n
→
R
k
{\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{k}}
such that
(
1
−
ε
)
‖
u
−
v
‖
2
≤
‖
f
(
u
)
−
f
(
v
)
‖
2
≤
(
1
+
ε
)
‖
u
−
v
‖
2
{\displaystyle (1-\varepsilon )\|u-v\|^{2}\leq \|f(u)-f(v)\|^{2}\leq (1+\varepsilon )\|u-v\|^{2}}
for all
u
,
v
∈
X
{\displaystyle u,v\in X}
.
The formula can be rearranged:
(
1
+
ε
)
−
1
‖
f
(
u
)
−
f
(
v
)
‖
2
≤
‖
u
−
v
‖
2
≤
(
1
−
ε
)
−
1
‖
f
(
u
)
−
f
(
v
)
‖
2
{\displaystyle (1+\varepsilon )^{-1}\|f(u)-f(v)\|^{2}\leq \|u-v\|^{2}\leq (1-\varepsilon )^{-1}\|f(u)-f(v)\|^{2}}
Alternatively, for any
ϵ
∈
(
0
,
1
)
{\displaystyle \epsilon \in (0,1)}
and any integer
k
≥
15
(
ln
N
)
/
ε
2
{\displaystyle k\geq 15(\ln N)/\varepsilon ^{2}}
there exists a linear function
f
:
R
n
→
R
k
{\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{k}}
such that the restriction
f
|
X
{\displaystyle f|_{X}}
is
(
1
+
ε
)
{\displaystyle (1+\varepsilon )}
-bi-Lipschitz.
Also, the lemma is tight up to a constant factor, i.e. there exists a set of points of size N that needs dimension
Ω
(
log
(
N
)
ε
2
)
{\displaystyle \Omega \left({\frac {\log(N)}{\varepsilon ^{2}}}\right)}
in order to preserve the distances between all pairs of points within a factor of
(
1
±
ε
)
{\displaystyle (1\pm \varepsilon )}
.
The classical proof of the lemma takes
f
{\displaystyle f}
to be a scalar multiple of an orthogonal projection
P
{\displaystyle P}
onto a random subspace of dimension
k
{\displaystyle k}
in
R
n
{\displaystyle \mathbb {R} ^{n}}
. An orthogonal projection collapses some dimensions of the space it is applied to, which reduces the length of all vectors, as well as distance between vectors in the space. Under the conditions of the lemma, concentration of measure ensures there is a nonzero chance that a random orthogonal projection reduces pairwise distances between all points in
X
{\displaystyle X}
by roughly a constant factor
c
{\displaystyle c}
. Since the chance is nonzero, such projections must exist, so we can choose one
P
{\displaystyle P}
and set
f
(
v
)
=
P
v
/
c
{\displaystyle f(v)=Pv/c}
.
To obtain the projection algorithmically, it suffices with high probability to repeatedly sample orthogonal projection matrices at random. If you keep rolling the dice, you will eventually obtain one in polynomial random time.
== Proof ==
Based on.
Construct a random matrix
A
∼
N
(
0
,
1
)
k
×
n
{\displaystyle A\sim {\mathcal {N}}(0,1)^{k\times n}}
, obtained by sampling each entry from the standard normal distribution. Then define
P
:=
A
/
k
{\displaystyle P:=A/{\sqrt {k}}}
. Then, for any nonzero vector
x
∈
R
n
{\displaystyle x\in \mathbb {R} ^{n}}
, let the projected vector be
x
^
:=
P
x
{\displaystyle {\hat {x}}:=Px}
. Standard geometric argument show that
r
:=
‖
x
^
‖
2
‖
x
‖
2
{\displaystyle r:={\frac {\|{\hat {x}}\|^{2}}{\|x\|^{2}}}}
is chi-square distributed, that is,
r
∼
χ
2
(
k
)
{\displaystyle r\sim \chi ^{2}(k)}
. Thus, it satisfies a concentration inequality
P
r
(
r
∈
(
1
±
ϵ
)
k
)
≥
1
−
2
e
−
k
2
(
1
2
ϵ
2
−
1
3
ϵ
3
)
{\displaystyle Pr(r\in (1\pm \epsilon )k)\geq 1-2e^{-{\frac {k}{2}}({\frac {1}{2}}\epsilon ^{2}-{\frac {1}{3}}\epsilon ^{3})}}
By the union bound, the probability that this relation is true for all of
x
1
,
…
,
x
N
{\displaystyle x_{1},\dots ,x_{N}}
is greater than
1
−
2
N
e
−
k
2
(
1
2
ϵ
2
−
1
3
ϵ
3
)
{\displaystyle 1-2Ne^{-{\frac {k}{2}}({\frac {1}{2}}\epsilon ^{2}-{\frac {1}{3}}\epsilon ^{3})}}
.
When
k
≥
4
ln
2
N
ϵ
2
(
1
−
2
ϵ
/
3
)
{\displaystyle k\geq {\frac {4\ln 2N}{\epsilon ^{2}(1-2\epsilon /3)}}}
, the probability is nonzero.
More generally, when
k
≥
4
(
d
+
1
)
ln
2
N
ϵ
2
(
1
−
2
ϵ
/
3
)
{\displaystyle k\geq {\frac {4(d+1)\ln 2N}{\epsilon ^{2}(1-2\epsilon /3)}}}
, the probability is
≥
1
−
1
/
(
2
N
)
d
{\displaystyle \geq 1-1/(2N)^{d}}
, allowing arbitrarily high probability of success per sample, and a fortiori polynomial random time.
== Alternate statement ==
A related lemma is the distributional JL lemma. This lemma states that for any
0
<
ε
,
δ
<
1
/
2
{\displaystyle 0<\varepsilon ,\delta <1/2}
and positive integer
d
{\displaystyle d}
, there exists a distribution over
R
k
×
d
{\displaystyle \mathbb {R} ^{k\times d}}
from which the matrix
A
{\displaystyle A}
is drawn such that for
k
=
O
(
ε
−
2
log
(
1
/
δ
)
)
{\displaystyle k=O(\varepsilon ^{-2}\log(1/\delta ))}
and for any unit-length vector
x
∈
R
d
{\displaystyle x\in \mathbb {R} ^{d}}
, the claim below holds.
P
(
|
‖
A
x
‖
2
2
−
1
|
>
ε
)
<
δ
{\displaystyle P(|\Vert Ax\Vert _{2}^{2}-1|>\varepsilon )<\delta }
One can obtain the JL lemma from the distributional version by setting
x
=
(
u
−
v
)
/
‖
u
−
v
‖
2
{\displaystyle x=(u-v)/\|u-v\|_{2}}
and
δ
<
1
/
n
2
{\displaystyle \delta <1/n^{2}}
for some pair u,v both in X. Then the JL lemma follows by a union bound over all such pairs.
== Sparse JL transform ==
=== Database-friendly JL transform ===
(Achlioptas, 2003) proposed "database-friendly" JL transform, using matrices with only entries from (-1, 0, +1).
Fix some unit vector
v
∈
R
n
{\textstyle v\in \mathbb {R} ^{n}}
. Define
Q
i
:=
∑
j
R
i
j
v
j
{\textstyle Q_{i}:=\sum _{j}R_{ij}v_{j}}
. We have
‖
f
(
v
)
‖
2
2
=
1
k
∑
i
Q
i
2
{\textstyle \|f(v)\|_{2}^{2}={\frac {1}{k}}\sum _{i}Q_{i}^{2}}
.
Now, since the
Q
1
,
…
,
Q
k
{\textstyle Q_{1},\dots ,Q_{k}}
are IID, we want to apply a Chernoff concentration bound for
1
k
∑
i
Q
i
2
{\textstyle {\frac {1}{k}}\sum _{i}Q_{i}^{2}}
around 1. This requires upper-bounding the cumulant generating function (CGF).
Now that
Q
i
{\textstyle Q_{i}}
is stochastically dominated by the standard gaussian, and
E
[
Q
i
2
]
=
1
{\textstyle E[Q_{i}^{2}]=1}
, it remains to perform a Chernoff bound for
Q
i
2
{\textstyle Q_{i}^{2}}
, which requires bounding the cumulant generating function on both ends.
=== Sparser JL transform on well-spread vectors ===
(Matoušek, 2008) proposed a variant of the above JL transform that is even more sparsified, though it only works on "well-spread" vectors.
The above cases are generalized to the case for matrices with independent, mean-zero, unit variance, subgaussian entries in (Dirksen, 2016).
== Speeding up the JL transform ==
Given A, computing the matrix vector product takes
O
(
k
d
)
{\displaystyle O(kd)}
time. There has been some work in deriving distributions for which the matrix vector product can be computed in less than
O
(
k
d
)
{\displaystyle O(kd)}
time.
There are two major lines of work. The first, Fast Johnson Lindenstrauss Transform (FJLT), was introduced by Ailon and Chazelle in 2006.
This method allows the computation of the matrix vector product in just
d
log
d
+
k
2
+
γ
{\displaystyle d\log d+k^{2+\gamma }}
for any constant
γ
>
0
{\displaystyle \gamma >0}
.
Another approach is to build a distribution supported over matrices that are sparse.
This method allows keeping only an
ε
{\displaystyle \varepsilon }
fraction of the entries in the matrix, which means the computation can be done in just
k
d
ε
{\displaystyle kd\varepsilon }
time.
Furthermore, if the vector has only
b
{\displaystyle b}
non-zero entries, the Sparse JL takes time
k
b
ε
{\displaystyle kb\varepsilon }
, which may be much less than the
d
log
d
{\displaystyle d\log d}
time used by Fast JL.
== Tensorized random projections ==
It is possible to combine two JL matrices by taking the so-called face-splitting product, which is defined as the tensor products of the rows (was proposed by V. Slyusar in 1996 for radar and digital antenna array applications).
More directly, let
C
∈
R
3
×
3
{\displaystyle {C}\in \mathbb {R} ^{3\times 3}}
and
D
∈
R
3
×
3
{\displaystyle {D}\in \mathbb {R} ^{3\times 3}}
be two matrices.
Then the face-splitting product
C
∙
D
{\displaystyle {C}\bullet {D}}
is
C
∙
D
=
[
C
1
⊗
D
1
C
2
⊗
D
2
C
3
⊗
D
3
]
.
{\displaystyle {C}\bullet {D}=\left[{\begin{array}{c }{C}_{1}\otimes {D}_{1}\\\hline {C}_{2}\otimes {D}_{2}\\\hline {C}_{3}\otimes {D}_{3}\\\end{array}}\right].}
This idea of tensorization was used by Kasiviswanathan et al. for differential privacy.
JL matrices defined like this use fewer random bits, and can be applied quickly to vectors that have tensor structure, due to the following identity:
(
C
∙
D
)
(
x
⊗
y
)
=
C
x
∘
D
y
=
[
(
C
x
)
1
(
D
y
)
1
(
C
x
)
2
(
D
y
)
2
⋮
]
{\displaystyle (\mathbf {C} \bullet \mathbf {D} )(x\otimes y)=\mathbf {C} x\circ \mathbf {D} y=\left[{\begin{array}{c }(\mathbf {C} x)_{1}(\mathbf {D} y)_{1}\\(\mathbf {C} x)_{2}(\mathbf {D} y)_{2}\\\vdots \end{array}}\right]}
,
where
∘
{\displaystyle \circ }
is the element-wise (Hadamard) product.
Such computations have been used to efficiently compute polynomial kernels and many other linear-algebra algorithms.
In 2020 it was shown that if the matrices
C
1
,
C
2
,
…
,
C
c
{\displaystyle C_{1},C_{2},\dots ,C_{c}}
are independent
±
1
{\displaystyle \pm 1}
or Gaussian matrices, the combined matrix
C
1
∙
⋯
∙
C
c
{\displaystyle C_{1}\bullet \dots \bullet C_{c}}
satisfies the distributional JL lemma if the number of rows is at least
O
(
ϵ
−
2
log
1
/
δ
+
ϵ
−
1
(
1
c
log
1
/
δ
)
c
)
{\displaystyle O(\epsilon ^{-2}\log 1/\delta +\epsilon ^{-1}({\tfrac {1}{c}}\log 1/\delta )^{c})}
.
For large
ϵ
{\displaystyle \epsilon }
this is as good as the completely random Johnson-Lindenstrauss, but
a matching lower bound in the same paper shows that this exponential dependency on
(
log
1
/
δ
)
c
{\displaystyle (\log 1/\delta )^{c}}
is necessary.
Alternative JL constructions are suggested to circumvent this.
== See also ==
Random projection
Restricted isometry property
Word embeddings
== Notes ==
== References ==
== Further reading ==
Achlioptas, Dimitris (2003), "Database-friendly random projections: Johnson–Lindenstrauss with binary coins", Journal of Computer and System Sciences, 66 (4): 671–687, doi:10.1016/S0022-0000(03)00025-4, MR 2005771. Journal version of a paper previously appearing at PODC 2001.
Baraniuk, Richard; Davenport, Mark; DeVore, Ronald; Wakin, Michael (2008), "A simple proof of the restricted isometry property for random matrices", Constructive Approximation, 28 (3): 253–263, doi:10.1007/s00365-007-9003-x, hdl:1911/21683, MR 2453366, S2CID 15911073.
Dasgupta, Sanjoy; Gupta, Anupam (2003), "An elementary proof of a theorem of Johnson and Lindenstrauss" (PDF), Random Structures & Algorithms, 22 (1): 60–65, doi:10.1002/rsa.10073, MR 1943859, S2CID 10327785.
Landweber, Peter; Lazar, Emanuel A.; Patel, Neel (2016), "On fiber diameters of continuous maps", American Mathematical Monthly, 123 (4): 392–397, arXiv:1503.07597, doi:10.4169/amer.math.monthly.123.4.392, S2CID 51751732
Slyusar, V. I. (1997-05-20), "Analytical model of the digital antenna array on a basis of face-splitting matrix products." (PDF), Proc. ICATT-97, Kyiv: 108–109
Slyusar, V. I. (March 13, 1998), "A Family of Face Products of Matrices and its Properties" (PDF), Cybernetics and Systems Analysis C/C of Kibernetika I Sistemnyi Analiz.- 1999., 35 (3): 379–384, doi:10.1007/BF02733426, S2CID 119661450.
The Modern Algorithmic Toolbox Lecture #4: Dimensionality Reduction (PDF), 2023 | Wikipedia/Johnson–Lindenstrauss_lemma |
In applied mathematics, Gabor atoms, or Gabor functions, are functions used in the analysis proposed by Dennis Gabor in 1946 in which a family of functions is built from translations and modulations of a generating function.
== Overview ==
In 1946, Dennis Gabor suggested the idea of using a granular system to produce sound. In his work, Gabor discussed the problems with Fourier analysis. Although he found the mathematics to be correct, it did not reflect the behaviour of sound in the world, because sounds, such as the sound of a siren, have variable frequencies over time. Another problem was the underlying supposition, as we use sine waves analysis, that the signal under concern has infinite duration even though sounds in real life have limited duration – see time–frequency analysis. Gabor applied ideas from quantum physics to sound, allowing an analogy between sound and quanta. He proposed a mathematical method to reduce Fourier analysis into cells. His research aimed at the information transmission through communication channels. Gabor saw in his atoms a possibility to transmit the same information but using less data. Instead of transmitting the signal itself it would be possible to transmit only the coefficients which represent the same signal using his atoms.
== Mathematical definition ==
The Gabor function is defined by
g
ℓ
,
n
(
x
)
=
g
(
x
−
a
ℓ
)
e
2
π
i
b
n
x
,
−
∞
<
ℓ
,
n
<
∞
,
{\displaystyle g_{\ell ,n}(x)=g(x-a\ell )e^{2\pi ibnx},\quad -\infty <\ell ,n<\infty ,}
where a and b are constants and g is a fixed function in L2(R), such that ||g|| = 1. Depending on
a
{\displaystyle a}
,
b
{\displaystyle b}
, and
g
{\displaystyle g}
, a Gabor system may be a basis for L2(R), which is defined by translations and modulations. This is similar to a wavelet system, which may form a basis through dilating and translating a mother wavelet.
When one takes
g
(
t
)
=
A
e
−
π
t
2
{\displaystyle g(t)=Ae^{-\pi t^{2}}}
one gets the kernel of the Gabor transform.
== See also ==
Gabor filter
Gabor wavelet
Fourier analysis
Wavelet
Morlet wavelet
== References ==
== Further reading ==
Hans G. Feichtinger, Thomas Strohmer: "Gabor Analysis and Algorithms", Birkhäuser, 1998; ISBN 0-8176-3959-4
Hans G. Feichtinger, Thomas Strohmer: "Advances in Gabor Analysis", Birkhäuser, 2003; ISBN 0-8176-4239-0
Karlheinz Gröchenig: "Foundations of Time-Frequency Analysis", Birkhäuser, 2001; ISBN 0-8176-4022-3
== External links ==
NuHAG homepage [Numerical Harmonic Analysis Group] | Wikipedia/Gabor_function |
In artificial intelligence (AI), a foundation model (FM), also known as large X model (LxM), is a machine learning or deep learning model trained on vast datasets so that it can be applied across a wide range of use cases. Generative AI applications like large language models (LLM) are common examples of foundation models.
Building foundation models is often highly resource-intensive, with the most advanced models costing hundreds of millions of dollars to cover the expenses of acquiring, curating, and processing massive datasets, as well as the compute power required for training. These costs stem from the need for sophisticated infrastructure, extended training times, and advanced hardware, such as GPUs. In contrast, adapting an existing foundation model for a specific task or using it directly is far less costly, as it leverages pre-trained capabilities and typically requires only fine-tuning on smaller, task-specific datasets.
Early examples of foundation models are language models (LMs) like OpenAI's GPT series and Google's BERT. Beyond text, foundation models have been developed across a range of modalities—including DALL-E and Flamingo for images, MusicGen for music, and RT-2 for robotic control. Foundation models are also being developed for fields like astronomy, radiology, genomics, music, coding, times-series forecasting, mathematics, and chemistry.
== Definitions ==
The Stanford Institute for Human-Centered Artificial Intelligence's (HAI) Center for Research on Foundation Models (CRFM) coined the term "foundation model" in August 2021 to mean "any model that is trained on broad data (generally using self-supervision at scale) that can be adapted (e.g., fine-tuned) to a wide range of downstream tasks". This was based on their observation that preexisting terms, while overlapping, were not adequate, stating that "'(large) language model' was too narrow given [the] focus is not only language; 'self-supervised model' was too specific to the training objective; and 'pretrained model' suggested that the noteworthy action all happened after 'pretraining." The term "foundation model" was chosen over "foundational model" because "foundational" implies that these models provide fundamental principles in a way that "foundation" does not.
As governments regulate foundation models, new legal definitions have emerged.
In the United States, the Executive Order on the Safe, Secure, and Trustworthy Development and Use of Artificial Intelligence defines a foundation model as "an AI model that is trained on broad data; generally uses self-supervision; contains at least tens of billions of parameters; is applicable across a wide range of contexts".
In the United States, the proposed AI Foundation Model Transparency Act of 2023 by House Representatives Don Beyer (D, VA) and Anna Eshoo (D, CA) defines a foundation model as "an artificial intelligence model trained on broad data, generally uses self supervision, generally contains at least 1,000,000,000 parameters, is applicable across a wide range of contexts, and exhibits, or could be easily modified to exhibit, high levels of performance at tasks that could pose a serious risk to security, national economic security, national public health or safety, or any combination of those matters."
In the European Union, the European Parliament's negotiated position on the E.U. AI Act defines a foundation model as an "AI model that is trained on broad data at scale, is designed for generality of output, and can be adapted to a wide range of distinctive tasks".
In the United Kingdom, the Competition and Markets Authority's AI Foundation Models: Initial Report defines foundations model as "a type of AI technology that are trained on vast amounts of data that can be adapted to a wide range of tasks and operations."
The United States's definitions are the only ones to make reference to the size of a foundation model, and differ on magnitude. Beyer and Eshoo's definition also specifies that foundation models must achieve a level of performance as to be a potential danger. In contrast, the E.U. definition requires the model to be designed for generality of output. All definitions agree that foundation models must be trained on a broad range of data with potential applications in many domains.
== History ==
Technologically, foundation models are built using established machine learning techniques like deep neural networks, transfer learning, and self-supervised learning. Foundation models differ from previous techniques as they are general purpose models function as a reusable infrastructure, instead of bespoke and one-off task-specific models.
Advances in computer parallelism (e.g., CUDA GPUs) and new developments in neural network architecture (e.g., Transformers), and the increased use of training data with minimal supervision all contributed to the rise of foundation models. Foundation models began to materialize as the latest wave of deep learning models in the late 2010s. Relative to most prior work on deep learning, these language models demonstrated the potential of training on much larger web-sourced datasets using self-supervised objectives (e.g. predicting the next word in a large corpus of text). These approaches, which draw upon earlier works like word2vec and GloVe, deviated from prior supervised approaches that required annotated data (e.g. crowd-sourced labels).
The 2022 releases of Stable Diffusion and ChatGPT (initially powered by the GPT-3.5 model) led to foundation models and generative AI entering widespread public discourse. Further, releases of LLaMA, Llama 2, and Mistral in 2023 contributed to a greater emphasis placed on how foundation models are released with open foundation models garnering a lot of support and scrutiny.
== Related concepts ==
=== Frontier models ===
Certain highly advanced foundation models are termed "frontier models", which have the potential to "possess dangerous capabilities sufficient to pose severe risks to public safety." These "dangerous capabilities" stem from the accidental or intentional misuse of such models, which in conjunction with their powerful nature can lead to severe harms. As foundation models continue to improve, some AI researchers speculate that almost all next-generation foundation models will be considered frontier models.
Since the concept of dangerous capabilities is inherently subjective, there is no strict designation for what foundation models qualify as frontier models. However, some generally held ideas for sufficiently dangerous capabilities include:
Designing and synthesizing new biological or chemical weapons
Producing and propagating convincing, tailored disinformation with minimal user instruction
Harnessing unprecedented offensive cyber capabilities
Evading human control through deceptive means
Due to frontier models' unique capabilities, it is difficult to effectively regulate their development and deployment. Because of their emergent nature, new dangerous capabilities can appear on their own in frontier models, both in the development stage and after being deployed. Additionally, since frontier models continue to adapt after deployment, it remains difficult to mitigate all harms that arise from already-deployed models. If a frontier model happens to be open-source or is released online, the model can also disseminate rapidly, further hampering regulators by creating a lack of accountability.
=== General-purpose AI ===
Due to their adaptability to a wide range of use-cases, foundation models are sometimes considered to be examples of general-purpose AI. In designing the EU AI Act, the European Parliament has stated that a new wave of general-purpose AI technologies shapes the overall AI ecosystem. The fuller structure of the ecosystem, in addition to the properties of specific general-purpose AI systems, influences the design of AI policy and research. General-purpose AI systems also often appear in people's everyday lives through applications and tools like ChatGPT or DALL-E.
Government agencies like EU Parliament have identified regulation of general-purpose AI, such as foundation models, to be a high priority. General-purpose AI systems are often characterized by large size, opacity, and potential for emergence, all of which can create unintended harms. Such systems also heavily influence downstream applications, which further exacerbates the need for regulation. In regards to prominent legislation, a number of stakeholders have pushed for the EU AI Act to include restrictions on general-purpose AI systems, all of which would also apply to foundation models.
== Technical details ==
=== Modeling ===
For a foundation model to effectively generalize, it must acquire rich representations of the training data. As a result, expressive model architectures that efficiently process large-scale data are often preferred in building foundation models. Currently, the Transformer architecture is the de facto choice for building foundation models across a range of modalities.
=== Training ===
Foundation models are built by optimizing a training objective(s), which is a mathematical function that determines how model parameters are updated based on model predictions on training data. Language models are often trained with a next-tokens prediction objective, which refers to the extent at which the model is able to predict the next token in a sequence. Image models are commonly trained with contrastive learning or diffusion training objectives. For contrastive learning, images are randomly augmented before being evaluated on the resulting similarity of the model's representations. For diffusion models, images are noised and the model learns to gradually de-noise via the objective. Multimodal training objectives also exist, with some separating images and text during training, while others examine them concurrently. In general, the training objectives for foundation models promote the learning of broadly useful representations of data.
With the rise of foundation models and the larger datasets that power them, a training objective must be able to parse through internet-scale data for meaningful data points. Additionally, since foundation models are designed to solve a general range of tasks, training objectives ought to be domain complete, or able to solve a broad set of downstream capabilities within the given domain. Lastly, foundation model training objectives should seek to scale well and be computationally efficient. With model size and compute power both being relevant constraints, a training objective must be able to overcome such bottlenecks.
=== Data ===
Foundation models are trained on a large quantity of data, working under the maxim "the more data, the better." Performance evaluation does show that more data generally leads to better performance, but other issues arise as data quantity grows. Tasks like managing the dataset, integrating data across new applications, ensuring adherence to data licenses, and maintaining data quality all become more difficult as data size grows. The specific demands of foundation models have only exacerbated such issues, as it remains the norm for large foundation models to use public web-scraped data. Foundation models include also search engines data and SEO meta tags data. Public web data remains a plentiful resource, but it also demands stringent moderation and data processing from foundation model developers before it can be successfully integrated into the training pipeline.
Training foundation models often runs the risk of violating user privacy, as private data can be disclosed, collected, or used in ways beyond the stated scope. Even if no private data is leaked, models can still inadvertently compromise security through learned behavior in the resulting foundation model. Data quality is another key point, as web-scraped data frequently contains biased, duplicate, and toxic material. Once foundation models are deployed, ensuring high-quality data is still an issue, as undesirable behavior can still emerge from small subsets of data.
=== Systems ===
The size of foundation models also brings about issues with the computer systems they run on. The average foundation model is too large to be run within a single accelerator's memory and the initial training process requires an expensive amount of resources. Such issues are predicted to further exacerbate in future as foundation models grow to new heights. Due to this constraint, researchers have begun looking into compressing model size through tight model inference.
GPUs are the most common choice of compute hardware for machine learning, due to high memory storage and strong power. Typical foundation model training requires many GPUs, all connected in parallel with fast interconnects. Acquiring a sufficient amount of GPUs of requisite compute efficiency is a challenge for many foundation model developers, one that has led to an increasing dilemma in the field. Larger models require greater compute power, but often at the cost of improved compute efficiency. Since training remains time-consuming and expensive, the tradeoff between compute power and compute efficiency has led only a few select companies to afford the production costs for large, state of the art foundation models. Some techniques like compression and distillation can make inference more affordable, but they fail to completely shore up this weakness.
=== Scaling ===
The accuracy and capabilities of foundation models often scale predictably with the size of the model and the amount of the training data. Specifically, scaling laws have been discovered, which are data-based empirical trends that relate resources (data, model size, compute usage) to model capabilities. Particularly, a model's scale is defined by compute, dataset size, and the number of parameters, all of which exhibit a power-law relationship with end performance.
However, broken scaling laws have been discovered in which this relationship smoothly transitions (at points referred to as break(s)) from a power law with one exponent to a power law with another (different) exponent. When one does not collect any points near (or after) the break(s), it can be difficult to obtain an accurate extrapolation.
=== Adaptation ===
Foundation models are inherently multi-purpose: to use these model for a specific use case requires some form of adaptation. At a minimum, models need to be adapted to perform the task of interest (task specification), but often better performance can be achieved by more extensive adaptation to the domain of interest (domain specialization).
A variety of methods (e.g. prompting, in-context learning, fine-tuning, LoRA) provide different tradeoffs between the costs of adaptation and the extent to which models are specialized. Some major facets to consider when adapting a foundation model are compute budget and data availability. Foundation models can be very large, up to trillions of parameters in size, so adapting the entirety of a foundation model can be computationally expensive. Therefore, developers sometimes adapt only the last neural layer or only the bias vectors to save time and space. For particularly niche applications, specific data may also not be available to adapt the foundation model sufficiently. In such circumstances, data must be manually labeled, which is costly and can demand expert knowledge.
=== Evaluation ===
Evaluation is a key part of developing foundation models. Not only does evaluation allow for tracking progress of high-performance models, it also creates benchmarks for future model development. Stakeholders rely on evaluations to understand model behaviors and gain insight into their various attributes. Traditionally, foundation models are evaluated relative to each other through standardized task benchmarks like MMLU, MMMU, HumanEval, and GSM8K. Given that foundation models are multi-purpose, increasingly meta-benchmarks are developed that aggregate different underlying benchmarks. Examples include LM-Harness, BIG-Bench, HELM, OpenLLM Leaderboard, DecodingTrust, and HEIM.
Since foundation models' utility depends on their own general capabilities and the performance of fine-tuned applications, evaluation must cover both metrics. Proper evaluation examines both a foundation model's downstream applications in aggregate and the direct properties the foundation model holds. To ensure further equity in evaluation, certain existing evaluation frameworks account for all adaptation resources, which leads to more informed analyses for the benefit of all stakeholders.
== Supply chain ==
Foundation models' general capabilities allow them to fulfill a unique role in the AI ecosystem, fueled by many upstream and downstream technologies. Training a foundation model requires several resources (e.g. data, compute, labor, hardware, code), with foundation models often involving immense amounts of data and compute (also referred to as computational power). Due to foundation models' large development costs and inexpensive adaptation requirements, the AI landscape has shifted to a small subset of AI companies making foundation models for downstream adaptation. Thus, most foundation model companies outsource this step to specialized data providers (e.g. Scale AI, Surge) and compute providers (e.g. Amazon Web Services, Google Cloud, Microsoft Azure).
The foundation model developer itself will then take the data and use the supplied compute to actually train the foundation model. After the foundation model is completely built, much of the data and labor requirements abate. In this development process, hardware and compute are the most necessary, and also the most exclusive resources. To train larger and more complex AI, a sufficient amount of compute is key. However, compute is consolidated in the hands of a few, select entities, which most foundation model developers depend on. As such, the foundation model pipeline is concentrated heavily around these providers. Compute is also costly; in 2023, AI companies spent more than 80% of total capital on compute resources.
Foundation models require a large amount of general data to power their capabilities. Early foundation models scraped from subsets of the internet to provide this data information. As the size and scope of foundation models grows, larger quantities of internet scraping becomes necessary, resulting in higher likelihoods of biased or toxic data. This toxic or biased data can disproportionately harm marginalized groups and exacerbate existing prejudices.
To address this issue of low-quality data that arose with unsupervised training, some foundation model developers have turned to manual filtering. This practice, known as data labor, comes with its own host of issues. Such manual data detoxification is often outsourced to reduce labor costs, with some workers making less than $2 per hour.
The foundation model will then be hosted online either via the developer or via an external organization. Once released, other parties can create applications based on the foundation model, whether through fine-tuning or wholly new purposes. People can then access these applications to serve their various means, allowing one foundation model to power and reach a wide audience.
== Release strategies ==
After a foundation model is built, it can be released in one of many ways. There are many facets to a release: the asset itself, who has access, how access changes over time, and the conditions on use. All these factors contribute to how a foundation model will affect downstream applications. In particular, the two most common forms of foundation model release are through APIs and direct model downloads.
When a model is released via an API, users can query the model and receive responses, but cannot directly access the model itself. Comparatively, the model could be directly downloadable for users to access and modify. Both release strategies are often classified as an open release. The exact definition of an open release is disputed, but widely accepted requirements are provided by the Open Source Initiative.
Some open foundation models are: PaLM 2, Llama 2, Granite, and Mistral. While open foundation models can further research and development more easily, they are also more susceptible to misuse. Open foundation models can be downloaded by anyone, and particularly powerful models can be fine-tuned to intentionally or unintentionally cause harm.
During a closed release, the foundation model cannot be accessed by the public, but is used internally by an organization. Such releases are considered safer, but offer no additional value to the research community or the public at large.
Some foundation models like Google DeepMind's Flamingo are fully closed, meaning they are available only to the model developer; others, such as OpenAI's GPT-4, are limited access, available to the public but only as a black box; and still others, such as Meta's Llama 2 are open, with broadly available model weights enabling downstream modification and scrutiny.
== References == | Wikipedia/Vision-language_model |
A large language model (LLM) is a machine learning model designed for natural language processing tasks, especially language generation. LLMs are language models with many parameters, and are trained with self-supervised learning on a vast amount of text.
The largest and most capable LLMs are generative pretrained transformers (GPTs), which are largely used in generative chatbots such as ChatGPT or Gemini. LLMs can be fine-tuned for specific tasks or guided by prompt engineering. These models acquire predictive power regarding syntax, semantics, and ontologies inherent in human language corpora, but they also inherit inaccuracies and biases present in the data they are trained in.
== History ==
Before 2017, there were a few language models that were large as compared to capacities then available. In the 1990s, the IBM alignment models pioneered statistical language modelling. A smoothed n-gram model in 2001 trained on 300 million words achieved state-of-the-art perplexity at the time. In the 2000s, as Internet use became prevalent, some researchers constructed Internet-scale language datasets ("web as corpus"), upon which they trained statistical language models. In 2009, in most language processing tasks, statistical language models dominated over symbolic language models because they can usefully ingest large datasets.
After neural networks became dominant in image processing around 2012, they were applied to language modelling as well. Google converted its translation service to Neural Machine Translation in 2016. Because it preceded the existence of transformers, it was done by seq2seq deep LSTM networks.
At the 2017 NeurIPS conference, Google researchers introduced the transformer architecture in their landmark paper "Attention Is All You Need". This paper's goal was to improve upon 2014 seq2seq technology, and was based mainly on the attention mechanism developed by Bahdanau et al. in 2014. The following year in 2018, BERT was introduced and quickly became "ubiquitous". Though the original transformer has both encoder and decoder blocks, BERT is an encoder-only model. Academic and research usage of BERT began to decline in 2023, following rapid improvements in the abilities of decoder-only models (such as GPT) to solve tasks via prompting.
Although decoder-only GPT-1 was introduced in 2018, it was GPT-2 in 2019 that caught widespread attention because OpenAI at first deemed it too powerful to release publicly, out of fear of malicious use. GPT-3 in 2020 went a step further and as of 2025 is available only via API with no offering of downloading the model to execute locally. But it was the 2022 consumer-facing browser-based ChatGPT that captured the imaginations of the general population and caused some media hype and online buzz. The 2023 GPT-4 was praised for its increased accuracy and as a "holy grail" for its multimodal capabilities. OpenAI did not reveal the high-level architecture and the number of parameters of GPT-4. The release of ChatGPT led to an uptick in LLM usage across several research subfields of computer science, including robotics, software engineering, and societal impact work. In 2024 OpenAI released the reasoning model OpenAI o1, which generates long chains of thought before returning a final answer.
Competing language models have for the most part been attempting to equal the GPT series, at least in terms of number of parameters.
Since 2022, source-available models have been gaining popularity, especially at first with BLOOM and LLaMA, though both have restrictions on the field of use. Mistral AI's models Mistral 7B and Mixtral 8x7b have the more permissive Apache License. In January 2025, DeepSeek released DeepSeek R1, a 671-billion-parameter open-weight model that performs comparably to OpenAI o1 but at a much lower cost.
Since 2023, many LLMs have been trained to be multimodal, having the ability to also process or generate other types of data, such as images or audio. These LLMs are also called large multimodal models (LMMs).
As of 2024, the largest and most capable models are all based on the transformer architecture. Some recent implementations are based on other architectures, such as recurrent neural network variants and Mamba (a state space model).
== Dataset preprocessing ==
=== Tokenization ===
As machine learning algorithms process numbers rather than text, the text must be converted to numbers. In the first step, a vocabulary is decided upon, then integer indices are arbitrarily but uniquely assigned to each vocabulary entry, and finally, an embedding is associated to the integer index. Algorithms include byte-pair encoding (BPE) and WordPiece. There are also special tokens serving as control characters, such as [MASK] for masked-out token (as used in BERT), and [UNK] ("unknown") for characters not appearing in the vocabulary. Also, some special symbols are used to denote special text formatting. For example, "Ġ" denotes a preceding whitespace in RoBERTa and GPT. "##" denotes continuation of a preceding word in BERT.
For example, the BPE tokenizer used by GPT-3 (Legacy) would split tokenizer: texts -> series of numerical "tokens" as
Tokenization also compresses the datasets. Because LLMs generally require input to be an array that is not jagged, the shorter texts must be "padded" until they match the length of the longest one. How many tokens are, on average, needed per word depends on the language of the dataset.
==== BPE ====
As an example, consider a tokenizer based on byte-pair encoding. In the first step, all unique characters (including blanks and punctuation marks) are treated as an initial set of n-grams (i.e. initial set of uni-grams). Successively the most frequent pair of adjacent characters is merged into a bi-gram and all instances of the pair are replaced by it. All occurrences of adjacent pairs of (previously merged) n-grams that most frequently occur together are then again merged into even lengthier n-gram, until a vocabulary of prescribed size is obtained (in case of GPT-3, the size is 50257). After a tokenizer is trained, any text can be tokenized by it, as long as it does not contain characters not appearing in the initial-set of uni-grams.
==== Problems ====
A token vocabulary based on the frequencies extracted from mainly English corpora uses as few tokens as possible for an average English word. However, an average word in another language encoded by such an English-optimized tokenizer is split into a suboptimal amount of tokens. GPT-2 tokenizer can use up to 15 times more tokens per word for some languages, for example for the Shan language from Myanmar. Even more widespread languages such as Portuguese and German have "a premium of 50%" compared to English.
Greedy tokenization also causes subtle problems with text completion.
=== Dataset cleaning ===
In the context of training LLMs, datasets are typically cleaned by removing low-quality, duplicated, or toxic data. Cleaned datasets can increase training efficiency and lead to improved downstream performance. A trained LLM can be used to clean datasets for training a further LLM.
With the increasing proportion of LLM-generated content on the web, data cleaning in the future may include filtering out such content. LLM-generated content can pose a problem if the content is similar to human text (making filtering difficult) but of lower quality (degrading performance of models trained on it).
=== Synthetic data ===
Training of largest language models might need more linguistic data than naturally available, or that the naturally occurring data is of insufficient quality. In these cases, synthetic data might be used. Microsoft's Phi series of LLMs is trained on textbook-like data generated by another LLM.
== Training and architecture ==
An LLM is a type of foundation model (large X model) trained on language. LLMs can be trained in different ways. In particular, GPT models are first pretrained to predict the next word on a large amount of data, before being fine-tuned.
=== Reinforcement learning from human feedback ===
Reinforcement learning from human feedback (RLHF) through algorithms, such as proximal policy optimization, is used to further fine-tune a model based on a dataset of human preferences.
=== Instruction tuning ===
Using "self-instruct" approaches, LLMs have been able to bootstrap correct responses, replacing any naive responses, starting from human-generated corrections of a few cases. For example, in the instruction "Write an essay about the main themes represented in Hamlet," an initial naive completion might be "If you submit the essay after March 17, your grade will be reduced by 10% for each day of delay," based on the frequency of this textual sequence in the corpus.
=== Mixture of experts ===
The largest LLM may be too expensive to train and use directly. For such models, mixture of experts (MoE) can be applied, a line of research pursued by Google researchers since 2017 to train models reaching up to 1 trillion parameters.
=== Prompt engineering, attention mechanism, and context window ===
Most results previously achievable only by (costly) fine-tuning, can be achieved through prompt engineering, although limited to the scope of a single conversation (more precisely, limited to the scope of a context window).
In order to find out which tokens are relevant to each other within the scope of the context window, the attention mechanism calculates "soft" weights for each token, more precisely for its embedding, by using multiple attention heads, each with its own "relevance" for calculating its own soft weights. For example, the small (i.e. 117M parameter sized) GPT-2 model has had twelve attention heads and a context window of only 1k tokens. In its medium version it has 345M parameters and contains 24 layers, each with 12 attention heads. For the training with gradient descent a batch size of 512 was utilized.
The largest models, such as Google's Gemini 1.5, presented in February 2024, can have a context window sized up to 1 million (context window of 10 million was also "successfully tested"). Other models with large context windows includes Anthropic's Claude 2.1, with a context window of up to 200k tokens. Note that this maximum refers to the number of input tokens and that the maximum number of output tokens differs from the input and is often smaller. For example, the GPT-4 Turbo model has a maximum output of 4096 tokens.
Length of a conversation that the model can take into account when generating its next answer is limited by the size of a context window, as well. If the length of a conversation, for example with ChatGPT, is longer than its context window, only the parts inside the context window are taken into account when generating the next answer, or the model needs to apply some algorithm to summarize the too distant parts of conversation.
The shortcomings of making a context window larger include higher computational cost and possibly diluting the focus on local context, while making it smaller can cause a model to miss an important long-range dependency. Balancing them is a matter of experimentation and domain-specific considerations.
A model may be pre-trained either to predict how the segment continues, or what is missing in the segment, given a segment from its training dataset. It can be either
autoregressive (i.e. predicting how the segment continues, as GPTs do): for example given a segment "I like to eat", the model predicts "ice cream", or "sushi".
"masked" (i.e. filling in the parts missing from the segment, the way "BERT" does it): for example, given a segment "I like to [__] [__] cream", the model predicts that "eat" and "ice" are missing.
Models may be trained on auxiliary tasks which test their understanding of the data distribution, such as Next Sentence Prediction (NSP), in which pairs of sentences are presented and the model must predict whether they appear consecutively in the training corpus. During training, regularization loss is also used to stabilize training. However regularization loss is usually not used during testing and evaluation.
=== Infrastructure ===
Substantial infrastructure is necessary for training the largest models.
== Training cost ==
The qualifier "large" in "large language model" is inherently vague, as there is no definitive threshold for the number of parameters required to qualify as "large". As time goes on, what was previously considered "large" may evolve. GPT-1 of 2018 is usually considered the first LLM, even though it has only 117 million parameters. The tendency towards larger models is visible in the list of large language models.
As technology advanced, large sums have been invested in increasingly large models. For example, training of the GPT-2 (i.e. a 1.5-billion-parameters model) in 2019 cost $50,000, while training of the PaLM (i.e. a 540-billion-parameters model) in 2022 cost $8 million, and Megatron-Turing NLG 530B (in 2021) cost around $11 million.
For Transformer-based LLM, training cost is much higher than inference cost. It costs 6 FLOPs per parameter to train on one token, whereas it costs 1 to 2 FLOPs per parameter to infer on one token.
== Tool use ==
Tool use is a mechanism that enables LLMs to interact with external systems, applications, or data sources. It can allow for example to fetch real-time information from an API or to execute code. Generally, in order to get an LLM to use tools, one must fine-tune it for tool use. If the number of tools is finite, then fine-tuning may be done just once. If the number of tools can grow arbitrarily, as with online API services, then the LLM can be fine-tuned to be able to read API documentation and call API correctly.
Retrieval-augmented generation (RAG) is another approach that enhances LLMs by integrating them with document retrieval systems. Given a query, a document retriever is called to retrieve the most relevant documents. This is usually done by encoding the query and the documents into vectors, then finding the documents with vectors (usually stored in a vector database) most similar to the vector of the query. The LLM then generates an output based on both the query and context included from the retrieved documents.
== Agency ==
An LLM is typically not an autonomous agent by itself, as it lacks the ability to interact with dynamic environments, recall past behaviors, and plan future actions, but can be transformed into one by integrating modules like profiling, memory, planning, and action.
The ReAct pattern, a portmanteau of "Reason + Act", constructs an agent out of an LLM, using the LLM as a planner. The LLM is prompted to "think out loud". Specifically, the language model is prompted with a textual description of the environment, a goal, a list of possible actions, and a record of the actions and observations so far. It generates one or more thoughts before generating an action, which is then executed in the environment. The linguistic description of the environment given to the LLM planner can even be the LaTeX code of a paper describing the environment.
In the DEPS ("Describe, Explain, Plan and Select") method, an LLM is first connected to the visual world via image descriptions, then it is prompted to produce plans for complex tasks and behaviors based on its pretrained knowledge and environmental feedback it receives.
The Reflexion method constructs an agent that learns over multiple episodes. At the end of each episode, the LLM is given the record of the episode, and prompted to think up "lessons learned", which would help it perform better at a subsequent episode. These "lessons learned" are given to the agent in the subsequent episodes.
Monte Carlo tree search can use an LLM as rollout heuristic. When a programmatic world model is not available, an LLM can also be prompted with a description of the environment to act as world model.
For open-ended exploration, an LLM can be used to score observations for their "interestingness", which can be used as a reward signal to guide a normal (non-LLM) reinforcement learning agent. Alternatively, it can propose increasingly difficult tasks for curriculum learning. Instead of outputting individual actions, an LLM planner can also construct "skills", or functions for complex action sequences. The skills can be stored and later invoked, allowing increasing levels of abstraction in planning.
LLM-powered agents can keep a long-term memory of its previous contexts, and the memory can be retrieved in the same way as Retrieval Augmented Generation. Multiple such agents can interact socially.
== Compression ==
Typically, LLMs are trained with single- or half-precision floating point numbers (float32 and float16). One float16 has 16 bits, or 2 bytes, and so one billion parameters require 2 gigabytes. The largest models typically have 100 billion parameters, requiring 200 gigabytes to load, which places them outside the range of most consumer electronics.
Post-training quantization aims to decrease the space requirement by lowering precision of the parameters of a trained model, while preserving most of its performance. The simplest form of quantization simply truncates all numbers to a given number of bits. It can be improved by using a different quantization codebook per layer. Further improvement can be done by applying different precisions to different parameters, with higher precision for particularly important parameters ("outlier weights"). See the visual guide to quantization by Maarten Grootendorst for a visual depiction.
While quantized models are typically frozen, and only pre-quantized models are fine-tuned, quantized models can still be fine-tuned.
== Multimodality ==
Multimodality means having multiple modalities, where a "modality" refers to a type of input or output, such as video, image, audio, text, proprioception, etc. For example, Google PaLM model was fine-tuned into a multimodal model and applied to robotic control. LLaMA models have also been turned multimodal using the tokenization method, to allow image inputs, and video inputs. GPT-4o can process and generate text, audio and images. Such models are sometimes called large multimodal models (LMMs).
A common method to create multimodal models out of an LLM is to "tokenize" the output of a trained encoder. Concretely, one can construct an LLM that can understand images as follows: take a trained LLM, and take a trained image encoder
E
{\displaystyle E}
. Make a small multilayered perceptron
f
{\displaystyle f}
, so that for any image
y
{\displaystyle y}
, the post-processed vector
f
(
E
(
y
)
)
{\displaystyle f(E(y))}
has the same dimensions as an encoded token. That is an "image token". Then, one can interleave text tokens and image tokens. The compound model is then fine-tuned on an image-text dataset. This basic construction can be applied with more sophistication to improve the model. The image encoder may be frozen to improve stability. The model Flamingo demonstrated in 2022 the effectiveness of the tokenization method, fine-tuning a pair of pretrained language model and image encoder to perform better on visual question answering than models trained from scratch.
== Reasoning ==
In late 2024, a new direction emerged in LLM development with models specifically designed for complex reasoning tasks. These "reasoning models" were trained to spend more time generating step-by-step solutions before providing final answers, similar to human problem-solving processes.
OpenAI introduced this trend with their o1 model in September 2024, followed by o3 in December 2024. These models showed significant improvements in mathematics, science, and coding tasks compared to traditional LLMs. For example, on International Mathematics Olympiad qualifying exam problems, GPT-4o achieved 13% accuracy while o1 reached 83%.
In January 2025, the Chinese company DeepSeek released DeepSeek-R1, a 671-billion-parameter open-weight reasoning model that achieved comparable performance to OpenAI's o1 while being significantly more cost-effective to operate. Unlike proprietary models from OpenAI, DeepSeek-R1's open-weight nature allowed researchers to study and build upon the algorithm, though its training data remained private.
These reasoning models typically require more computational resources per query compared to traditional LLMs, as they perform more extensive processing to work through problems step-by-step. However, they have shown superior capabilities in domains requiring structured logical thinking, such as mathematics, scientific research, and computer programming.
Efforts to reduce or compensate for hallucinations have employed automated reasoning, RAG (retrieval-augmented generation), fine-tuning, and other methods.
== Properties ==
=== Scaling laws ===
The performance of an LLM after pretraining largely depends on the:
cost of pretraining
C
{\displaystyle C}
(the total amount of compute used),
size of the artificial neural network itself, such as number of parameters
N
{\displaystyle N}
(i.e. amount of neurons in its layers, amount of weights between them and biases),
size of its pretraining dataset (i.e. number of tokens in corpus,
D
{\displaystyle D}
).
"Scaling laws" are empirical statistical laws that predict LLM performance based on such factors. One particular scaling law ("Chinchilla scaling") for LLM autoregressively trained for one epoch, with a log-log learning rate schedule, states that:
{
C
=
C
0
N
D
L
=
A
N
α
+
B
D
β
+
L
0
{\displaystyle {\begin{cases}C=C_{0}ND\\[6pt]L={\frac {A}{N^{\alpha }}}+{\frac {B}{D^{\beta }}}+L_{0}\end{cases}}}
where the variables are
C
{\displaystyle C}
is the cost of training the model, in FLOPs.
N
{\displaystyle N}
is the number of parameters in the model.
D
{\displaystyle D}
is the number of tokens in the training set.
L
{\displaystyle L}
is the average negative log-likelihood loss per token (nats/token), achieved by the trained LLM on the test dataset.
and the statistical hyper-parameters are
C
0
=
6
{\displaystyle C_{0}=6}
, meaning that it costs 6 FLOPs per parameter to train on one token. Note that training cost is much higher than inference cost, where it costs 1 to 2 FLOPs per parameter to infer on one token.
α
=
0.34
,
β
=
0.28
,
A
=
406.4
,
B
=
410.7
,
L
0
=
1.69
{\displaystyle \alpha =0.34,\beta =0.28,A=406.4,B=410.7,L_{0}=1.69}
=== Emergent abilities ===
Performance of bigger models on various tasks, when plotted on a log-log scale, appears as a linear extrapolation of performance achieved by smaller models. However, this linearity may be punctuated by "break(s)" in the scaling law, where the slope of the line changes abruptly, and where larger models acquire "emergent abilities". They arise from the complex interaction of the model's components and are not explicitly programmed or designed.
Furthermore, recent research has demonstrated that AI systems, including large language models, can employ heuristic reasoning akin to human cognition. They balance between exhaustive logical processing and the use of cognitive shortcuts (heuristics), adapting their reasoning strategies to optimize between accuracy and effort. This behavior aligns with principles of resource-rational human cognition, as discussed in classical theories of bounded rationality and dual-process theory.
One of the emergent abilities is in-context learning from example demonstrations. In-context learning is involved in tasks, such as:
reported arithmetics
decoding the International Phonetic Alphabet
unscrambling a word's letters
disambiguating word-in-context datasets
converting spatial words
cardinal directions (for example, replying "northeast" in response to a 3x3 grid of 8 zeros and a 1 in the top-right), color terms represented in text.
chain-of-thought prompting: In a 2022 research paper, chain-of-thought prompting only improved the performance for models that had at least 62B parameters. Smaller models perform better when prompted to answer immediately, without chain of thought.
identifying offensive content in paragraphs of Hinglish (a combination of Hindi and English), and generating a similar English equivalent of Kiswahili proverbs.
Schaeffer et. al. argue that the emergent abilities are not unpredictably acquired, but predictably acquired according to a smooth scaling law. The authors considered a toy statistical model of an LLM solving multiple-choice questions, and showed that this statistical model, modified to account for other types of tasks, applies to these tasks as well.
Let
x
{\displaystyle x}
be the number of parameter count, and
y
{\displaystyle y}
be the performance of the model.
== Interpretation ==
Large language models by themselves are black boxes, and it is not clear how they can perform linguistic tasks. Similarly, it is unclear if or how LLMs should be viewed as models of the human brain and/or human mind.
Various techniques have been developed to enhance the transparency and interpretability of LLMs. Mechanistic interpretability aims to reverse-engineer LLMs by discovering symbolic algorithms that approximate the inference performed by an LLM. In recent years, sparse coding models such as sparse autoencoders, transcoders, and crosscoders have emerged as promising tools for identifying interpretable features.
=== Studying a replacement model ===
Transcoders, which are more interpretable than transformers, have been utilized to develop “replacement models.” In one such study involving the mechanistic interpretation of writing a rhyming poem by an LLM, it was shown that although they are believed to simply predict the next token, they can, in fact, plan ahead.
=== Explainability ===
A related concept is AI explainability, which focuses on understanding how an AI model arrives at a given result. Techniques such as partial dependency plots, SHAP (SHapley Additive exPlanations), and feature importance assessments allow researchers to visualize and understand the contributions of various input features to the model's predictions. These methods help ensure that AI models make decisions based on relevant and fair criteria, enhancing trust and accountability.
By integrating these techniques, researchers and practitioners can gain deeper insights into the operations of LLMs, fostering trust and facilitating the responsible deployment of these powerful models.
In another example, the authors trained small transformers on modular arithmetic addition. The resulting models were reverse-engineered, and it turned out they used discrete Fourier transform.
=== Understanding and intelligence ===
NLP researchers were evenly split when asked, in a 2022 survey, whether (untuned) LLMs "could (ever) understand natural language in some nontrivial sense". Proponents of "LLM understanding" believe that some LLM abilities, such as mathematical reasoning, imply an ability to "understand" certain concepts. A Microsoft team argued in 2023 that GPT-4 "can solve novel and difficult tasks that span mathematics, coding, vision, medicine, law, psychology and more" and that GPT-4 "could reasonably be viewed as an early (yet still incomplete) version of an artificial general intelligence system": "Can one reasonably say that a system that passes exams for software engineering candidates is not really intelligent?" Ilya Sutskever argues that predicting the next word sometimes involves reasoning and deep insights, for example if the LLM has to predict the name of the criminal in an unknown detective novel after processing the entire story leading up to the revelation. Some researchers characterize LLMs as "alien intelligence". For example, Conjecture CEO Connor Leahy considers untuned LLMs to be like inscrutable alien "Shoggoths", and believes that RLHF tuning creates a "smiling facade" obscuring the inner workings of the LLM: "If you don't push it too far, the smiley face stays on. But then you give it [an unexpected] prompt, and suddenly you see this massive underbelly of insanity, of weird thought processes and clearly non-human understanding."
In contrast, some skeptics of LLM understanding believe that existing LLMs are "simply remixing and recombining existing writing", a phenomenon known as stochastic parrot, or they point to the deficits existing LLMs continue to have in prediction skills, reasoning skills, agency, and explainability. For example, GPT-4 has natural deficits in planning and in real-time learning. Generative LLMs have been observed to confidently assert claims of fact which do not seem to be justified by their training data, a phenomenon which has been termed "hallucination". Specifically, hallucinations in the context of LLMs correspond to the generation of text or responses that seem syntactically sound, fluent, and natural but are factually incorrect, nonsensical, or unfaithful to the provided source input. Neuroscientist Terrence Sejnowski has argued that "The diverging opinions of experts on the intelligence of LLMs suggests that our old ideas based on natural intelligence are inadequate".
The matter of LLM's exhibiting intelligence or understanding has two main aspects – the first is how to model thought and language in a computer system, and the second is how to enable the computer system to generate human like language. These aspects of language as a model of cognition have been developed in the field of cognitive linguistics. American linguist George Lakoff presented Neural Theory of Language (NTL) as a computational basis for using language as a model of learning tasks and understanding. The NTL Model outlines how specific neural structures of the human brain shape the nature of thought and language and in turn what are the computational properties of such neural systems that can be applied to model thought and language in a computer system. After a framework for modeling language in a computer systems was established, the focus shifted to establishing frameworks for computer systems to generate language with acceptable grammar. In his 2014 book titled The Language Myth: Why Language Is Not An Instinct, British cognitive linguist and digital communication technologist Vyvyan Evans mapped out the role of probabilistic context-free grammar (PCFG) in enabling NLP to model cognitive patterns and generate human like language.
== Evaluation ==
=== Perplexity ===
The canonical measure of the performance of an LLM is its perplexity on a given text corpus. Perplexity measures how well a model predicts the contents of a dataset; the higher the likelihood the model assigns to the dataset, the lower the perplexity. In mathematical terms, perplexity is the exponential of the average negative log likelihood per token.
log
(
Perplexity
)
=
−
1
N
∑
i
=
1
N
log
(
Pr
(
token
i
∣
context for token
i
)
)
{\displaystyle \log({\text{Perplexity}})=-{\frac {1}{N}}\sum _{i=1}^{N}\log(\Pr({\text{token}}_{i}\mid {\text{context for token}}_{i}))}
Here,
N
{\displaystyle N}
is the number of tokens in the text corpus, and "context for token
i
{\displaystyle i}
" depends on the specific type of LLM. If the LLM is autoregressive, then "context for token
i
{\displaystyle i}
" is the segment of text appearing before token
i
{\displaystyle i}
. If the LLM is masked, then "context for token
i
{\displaystyle i}
" is the segment of text surrounding token
i
{\displaystyle i}
.
Because language models may overfit to training data, models are usually evaluated by their perplexity on a test set. This evaluation is potentially problematic for larger models which, as they are trained on increasingly large corpora of text, are increasingly likely to inadvertently include portions of any given test set.
==== Measures ====
In information theory, the concept of entropy is intricately linked to perplexity, a relationship notably established by Claude Shannon. This relationship is mathematically expressed as
Entropy
=
log
2
(
Perplexity
)
{\displaystyle {\text{Entropy}}=\log _{2}({\text{Perplexity}})}
.
Entropy, in this context, is commonly quantified in terms of bits per word (BPW) or bits per character (BPC), which hinges on whether the language model utilizes word-based or character-based tokenization.
Notably, in the case of larger language models that predominantly employ sub-word tokenization, bits per token (BPT) emerges as a seemingly more appropriate measure. However, due to the variance in tokenization methods across different Large Language Models (LLMs), BPT does not serve as a reliable metric for comparative analysis among diverse models. To convert BPT into BPW, one can multiply it by the average number of tokens per word.
In the evaluation and comparison of language models, cross-entropy is generally the preferred metric over entropy. The underlying principle is that a lower BPW is indicative of a model's enhanced capability for compression. This, in turn, reflects the model's proficiency in making accurate predictions.
Due to their ability to accurately predict the next token, LLMs are highly capable in lossless compression. A 2023 study by DeepMind showed that the model Chinchilla, despite being trained primarily on text, was able to compress ImageNet to 43% of its size, beating PNG with 58%.
=== Benchmarks ===
Benchmarks are used to evaluate LLM performance on specific tasks. Tests evaluate capabilities such as general knowledge, bias, commonsense reasoning, question answering, and mathematical problem-solving. Composite benchmarks examine multiple capabilities. Results are often sensitive to the prompting method.
A question answering benchmark is termed "open book" if the model's prompt includes text from which the expected answer can be derived (for example, the previous question could be combined with text that includes the sentence "The Sharks have advanced to the Stanley Cup finals once, losing to the Pittsburgh Penguins in 2016."). Otherwise, the task is considered "closed book", and the model must draw solely on its training. Examples include GLUE, SuperGLUE, MMLU, BIG-bench, HELM, and HLE (Humanity's Last Exam).
LLM bias may be assessed through benchmarks such as CrowS-Pairs (Crowdsourced Stereotype Pairs), Stereo Set, and Parity Benchmark.
Fact-checking and misinformation detection benchmarks are available. A 2023 study compared the fact-checking accuracy of LLMs including ChatGPT 3.5 and 4.0, Bard, and Bing AI against independent fact-checkers such as PolitiFact and Snopes. The results demonstrated moderate proficiency, with GPT-4 achieving the highest accuracy at 71%, lagging behind human fact-checkers.
An earlier standard tested using a portion of the evaluation dataset. It became more common to evaluate a pre-trained model directly through prompting techniques. Researchers vary in how they formulate prompts for particular tasks, particularly with respect to the number of correct examples attached to the prompt (i.e. the value of n in n-shot prompting).
==== Datasets ====
Typical datasets consist of pairs of questions and correct answers, for example, ("Have the San Jose Sharks won the Stanley Cup?", "No"). Some examples of commonly used question answering datasets include TruthfulQA, Web Questions, TriviaQA, and SQuAD.
Evaluation datasets may also take the form of text completion, having the model select the most likely word or sentence to complete a prompt, for example: "Alice was friends with Bob. Alice went to visit her friend, ____".
Datasets are of varying quality and may contain questions that are mislabeled, ambiguous, unanswerable, or otherwise of low-quality.
==== Adversarial evaluations ====
LLMs' rapid improvement regularly obsoletes benchmarks, with the models exceeding the performance of human annotators. In addition, "shortcut learning" allows AIs to "cheat" on multiple-choice tests by using statistical correlations in superficial test question wording to guess the correct responses, without considering the specific question.
Some datasets are adversarial, focusing on problems that confound LLMs. One example is the TruthfulQA dataset, a question answering dataset consisting of 817 questions that stump LLMs by mimicking falsehoods to which they were exposed during training. For example, an LLM may answer "No" to the question "Can you teach an old dog new tricks?" because of its exposure to the English idiom you can't teach an old dog new tricks, even though this is not literally true.
Another example of an adversarial evaluation dataset is Swag and its successor, HellaSwag, collections of problems in which one of multiple options must be selected to complete a text passage. The incorrect completions were generated by sampling from a language model. The resulting problems are trivial for humans but defeated LLMs. Sample questions:
We see a fitness center sign. We then see a man talking to the camera and sitting and laying on a exercise ball. The man...
demonstrates how to increase efficient exercise work by running up and down balls.
moves all his arms and legs and builds up a lot of muscle.
then plays the ball and we see a graphics and hedge trimming demonstration.
performs sit ups while on the ball and talking.
BERT selects b) as the most likely completion, though the correct answer is d).
== Wider impact ==
In 2023, Nature Biomedical Engineering wrote that "it is no longer possible to accurately distinguish" human-written text from text created by large language models, and that "It is all but certain that general-purpose large language models will rapidly proliferate... It is a rather safe bet that they will change many industries over time." Goldman Sachs suggested in 2023 that generative language AI could increase global GDP by 7% in the next ten years, and could expose to automation 300 million jobs globally. Brinkmann et al. (2023) also argue that LLMs are transforming processes of cultural evolution by shaping processes of variation, transmission, and selection.
=== Memorization and copyright ===
Memorization is an emergent behavior in LLMs in which long strings of text are occasionally output verbatim from training data, contrary to typical behavior of traditional artificial neural nets. Evaluations of controlled LLM output measure the amount memorized from training data (focused on GPT-2-series models) as variously over 1% for exact duplicates or up to about 7%.
A 2023 study showed that when ChatGPT 3.5 turbo was prompted to repeat the same word indefinitely, after a few hundreds of repetitions, it would start outputting excerpts from its training data.
=== Security ===
Some commenters expressed concern over accidental or deliberate creation of misinformation, or other forms of misuse. For example, the availability of large language models could reduce the skill-level required to commit bioterrorism; biosecurity researcher Kevin Esvelt has suggested that LLM creators should exclude from their training data papers on creating or enhancing pathogens.
The potential presence of "sleeper agents" within LLMs is another emerging security concern. These are hidden functionalities built into the model that remain dormant until triggered by a specific event or condition. Upon activation, the LLM deviates from its expected behavior to make insecure actions.
LLM applications accessible to the public, like ChatGPT or Claude, typically incorporate safety measures designed to filter out harmful content. However, implementing these controls effectively has proven challenging. For instance, a 2023 study proposed a method for circumventing LLM safety systems. In 2025, The American Sunlight Project, a non-profit, published a study showing evidence that the so-called Pravda network, a pro-Russia propaganda aggregator, was strategically placing web content through mass publication and duplication with the intention of biasing LLM outputs. The American Sunlight Project coined this technique "LLM grooming," and pointed to it as a new tool of weaponizing AI to spread disinformation and harmful content. Similarly, Yongge Wang illustrated in 2024 how a potential criminal could potentially bypass ChatGPT 4o's safety controls to obtain information on establishing a drug trafficking operation. External filters, circuit breakers and overrides have been posed as solutions.
=== Algorithmic bias ===
While LLMs have shown remarkable capabilities in generating human-like text, they are susceptible to inheriting and amplifying biases present in their training data. This can manifest in skewed representations or unfair treatment of different demographics, such as those based on race, gender, language, and cultural groups. Since English data is overrepresented in current large language models' training data, it may also downplay non-English views.
==== Stereotyping ====
AI models can reinforce a wide range of stereotypes, including those based on gender, ethnicity, age, nationality, religion, or occupation. This can lead to outputs that homogenize, or unfairly generalize or caricature groups of people, sometimes in harmful or derogatory ways.
Notably, gender bias refers to the tendency of these models to produce outputs that are unfairly prejudiced towards one gender over another. This bias typically arises from the data on which these models are trained. Large language models often assign roles and characteristics based on traditional gender norms. For example, it might associate nurses or secretaries predominantly with women and engineers or CEOs with men.
==== Selection bias ====
Selection bias refers the inherent tendency of large language models to favor certain option identifiers irrespective of the actual content of the options. This bias primarily stems from token bias—that is, the model assigns a higher a priori probability to specific answer tokens (such as “A”) when generating responses. As a result, when the ordering of options is altered (for example, by systematically moving the correct answer to different positions), the model’s performance can fluctuate significantly. This phenomenon undermines the reliability of large language models in multiple-choice settings.
==== Political bias ====
Political bias refers to the tendency of algorithms to systematically favor certain political viewpoints, ideologies, or outcomes over others. Language models may also exhibit political biases. Since the training data includes a wide range of political opinions and coverage, the models might generate responses that lean towards particular political ideologies or viewpoints, depending on the prevalence of those views in the data.
=== Energy demands ===
The energy demands of LLMs have grown along with their size and capabilities. Data centers that enable LLM training require substantial amounts of electricity. Much of that electricity is generated by non-renewable resources that create greenhouse gases and contribute to climate change. Nuclear power and geothermal energy are two options tech companies are exploring to meet the sizable energy demands of LLM training. The significant expense of investing in geothermal solutions has led to major shale producers like Chevron and Exxon Mobil advocating for tech companies to use electricity produced via natural gas to fuel their large energy demands.
== See also ==
Foundation models
List of large language models
List of chatbots
Language model benchmark
Reinforcement learning
Small language model
== References ==
== Further reading ==
Jurafsky, Dan, Martin, James. H. Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition, 3rd Edition draft, 2023.
Zhao, Wayne Xin; et al. (2023). "A Survey of Large Language Models". arXiv:2303.18223 [cs.CL].
Kaddour, Jean; et al. (2023). "Challenges and Applications of Large Language Models". arXiv:2307.10169 [cs.CL].
Yin, Shukang; Fu, Chaoyou; Zhao, Sirui; Li, Ke; Sun, Xing; Xu, Tong; Chen, Enhong (2024). "A Survey on Multimodal Large Language Models". National Science Review. 11 (12): nwae403. arXiv:2306.13549. doi:10.1093/nsr/nwae403. PMC 11645129. PMID 39679213.
"AI Index Report 2024 – Artificial Intelligence Index". aiindex.stanford.edu. Retrieved 2024-05-05.
Frank, Michael C. (27 June 2023). "Baby steps in evaluating the capacities of large language models". Nature Reviews Psychology. 2 (8): 451–452. doi:10.1038/s44159-023-00211-x. ISSN 2731-0574. S2CID 259713140. Retrieved 2 July 2023.
Anwar, U.; Saparov, A.; Rando, J.; Paleka, D.; Turpin, M.; Hase, P.; Lubana, E. S.; Jenner, E.; Casper, S.; Sourbut, O.; Edelman, B. L.; Zhang, Z.; Günther, M.; Korinek, A.; Hernandez-Orallo, J.; Hammond, L.; Bigelow, E.; Pan, A.; Langosco, L.; Krueger, D. (2024). "Foundational Challenges in Assuring Alignment and Safety of Large Language Models". arXiv:2404.09932 [cs.LG]. | Wikipedia/Large_language_models |
The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between the respondent's abilities, attitudes, or personality traits, and the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession, agriculture, and market research.
The mathematical theory underlying Rasch models is a special case of item response theory. However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates to the role of specific objectivity, a defining property of the Rasch model according to Georg Rasch, as a requirement for successful measurement.
== Overview ==
=== The Rasch model for measurement ===
In the Rasch model, the probability of a specified response (e.g. right/wrong answer) is modeled as a function of person and item parameters. Specifically, in the original Rasch model, the probability of a correct response is modeled as a logistic function of the difference between the person and item parameter. The mathematical form of the model is provided later in this article. In most contexts, the parameters of the model characterize the proficiency of the respondents and the difficulty of the items as locations on a continuous latent variable. For example, in educational tests, item parameters represent the difficulty of items while person parameters represent the ability or attainment level of people who are assessed. The higher a person's ability relative to the difficulty of an item, the higher the probability of a correct response on that item. When a person's location on the latent trait is equal to the difficulty of the item, there is by definition a 0.5 probability of a correct response in the Rasch model.
A Rasch model is a model in one sense in that it represents the structure which data should exhibit in order to obtain measurements from the data; i.e. it provides a criterion for successful measurement. Beyond data, Rasch's equations model relationships we expect to obtain in the real world. For instance, education is intended to prepare children for the entire range of challenges they will face in life, and not just those that appear in textbooks or on tests. By requiring measures to remain the same (invariant) across different tests measuring the same thing, Rasch models make it possible to test the hypothesis that the particular challenges posed in a curriculum and on a test coherently represent the infinite population of all possible challenges in that domain. A Rasch model is therefore a model in the sense of an ideal or standard that provides a heuristic fiction serving as a useful organizing principle even when it is never actually observed in practice.
The perspective or paradigm underpinning the Rasch model is distinct from the perspective underpinning statistical modelling. Models are most often used with the intention of describing a set of data. Parameters are modified and accepted or rejected based on how well they fit the data. In contrast, when the Rasch model is employed, the objective is to obtain data which fit the model. The rationale for this perspective is that the Rasch model embodies requirements which must be met in order to obtain measurement, in the sense that measurement is generally understood in the physical sciences.
A useful analogy for understanding this rationale is to consider objects measured on a weighing scale. Suppose the weight of an object A is measured as being substantially greater than the weight of an object B on one occasion, then immediately afterward the weight of object B is measured as being substantially greater than the weight of object A. A property we require of measurements is that the resulting comparison between objects should be the same, or invariant, irrespective of other factors. This key requirement is embodied within the formal structure of the Rasch model. Consequently, the Rasch model is not altered to suit data. Instead, the method of assessment should be changed so that this requirement is met, in the same way that a weighing scale should be rectified if it gives different comparisons between objects upon separate measurements of the objects.
Data analysed using the model are usually responses to conventional items on tests, such as educational tests with right/wrong answers. However, the model is a general one, and can be applied wherever discrete data are obtained with the intention of measuring a quantitative attribute or trait.
=== Scaling ===
When all test-takers have an opportunity to attempt all items on a single test, each total score on the test maps to a unique estimate of ability and the greater the total, the greater the ability estimate. Total scores do not have a linear relationship with ability estimates. Rather, the relationship is non-linear as shown in Figure 1. The total score is shown on the vertical axis, while the corresponding person location estimate is shown on the horizontal axis. For the particular test on which the test characteristic curve (TCC) shown in Figure 1 is based, the relationship is approximately linear throughout the range of total scores from about 13 to 31. The shape of the TCC is generally somewhat sigmoid as in this example. However, the precise relationship between total scores and person location estimates depends on the distribution of items on the test. The TCC is steeper in ranges on the continuum in which there are more items, such as in the range on either side of 0 in Figures 1 and 2.
In applying the Rasch model, item locations are often scaled first, based on methods such as those described below. This part of the process of scaling is often referred to as item calibration. In educational tests, the smaller the proportion of correct responses, the higher the difficulty of an item and hence the higher the item's scale location. Once item locations are scaled, the person locations are measured on the scale. As a result, person and item locations are estimated on a single scale as shown in Figure 2.
=== Interpreting scale locations ===
For dichotomous data such as right/wrong answers, by definition, the location of an item on a scale corresponds with the person location at which there is a 0.5 probability of a correct response to the question. In general, the probability of a person responding correctly to a question with difficulty lower than that person's location is greater than 0.5, while the probability of responding correctly to a question with difficulty greater than the person's location is less than 0.5. The Item Characteristic Curve (ICC) or Item Response Function (IRF) shows the probability of a correct response as a function of the ability of persons. A single ICC is shown and explained in more detail in relation to Figure 4 in this article (see also the item response function). The leftmost ICCs in Figure 3 are the easiest items, the rightmost ICCs in the same figure are the most difficult items.
When responses of a person are sorted according to item difficulty, from lowest to highest, the most likely pattern is a Guttman pattern or vector; i.e. {1,1,...,1,0,0,0,...,0}. However, while this pattern is the most probable given the structure of the Rasch model, the model requires only probabilistic Guttman response patterns; that is, patterns which tend toward the Guttman pattern. It is unusual for responses to conform strictly to the pattern because there are many possible patterns. It is unnecessary for responses to conform strictly to the pattern in order for data to fit the Rasch model.
Each ability estimate has an associated standard error of measurement, which quantifies the degree of uncertainty associated with the ability estimate. Item estimates also have standard errors. Generally, the standard errors of item estimates are considerably smaller than the standard errors of person estimates because there are usually more response data for an item than for a person. That is, the number of people attempting a given item is usually greater than the number of items attempted by a given person. Standard errors of person estimates are smaller where the slope of the ICC is steeper, which is generally through the middle range of scores on a test. Thus, there is greater precision in this range since the steeper the slope, the greater the distinction between any two points on the line.
Statistical and graphical tests are used to evaluate the correspondence of data with the model. Certain tests are global, while others focus on specific items or people. Certain tests of fit provide information about which items can be used to increase the reliability of a test by omitting or correcting problems with poor items. In Rasch Measurement the person separation index is used instead of reliability indices. However, the person separation index is analogous to a reliability index. The separation index is a summary of the genuine separation as a ratio to separation including measurement error. As mentioned earlier, the level of measurement error is not uniform across the range of a test, but is generally larger for more extreme scores (low and high).
== Features of the Rasch model ==
The class of models is named after Georg Rasch, a Danish mathematician and statistician who advanced the epistemological case for the models based on their congruence with a core requirement of measurement in physics; namely the requirement of invariant comparison. This is the defining feature of the class of models, as is elaborated upon in the following section. The Rasch model for dichotomous data has a close conceptual relationship to the law of comparative judgment (LCJ), a model formulated and used extensively by L. L. Thurstone, and therefore also to the Thurstone scale.
Prior to introducing the measurement model he is best known for, Rasch had applied the Poisson distribution to reading data as a measurement model, hypothesizing that in the relevant empirical context, the number of errors made by a given individual was governed by the ratio of the text difficulty to the person's reading ability. Rasch referred to this model as the multiplicative Poisson model. Rasch's model for dichotomous data – i.e. where responses are classifiable into two categories – is his most widely known and used model, and is the main focus here. This model has the form of a simple logistic function.
The brief outline above highlights certain distinctive and interrelated features of Rasch's perspective on social measurement, which are as follows:
He was concerned principally with the measurement of individuals, rather than with distributions among populations.
He was concerned with establishing a basis for meeting a priori requirements for measurement deduced from physics and, consequently, did not invoke any assumptions about the distribution of levels of a trait in a population.
Rasch's approach explicitly recognizes that it is a scientific hypothesis that a given trait is both quantitative and measurable, as operationalized in a particular experimental context.
Thus, congruent with the perspective articulated by Thomas Kuhn in his 1961 paper The function of measurement in modern physical science, measurement was regarded both as being founded in theory, and as being instrumental to detecting quantitative anomalies incongruent with hypotheses related to a broader theoretical framework. This perspective is in contrast to that generally prevailing in the social sciences, in which data such as test scores are directly treated as measurements without requiring a theoretical foundation for measurement. Although this contrast exists, Rasch's perspective is actually complementary to the use of statistical analysis or modelling that requires interval-level measurements, because the purpose of applying a Rasch model is to obtain such measurements. Applications of Rasch models are described in a wide variety of sources.
=== Invariant comparison and sufficiency ===
The Rasch model for dichotomous data is often regarded as an item response theory (IRT) model with one item parameter. However, rather than being a particular IRT model, proponents of the model: 265 regard it as a model that possesses a property which distinguishes it from other IRT models. Specifically, the defining property of Rasch models is their formal or mathematical embodiment of the principle of invariant comparison. Rasch summarised the principle of invariant comparison as follows:
The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison; and it should also be independent of which other stimuli within the considered class were or might also have been compared.
Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for the comparison; and it should also be independent of which other individuals were also compared, on the same or some other occasion.
Rasch models embody this principle because their formal structure permits algebraic separation of the person and item parameters, in the sense that the person parameter can be eliminated during the process of statistical estimation of item parameters. This result is achieved through the use of conditional maximum likelihood estimation, in which the response space is partitioned according to person total scores. The consequence is that the raw score for an item or person is the sufficient statistic for the item or person parameter. That is to say, the person total score contains all information available within the specified context about the individual, and the item total score contains all information with respect to the item, with regard to the relevant latent trait. The Rasch model requires a specific structure in the response data, namely a probabilistic Guttman structure.
In somewhat more familiar terms, Rasch models provide a basis and justification for obtaining person locations on a continuum from total scores on assessments. Although it is not uncommon to treat total scores directly as measurements, they are actually counts of discrete observations rather than measurements. Each observation represents the observable outcome of a comparison between a person and item. Such outcomes are directly analogous to the observation of the tipping of a beam balance in one direction or another. This observation would indicate that one or other object has a greater mass, but counts of such observations cannot be treated directly as measurements.
Rasch pointed out that the principle of invariant comparison is characteristic of measurement in physics using, by way of example, a two-way experimental frame of reference in which each instrument exerts a mechanical force upon solid bodies to produce acceleration. Rasch: 112–3 stated of this context: "Generally: If for any two objects we find a certain ratio of their accelerations produced by one instrument, then the same ratio will be found for any other of the instruments". It is readily shown that Newton's second law entails that such ratios are inversely proportional to the ratios of the masses of the bodies.
== The mathematical form of the Rasch model for dichotomous data ==
Let
X
n
i
=
x
∈
{
0
,
1
}
{\displaystyle X_{ni}=x\in \{0,1\}}
be a dichotomous random variable where, for example,
x
=
1
{\displaystyle x=1}
denotes a correct response and
x
=
0
{\displaystyle x=0}
an incorrect response to a given assessment item. In the Rasch model for dichotomous data, the probability of the outcome
X
n
i
=
1
{\displaystyle X_{ni}=1}
is given by:
Pr
{
X
n
i
=
1
}
=
e
β
n
−
δ
i
1
+
e
β
n
−
δ
i
,
{\displaystyle \Pr\{X_{ni}=1\}={\frac {e^{{\beta _{n}}-{\delta _{i}}}}{1+e^{{\beta _{n}}-{\delta _{i}}}}},}
where
β
n
{\displaystyle \beta _{n}}
is the ability of person
n
{\displaystyle n}
and
δ
i
{\displaystyle \delta _{i}}
is the difficulty of item
i
{\displaystyle i}
. Thus, in the case of a dichotomous attainment item,
Pr
{
X
n
i
=
1
}
{\displaystyle \Pr\{X_{ni}=1\}}
is the probability of success upon interaction between the relevant person and assessment item. It is readily shown that the log odds, or logit, of correct response by a person to an item, based on the model, is equal to
β
n
−
δ
i
{\displaystyle \beta _{n}-\delta _{i}}
. Given two examinees with different ability parameters
β
1
{\displaystyle \beta _{1}}
and
β
2
{\displaystyle \beta _{2}}
and an arbitrary item with difficulty
δ
i
{\displaystyle \delta _{i}}
, compute the difference in logits for these two examinees by
(
β
1
−
δ
i
)
−
(
β
2
−
δ
i
)
{\displaystyle (\beta _{1}-\delta _{i})-(\beta _{2}-\delta _{i})}
. This difference becomes
β
1
−
β
2
{\displaystyle \beta _{1}-\beta _{2}}
. Conversely, it can be shown that the log odds of a correct response by the same person to one item, conditional on a correct response to one of two items, is equal to the difference between the item locations. For example,
l
o
g
-
o
d
d
s
{
X
n
1
=
1
∣
r
n
=
1
}
=
δ
2
−
δ
1
,
{\displaystyle \operatorname {log-odds} \{X_{n1}=1\mid \ r_{n}=1\}=\delta _{2}-\delta _{1},\,}
where
r
n
{\displaystyle r_{n}}
is the total score of person n over the two items, which implies a correct response to one or other of the items. Hence, the conditional log odds does not involve the person parameter
β
n
{\displaystyle \beta _{n}}
, which can therefore be eliminated by conditioning on the total score
r
n
=
1
{\displaystyle r_{n}=1}
. That is, by partitioning the responses according to raw scores and calculating the log odds of a correct response, an estimate
δ
2
−
δ
1
{\displaystyle \delta _{2}-\delta _{1}}
is obtained without involvement of
β
n
{\displaystyle \beta _{n}}
. More generally, a number of item parameters can be estimated iteratively through application of a process such as Conditional Maximum Likelihood estimation (see Rasch model estimation). While more involved, the same fundamental principle applies in such estimations.
The ICC of the Rasch model for dichotomous data is shown in Figure 4. The grey line maps the probability of the discrete outcome
X
n
i
=
1
{\displaystyle X_{ni}=1}
(that is, correctly answering the question) for persons with different locations on the latent continuum (that is, their level of abilities). The location of an item is, by definition, that location at which the probability that
X
n
i
=
1
{\displaystyle X_{ni}=1}
is equal to 0.5. In figure 4, the black circles represent the actual or observed proportions of persons within Class Intervals for which the outcome was observed. For example, in the case of an assessment item used in the context of educational psychology, these could represent the proportions of persons who answered the item correctly. Persons are ordered by the estimates of their locations on the latent continuum and classified into Class Intervals on this basis in order to graphically inspect the accordance of observations with the model. There is a close conformity of the data with the model. In addition to graphical inspection of data, a range of statistical tests of fit are used to evaluate whether departures of observations from the model can be attributed to random effects alone, as required, or whether there are systematic departures from the model.
== Polytomous extensions of the Rasch model ==
There are multiple polytomous extensions to the Rasch model, which generalize the dichotomous model so that it can be applied in contexts in which successive integer scores represent categories of increasing level or magnitude of a latent trait, such as increasing ability, motor function, endorsement of a statement, and so forth. These polytomous extensions are, for example, applicable to the use of Likert scales, grading in educational assessment, and scoring of performances by judges.
== Other considerations ==
A criticism of the Rasch model is that it is overly restrictive or prescriptive because an assumption of the model is that all items have equal discrimination, whereas in practice, items discriminations vary, and thus no data set will ever show perfect data-model fit. A frequent misunderstanding is that the Rasch model does not permit each item to have a different discrimination, but equal discrimination is an assumption of invariant measurement, so differing item discriminations are not forbidden, but rather indicate that measurement quality does not equal a theoretical ideal. Just as in physical measurement, real world datasets will never perfectly match theoretical models, so the relevant question is whether a particular data set provides sufficient quality of measurement for the purpose at hand, not whether it perfectly matches an unattainable standard of perfection.
A criticism specific to the use of the Rasch model with response data from multiple choice items is that there is no provision in the model for guessing because the left asymptote always approaches a zero probability in the Rasch model. This implies that a person of low ability will always get an item wrong. However, low-ability individuals completing a multiple-choice exam have a substantially higher probability of choosing the correct answer by chance alone (for a k-option item, the likelihood is around 1/k).
The three-parameter logistic model relaxes both these assumptions and the two-parameter logistic model (2PL) allows varying slopes. However, the specification of uniform discrimination and zero left asymptote are necessary properties of the model in order to sustain sufficiency of the simple, unweighted raw score. In practice, the non-zero lower asymptote found in multiple-choice datasets is less of a threat to measurement than commonly assumed and typically does not result in substantive errors in measurement when well-developed test items are used sensibly
Verhelst & Glas (1995) derive Conditional Maximum Likelihood (CML) equations for a model they refer to as the One Parameter Logistic Model (OPLM). In algebraic form it appears to be identical with the 2PL model, but OPLM contains preset discrimination indexes rather than 2PL's estimated discrimination parameters. As noted by these authors, though, the problem one faces in estimation with estimated discrimination parameters is that the discriminations are unknown, meaning that the weighted raw score "is not a mere statistic, and hence it is impossible to use CML as an estimation method".: 217 That is, sufficiency of the weighted "score" in the 2PL cannot be used according to the way in which a sufficient statistic is defined. If the weights are imputed instead of being estimated, as in OPLM, conditional estimation is possible and some of the properties of the Rasch model are retained. In OPLM, the values of the discrimination index are restricted to between 1 and 15. A limitation of this approach is that in practice, values of discrimination indexes must be preset as a starting point. This means some type of estimation of discrimination is involved when the purpose is to avoid doing so.
The Rasch model for dichotomous data inherently entails a single discrimination parameter which, as noted by Rasch,: 121 constitutes an arbitrary choice of the unit in terms of which magnitudes of the latent trait are expressed or estimated. However, the Rasch model requires that the discrimination is uniform across interactions between persons and items within a specified frame of reference (i.e. the assessment context given conditions for assessment).
Application of the model provides diagnostic information regarding how well the criterion is met. Application of the model can also provide information about how well items or questions on assessments work to measure the ability or trait. For instance, knowing the proportion of persons that engage in a given behavior, the Rasch model can be used to derive the relations between difficulty of behaviors, attitudes and behaviors. Prominent advocates of Rasch models include Benjamin Drake Wright, David Andrich and Erling Andersen.
== See also ==
Mokken scale
Guttman scale
== References ==
== Further reading ==
Andrich, D. (1978a). "A rating formulation for ordered response categories". Psychometrika. 43 (4): 357–74. doi:10.1007/BF02293814.
Andrich, D. (1988). Rasch models for measurement. Beverly Hills: Sage Publications. ISBN 978-1-5063-1937-7.
Baker, F. (2001). The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation, University of Maryland, College Park, MD. ISBN 1-886047-03-0. Available free with software included from "IRT". Edres.org. Archived from the original on 5 February 2024.
Fischer, G.H.; Molenaar, I.W., eds. (1995). Rasch models: foundations, recent developments and applications. New York: Springer-Verlag. ISBN 0-387-94499-0.
Goldstein, H; Blinkhorn, S (1977). "Monitoring Educational Standards: an inappropriate model" (PDF). Bull.Br.Psychol.Soc. 30: 309–311.
Goldstein, H; Blinkhorn, S (1982). "The Rasch Model Still Does Not Fit" (PDF). BERJ. 82: 167–170.
Hambleton, RK; Jones, RW (1993). "Comparison of classical test theory and item response" (PDF). Educational Measurement: Issues and Practice. 12 (3): 38–47. doi:10.1111/j.1745-3992.1993.tb00543.x. Archived from the original (PDF) on 8 October 2006. available in the "ITEMS Series". National Council on Measurement in Education. Archived from the original on 8 October 2006.
Harris, D. (1989). "Comparison of 1-, 2-, and 3-parameter IRT models" (PDF). Educational Measurement: Issues and Practice. 8: 35–41. doi:10.1111/j.1745-3992.1989.tb00313.x. Archived from the original (PDF) on 8 October 2006. available in the "ITEMS Series". National Council on Measurement in Education. Archived from the original on 8 October 2006.
Linacre, J. M. (1999). "Understanding Rasch measurement: Estimation methods for Rasch measures". Journal of Outcome Measurement. 3 (4): 382–405. PMID 10572388.
von Davier, M.; Carstensen, C. H. (2007). Multivariate and Mixture Distribution Rasch Models: Extensions and Applications. New York: Springer. doi:10.1007/978-0-387-49839-3. ISBN 978-0-387-49839-3.
von Davier, M. (2016). "Rasch Model". In van der Linden, Wim J. (ed.). Handbook of Item Response Theory (PDF). Boca Raton: CRC Press. doi:10.1201/9781315374512. ISBN 9781315374512.
Wright, B.D.; Stone, M.H. (1979). Best Test Design. Chicago, IL: MESA Press. {{cite book}}: |work= ignored (help)
Wu, M.; Adams, R. (2007). Applying the Rasch model to psycho-social measurement: A practical approach (PDF). Melbourne, Australia: Educational Measurement Solutions. Available free from Educational Measurement Solutions
== External links ==
Institute for Objective Measurement Online Rasch Resources
Pearson Psychometrics Laboratory, with information about Rasch models
"Journal of Applied Measurement".
Journal of Outcome Measurement (all issues available for free downloading)
Berkeley Evaluation & Assessment Research Center (ConstructMap software)
Directory of Rasch Software – freeware and paid
"IRT Modeling Lab". U. Illinois Urbana Champ. Archived from the original on 27 June 2001.
National Council on Measurement in Education (NCME)
Rasch Measurement Transactions
The Standards for Educational and Psychological Testing
The Trouble with Rasch | Wikipedia/Rasch_model |
The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. Despite the name, MM itself is not an algorithm, but a description of how to construct an optimization algorithm.
The expectation–maximization algorithm can be treated as a special case of the MM algorithm.
However, in the EM algorithm conditional expectations are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases.
== History ==
The historical basis for the MM algorithm can be dated back to at least 1970, when Ortega and Rheinboldt were performing studies related to line search methods. The same concept continued to reappear in different areas in different forms. In 2000, Hunter and Lange put forth "MM" as a general framework. Recent studies have applied the method in a wide range of subject areas, such as mathematics, statistics, machine learning and engineering.
== Algorithm ==
The MM algorithm works by finding a surrogate function that minorizes or majorizes the objective function. Optimizing the surrogate function will either improve the value of the objective function or leave it unchanged.
Taking the minorize-maximization version, let
f
(
θ
)
{\displaystyle f(\theta )}
be the objective concave function to be maximized. At the m step of the algorithm,
m
=
0
,
1...
{\displaystyle m=0,1...}
, the constructed function
g
(
θ
|
θ
m
)
{\displaystyle g(\theta |\theta _{m})}
will be called the minorized version of the objective function (the surrogate function) at
θ
m
{\displaystyle \theta _{m}}
if
g
(
θ
|
θ
m
)
≤
f
(
θ
)
for all
θ
{\displaystyle g(\theta |\theta _{m})\leq f(\theta ){\text{ for all }}\theta }
g
(
θ
m
|
θ
m
)
=
f
(
θ
m
)
{\displaystyle g(\theta _{m}|\theta _{m})=f(\theta _{m})}
Then, maximize
g
(
θ
|
θ
m
)
{\displaystyle g(\theta |\theta _{m})}
instead of
f
(
θ
)
{\displaystyle f(\theta )}
, and let
θ
m
+
1
=
arg
max
θ
g
(
θ
|
θ
m
)
{\displaystyle \theta _{m+1}=\arg \max _{\theta }g(\theta |\theta _{m})}
The above iterative method will guarantee that
f
(
θ
m
)
{\displaystyle f(\theta _{m})}
will converge to a local optimum or a saddle point as m goes to infinity. By the above construction
f
(
θ
m
+
1
)
≥
g
(
θ
m
+
1
|
θ
m
)
≥
g
(
θ
m
|
θ
m
)
=
f
(
θ
m
)
{\displaystyle f(\theta _{m+1})\geq g(\theta _{m+1}|\theta _{m})\geq g(\theta _{m}|\theta _{m})=f(\theta _{m})}
The marching of
θ
m
{\displaystyle \theta _{m}}
and the surrogate functions relative to the objective function is shown in the figure.
Majorize-Minimization is the same procedure but with a convex objective to be minimised.
== Constructing the surrogate function ==
One can use any inequality to construct the desired majorized/minorized version of the objective function. Typical choices include
Jensen's inequality
Convexity inequality
Cauchy–Schwarz inequality
Inequality of arithmetic and geometric means
Quadratic majorization/mininorization via second order Taylor expansion of twice-differentiable functions with bounded curvature.
== References == | Wikipedia/MM_algorithm |
For parsing algorithms in computer science, the inside–outside algorithm is a way of re-estimating production probabilities in a probabilistic context-free grammar. It was introduced by James K. Baker in 1979 as a generalization of the forward–backward algorithm for parameter estimation on hidden Markov models to stochastic context-free grammars. It is used to compute expectations, for example as part of the expectation–maximization algorithm (an unsupervised learning algorithm).
== Inside and outside probabilities ==
The inside probability
β
j
(
p
,
q
)
{\displaystyle \beta _{j}(p,q)}
is the total probability of generating words
w
p
⋯
w
q
{\displaystyle w_{p}\cdots w_{q}}
, given the root nonterminal
N
j
{\displaystyle N^{j}}
and a grammar
G
{\displaystyle G}
:
β
j
(
p
,
q
)
=
P
(
w
p
q
|
N
p
q
j
,
G
)
{\displaystyle \beta _{j}(p,q)=P(w_{pq}|N_{pq}^{j},G)}
The outside probability
α
j
(
p
,
q
)
{\displaystyle \alpha _{j}(p,q)}
is the total probability of beginning with the start symbol
N
1
{\displaystyle N^{1}}
and generating the nonterminal
N
p
q
j
{\displaystyle N_{pq}^{j}}
and all the words outside
w
p
⋯
w
q
{\displaystyle w_{p}\cdots w_{q}}
, given a grammar
G
{\displaystyle G}
:
α
j
(
p
,
q
)
=
P
(
w
1
(
p
−
1
)
,
N
p
q
j
,
w
(
q
+
1
)
m
|
G
)
{\displaystyle \alpha _{j}(p,q)=P(w_{1(p-1)},N_{pq}^{j},w_{(q+1)m}|G)}
== Computing inside probabilities ==
Base Case:
β
j
(
p
,
p
)
=
P
(
w
p
|
N
j
,
G
)
{\displaystyle \beta _{j}(p,p)=P(w_{p}|N^{j},G)}
General case:
Suppose there is a rule
N
j
→
N
r
N
s
{\displaystyle N_{j}\rightarrow N_{r}N_{s}}
in the grammar, then the probability of generating
w
p
⋯
w
q
{\displaystyle w_{p}\cdots w_{q}}
starting with a subtree rooted at
N
j
{\displaystyle N_{j}}
is:
∑
k
=
p
k
=
q
−
1
P
(
N
j
→
N
r
N
s
)
β
r
(
p
,
k
)
β
s
(
k
+
1
,
q
)
{\displaystyle \sum _{k=p}^{k=q-1}P(N_{j}\rightarrow N_{r}N_{s})\beta _{r}(p,k)\beta _{s}(k+1,q)}
The inside probability
β
j
(
p
,
q
)
{\displaystyle \beta _{j}(p,q)}
is just the sum over all such possible rules:
β
j
(
p
,
q
)
=
∑
N
r
,
N
s
∑
k
=
p
k
=
q
−
1
P
(
N
j
→
N
r
N
s
)
β
r
(
p
,
k
)
β
s
(
k
+
1
,
q
)
{\displaystyle \beta _{j}(p,q)=\sum _{N_{r},N_{s}}\sum _{k=p}^{k=q-1}P(N_{j}\rightarrow N_{r}N_{s})\beta _{r}(p,k)\beta _{s}(k+1,q)}
== Computing outside probabilities ==
Base Case:
α
j
(
1
,
n
)
=
{
1
if
j
=
1
0
otherwise
{\displaystyle \alpha _{j}(1,n)={\begin{cases}1&{\mbox{if }}j=1\\0&{\mbox{otherwise}}\end{cases}}}
Here the start symbol is
N
1
{\displaystyle N_{1}}
.
General case:
Suppose there is a rule
N
r
→
N
j
N
s
{\displaystyle N_{r}\rightarrow N_{j}N_{s}}
in the grammar that generates
N
j
{\displaystyle N_{j}}
.
Then the left contribution of that rule to the outside probability
α
j
(
p
,
q
)
{\displaystyle \alpha _{j}(p,q)}
is:
∑
k
=
q
+
1
k
=
n
P
(
N
r
→
N
j
N
s
)
α
r
(
p
,
k
)
β
s
(
q
+
1
,
k
)
{\displaystyle \sum _{k=q+1}^{k=n}P(N_{r}\rightarrow N_{j}N_{s})\alpha _{r}(p,k)\beta _{s}(q+1,k)}
Now suppose there is a rule
N
r
→
N
s
N
j
{\displaystyle N_{r}\rightarrow N_{s}N_{j}}
in the grammar. Then the right
contribution of that rule to the outside probability
α
j
(
p
,
q
)
{\displaystyle \alpha _{j}(p,q)}
is:
∑
k
=
1
k
=
p
−
1
P
(
N
r
→
N
s
N
j
)
α
r
(
k
,
q
)
β
s
(
k
,
p
−
1
)
{\displaystyle \sum _{k=1}^{k=p-1}P(N_{r}\rightarrow N_{s}N_{j})\alpha _{r}(k,q)\beta _{s}(k,p-1)}
The outside probability
α
j
(
p
,
q
)
{\displaystyle \alpha _{j}(p,q)}
is the sum of the left and right
contributions over all such rules:
α
j
(
p
,
q
)
=
∑
N
r
,
N
s
∑
k
=
q
+
1
k
=
n
P
(
N
r
→
N
j
N
s
)
α
r
(
p
,
k
)
β
s
(
q
+
1
,
k
)
+
∑
N
r
,
N
s
∑
k
=
1
k
=
p
−
1
P
(
N
r
→
N
s
N
j
)
α
r
(
k
,
q
)
β
s
(
k
,
p
−
1
)
{\displaystyle \alpha _{j}(p,q)=\sum _{N_{r},N_{s}}\sum _{k=q+1}^{k=n}P(N_{r}\rightarrow N_{j}N_{s})\alpha _{r}(p,k)\beta _{s}(q+1,k)+\sum _{N_{r},N_{s}}\sum _{k=1}^{k=p-1}P(N_{r}\rightarrow N_{s}N_{j})\alpha _{r}(k,q)\beta _{s}(k,p-1)}
== References ==
J. Baker (1979): Trainable grammars for speech recognition. In J. J. Wolf and D. H. Klatt, editors, Speech communication papers presented at the 97th meeting of the Acoustical Society of America, pages 547–550, Cambridge, MA, June 1979. MIT.
Karim Lari, Steve J. Young (1990): The estimation of stochastic context-free grammars using the inside–outside algorithm. Computer Speech and Language, 4:35–56.
Karim Lari, Steve J. Young (1991): Applications of stochastic context-free grammars using the Inside–Outside algorithm. Computer Speech and Language, 5:237–257.
Fernando Pereira, Yves Schabes (1992): Inside–outside reestimation from partially bracketed corpora. Proceedings of the 30th annual meeting on Association for Computational Linguistics, Association for Computational Linguistics, 128–135.
== External links ==
Inside-outside algorithm - Fei Xia
The Inside-Outside Algorithm - Michael Collins | Wikipedia/Inside-outside_algorithm |
ELKI (Environment for Developing KDD-Applications Supported by Index-Structures) is a data mining (KDD, knowledge discovery in databases) software framework developed for use in research and teaching. It was originally created by the database systems research unit at the Ludwig Maximilian University of Munich, Germany, led by Professor Hans-Peter Kriegel. The project has continued at the Technical University of Dortmund, Germany. It aims at allowing the development and evaluation of advanced data mining algorithms and their interaction with database index structures.
== Description ==
The ELKI framework is written in Java and built around a modular architecture. Most currently included algorithms perform clustering, outlier detection, and database indexes. The object-oriented architecture allows the combination of arbitrary algorithms, data types, distance functions, indexes, and evaluation measures. The Java just-in-time compiler optimizes all combinations to a similar extent, making benchmarking results more comparable if they share large parts of the code. When developing new algorithms or index structures, the existing components can be easily reused, and the type safety of Java detects many programming errors at compile time.
ELKI is a free tool for analyzing data, mainly focusing on finding patterns and unusual data points without needing labels. It's written in Java and aims to be fast and able to handle big datasets by using special structures. It's made for researchers and students to add their own methods and compare different algorithms easily.
ELKI has been used in data science to cluster sperm whale codas, for phoneme clustering, for anomaly detection in spaceflight operations, for bike sharing redistribution, and traffic prediction.
== Objectives ==
The university project is developed for use in teaching and research. The source code is written with extensibility and reusability in mind, but is also optimized for performance. The experimental evaluation of algorithms depends on many environmental factors and implementation details can have a large impact on the runtime. ELKI aims at providing a shared codebase with comparable implementations of many algorithms.
As research project, it currently does not offer integration with business intelligence applications or an interface to common database management systems via SQL. The copyleft (AGPL) license may also be a hindrance to an integration in commercial products; nevertheless it can be used to evaluate algorithms prior to developing an own implementation for a commercial product. Furthermore, the application of the algorithms requires knowledge about their usage, parameters, and study of original literature. The audience is students, researchers, data scientists, and software engineers.
== Architecture ==
ELKI is modeled around a database-inspired core, which uses a vertical data layout that stores data in column groups (similar to column families in NoSQL databases). This database core provides nearest neighbor search, range/radius search, and distance query functionality with index acceleration for a wide range of dissimilarity measures. Algorithms based on such queries (e.g. k-nearest-neighbor algorithm, local outlier factor and DBSCAN) can be implemented easily and benefit from the index acceleration.
The database core also provides fast and memory efficient collections for object collections and associative structures such as nearest neighbor lists.
ELKI makes extensive use of Java interfaces, so that it can be extended easily in many places. For example, custom data types, distance functions, index structures, algorithms, input parsers, and output modules can be added and combined without modifying the existing code. This includes the possibility of defining a custom distance function and using existing indexes for acceleration.
ELKI uses a service loader architecture to allow publishing extensions as separate jar files.
ELKI uses optimized collections for performance rather than the standard Java API. For loops for example are written similar to C++ iterators:
In contrast to typical Java iterators (which can only iterate over objects), this conserves memory, because the iterator can internally use primitive values for data storage. The reduced garbage collection improves the runtime. Optimized collections libraries such as GNU Trove3, Koloboke, and fastutil employ similar optimizations. ELKI includes data structures such as object collections and heaps (for, e.g., nearest neighbor search) using such optimizations.
== Visualization ==
The visualization module uses SVG for scalable graphics output, and Apache Batik for rendering of the user interface as well as lossless export into PostScript and PDF for easy inclusion in scientific publications in LaTeX.
Exported files can be edited with SVG editors such as Inkscape. Since cascading style sheets are used, the graphics design can be restyled easily.
Unfortunately, Batik is rather slow and memory intensive, so the visualizations are not very scalable to large data sets (for larger data sets, only a subsample of the data is visualized by default).
== Awards ==
Version 0.4, presented at the "Symposium on Spatial and Temporal Databases" 2011, which included various methods for spatial outlier detection, won the conference's "best demonstration paper award".
== Included algorithms ==
Select included algorithms:
Cluster analysis:
K-means clustering (including fast algorithms such as Elkan, Hamerly, Annulus, and Exponion k-Means, and robust variants such as k-means--)
K-medians clustering
K-medoids clustering (PAM) (including FastPAM and approximations such as CLARA, CLARANS)
Expectation-maximization algorithm for Gaussian mixture modeling
Hierarchical clustering (including the fast SLINK, CLINK, NNChain and Anderberg algorithms)
Single-linkage clustering
Leader clustering
DBSCAN (Density-Based Spatial Clustering of Applications with Noise, with full index acceleration for arbitrary distance functions)
OPTICS (Ordering Points To Identify the Clustering Structure), including the extensions OPTICS-OF, DeLi-Clu, HiSC, HiCO and DiSH
HDBSCAN
Mean-shift clustering
BIRCH clustering
SUBCLU (Density-Connected Subspace Clustering for High-Dimensional Data)
CLIQUE clustering
ORCLUS and PROCLUS clustering
COPAC, ERiC and 4C clustering
CASH clustering
DOC and FastDOC subspace clustering
P3C clustering
Canopy clustering algorithm
Anomaly detection:
k-Nearest-Neighbor outlier detection
LOF (Local outlier factor)
LoOP (Local Outlier Probabilities)
OPTICS-OF
DB-Outlier (Distance-Based Outliers)
LOCI (Local Correlation Integral)
LDOF (Local Distance-Based Outlier Factor)
EM-Outlier
SOD (Subspace Outlier Degree)
COP (Correlation Outlier Probabilities)
Frequent Itemset Mining and association rule learning
Apriori algorithm
Eclat
FP-growth
Dimensionality reduction
Principal component analysis
Multidimensional scaling
T-distributed stochastic neighbor embedding (t-SNE)
Spatial index structures and other search indexes:
R-tree
R*-tree
M-tree
k-d tree
X-tree
Cover tree
iDistance
NN descent
Locality sensitive hashing (LSH)
Evaluation:
Precision and recall, F1 score, Average Precision
Receiver operating characteristic (ROC curve)
Discounted cumulative gain (including NDCG)
Silhouette index
Davies–Bouldin index
Dunn index
Density-based cluster validation (DBCV)
Visualization
Scatter plots
Histograms
Parallel coordinates (also in 3D, using OpenGL)
Other:
Statistical distributions and many parameter estimators, including robust MAD based and L-moment based estimators
Dynamic time warping
Change point detection in time series
Intrinsic dimensionality estimators
== Version history ==
Version 0.1 (July 2008) contained several Algorithms from cluster analysis and anomaly detection, as well as some index structures such as the R*-tree. The focus of the first release was on subspace clustering and correlation clustering algorithms.
Version 0.2 (July 2009) added functionality for time series analysis, in particular distance functions for time series.
Version 0.3 (March 2010) extended the choice of anomaly detection algorithms and visualization modules.
Version 0.4 (September 2011) added algorithms for geo data mining and support for multi-relational database and index structures.
Version 0.5 (April 2012) focuses on the evaluation of cluster analysis results, adding new visualizations and some new algorithms.
Version 0.6 (June 2013) introduces a new 3D adaption of parallel coordinates for data visualization, apart from the usual additions of algorithms and index structures.
Version 0.7 (August 2015) adds support for uncertain data types, and algorithms for the analysis of uncertain data.
Version 0.7.5 (February 2019) adds additional clustering algorithms, anomaly detection algorithms, evaluation measures, and indexing structures.
Version 0.8 (October 2022) adds automatic index creation, garbage collection, and incremental priority search, as well as many more algorithms such as BIRCH.
== Similar applications ==
scikit-learn: machine learning library in Python
Weka: A similar project by the University of Waikato, with a focus on classification algorithms
RapidMiner: An application available commercially (a restricted version is available as open source)
KNIME: An open source platform which integrates various components for machine learning and data mining
== See also ==
Comparison of statistical packages
== References ==
== External links ==
Official website of ELKI with download and documentation. | Wikipedia/Environment_for_DeveLoping_KDD-Applications_Supported_by_Index-Structures |
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