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  PenTile matrix family

  PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also

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  Wake-sleep algorithm

  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.

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  Huber loss

  In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. == Definition == The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by L δ ( a ) = { 1 2 a 2 for | a | ≤ δ , δ ⋅ ( | a | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\[4pt]\delta \cdot \left(|a|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where | a | = δ {\displaystyle |a|=\delta } . The variable a often refers to the residuals, that is to the difference between the observed and predicted values a = y − f ( x ) {\displaystyle a=y-f(x)} , so the former can be expanded to L δ ( y , f ( x ) ) = { 1 2 ( y − f ( x ) ) 2 for | y − f ( x ) | ≤ δ , δ ⋅ ( | y − f ( x ) | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(y,f(x))={\begin{cases}{\frac {1}{2}}{\left(y-f(x)\right)}^{2}&{\text{for }}\left|y-f(x)\right|\leq \delta ,\\[4pt]\delta \ \cdot \left(\left|y-f(x)\right|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus it "smoothens out" the former's corner at the origin. == Motivation == Two very commonly used loss functions are the squared loss, L ( a ) = a 2 {\displaystyle L(a)=a^{2}} , and the absolute loss, L ( a ) = | a | {\displaystyle L(a)=|a|} . The squared loss function results in an arithmetic mean-unbiased estimator, and the absolute-value loss function results in a median-unbiased estimator (in the one-dimensional case, and a geometric median-unbiased estimator for the multi-dimensional case). The squared loss has the disadvantage that it has the tendency to be dominated by outliers—when summing over a set of a {\displaystyle a} 's (as in ∑ i = 1 n L ( a i ) {\textstyle \sum _{i=1}^{n}L(a_{i})} ), the sample mean is influenced too much by a few particularly large a {\displaystyle a} -values when the distribution is heavy tailed: in terms of estimation theory, the asymptotic relative efficiency of the mean is poor for heavy-tailed distributions. As defined above, the Huber loss function is strongly convex in a uniform neighborhood of its minimum a = 0 {\displaystyle a=0} ; at the boundary of this uniform neighborhood, the Huber loss function has a differentiable extension to an affine function at points a = − δ {\displaystyle a=-\delta } and a = δ {\displaystyle a=\delta } . These properties allow it to combine much of the sensitivity of the mean-unbiased, minimum-variance estimator of the mean (using the quadratic loss function) and the robustness of the median-unbiased estimator (using the absolute value function). == Pseudo-Huber loss function == The Pseudo-Huber loss function can be used as a smooth approximation of the Huber loss function. It combines the best properties of L2 squared loss and L1 absolute loss by being strongly convex when close to the target/minimum and less steep for extreme values. The scale at which the Pseudo-Huber loss function transitions from L2 loss for values close to the minimum to L1 loss for extreme values and the steepness at extreme values can be controlled by the δ {\displaystyle \delta } value. The Pseudo-Huber loss function ensures that derivatives are continuous for all degrees. It is defined as L δ ( a ) = δ 2 ( 1 + ( a / δ ) 2 − 1 ) . {\displaystyle L_{\delta }(a)=\delta ^{2}\left({\sqrt {1+(a/\delta )^{2}}}-1\right).} As such, this function approximates a 2 / 2 {\displaystyle a^{2}/2} for small values of a {\displaystyle a} , and approximates a straight line with slope δ {\displaystyle \delta } for large values of a {\displaystyle a} . While the above is the most common form, other smooth approximations of the Huber loss function also exist. == Variant for classification == For classification purposes, a variant of the Huber loss called modified Huber is sometimes used. Given a prediction f ( x ) {\displaystyle f(x)} (a real-valued classifier score) and a true binary class label y ∈ { + 1 , − 1 } {\displaystyle y\in \{+1,-1\}} , the modified Huber loss is defined as L ( y , f ( x ) ) = { max ( 0 , 1 − y f ( x ) ) 2 for y f ( x ) > − 1 , − 4 y f ( x ) otherwise. {\displaystyle L(y,f(x))={\begin{cases}\max(0,1-y\,f(x))^{2}&{\text{for }}\,\,y\,f(x)>-1,\\[4pt]-4y\,f(x)&{\text{otherwise.}}\end{cases}}} The term max ( 0 , 1 − y f ( x ) ) {\displaystyle \max(0,1-y\,f(x))} is the hinge loss used by support vector machines; the quadratically smoothed hinge loss is a generalization of L {\displaystyle L} . == Applications == The Huber loss function is used in robust statistics, M-estimation and additive modelling.

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  ImageNets

  ImageNets is an open source framework for rapid prototyping of machine vision algorithms, developed by the Institute of Automation. == Description == ImageNets is an open source and platform independent (Windows & Linux) framework for rapid prototyping of machine vision algorithms. With the GUI ImageNet Designer, no programming knowledge is required to perform operations on images. A configured ImageNet can be loaded and executed from C++ code without the need for loading the ImageNet Designer GUI to achieve higher execution performance. == History == ImageNets was developed by the Institute of Automation, University of Bremen, Germany. The software was first publicly released in 2010. Originally, ImageNets was developed for the Care-Providing Robot FRIEND but it can be used for a wide range of computer vision applications.

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  Secure element

  A secure element (SE) is a secure operating system (OS) in a tamper-resistant processor chip or secure component. It can protect assets (root of trust, sensitive data, keys, certificates, applications) against high-level software and hardware attacks. Applications that process this sensitive data on an SE are isolated and so operate within a controlled environment not affected by software (including possible malware) found elsewhere on the OS. The hardware and embedded software meet the requirements of the Security IC Platform Protection Profile [PP 0084] including resistance to physical tampering scenarios described within it. More than 96 billion secure elements were produced and shipped between 2010 and 2021. SEs exist in various form factors, as devices such as smart cards, UICCs, or smart microSD cards, or embedded, or integrated, as parts of larger devices. SEs are an evolution of the chips in earlier smart cards, which have been adapted to suit the needs of numerous use cases, such as smartphones, tablets, set-top boxes, wearables, connected cars, and other internet of things (IoT) devices. The technology is widely used by technology firms such as Oracle, Apple and Samsung. SEs provide secure isolation, storage and processing for applications (called applets) they host while being isolated from the external world (e.g. rich OS and application processor when embedded in a smartphone) and from other applications running on the SE. Java Card and MULTOS are the most deployed standardized multi-application operating systems currently used to develop applications running on SEs. Since 1999, GlobalPlatform has been the body responsible for standardizing secure element technologies to support a dynamic model of application management in a multi-actor model. GlobalPlatform also runs Functional and Security Certification programmes for secure elements, and hosts a list of Functional Certified and Security Certified products. GlobalPlatform technology is also embedded in other standards such as ETSI SCP (now SET) since release 7. A Common Criteria Secure Element Protection Profile has been released targeting EAL4+ level with ALC_DVS.2 and AVA_VAN.5 extension to standardize the security features of a secure element across markets.

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  Multiple kernel learning

  Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination of kernels as part of the algorithm. Reasons to use multiple kernel learning include a) the ability to select for an optimal kernel and parameters from a larger set of kernels, reducing bias due to kernel selection while allowing for more automated machine learning methods, and b) combining data from different sources (e.g. sound and images from a video) that have different notions of similarity and thus require different kernels. Instead of creating a new kernel, multiple kernel algorithms can be used to combine kernels already established for each individual data source. Multiple kernel learning approaches have been used in many applications, such as event recognition in video, object recognition in images, and biomedical data fusion. == Algorithms == Multiple kernel learning algorithms have been developed for supervised, semi-supervised, as well as unsupervised learning. Most work has been done on the supervised learning case with linear combinations of kernels, however, many algorithms have been developed. The basic idea behind multiple kernel learning algorithms is to add an extra parameter to the minimization problem of the learning algorithm. As an example, consider the case of supervised learning of a linear combination of a set of n {\displaystyle n} kernels K {\displaystyle K} . We introduce a new kernel K ′ = ∑ i = 1 n β i K i {\displaystyle K'=\sum _{i=1}^{n}\beta _{i}K_{i}} , where β {\displaystyle \beta } is a vector of coefficients for each kernel. Because the kernels are additive (due to properties of reproducing kernel Hilbert spaces), this new function is still a kernel. For a set of data X {\displaystyle X} with labels Y {\displaystyle Y} , the minimization problem can then be written as min β , c E ( Y , K ′ c ) + R ( K , c ) {\displaystyle \min _{\beta ,c}\mathrm {E} (Y,K'c)+R(K,c)} where E {\displaystyle \mathrm {E} } is an error function and R {\displaystyle R} is a regularization term. E {\displaystyle \mathrm {E} } is typically the square loss function (Tikhonov regularization) or the hinge loss function (for SVM algorithms), and R {\displaystyle R} is usually an ℓ n {\displaystyle \ell _{n}} norm or some combination of the norms (i.e. elastic net regularization). This optimization problem can then be solved by standard optimization methods. Adaptations of existing techniques such as the Sequential Minimal Optimization have also been developed for multiple kernel SVM-based methods. === Supervised learning === For supervised learning, there are many other algorithms that use different methods to learn the form of the kernel. The following categorization has been proposed by Gonen and Alpaydın (2011) ==== Fixed rules approaches ==== Fixed rules approaches such as the linear combination algorithm described above use rules to set the combination of the kernels. These do not require parameterization and use rules like summation and multiplication to combine the kernels. The weighting is learned in the algorithm. Other examples of fixed rules include pairwise kernels, which are of the form k ( ( x 1 i , x 1 j ) , ( x 2 i , x 2 j ) ) = k ( x 1 i , x 2 i ) k ( x 1 j , x 2 j ) + k ( x 1 i , x 2 j ) k ( x 1 j , x 2 i ) {\displaystyle k((x_{1i},x_{1j}),(x_{2i},x_{2j}))=k(x_{1i},x_{2i})k(x_{1j},x_{2j})+k(x_{1i},x_{2j})k(x_{1j},x_{2i})} . These pairwise approaches have been used in predicting protein-protein interactions. ==== Heuristic approaches ==== These algorithms use a combination function that is parameterized. The parameters are generally defined for each individual kernel based on single-kernel performance or some computation from the kernel matrix. Examples of these include the kernel from Tenabe et al. (2008). Letting π m {\displaystyle \pi _{m}} be the accuracy obtained using only K m {\displaystyle K_{m}} , and letting δ {\displaystyle \delta } be a threshold less than the minimum of the single-kernel accuracies, we can define β m = π m − δ ∑ h = 1 n ( π h − δ ) {\displaystyle \beta _{m}={\frac {\pi _{m}-\delta }{\sum _{h=1}^{n}(\pi _{h}-\delta )}}} Other approaches use a definition of kernel similarity, such as A ( K 1 , K 2 ) = ⟨ K 1 , K 2 ⟩ ⟨ K 1 , K 1 ⟩ ⟨ K 2 , K 2 ⟩ {\displaystyle A(K_{1},K_{2})={\frac {\langle K_{1},K_{2}\rangle }{\sqrt {\langle K_{1},K_{1}\rangle \langle K_{2},K_{2}\rangle }}}} Using this measure, Qui and Lane (2009) used the following heuristic to define β m = A ( K m , Y Y T ) ∑ h = 1 n A ( K h , Y Y T ) {\displaystyle \beta _{m}={\frac {A(K_{m},YY^{T})}{\sum _{h=1}^{n}A(K_{h},YY^{T})}}} ==== Optimization approaches ==== These approaches solve an optimization problem to determine parameters for the kernel combination function. This has been done with similarity measures and structural risk minimization approaches. For similarity measures such as the one defined above, the problem can be formulated as follows: max β , tr ⁡ ( K t r a ′ ) = 1 , K ′ ≥ 0 A ( K t r a ′ , Y Y T ) . {\displaystyle \max _{\beta ,\operatorname {tr} (K'_{tra})=1,K'\geq 0}A(K'_{tra},YY^{T}).} where K t r a ′ {\displaystyle K'_{tra}} is the kernel of the training set. Structural risk minimization approaches that have been used include linear approaches, such as that used by Lanckriet et al. (2002). We can define the implausibility of a kernel ω ( K ) {\displaystyle \omega (K)} to be the value of the objective function after solving a canonical SVM problem. We can then solve the following minimization problem: min tr ⁡ ( K t r a ′ ) = c ω ( K t r a ′ ) {\displaystyle \min _{\operatorname {tr} (K'_{tra})=c}\omega (K'_{tra})} where c {\displaystyle c} is a positive constant. Many other variations exist on the same idea, with different methods of refining and solving the problem, e.g. with nonnegative weights for individual kernels and using non-linear combinations of kernels. ==== Bayesian approaches ==== Bayesian approaches put priors on the kernel parameters and learn the parameter values from the priors and the base algorithm. For example, the decision function can be written as f ( x ) = ∑ i = 0 n α i ∑ m = 1 p η m K m ( x i m , x m ) {\displaystyle f(x)=\sum _{i=0}^{n}\alpha _{i}\sum _{m=1}^{p}\eta _{m}K_{m}(x_{i}^{m},x^{m})} η {\displaystyle \eta } can be modeled with a Dirichlet prior and α {\displaystyle \alpha } can be modeled with a zero-mean Gaussian and an inverse gamma variance prior. This model is then optimized using a customized multinomial probit approach with a Gibbs sampler. These methods have been used successfully in applications such as protein fold recognition and protein homology problems ==== Boosting approaches ==== Boosting approaches add new kernels iteratively until some stopping criteria that is a function of performance is reached. An example of this is the MARK model developed by Bennett et al. (2002) f ( x ) = ∑ i = 1 N ∑ m = 1 P α i m K m ( x i m , x m ) + b {\displaystyle f(x)=\sum _{i=1}^{N}\sum _{m=1}^{P}\alpha _{i}^{m}K_{m}(x_{i}^{m},x^{m})+b} The parameters α i m {\displaystyle \alpha _{i}^{m}} and b {\displaystyle b} are learned by gradient descent on a coordinate basis. In this way, each iteration of the descent algorithm identifies the best kernel column to choose at each particular iteration and adds that to the combined kernel. The model is then rerun to generate the optimal weights α i {\displaystyle \alpha _{i}} and b {\displaystyle b} . === Semisupervised learning === Semisupervised learning approaches to multiple kernel learning are similar to other extensions of supervised learning approaches. An inductive procedure has been developed that uses a log-likelihood empirical loss and group LASSO regularization with conditional expectation consensus on unlabeled data for image categorization. We can define the problem as follows. Let L = ( x i , y i ) {\displaystyle L={(x_{i},y_{i})}} be the labeled data, and let U = x i {\displaystyle U={x_{i}}} be the set of unlabeled data. Then, we can write the decision function as follows. f ( x ) = α 0 + ∑ i = 1 | L | α i K i ( x ) {\displaystyle f(x)=\alpha _{0}+\sum _{i=1}^{|L|}\alpha _{i}K_{i}(x)} The problem can be written as min f L ( f ) + λ R ( f ) + γ Θ ( f ) {\displaystyle \min _{f}L(f)+\lambda R(f)+\gamma \Theta (f)} where L {\displaystyle L} is the loss function (weighted negative log-likelihood in this case), R {\displaystyle R} is the regularization parameter (Group LASSO in this case), and Θ {\displaystyle \Theta } is the conditional expectation consensus (CEC) penalty on unlabeled data. The CEC penalty is defined as follows. Let the marginal kernel density for all the data be g m π ( x ) = ⟨ ϕ m π , ψ m ( x ) ⟩ {\displaystyle g_{m}^{\pi }(x)=\langle \phi _{m}^{\pi },\psi _{m}(x)\rangle } where ψ m ( x ) = [ K m ( x 1 , x ) , … , K m ( x L , x ) ] T {\displaystyle \psi _{m}(x)=[K_{m}(x_{1},x),\ldots ,K_{m}(x_{L},x)]^{T}} (the kernel distance between the labe

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  Vapnik–Chervonenkis dimension

  In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that the function class can shatter—that is, for which all possible binary labelings can be realized by some function in the class. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis. Informally, the capacity of a classification model is related to how complicated it can be. For example, consider the thresholding of a high-degree polynomial: if the polynomial evaluates above zero, that point is classified as positive, otherwise as negative. A high-degree polynomial can be wiggly, so that it can fit a given set of training points well. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity. This notion of capacity is made rigorous below. == Definitions == === VC dimension of a set-family === Let C = { C } C ∈ C {\displaystyle {\mathcal {C}}=\{C\}_{C\in {\mathcal {C}}}} be a family of sets (also called set family, collection of sets or set of sets) and X {\displaystyle X} a set. Their intersection is defined as the following set family: C ∩ X := { C ∩ X ∣ C ∈ C } . {\displaystyle {\mathcal {C}}\cap X:=\{C\cap X\mid C\in {\mathcal {C}}\}.} Here typically X {\displaystyle X} and each C ∈ C {\displaystyle C\in {\mathcal {C}}} are subsets of a big "universe" of possibilities U {\displaystyle U} where intersection takes place. We say that a set X {\displaystyle X} is shattered by C {\displaystyle {\mathcal {C}}} if P ( X ) = C ∩ X {\displaystyle {\mathcal {P}}(X)={\mathcal {C}}\cap X} i.e. the set of intersections contains (hence is equal to) all the subsets of X {\displaystyle X} . For finite sets X {\displaystyle X} this is equivalent to | C ∩ X | = 2 | X | . {\displaystyle |{\mathcal {C}}\cap X|=2^{|X|}.} The VC dimension D {\displaystyle D} of C {\displaystyle {\mathcal {C}}} is the cardinality of the largest set that is shattered by C {\displaystyle {\mathcal {C}}} . If arbitrarily large sets can be shattered, the VC dimension of C {\displaystyle {\mathcal {C}}} is ∞ {\displaystyle \infty } . === VC dimension of a classification model === A binary classification model f {\displaystyle f} with some parameter vector θ {\displaystyle \theta } is said to shatter a set of generally positioned data points ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} if, for every assignment of labels to those points, there exists a θ {\displaystyle \theta } such that the model f {\displaystyle f} makes no errors when evaluating that set of data points. The VC dimension of a model f {\displaystyle f} is the maximum number of points that can be arranged so that f {\displaystyle f} shatters them. More formally, it is the maximum cardinal D {\displaystyle D} such that there exists a generally positioned data point set of cardinality D {\displaystyle D} that can be shattered by f {\displaystyle f} . == Examples == f {\displaystyle f} is a constant classifier (with no parameters); Its VC dimension is 0 since it cannot shatter even a single point. In general, the VC dimension of a finite classification model, which can return at most 2 d {\displaystyle 2^{d}} different classifiers, is at most d {\displaystyle d} (this is an upper bound on the VC dimension; the Sauer–Shelah lemma gives a lower bound on the dimension). f {\displaystyle f} is a single-parametric threshold classifier on real numbers; i.e., for a certain threshold θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number is larger than θ {\displaystyle \theta } and 0 otherwise. The VC dimension of f {\displaystyle f} is 1 because: (a) It can shatter a single point. For every point x {\displaystyle x} , a classifier f θ {\displaystyle f_{\theta }} labels it as 0 if θ > x {\displaystyle \theta >x} and labels it as 1 if θ < x {\displaystyle \theta x + 2 {\displaystyle \theta >x+2} , as (1,0) if θ ∈ [ x − 4 , x − 2 ) {\displaystyle \theta \in [x-4,x-2)} , as (1,1) if θ ∈ [ x − 2 , x ] {\displaystyle \theta \in [x-2,x]} , and as (0,1) if θ ∈ ( x , x + 2 ] {\displaystyle \theta \in (x,x+2]} . (b) It cannot shatter any set of three points. For every set of three numbers, if the smallest and the largest are labeled 1, then the middle one must also be labeled 1, so not all labelings are possible. f {\displaystyle f} is a straight line as a classification model on points in a two-dimensional plane (this is the model used by a perceptron). The line should separate positive data points from negative data points. There exist sets of 3 points that can indeed be shattered using this model (any 3 points that are not collinear can be shattered). However, no set of 4 points can be shattered: by Radon's theorem, any four points can be partitioned into two subsets with intersecting convex hulls, so it is not possible to separate one of these two subsets from the other. Thus, the VC dimension of this particular classifier is 3. It is important to remember that while one can choose any arrangement of points, the arrangement of those points cannot change when attempting to shatter for some label assignment. Note, only 3 of the 23 = 8 possible label assignments are shown for the three points. f {\displaystyle f} is a single-parametric sine classifier, i.e., for a certain parameter θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number x {\displaystyle x} has sin ⁡ ( θ x ) > 0 {\displaystyle \sin(\theta x)>0} and 0 otherwise. The VC dimension of f {\displaystyle f} is infinite, since it can shatter any finite subset of the set { 2 − m ∣ m ∈ N } {\displaystyle \{2^{-m}\mid m\in \mathbb {N} \}} . == Uses == === In statistical learning theory === The VC dimension can predict a probabilistic upper bound on the test error of a classification model. Vapnik proved that the probability of the test error (i.e., risk with 0–1 loss function) distancing from an upper bound (on data that is drawn i.i.d. from the same distribution as the training set) is given by: Pr ( test error ⩽ training error + 1 N [ D ( log ⁡ ( 2 N D ) + 1 ) − log ⁡ ( η 4 ) ] ) = 1 − η , {\displaystyle \Pr \left({\text{test error}}\leqslant {\text{training error}}+{\sqrt {{\frac {1}{N}}\left[D\left(\log \left({\tfrac {2N}{D}}\right)+1\right)-\log \left({\tfrac {\eta }{4}}\right)\right]}}\,\right)=1-\eta ,} where D {\displaystyle D} is the VC dimension of the classification model, 0 < η ⩽ 1 {\displaystyle 0<\eta \leqslant 1} , and N {\displaystyle N} is the size of the training set (restriction: this formula is valid when D ≪ N {\displaystyle D\ll N} . When D {\displaystyle D} is larger, the test-error may be much higher than the training-error. This is due to overfitting). The VC dimension also appears in sample-complexity bounds. A space of binary functions with VC dimension D {\displaystyle D} can be learned with: N = Θ ( D + ln ⁡ 1 δ ε 2 ) {\displaystyle N=\Theta \left({\frac {D+\ln {1 \over \delta }}{\varepsilon ^{2}}}\right)} samples, where ε {\displaystyle \varepsilon } is the learning error and δ {\displaystyle \delta } is the failure probability. Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. === In computational geometry === The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. == Bounds == The VC dimension of the dual set-family of C {\displaystyle {\mathcal {C}}} is strictly less than 2 vc ⁡ ( C ) + 1 {\displaystyle 2^{\operatorname {vc} ({\mathcal {C}})+1}} , and this is best possible. The VC dimension of a finite set-family C {\displaystyle {\mathcal {C}}} is at most log 2 ⁡ | C | {\displaystyle \log _{2}|{\mathcal {C}}|} . This is because | C ∩ X | ≤ | X | {\displaystyle |{\mathcal {C}}\cap X|\leq |X|} by definition. Given a set-fa

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  Correspondence analysis

  Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a manner similar to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. Its aim is to display in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since the variant of CA described here can be applied either with a focus on the rows or on the columns it should in fact be called simple (symmetric) correspondence analysis. It is traditionally applied to the contingency table of a pair of nominal variables where each cell contains either a count or a zero value. If more than two categorical variables are to be summarized, a variant called multiple correspondence analysis should be chosen instead. CA may also be applied to binary data given the presence/absence coding represents simplified count data i.e. a 1 describes a positive count and 0 stands for a count of zero. Depending on the scores used CA preserves the chi-square distance between either the rows or the columns of the table. Because CA is a descriptive technique, it can be applied to tables regardless of a significant chi-squared test. Although the χ 2 {\displaystyle \chi ^{2}} statistic used in inferential statistics and the chi-square distance are computationally related they should not be confused since the latter works as a multivariate statistical distance measure in CA while the χ 2 {\displaystyle \chi ^{2}} statistic is in fact a scalar not a metric. == Details == Like principal components analysis, correspondence analysis creates orthogonal components (or axes) and, for each item in a table i.e. for each row, a set of scores (sometimes called factor scores, see Factor analysis). Correspondence analysis is performed on the data table, conceived as matrix C of size m × n where m is the number of rows and n is the number of columns. In the following mathematical description of the method capital letters in italics refer to a matrix while letters in italics refer to vectors. Understanding the following computations requires knowledge of matrix algebra. === Preprocessing === Before proceeding to the central computational step of the algorithm, the values in matrix C have to be transformed. First compute a set of weights for the columns and the rows (sometimes called masses), where row and column weights are given by the row and column vectors, respectively: w m = 1 n C C 1 , w n = 1 n C 1 T C . {\displaystyle w_{m}={\frac {1}{n_{C}}}C\mathbf {1} ,\quad w_{n}={\frac {1}{n_{C}}}\mathbf {1} ^{T}C.} Here n C = ∑ i = 1 n ∑ j = 1 m C i j {\displaystyle n_{C}=\sum _{i=1}^{n}\sum _{j=1}^{m}C_{ij}} is the sum of all cell values in matrix C, or short the sum of C, and 1 {\displaystyle \mathbf {1} } is a column vector of ones with the appropriate dimension. Put in simple words, w m {\displaystyle w_{m}} is just a vector whose elements are the row sums of C divided by the sum of C, and w n {\displaystyle w_{n}} is a vector whose elements are the column sums of C divided by the sum of C. The weights are transformed into diagonal matrices W m = diag ⁡ ( 1 / w m ) {\displaystyle W_{m}=\operatorname {diag} (1/{\sqrt {w_{m}}})} and W n = diag ⁡ ( 1 / w n ) {\displaystyle W_{n}=\operatorname {diag} (1/{\sqrt {w_{n}}})} where the diagonal elements of W n {\displaystyle W_{n}} are 1 / w n {\displaystyle 1/{\sqrt {w_{n}}}} and those of W m {\displaystyle W_{m}} are 1 / w m {\displaystyle 1/{\sqrt {w_{m}}}} respectively i.e. the vector elements are the inverses of the square roots of the masses. The off-diagonal elements are all 0. Next, compute matrix P {\displaystyle P} by dividing C {\displaystyle C} by its sum P = 1 n C C . {\displaystyle P={\frac {1}{n_{C}}}C.} In simple words, Matrix P {\displaystyle P} is just the data matrix (contingency table or binary table) transformed into portions i.e. each cell value is just the cell portion of the sum of the whole table. Finally, compute matrix S {\displaystyle S} , sometimes called the matrix of standardized residuals, by matrix multiplication as S = W m ( P − w m w n ) W n {\displaystyle S=W_{m}(P-w_{m}w_{n})W_{n}} Note, the vectors w m {\displaystyle w_{m}} and w n {\displaystyle w_{n}} are combined in an outer product resulting in a matrix of the same dimensions as P {\displaystyle P} . In words the formula reads: matrix outer ⁡ ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} is subtracted from matrix P {\displaystyle P} and the resulting matrix is scaled (weighted) by the diagonal matrices W m {\displaystyle W_{m}} and W n {\displaystyle W_{n}} . Multiplying the resulting matrix by the diagonal matrices is equivalent to multiply the i-th row (or column) of it by the i-th element of the diagonal of W m {\displaystyle W_{m}} or W n {\displaystyle W_{n}} , respectively. === Interpretation of preprocessing === The vectors w m {\displaystyle w_{m}} and w n {\displaystyle w_{n}} are the row and column masses or the marginal probabilities for the rows and columns, respectively. Subtracting matrix outer ⁡ ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} from matrix P {\displaystyle P} is the matrix algebra version of double centering the data. Multiplying this difference by the diagonal weighting matrices results in a matrix containing weighted deviations from the origin of a vector space. This origin is defined by matrix outer ⁡ ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} . In fact matrix outer ⁡ ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} is identical with the matrix of expected frequencies in the chi-squared test. Therefore S {\displaystyle S} is computationally related to the independence model used in that test. But since CA is not an inferential method the term independence model is inappropriate here. === Orthogonal components === The table S {\displaystyle S} is then decomposed by a singular value decomposition as S = U Σ V ∗ {\displaystyle S=U\Sigma V^{}\,} where U {\displaystyle U} and V {\displaystyle V} are the left and right singular vectors of S {\displaystyle S} and Σ {\displaystyle \Sigma } is a square diagonal matrix with the singular values σ i {\displaystyle \sigma _{i}} of S {\displaystyle S} on the diagonal. Σ {\displaystyle \Sigma } is of dimension p ≤ ( min ( m , n ) − 1 ) {\displaystyle p\leq (\min(m,n)-1)} hence U {\displaystyle U} is of dimension m×p and V {\displaystyle V} is of n×p. As orthonormal vectors U {\displaystyle U} and V {\displaystyle V} fulfill U ∗ U = V ∗ V = I {\displaystyle U^{}U=V^{}V=I} . In other words, the multivariate information that is contained in C {\displaystyle C} as well as in S {\displaystyle S} is now distributed across two (coordinate) matrices U {\displaystyle U} and V {\displaystyle V} and a diagonal (scaling) matrix Σ {\displaystyle \Sigma } . The vector space defined by them has as number of dimensions p, that is the smaller of the two values, number of rows and number of columns, minus 1. === Inertia === While a principal component analysis may be said to decompose the (co)variance, and hence its measure of success is the amount of (co-)variance covered by the first few PCA axes - measured in eigenvalue -, a CA works with a weighted (co-)variance which is called inertia. The sum of the squared singular values is the total inertia I {\displaystyle \mathrm {I} } of the data table, computed as I = ∑ i = 1 p σ i 2 . {\displaystyle \mathrm {I} =\sum _{i=1}^{p}\sigma _{i}^{2}.} The total inertia I {\displaystyle \mathrm {I} } of the data table can also computed directly from S {\displaystyle S} as I = ∑ i = 1 n ∑ j = 1 m s i j 2 . {\displaystyle \mathrm {I} =\sum _{i=1}^{n}\sum _{j=1}^{m}s_{ij}^{2}.} The amount of inertia covered by the i-th set of singular vectors is ι i {\displaystyle \iota _{i}} , the principal inertia. The higher the portion of inertia covered by the first few singular vectors i.e. the larger the sum of the principal inertiae in comparison to the total inertia, the more successful a CA is. Therefore, all principal inertia values are expressed as portion ϵ i {\displaystyle \epsilon _{i}} of the total inertia ϵ i = σ i 2 / ∑ i = 1 p σ i 2 {\displaystyle \epsilon _{i}=\sigma _{i}^{2}/\sum _{i=1}^{p}\sigma _{i}^{2}} and are presented in the form of a scree plot. In fact a scree plot is just a bar plot of all principal inertia portions ϵ i {\displaystyle \epsilon _{i}} . === Coordinates === To transform the singular vectors to coordinates which preserve the chi-square distances between rows or columns an additional weighting step is necessary. The resulting coordinates are called principal coordinates in CA text books. If principal coordinates are used for

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  AI anthropomorphism

  AI anthropomorphism is the attribution of human-like feelings, mental states, and behavioral characteristics to artificial intelligence systems. Factors related to the user of the AI – such as culture, age, education, gender, and personality traits – are also important determinants of the strength of anthropomorphic effects. Since the earliest days of AI development, humans have interpreted machine outputs through anthropomorphic frameworks, but the recent emergence of generative AI has amplified these tendencies. In research and engineering, there is a distinction between anthropomorphism and anthropomorphic design. The former is an innate human tendency toward non-human entities. The latter is the scientific community effort to “design anthropomorphism”. Such a design can involve the manipulation of cues, including AI appearance, behaviour and language. Contemporary AI systems today can generate extremely human-like outputs and are often designed specifically to do so, meaning that their anthropomorphic effects can be especially powerful. In some cases, anthropomorphism is accompanied with explicit beliefs that AI systems are capable of empathy, goodwill, understanding, or consciousness. == Background == === In early AIs === Views of artificial agents possessing a human-like intelligence have existed since the early development of computers in the mid-1900s. The use of the human mind as a metaphor for understanding the workings of machine systems was prevalent among researchers in the early days of computer science, with multiple influential works widely distributing the idea of intelligent machines. Among the most widely cited papers of this period was Alan Turing's "Computing Machinery and Intelligence" in which he introduced the Turing Test, stating that a machine was intelligent if it could produce conversation that was indistinguishable from that of a human. These academic works in the 1940s and 1950s gave early credibility to the idea that machine workings could be thought of similarly to human minds. The public quickly came to view artificial systems similarly, with often exaggerated conceptions of the capabilities of early machines. Among the most well-known demonstrations of this was through the chatbot ELIZA designed by Joseph Weizenbaum in 1966. ELIZA responded to user inputs with a rudimentary text-processing approach that could not be considered anything resembling true understanding of the inputs, yet users, even when operating with full conscious knowledge of ELIZA's limitations, often began to ascribe motivation and understanding to the program's output. Weizenbaum later wrote, "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people." Comparisons between the intellectual capabilities of artificial intelligence and human intelligence were continually intensified by the attempts of computer scientists to develop machines that could perform human tasks at a level equal to or better than humans. A symbolic turning point was achieved in 1997, when IBM's chess supercomputer Deep Blue defeated then-world champion Garry Kasparov in a highly publicized six-game match. The defeat of a human by a machine for the first time in chess – a game viewed as a canonical example of human intellect – and the media attention surrounding the match led to a significant shift, where views of parallels between human and artificial intelligence moved from abstract speculation to being concretely demonstrated. A similar achievement was reached in the board game Go in 2017, when the program AlphaGo defeated world top-ranked Ke Jie. === Large language models === The AI boom of the 2020s brought about the widespread emergence of generative AI; in particular, chatbots such as ChatGPT, Gemini, and Claude based on large language models (LLMs) have become increasingly pervasive in everyday society. These systems are notable for the fact that they are able to respond to a wide range of prompts across contexts while producing strikingly human-like outputs – research has shown that humans are often unable to distinguish human-generated text from AI-generated text, and modern AI chatbots have formally been shown to pass the Turing test. As such, the anthropomorphic effects of AI are more powerful than ever. Given that LLMs have brought AI into the technological mainstream, considerable scientific effort has been devoted in recent years to understand existing and potential ramifications of AI in the public sphere; the prevalence and effects of anthropomorphism is one of those domains where much of this effort has been directed. == Current anthropomorphic attributions == === In the general public === Surveys have shown that a substantial portion of the public attributes human-like qualities to AI. In one sample of U.S. adults from 2024, two-thirds of people believed that ChatGPT is possibly conscious on some level, though other research has shown that the public still views the likelihood itself of AI consciousness as comparatively low. Another study conducted in 2025 found that women, people of color, and older individuals were most likely to anthropomorphize AI, as well as that – in general – humans view AIs as warm and competent, and anthropomorphic attributions to AI had increased by 34% in the past year. A YouGov poll reported that 46% of Americans believe that people should display politeness to AI chatbots by saying "please" and "thank you", demonstrating the application of social norms to AI. These beliefs extend to behavior, where majorities of AI users claim to always be polite to chatbots; of those who behave politely, most say they do so simply because it is the "nice" thing to do. In many recent cases, humans have developed robust interpersonal bonds with AI systems. For example: users of social chatbots like Replika and Character.ai have been documented to fall in love with the AIs, or to otherwise treat the AIs as intimate companions, and it has become increasingly common for individuals to use LLMs like ChatGPT as therapists. Chatbots are able to produce responses deeply attuned to users, as they are often designed to maximize agreeableness and mirror users' emotions; this can create compelling illusions of intimacy. === In the research community === In many cases, even AI researchers anthropomorphize AI systems in some capacity. Among the most extreme and well-publicized of these instances occurred in 2022, when engineer Blake Lemoine publicly claimed that Google's LLM LaMDA was conscious. Lemoine published the transcript of a conversation he had had with LaMDA regarding self identity and morality which he claimed was evidence of its sentience; he asserted that LaMDA was "a person" as defined by the United States Constitution and compared its mental capability to that of a 7- or 8-year-old. Lemoine's claims were widely dismissed by the scientific community and by Google itself, which described Lemoine's conclusions as "wholly unfounded" and fired him on the grounds that he had violated policies "to safeguard product information". It is much more common that AI researchers unintentionally imply humanness of AI through the ordinary use of anthropomorphic language to describe nonhuman agents. This kind of language, which Daniel Dennett coined the "intentional stance", is very common in everyday life in a variety of different contexts (e.g., "My computer doesn't want to turn on today"). For AI agents that may actually appear to very closely replicate some human abilities, however, the casual use of such anthropomorphic language in research has been scrutinized for being potentially misleading to the public. As early as 1976, Drew McDermott criticized the research community for the use of "wishful mnemonics", where AIs were referred to with terms like "understand" and "learn". In the LLM era, these criticisms have further intensified, with the negative effects of AI anthropomorphism in the public posing an especially salient danger given the elevated accessibility of modern AI. In some cases, the use of anthropomorphic language for AI is not unintentional, but is willfully used by researchers in order to promote better understanding of the brain – the idea being that, as AI can be functionally similar in some ways to the human brain, we may gain new insights and ideas from treating AI as a kind of model of the brain's workings. In particular, deep neuronal networks (DNNs) are often explicitly compared to the human brain, and significant advances in DNN research have stirred considerable enthusiasm about the ability of AI to emulate the human abilities. Caution has been urged in this domain as well, however; the use of anthropomorphic language can mask important differences that fundamentally distinguish AI from human intelligence. When it comes to DNNs, for example, it has been pointed out that they are still structurally quite different

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  Margin-infused relaxed algorithm

  Margin-infused relaxed algorithm (MIRA) is a machine learning and online algorithm for multiclass classification problems. It is designed to learn a set of parameters (vector or matrix) by processing all the given training examples one-by-one and updating the parameters according to each training example, so that the current training example is classified correctly with a margin against incorrect classifications at least as large as their loss. The change of the parameters is kept as small as possible. A two-class version called binary MIRA simplifies the algorithm by not requiring the solution of a quadratic programming problem (see below). When used in a one-vs-all configuration, binary MIRA can be extended to a multiclass learner that approximates full MIRA, but may be faster to train. The flow of the algorithm looks as follows: The update step is then formalized as a quadratic programming problem: Find m i n ‖ w ( i + 1 ) − w ( i ) ‖ {\displaystyle min\|w^{(i+1)}-w^{(i)}\|} , so that s c o r e ( x t , y t ) − s c o r e ( x t , y ′ ) ≥ L ( y t , y ′ ) ∀ y ′ {\displaystyle score(x_{t},y_{t})-score(x_{t},y')\geq L(y_{t},y')\ \forall y'} , i.e. the score of the current correct training y {\displaystyle y} must be greater than the score of any other possible y ′ {\displaystyle y'} by at least the loss (number of errors) of that y ′ {\displaystyle y'} in comparison to y {\displaystyle y} .

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  Sharpness aware minimization

  Sharpness Aware Minimization (SAM) is an optimization algorithm used in machine learning that aims to improve model generalization. The method seeks to find model parameters that are located in regions of the loss landscape with uniformly low loss values, rather than parameters that only achieve a minimal loss value at a single point. This approach is described as finding "flat" minima instead of "sharp" ones. The rationale is that models trained this way are less sensitive to variations between training and test data, which can lead to better performance on unseen data. The algorithm was introduced in a 2020 paper by a team of researchers including Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. == Underlying Principle == SAM modifies the standard training objective by minimizing a "sharpness-aware" loss. This is formulated as a minimax problem where the inner objective seeks to find the highest loss value in the immediate neighborhood of the current model weights, and the outer objective minimizes this value: min w max ‖ ϵ ‖ p ≤ ρ L train ( w + ϵ ) + λ ‖ w ‖ 2 2 {\displaystyle \min _{w}\max _{\|\epsilon \|_{p}\leq \rho }L_{\text{train}}(w+\epsilon )+\lambda \|w\|_{2}^{2}} In this formulation: w {\displaystyle w} represents the model's parameters (weights). L train {\displaystyle L_{\text{train}}} is the loss calculated on the training data. ϵ {\displaystyle \epsilon } is a perturbation applied to the weights. ρ {\displaystyle \rho } is a hyperparameter that defines the radius of the neighborhood (an L p {\displaystyle L_{p}} ball) to search for the highest loss. An optional L2 regularization term, scaled by λ {\displaystyle \lambda } , can be included. A direct solution to the inner maximization problem is computationally expensive. SAM approximates it by taking a single gradient ascent step to find the perturbation ϵ {\displaystyle \epsilon } . This is calculated as: ϵ ( w ) = ρ ∇ L train ( w ) ‖ ∇ L train ( w ) ‖ 2 {\displaystyle \epsilon (w)=\rho {\frac {\nabla L_{\text{train}}(w)}{\|\nabla L_{\text{train}}(w)\|_{2}}}} The optimization process for each training step involves two stages. First, an "ascent step" computes a perturbed set of weights, w adv = w + ϵ ( w ) {\displaystyle w_{\text{adv}}=w+\epsilon (w)} , by moving towards the direction of the highest local loss. Second, a "descent step" updates the original weights w {\displaystyle w} using the gradient calculated at these perturbed weights, ∇ L train ( w adv ) {\displaystyle \nabla L_{\text{train}}(w_{\text{adv}})} . This update is typically performed using a standard optimizer like SGD or Adam. == Application and Performance == SAM has been applied in various machine learning contexts, primarily in computer vision. Research has shown it can improve generalization performance in models such as Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) on image datasets including ImageNet, CIFAR-10, and CIFAR-100. The algorithm has also been found to be effective in training models with noisy labels, where it performs comparably to methods designed specifically for this problem. Some studies indicate that SAM and its variants can improve out-of-distribution (OOD) generalization, which is a model's ability to perform well on data from distributions not seen during training. Other areas where it has been applied include gradual domain adaptation and mitigating overfitting in scenarios with repeated exposure to training examples. == Limitations == A primary limitation of SAM is its computational cost. By requiring two gradient computations (one for the ascent and one for the descent) per optimization step, it approximately doubles the training time compared to standard optimizers. The theoretical convergence properties of SAM are still under investigation. Some research suggests that with a constant step size, SAM may not converge to a stationary point. The accuracy of the single gradient step approximation for finding the worst-case perturbation may also decrease during the training process. The effectiveness of SAM can also be domain-dependent. While it has shown benefits for computer vision tasks, its impact on other areas, such as GPT-style language models where each training example is seen only once, has been reported as limited in some studies. Furthermore, while SAM seeks flat minima, some research suggests that not all flat minima necessarily lead to good generalization. The algorithm also introduces the neighborhood size ρ {\displaystyle \rho } as a new hyperparameter, which requires tuning. == Research, Variants, and Enhancements == Active research on SAM focuses on reducing its computational overhead and improving its performance. Several variants have been proposed to make the algorithm more efficient. These include methods that attempt to parallelize the two gradient computations, apply the perturbation to only a subset of parameters, or reduce the number of computation steps required. Other approaches use historical gradient information or apply SAM steps intermittently to lower the computational burden. To improve performance and robustness, variants have been developed that adapt the neighborhood size based on model parameter scales (Adaptive SAM or ASAM) or incorporate information about the curvature of the loss landscape (Curvature Regularized SAM or CR-SAM). Other research explores refining the perturbation step by focusing on specific components of the gradient or combining SAM with techniques like random smoothing. Theoretical work continues to analyze the algorithm's behavior, including its implicit bias towards flatter minima and the development of broader frameworks for sharpness-aware optimization that use different measures of sharpness.

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  Reservoir computing

  Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a "black box," a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost. == History == The first examples of reservoir neural networks demonstrated that randomly connected recurrent neural networks could be used for sensorimotor sequence learning, and simple forms of interval and speech discrimination. In these early models the memory in the network took the form of both short-term synaptic plasticity and activity mediated by recurrent connections. In other early reservoir neural network models the memory of the recent stimulus history was provided solely by the recurrent activity. Overall, the general concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system. It is a generalisation of earlier neural network architectures such as recurrent neural networks, liquid-state machines and echo-state networks. Reservoir computing also extends to physical systems that are not networks in the classical sense, but rather continuous systems in space and/or time: e.g. a literal "bucket of water" can serve as a reservoir that performs computations on inputs given as perturbations of the surface. The resultant complexity of such recurrent neural networks was found to be useful in solving a variety of problems including language processing and dynamic system modeling. However, training of recurrent neural networks is challenging and computationally expensive. Reservoir computing reduces those training-related challenges by fixing the dynamics of the reservoir and only training the linear output layer. A large variety of nonlinear dynamical systems can serve as a reservoir that performs computations. In recent years semiconductor lasers have attracted considerable interest as computation can be fast and energy efficient compared to electrical components. Recent advances in both AI and quantum information theory have given rise to the concept of quantum neural networks. These hold promise in quantum information processing, which is challenging to classical networks, but can also find application in solving classical problems. In 2018, a physical realization of a quantum reservoir computing architecture was demonstrated in the form of nuclear spins within a molecular solid. However, the nuclear spin experiments in did not demonstrate quantum reservoir computing per se as they did not involve processing of sequential data. Rather the data were vector inputs, which makes this more accurately a demonstration of quantum implementation of a random kitchen sink algorithm (also going by the name of extreme learning machines in some communities). In 2019, another possible implementation of quantum reservoir processors was proposed in the form of two-dimensional fermionic lattices. In 2020, realization of reservoir computing on gate-based quantum computers was proposed and demonstrated on cloud-based IBM superconducting near-term quantum computers. Reservoir computers have been used for time-series analysis purposes. In particular, some of their usages involve chaotic time-series prediction, separation of chaotic signals, and link inference of networks from their dynamics. == Classical reservoir computing == === Reservoir === The 'reservoir' in reservoir computing is the internal structure of the computer, and must have two properties: it must be made up of individual, non-linear units, and it must be capable of storing information. The non-linearity describes the response of each unit to input, which is what allows reservoir computers to solve complex problems. Reservoirs are able to store information by connecting the units in recurrent loops, where the previous input affects the next response. The change in reaction due to the past allows the computers to be trained to complete specific tasks. Reservoirs can be virtual or physical. Virtual reservoirs are typically randomly generated and are designed like neural networks. Virtual reservoirs can be designed to have non-linearity and recurrent loops, but, unlike neural networks, the connections between units are randomized and remain unchanged throughout computation. Physical reservoirs are possible because of the inherent non-linearity of certain natural systems. The interaction between ripples on the surface of water contains the nonlinear dynamics required in reservoir creation, and a pattern recognition RC was developed by first inputting ripples with electric motors then recording and analyzing the ripples in the readout. === Readout === The readout is a neural network layer that performs a linear transformation on the output of the reservoir. The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as a linear regression or a Ridge regression. As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir. For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid. === Types === ==== Context reverberation network ==== An early example of reservoir computing was the context reverberation network. In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction–diffusion system inspired by Alan Turing's model of morphogenesis. At the trainable layer, the perceptron associates current inputs with the signals that reverberate in the dynamical system; the latter were said to provide a dynamic "context" for the inputs. In the language of later work, the reaction–diffusion system served as the reservoir. ==== Echo state network ==== The tree echo state network (TreeESN) model represents a generalization of the reservoir computing framework to tree structured data. ==== Liquid-state machine ==== Chaotic liquid state machine The liquid (i.e. reservoir) of a chaotic liquid state machine (CLSM), or chaotic reservoir, is made from chaotic spiking neurons but which stabilize their activity by settling to a single hypothesis that describes the trained inputs of the machine. This is in contrast to general types of reservoirs that don't stabilize. The liquid stabilization occurs via synaptic plasticity and chaos control that govern neural connections inside the liquid. CLSM showed promising results in learning sensitive time series data. ==== Nonlinear transient computation ==== This type of information processing is most relevant when time-dependent input signals depart from the mechanism's internal dynamics. These departures cause transients or temporary altercations which are represented in the device's output. ==== Deep reservoir computing ==== The extension of the reservoir computing framework towards deep learning, with the introduction of deep reservoir computing and of the deep echo state network (DeepESN) model allows to develop efficiently trained models for hierarchical processing of temporal data, at the same time enabling the investigation on the inherent role of layered composition in recurrent neural networks. == Quantum reservoir computing == Quantum reservoir computing may use the nonlinear nature of quantum mechanical interactions or processes to form the characteristic nonlinear reservoirs but may also be done with linear reservoirs when the injection of the input to the reservoir creates the nonlinearity. The marriage of machine learning and quantum devices is leading to the emergence of quantum neuromorphic computing as a new research area. === Types === ==== Gaussian states of interacting quantum harmonic oscillators ==== Gaussian states are a paradigmatic class of states of continuous variable quantum systems. Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms, naturally robust to decoherence, it is well-known that they are not sufficient for, e.g., universal quantum computing because transformations that preserve the Gaussian nature of a state are linear. Normally, linear dynamics would not be sufficient for nontrivial reser

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  Relational data mining

  Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.

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  Ground truth

  Ground truth is information that is known to be real or true, provided by direct observation and measurement (i.e. empirical evidence) as opposed to information provided by inference. The term ground truth appeared in remote sensing literature as early as 1972, when NASA described it as essential "data about ... materials on the earth's surface" used to calibrate measurements. It was later adopted by the statistical modeling and machine learning communities. == Etymology == The Oxford English Dictionary (s.v. ground truth) records the use of the word Groundtruth in the sense of 'fundamental truth' from Henry Ellison's poem "The Siberian Exile's Tale", published in 1833. == Usage == The term "ground truth" can be used as a noun, adjective, and verb. Noun: "ground truth" (no hyphen). Example: "The ground truth is essential for training accurate models." Adjective: "ground-truth" (hyphenated compound adjective). Example: "We need to use ground-truth data to validate the model." Verb: "to ground-truth" or "to groundtruth" (compound verb,). Example: "We need to ground-truth the results to ensure their accuracy." == Statistics and machine learning == In statistics and machine learning, ground truth is the ideal expected result, used in statistical models to prove or disprove research hypotheses. "Ground truthing" is the process of gathering the good data for this test. Ground truth is typically included in labeled data. In machine learning, "ground truth" is not necessarily objectively correct or true. For example, in training AI models or relevance rankers, it may be a set of judgments made by people or inferred from user behavior, which may depend on context. For example, in Bayesian spam filtering, a supervised learning system is typically trained by examples labeled as spam and non-spam. Although these labels may be subjective or inaccurate, they are considered ground truth. True ground truth in machine learning is objective data. For example, suppose we are testing a stereo vision system to see how well it can estimate 3D positions. A calibrated laser rangefinder may provide accurate distances as ground truth. == Remote sensing == In remote sensing, "ground truth" refers to information collected at the imaged location. Ground truth allows image data to be related to real features and materials on the ground. The collection of ground truth data enables calibration of remote-sensing data, and aids in the interpretation and analysis of what is being sensed. Examples include cartography, meteorology, analysis of aerial photographs, satellite imagery and other techniques in which data are gathered at a distance. More specifically, ground truth may refer to a process in which "pixels" on a satellite image are compared to what is imaged (at the time of capture) in order to verify the contents of the "pixels" in the image (noting that the concept of "pixel" is imaging-system-dependent). In the case of a classified image, supervised classification can help to determine the accuracy of the classification by the remote sensing system which can minimize error in the classification. Ground truth is usually done on site, correlating what is known with surface observations and measurements of various properties of the features of the ground resolution cells under study in the remotely sensed digital image. The process also involves taking geographic coordinates of the ground resolution cell with GPS technology and comparing those with the coordinates of the "pixel" being studied provided by the remote sensing software to understand and analyze the location errors and how it may affect a particular study. Ground truth is important in the initial supervised classification of an image. When the identity and location of land cover types are known through a combination of field work, maps, and personal experience these areas are known as training sites. The spectral characteristics of these areas are used to train the remote sensing software using decision rules for classifying the rest of the image. These decision rules such as Maximum Likelihood Classification, Parallelopiped Classification, and Minimum Distance Classification offer different techniques to classify an image. Additional ground truth sites allow the remote sensor to establish an error matrix that validates the accuracy of the classification method used. Different classification methods may have different percentages of error for a given classification project. It is important that the remote sensor chooses a classification method that works best with the number of classifications used while providing the least amount of error. Ground truth also helps with atmospheric correction. Since images from satellites have to pass through the atmosphere, they can get distorted because of absorption in the atmosphere. So ground truth can help fully identify objects in satellite photos. === Errors of commission === An example of an error of commission is when a pixel reports the presence of a feature (such a tree) that, in reality, is absent (no tree is actually present). Ground truthing ensures that the error matrices have a higher accuracy percentage than would be the case if no pixels were ground-truthed. This value is the complement of the user's accuracy, i.e. Commission Error = 1 - user's accuracy. === Errors of omission === An example of an error of omission is when pixels of a certain type, for example, maple trees, are not classified as maple trees. The process of ground-truthing helps to ensure that the pixel is classified correctly and the error matrices are more accurate. This value is the complement of the producer's accuracy, i.e. Omission Error = 1 - producer's accuracy == Geographical information systems == In GIS the spatial data is modeled as field (like in remote sensing raster images) or as object (like in vectorial map representation). They are modeled from the real world (also named geographical reality), typically by a cartographic process (illustrated). Geographic information systems such as GIS, GPS, and GNSS, have become so widespread that the term "ground truth" has taken on special meaning in that context. If the location coordinates returned by a location method such as GPS are an estimate of a location, then the "ground truth" is the actual location on Earth. A smart phone might return a set of estimated location coordinates such as 43.87870, −103.45901. The ground truth being estimated by those coordinates is the tip of George Washington's nose on Mount Rushmore. The accuracy of the estimate is the maximum distance between the location coordinates and the ground truth. We could say in this case that the estimate accuracy is 10 meters, meaning that the point on Earth represented by the location coordinates is thought to be within 10 meters of George's nose—the ground truth. In slang, the coordinates indicate where we think George Washington's nose is located, and the ground truth is where it really is. In practice a smart phone or hand-held GPS unit is routinely able to estimate the ground truth within 6–10 meters. Specialized instruments can reduce GPS measurement error to under a centimeter. == Military usage == US military slang uses "ground truth" to refer to the facts comprising a tactical situation—as opposed to intelligence reports, mission plans, and other descriptions reflecting the conative or policy-based projections of the industrial·military complex. The term appears in the title of the Iraq War documentary film The Ground Truth (2006), and also in military publications, for example Stars and Stripes saying: "Stripes decided to figure out what the ground truth was in Iraq."

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  Log-linear model

  A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form exp ⁡ ( c + ∑ i w i f i ( X ) ) {\displaystyle \exp \left(c+\sum _{i}w_{i}f_{i}(X)\right)} , in which the fi(X) are quantities that are functions of the variable X, in general a vector of values, while c and the wi stand for the model parameters. The term may specifically be used for: A log-linear plot or graph, which is a type of semi-log plot. Poisson regression for contingency tables, a type of generalized linear model. The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables X, or more immediately, the transformed quantities fi(X) in the range −∞ to +∞. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. Thus the contexts where these models are useful or realistic often depends on the range of the values being modelled.

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