A digital on-screen graphic, digitally originated graphic (DOG, bug, network bug, on-screen bug or screenbug) is a watermark-like station logo that most television broadcasters overlay over a portion of the screen area of their programs to identify the channel. They are thus a form of permanent visual station identification, increasing brand recognition and asserting ownership of the video signal. The graphic identifies the source of programming, even if it has been time-shifted or recorded. Many of these technologies allow viewers to skip or omit traditional between-programming station identification; thus the use of a DOG enables the station or network to enforce brand identification even when standard commercials are skipped. DOG watermarking helps to reduce off-the-air copyright infringement—for example, the distribution of a current series' episodes on DVD: the watermarked content is easily differentiated from "official" DVD releases, and can help identify not only the station from which the broadcast was captured, but usually the actual date of the broadcast as well. Graphics may be used to identify if the correct subscription is being used for a type of venue. For example, showing Sky Sports within a pub in the United Kingdom requires a more expensive subscription; a channel authorized under this subscription adds a pint glass graphic to the bottom of the screen for inspectors to see. The graphic changes at certain times, making it harder to counterfeit. On the other hand, watermarks pollute the picture, distract viewers' attention and may cover an important piece of information presented in the television program. Extremely bright watermarks may cause screen burn-in or image persistence on some types of television sets such as the now mostly discontinued and rarely used plasma and CRT displays, and currently commonly used OLED and LCD displays. Usage of visually perceptible embedded watermarks requires the program author to have a separate clean copy for archival purposes, but this practice was not common decades ago when watermarking became popular among broadcasters. Watermarks present an issue when archival videos are used for a documentary that strives to create a coherent story. In some cases, watermarks are blurred or digitally removed if possible to clean up the picture. In the absence of visually perceptible watermarks, content control can be ensured with visually imperceptible digital watermarks. In some cases, the graphic also shows the name of the current program. Some television networks may place additional logos or text alongside their DOG to advertise significant upcoming programs. For example, broadcasters of the Olympic Games (most notably United States broadcaster NBC) often add the Olympic rings to their DOG for a period of time leading up to and during the Games. == Usage == == Connections with sponsor tags == Another graphic on television usually connected with sports (particularly in North America, though not in Europe) is the sponsor tag. It shows the logos of certain sponsors, accompanied by some background relevant to the game, the network logo, announcement and music of some kind. == Usage in ham radio and television == In most countries, the ham station is required to periodically identify their amateur-television transmission. Such stations frequently overlay their callsign on the signal instead of placing a card in the background. Most hams use homebuilt devices or old consumer character generators to generate such identifications rather than using graphical superimposes of high cost to do so. Only rarely one can see real graphics, as the callsign is usually written in the "OSD font". == Live DOGs by hobbyists == One of the easiest and most sought-after devices used to generate DOGs by hobbyists is the 1980s vintage Sony XV-T500 video superimposer. This device can luma-key a signal, capture a still frame into memory and then overlay the keyed graphic in one of eight colors onto any CVBS signal. Another method commonly used by hobbyists and even low-budgeted television stations was Amiga computers with genlock interfaces.
Radioplayer
Radioplayer is a radio technology platform, owned by UK radio broadcasters and operated under licence in some other countries. It operates an internet radio web tuner, a set of mobile phone apps, an in-car adaptor, and a growing range of integrations with other connected devices and platforms. Radioplayer is operated by UK Radioplayer Ltd which is a not-for-profit organisation owned by UK radio broadcasters. Initial shareholders were the BBC, Global Radio, GMG Radio, Absolute Radio and RadioCentre. After consolidation in the radio market, current shareholders are the BBC, Global Radio, Bauer Media Group and RadioCentre. == History == Launched in the UK on 31 March 2011, Radioplayer set out to offer a simple and accessible way to listen to radio via the internet. It contained 157 stations at launch. Initially working internally at the BBC for Tim Davie, then Director of BBC Audio & Music, Michael Hill led the project since March 2009; he was made Managing Director of UK Radioplayer Ltd on 28 July 2010. At launch, Radioplayer was a simple and straightforward Flash-based radio player, linked-to by radio stations on their own website. The player included searching and bookmarking across all of UK radio station content. On 5 October 2012, Radioplayer launched a mobile app on iOS phones with an Android version following shortly afterwards. The apps are unavailable for download outside the United Kingdom. This was followed by a tablet app on 25 September 2013. The apps also support Android Wear, Android Auto, Smart Device Link, Apple Watch and Apple CarPlay. They are also compatible with Chromecast and Airplay. In September 2016, Radioplayer announced it had been chosen by Amazon to integrate with their new voice-controlled 'Echo' device, ahead of its UK launch. In July 2017, Radioplayer integrated with the Sonos and Bose multi-room speaker platforms. UK Radioplayer currently contains around 500 UK stations, from Ofcom-licensed broadcasters. Online-only 'sister-stations' can also be added, but only by broadcasters with Ofcom licences which have been on the platform for over a year. == Radioplayer Car == Radioplayer Car was announced in September 2014 as a hybrid radio receiver that switches between FM, DAB and streaming to find the strongest signal. Speaking in Oslo in June 2015, Michael Hill said that he hoped to launch the product in the UK and Norway during the summer of 2015. In February 2017, Radioplayer Car was launched. It was marketed as the world’s first voice-controlled hybrid radio adaptor for car stereos. A small box, fitted behind the dashboard, links to the auxiliary input on an existing car radio. It connects wirelessly via Bluetooth to the driver’s smartphone by an app. The adaptor enabled drivers to listen to their own smartphone music collections using Bluetooth, take hands-free calls, listen to inbound text messages and receive instant audio travel news, customised by GPS to their location and direction of travel. The hardware was manufactured under licence by car audio interfaces supplier Connects2, and Hyde Park Corner was promoted as the preferred installer of the audio equipment. There were several spin-off benefits of the Radioplayer Car project, including the creation of the hybrid radio metadata API for cars, known as the 'WRAPI' (Worldwide Radioplayer API). == International == Through a separate company called Radioplayer Worldwide, Radioplayer technology is licensed to a number of different territories.
Artificial general intelligence
Artificial general intelligence (AGI) is a hypothetical type of artificial intelligence that matches or surpasses human capabilities across virtually all cognitive tasks. Beyond AGI, artificial superintelligence (ASI) would outperform the best human abilities across every domain by a wide margin. Unlike artificial narrow intelligence (ANI), whose competence is confined to well‑defined tasks, an AGI system can generalise knowledge, transfer skills between domains, and solve novel problems without task‑specific reprogramming. Creating AGI is a stated goal of technology companies such as OpenAI, Google, xAI, and Meta. A 2020 survey identified 72 active AGI research and development projects across 37 countries. AGI is a common topic in science fiction and futures studies. Contention exists over whether AGI represents an existential risk. Some AI experts and industry figures have stated that mitigating the risk of human extinction posed by AGI should be a global priority. Others find the development of AGI to be in too remote a stage to present such a risk. == Terminology == AGI is also known as strong AI, full AI, human-level AI, human-level intelligent AI, or general intelligent action. The term "artificial general intelligence" was used in 1997 by Mark Gubrud in a discussion of the implications of fully automated military production and operations. A mathematical formalism of AGI named AIXI was proposed in 2000 by Marcus Hutter, who defines intelligence as "an agent’s ability to achieve goals or succeed in a wide range of environments". This type of AGI has also been called "universal artificial intelligence". The term AGI was re-introduced and popularized by Shane Legg and Ben Goertzel around 2002. Some academic sources reserve the term "strong AI" for computer programs that will experience sentience or consciousness. In contrast, weak AI (or narrow AI) can solve a specific problem but lacks general cognitive abilities. Some academic sources use "weak AI" to refer more broadly to any programs that neither experience consciousness nor have a mind in the same sense as humans. Related concepts include artificial superintelligence and transformative AI. An artificial superintelligence (ASI) is a hypothetical type of AGI that is much more generally intelligent than humans, while the notion of transformative AI relates to AI having a large impact on society, for example, similar to the agricultural or industrial revolution. A framework for classifying AGI was proposed in 2023 by Google DeepMind researchers. They define five performance levels of AGI: emerging, competent, expert, virtuoso, and superhuman. For example, a competent AGI is defined as an AI that outperforms 50% of skilled adults in a wide range of non-physical tasks, and a superhuman AGI (i.e., an artificial superintelligence) is similarly defined but with a threshold of 100%. They consider large language models like ChatGPT or LLaMA 2 to be instances of emerging AGI (comparable to unskilled humans). Regarding the autonomy of AGI and associated risks, they define five levels: tool (fully in human control), consultant, collaborator, expert, and agent (fully autonomous). == Characteristics == There is no single agreed-upon definition of intelligence as applied to computers. Computer scientist John McCarthy wrote in 2007: "We cannot yet characterize in general what kinds of computational procedures we want to call intelligent." === Intelligence traits === Researchers generally hold that a system is required to do all of the following to be regarded as an AGI: reason, use strategy, solve puzzles, and make judgments under uncertainty, represent knowledge, including common sense knowledge, plan, learn, communicate in natural language, if necessary, integrate these skills in completion of any given goal. Many interdisciplinary approaches (e.g. cognitive science, computational intelligence, and decision making) consider additional traits such as imagination (the ability to form novel mental images and concepts) and autonomy. Computer-based systems exhibiting these capabilities are now widespread, with modern large language models demonstrating computational creativity, automated reasoning, and decision support simultaneously across domains. === Physical traits === Other capabilities are considered desirable in intelligent systems, as they may affect intelligence or aid in its expression. These include: the ability to sense (e.g. see, hear, etc.), and the ability to act (e.g. move and manipulate objects, change location to explore, etc.) This includes the ability to detect and respond to hazard. === Tests for human-level AGI === Several tests meant to confirm human-level AGI have been considered. ==== Turing test ==== The Turing test was proposed by Alan Turing in his 1950 paper "Computing Machinery and Intelligence". This test involves a human judge engaging in natural language conversations with both a human and a machine designed to generate human-like responses. The machine passes the test if it can convince the judge that it is human a significant fraction of the time. Turing proposed this as a practical measure of machine intelligence, focusing on the ability to produce human-like responses rather than on the internal workings of the machine. The idea of the test is that the machine has to try and pretend to be a man, by answering questions put to it, and it will only pass if the pretence is reasonably convincing. A considerable portion of a jury, who should not be experts about machines, must be taken in by the pretence. In 2014, a chatbot named Eugene Goostman, designed to imitate a 13-year-old Ukrainian boy, reportedly passed a Turing Test event by convincing 33% of judges that it was human. However, this claim was met with significant skepticism from the AI research community, who questioned the test's implementation and its relevance to AGI. A 2025 pre‑registered, three‑party Turing‑test study by Cameron R. Jones and Benjamin K. Bergen showed that GPT-4.5 was judged to be the human in 73% of five‑minute text conversations—surpassing the 67% humanness rate of real confederates and meeting the researchers' criterion for having passed the test. ==== Ikea test ==== The "Ikea test", also known as the Flat Pack Furniture Test, involves an AI controlling a robot which attempts to assemble an Ikea flat-pack furniture product after having been shown the parts and instructions. As early as 2013, MIT's IkeaBot demonstrated fully autonomous multi-robot assembly of an IKEA Lack table in ten minutes, with no human intervention and no pre-programmed assembly instructions. The robots inferred the assembly sequence from the geometry of the parts alone. ==== Coffee test ==== Steve Wozniak proposed a test where a machine is required to enter an average American home and figure out how to make coffee. It must find the coffee machine, find the coffee, add water, find a mug, and brew the coffee by pushing the proper buttons. This test has been substantially approached across multiple systems. In January 2024, Figure AI's Figure 01 humanoid learned to operate a Keurig coffee machine autonomously after watching video demonstrations, using end-to-end neural networks to translate visual input into motor actions. In 2025, researchers at the University of Edinburgh published the ELLMER framework in Nature Machine Intelligence, demonstrating a robotic arm that interprets verbal instructions, analyses its surroundings, and autonomously makes coffee in dynamic kitchen environments — adapting to unforeseen obstacles in real time rather than following pre-programmed sequences. ==== Suleyman's test ==== Mustafa Suleyman's test proposes giving an AI model US$100,000 and asking it to obtain US$1 million. ==== Use of video-games ==== Adams, et al. propose that the ability to learn and succeed in a wide range of video games can be used to test AI intelligence. This range would include games unknown to the AGI developers before the test is administered. === AI-complete problems === A problem is informally called "AI-complete" or "AI-hard" if it is believed that AGI would be needed to solve it, because the solution is beyond the capabilities of a purpose-specific algorithm. == History == === Classical AI === Modern AI research began in the mid-1950s. The first generation of AI researchers were convinced that artificial general intelligence was possible and that it would exist in just a few decades. AI pioneer Herbert A. Simon wrote in 1965: "machines will be capable, within twenty years, of doing any work a man can do". Their predictions were the inspiration for Stanley Kubrick and Arthur C. Clarke's fictional character HAL 9000, who embodied what AI researchers believed they could create by the year 2001. AI pioneer Marvin Minsky was a consultant on the project of making HAL 9000 as realistic as possible according to the consensus predictions of the time. He said in 1967, "Within a generation... the problem of
Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise when the number of datapoints is small (in a suitably defined sense) relative to the intrinsic dimension of the data. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting areas where objects form groups with similar properties; in high dimensional data, however, all objects appear to be sparse and dissimilar in many ways, which prevents common data organization strategies from being efficient. == Domains == === Combinatorics === In some problems, each variable can take one of several discrete values, or the range of possible values is divided to give a finite number of possibilities. Taking the variables together, a huge number of combinations of values must be considered. This effect is also known as the combinatorial explosion. Even in the simplest case of d {\displaystyle d} binary variables, the number of possible combinations already is 2 d {\displaystyle 2^{d}} , exponential in the dimensionality. Naively, each additional dimension doubles the effort needed to try all combinations. === Sampling === There is an exponential increase in volume associated with adding extra dimensions to a mathematical space. For example, 102 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube, i.e. a line) with no more than 10−2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10−2 = 0.01 between adjacent points would require 1020 = [(102)10] sample points. In general, with a spacing distance of 10−n the 10-dimensional hypercube appears to be a factor of 10n(10−1) = [(10n)10/(10n)] "larger" than the 1-dimensional hypercube, which is the unit interval. In the above example n = 2: when using a sampling distance of 0.01 the 10-dimensional hypercube appears to be 1018 "larger" than the unit interval. This effect is a combination of the combinatorics problems above and the distance function problems explained below. === Optimization === When solving dynamic optimization problems by numerical backward induction, the objective function must be computed for each combination of values. This is a significant obstacle when the dimension of the "state variable" is large. === Machine learning === In machine learning problems that involve learning a "state-of-nature" from a finite number of data samples in a high-dimensional feature space with each feature having a range of possible values, typically an enormous amount of training data is required to ensure that there are several samples with each combination of values. In an abstract sense, as the number of features or dimensions grows, the amount of data we need to generalize accurately grows exponentially. A typical rule of thumb is that there should be at least 5 training examples for each dimension in the representation. In machine learning and insofar as predictive performance is concerned, the curse of dimensionality is used interchangeably with the peaking phenomenon, which is also known as Hughes phenomenon. This phenomenon states that with a fixed number of training samples, the average (expected) predictive power of a classifier or regressor first increases as the number of dimensions or features used is increased but beyond a certain dimensionality it starts deteriorating instead of improving steadily. Nevertheless, in the context of a simple classifier (e.g., linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix), Zollanvari et al. showed both analytically and empirically that as long as the relative cumulative efficacy of an additional feature set (with respect to features that are already part of the classifier) is greater (or less) than the size of this additional feature set, the expected error of the classifier constructed using these additional features will be less (or greater) than the expected error of the classifier constructed without them. In other words, both the size of additional features and their (relative) cumulative discriminatory effect are important in observing a decrease or increase in the average predictive power. In metric learning, higher dimensions can sometimes allow a model to achieve better performance. After normalizing embeddings to the surface of a hypersphere, FaceNet achieves the best performance using 128 dimensions as opposed to 64, 256, or 512 dimensions in one ablation study. A loss function for unitary-invariant dissimilarity between word embeddings was found to be minimized in high dimensions. === Data mining === In data mining, the curse of dimensionality refers to a data set with too many features. Consider the first table, which depicts 200 individuals and 2000 genes (features) with a 1 or 0 denoting whether or not they have a genetic mutation in that gene. A data mining application to this data set may be finding the correlation between specific genetic mutations and creating a classification algorithm such as a decision tree to determine whether an individual has cancer or not. A common practice of data mining in this domain would be to create association rules between genetic mutations that lead to the development of cancers. To do this, one would have to loop through each genetic mutation of each individual and find other genetic mutations that occur over a desired threshold and create pairs. They would start with pairs of two, then three, then four until they result in an empty set of pairs. The complexity of this algorithm can lead to calculating all permutations of gene pairs for each individual or row. Given the formula for calculating the permutations of n items with a group size of r is: n ! ( n − r ) ! {\displaystyle {\frac {n!}{(n-r)!}}} , calculating the number of three pair permutations of any given individual would be 7988004000 different pairs of genes to evaluate for each individual. The number of pairs created will grow by an order of factorial as the size of the pairs increase. The growth is depicted in the permutation table (see right). As we can see from the permutation table above, one of the major problems data miners face regarding the curse of dimensionality is that the space of possible parameter values grows exponentially or factorially as the number of features in the data set grows. This problem critically affects both computational time and space when searching for associations or optimal features to consider. Another problem data miners may face when dealing with too many features is that the number of false predictions or classifications tends to increase as the number of features grows in the data set. In terms of the classification problem discussed above, keeping every data point could lead to a higher number of false positives and false negatives in the model. This may seem counterintuitive, but consider the genetic mutation table from above, depicting all genetic mutations for each individual. Each genetic mutation, whether they correlate with cancer or not, will have some input or weight in the model that guides the decision-making process of the algorithm. There may be mutations that are outliers or ones that dominate the overall distribution of genetic mutations when in fact they do not correlate with cancer. These features may be working against one's model, making it more difficult to obtain optimal results. This problem is up to the data miner to solve, and there is no universal solution. The first step any data miner should take is to explore the data, in an attempt to gain an understanding of how it can be used to solve the problem. One must first understand what the data means, and what they are trying to discover before they can decide if anything must be removed from the data set. Then they can create or use a feature selection or dimensionality reduction algorithm to remove samples or features from the data set if they deem it necessary. One example of such methods is the interquartile range method, used to remove outliers in a data set by calculating the standard deviation of a feature or occurrence. === Distance function === When a measure such as a Euclidean distance is defined using many coordinat
Deep tomographic reconstruction
Deep Tomographic Reconstruction is a set of methods for using deep learning methods to perform tomographic reconstruction of medical and industrial images. It uses artificial intelligence and machine learning, especially deep artificial neural networks or deep learning, to overcome challenges such as measurement noise, data sparsity, image artifacts, and computational inefficiency. This approach has been applied across various imaging modalities, including CT, MRI, PET, SPECT, ultrasound, and optical imaging == Historical background == Traditional tomographic reconstruction relies on analytic methods such as filtered back-projection, or iterative methods which incrementally compute inverse transformations from measurement data (e.g., Radon or Fourier transform data). However, these approaches are not sufficient for certain imaging techniques such as low-dose CT and fast MRI, or scenarios involving metal artifacts and patient motion. == Use in imaging modalities == === Computed tomography (CT) === In CT, deep learning models can be particularly effective in reducing radiation exposure while maintaining image quality. Deep neural networks can also be able to reconstruct images of fair quality from sparsely sampled data without sacrificing diagnostic performance. Deep learning-based generative AI models can reduce CT metal artifacts. === Magnetic resonance imaging (MRI) === In magnetic resonance imaging (MRI), deep learning can lead to reduced MRI motion artifacts, and increased acquisition speed, referred to as fast MRI. Despite suffering from disadvantages such as lower signal-to-noise ratio (SNR), deep learning can enhance image quality in low field MRI, making these systems clinically viable. === Positron emission tomography (PET) and single-photon emission CT (SPECT) === For PET imaging, deep learning models can provide substantial improvements in low-dose imaging and motion artifact correction. Also, deep learning can help SPECT for generation of attenuation background. A notable technique for PET denoising involves integrating MR data through multimodal networks, which use anatomical information from MRI to enhance PET image quality. === Ultrasound imaging === Deep learning can enhance ultrasound imaging by reducing speckle noise and motion blur. For ultrasound beamforming, deep neural networks can allow superior image quality with limited data at high speed. === Optical imaging and microscopy === Diffuse optical tomography, optical coherence tomography and microscopy can be improved by deep neural networks beyond traditional methods. Furthermore, deep learning can also enhance Photoacoustic imaging (see Deep learning in photoacoustic imaging), addressing challenges like high noise, low contrast, and limited resolution. Deep learning has also been applied to label-free live-cell imaging, where convolutional neural networks predict fluorescence labels from transmitted light images, a technique known as in silico labeling. This method can enable high-throughput, non-invasive cell analysis and phenotyping without the need for traditional fluorescent dyes.
Weight initialization
In deep learning, weight initialization or parameter initialization describes the initial step in creating a neural network. A neural network contains trainable parameters that are modified during training: weight initialization is the pre-training step of assigning initial values to these parameters. The choice of weight initialization method affects the speed of convergence, the scale of neural activation within the network, the scale of gradient signals during backpropagation, and the quality of the final model. Proper initialization is necessary for avoiding issues such as vanishing and exploding gradients and activation function saturation. Note that even though this article is titled "weight initialization", both weights and biases are used in a neural network as trainable parameters, so this article describes how both of these are initialized. Similarly, trainable parameters in convolutional neural networks (CNNs) are called kernels and biases, and this article also describes these. == Constant initialization == We discuss the main methods of initialization in the context of a multilayer perceptron (MLP). Specific strategies for initializing other network architectures are discussed in later sections. For an MLP, there are only two kinds of trainable parameters, called weights and biases. Each layer l {\displaystyle l} contains a weight matrix W ( l ) ∈ R n l − 1 × n l {\displaystyle W^{(l)}\in \mathbb {R} ^{n_{l-1}\times n_{l}}} and a bias vector b ( l ) ∈ R n l {\displaystyle b^{(l)}\in \mathbb {R} ^{n_{l}}} , where n l {\displaystyle n_{l}} is the number of neurons in that layer. A weight initialization method is an algorithm for setting the initial values for W ( l ) , b ( l ) {\displaystyle W^{(l)},b^{(l)}} for each layer l {\displaystyle l} . The simplest form is zero initialization: W ( l ) = 0 , b ( l ) = 0 {\displaystyle W^{(l)}=0,b^{(l)}=0} Zero initialization is usually used for initializing biases, but it is not used for initializing weights, as it leads to symmetry in the network, causing all neurons to learn the same features. In this page, we assume b = 0 {\displaystyle b=0} unless otherwise stated. Recurrent neural networks typically use activation functions with bounded range, such as sigmoid and tanh, since unbounded activation may cause exploding values. (Le, Jaitly, Hinton, 2015) suggested initializing weights in the recurrent parts of the network to identity and zero bias, similar to the idea of residual connections and LSTM with no forget gate. In most cases, the biases are initialized to zero, though some situations can use a nonzero initialization. For example, in multiplicative units, such as the forget gate of LSTM, the bias can be initialized to 1 to allow good gradient signal through the gate. For neurons with ReLU activation, one can initialize the bias to a small positive value like 0.1, so that the gradient is likely nonzero at initialization, avoiding the dying ReLU problem. == Random initialization == Random initialization means sampling the weights from a normal distribution or a uniform distribution, usually independently. === LeCun initialization === LeCun initialization, popularized in (LeCun et al., 1998), is designed to preserve the variance of neural activations during the forward pass. It samples each entry in W ( l ) {\displaystyle W^{(l)}} independently from a distribution with mean 0 and variance 1 / n l − 1 {\displaystyle 1/n_{l-1}} . For example, if the distribution is a continuous uniform distribution, then the distribution is U ( ± 3 / n l − 1 ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {3/n_{l-1}}})} . === Glorot initialization === Glorot initialization (or Xavier initialization) was proposed by Xavier Glorot and Yoshua Bengio. It was designed as a compromise between two goals: to preserve activation variance during the forward pass and to preserve gradient variance during the backward pass. For uniform initialization, it samples each entry in W ( l ) {\displaystyle W^{(l)}} independently and identically from U ( ± 6 / ( n l + 1 + n l − 1 ) ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {6/(n_{l+1}+n_{l-1})}})} . In the context, n l − 1 {\displaystyle n_{l-1}} is also called the "fan-in", and n l + 1 {\displaystyle n_{l+1}} the "fan-out". When the fan-in and fan-out are equal, then Glorot initialization is the same as LeCun initialization. === He initialization === As Glorot initialization performs poorly for ReLU activation, He initialization (or Kaiming initialization) was proposed by Kaiming He et al. for networks with ReLU activation. It samples each entry in W ( l ) {\displaystyle W^{(l)}} from N ( 0 , 2 / n l − 1 ) {\displaystyle {\mathcal {N}}(0,2/n_{l-1})} . === Orthogonal initialization === (Saxe et al. 2013) proposed orthogonal initialization: initializing weight matrices as uniformly random (according to the Haar measure) semi-orthogonal matrices, multiplied by a factor that depends on the activation function of the layer. It was designed so that if one initializes a deep linear network this way, then its training time until convergence is independent of depth. Sampling a uniformly random semi-orthogonal matrix can be done by initializing X {\displaystyle X} by IID sampling its entries from a standard normal distribution, then calculate ( X X ⊤ ) − 1 / 2 X {\displaystyle \left(XX^{\top }\right)^{-1/2}X} or its transpose, depending on whether X {\displaystyle X} is tall or wide. For CNN kernels with odd widths and heights, orthogonal initialization is done this way: initialize the central point by a semi-orthogonal matrix, and fill the other entries with zero. As an illustration, a kernel K {\displaystyle K} of shape 3 × 3 × c × c ′ {\displaystyle 3\times 3\times c\times c'} is initialized by filling K [ 2 , 2 , : , : ] {\displaystyle K[2,2,:,:]} with the entries of a random semi-orthogonal matrix of shape c × c ′ {\displaystyle c\times c'} , and the other entries with zero. (Balduzzi et al., 2017) used it with stride 1 and zero-padding. This is sometimes called the Orthogonal Delta initialization. Related to this approach, unitary initialization proposes to parameterize the weight matrices to be unitary matrices, with the result that at initialization they are random unitary matrices (and throughout training, they remain unitary). This is found to improve long-sequence modelling in LSTM. Orthogonal initialization has been generalized to layer-sequential unit-variance (LSUV) initialization. It is a data-dependent initialization method, and can be used in convolutional neural networks. It first initializes weights of each convolution or fully connected layer with orthonormal matrices. Then, proceeding from the first to the last layer, it runs a forward pass on a random minibatch, and divides the layer's weights by the standard deviation of its output, so that its output has variance approximately 1. === Fixup initialization === In 2015, the introduction of residual connections allowed very deep neural networks to be trained, much deeper than the ~20 layers of the previous state of the art (such as the VGG-19). Residual connections gave rise to their own weight initialization problems and strategies. These are sometimes called "normalization-free" methods, since using residual connection could stabilize the training of a deep neural network so much that normalizations become unnecessary. Fixup initialization is designed specifically for networks with residual connections and without batch normalization, as follows: Initialize the classification layer and the last layer of each residual branch to 0. Initialize every other layer using a standard method (such as He initialization), and scale only the weight layers inside residual branches by L − 1 2 m − 2 {\displaystyle L^{-{\frac {1}{2m-2}}}} . Add a scalar multiplier (initialized at 1) in every branch and a scalar bias (initialized at 0) before each convolution, linear, and element-wise activation layer. Similarly, T-Fixup initialization is designed for Transformers without layer normalization. === Others === Instead of initializing all weights with random values on the order of O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} , sparse initialization initialized only a small subset of the weights with larger random values, and the other weights zero, so that the total variance is still on the order of O ( 1 ) {\displaystyle O(1)} . Random walk initialization was designed for MLP so that during backpropagation, the L2 norm of gradient at each layer performs an unbiased random walk as one moves from the last layer to the first. Looks linear initialization was designed to allow the neural network to behave like a deep linear network at initialization, since W R e L U ( x ) − W R e L U ( − x ) = W x {\displaystyle W\;\mathrm {ReLU} (x)-W\;\mathrm {ReLU} (-x)=Wx} . It initializes a matrix W {\displaystyle W} of shape R n 2 × m {\displaystyle \mathbb {R} ^{{\frac {n}{2}}\times m}} by any method, such as orthogonal initialization, t
Maximum inner-product search
Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. Formally, for a database of vectors x i {\displaystyle x_{i}} defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } defined on it, MIPS search can be defined as the problem of determining a r g m a x i ∈ S ⟨ x i , q ⟩ {\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle } for a given query q {\displaystyle q} . Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. Like other forms of NNS, MIPS algorithms may be approximate or exact. MIPS search is used as part of DeepMind's RETRO algorithm.