AI Google Grammar Checker

AI Google Grammar Checker — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Meta-Labeling

  Meta-labeling, also known as corrective AI, is a machine learning (ML) technique utilized in quantitative finance to enhance the performance of investment and trading strategies, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. The core idea is to separate the decision of trade direction (side) from the decision of trade sizing, addressing the inefficiencies of simultaneously learning both side and size predictions. The side decision involves forecasting market movements (long, short, neutral), while the size decision focuses on risk management and profitability. It serves as a secondary decision-making layer that evaluates the signals generated by a primary predictive model. By assessing the confidence and likely profitability of those signals, meta-labeling allows investors and algorithms to dynamically size positions and suppress false positives. == Motivation == Meta-labeling is designed to improve precision without sacrificing recall. As noted by López de Prado, attempting to model both the direction and the magnitude of a trade using a single algorithm can result in poor generalization. By separating these tasks, meta-labeling enables greater flexibility and robustness: Enhances control over capital allocation. Reduces overfitting by limiting model complexity. Allows the use of interpretability tools and tailored thresholds to manage risk. Enables dynamic trade suppression in unfavorable regimes. == Applications == Meta-labeling has been applied in a variety of financial ML contexts, including: Algorithmic trading: Filtering and sizing trades to reduce false positives. Portfolio optimization: Scaling exposure across multiple signals with differing confidence levels. Risk management: Dynamically disabling strategies in adverse market conditions. Model validation: Interpreting when and why a model may be underperforming due to regime shifts. == General architecture == Meta-labeling decouples two core components of systematic trading strategies: directional prediction and position sizing. The process involves training a primary model to generate trade signals (e.g., buy, sell, or hold) and then training a secondary model to determine whether each signal is likely to lead to a profitable trade. The second model outputs a probability that is interpreted as the confidence in the forecast, which can be used to adjust the position size or to filter out unreliable trades. Meta-labeling is typically implemented as a three-stage process: Primary model (M1): Predicts the direction or label of a financial outcome using features such as market prices, returns, or volatility indicators. A typical output is directional, e.g., Y ∈ {−1,0,1}, representing short, neutral, or long positions. Secondary model (M2): A binary classifier trained to predict whether the primary model's prediction will be profitable. The target variable is a binary meta-label F ∈ { 0 , 1 } {\displaystyle F\in \{0,1\}} . Inputs can include features used in the primary model, performance diagnostics, or market regime data. Position sizing algorithm (M3): Translates the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 1: Forecasting side === Primary model architecture Figure 1 Figure 1 presents the architecture of a primary model. It focuses on forecasting the side of the trade. Following the example, this model (M1) takes in input data – such as open-high-low-close data and determines the side of the position to take: a negative number is a short position, and positive number is a long position, the range is set between −1 and 1 (the closer it is to −1 or 1, the stronger the models conviction is). When training the model, the labels are −1 and 1, based on the direction of forward returns for some predefined investment horizon. The researcher may decide to apply a recall check (τ: "Tau") by setting a minimum threshold that the initial output needs to be to qualify of a short or long position (if the threshold is not met, no side forecast is predicted, leading to closing of any open positions), this leads to the primary model output which is one of three possible side forecasts: −1, 0, or 1. The primary model also generates evaluation data which can be used by the secondary model, to improve performance of size forecasts. Some examples of evaluation data include rolling accuracy, F1, recall, precision, and AUC scores. === Stage 2: Filtering out false positives === General meta-labeling architecture Figure 2 Next comes the phase of filtering out false positives, by applying a secondary machine learning model (M2), which is a binary classifier trained to determine if the trade will be profitable or not. The model takes as input four general groupings of data: General input data which is predictive of a false positive. For example the last 30 days rolling volatility of the underlying asset. Evaluation data. Market state and regime data, one may find that macro economic data or clustering the market into regimes may help as specific trading strategies are known to perform better in particular regimes. Example: momentum based strategies perform best in periods with low volatility and strong directional moves. Primary models initial input which is a value between −1 and 1. This highlights the strength of the primary models conviction. The output of the model is a value between −1 and 1 (if using a Tanh function) which will indicate the strength of the conviction that a short or long position is profitable, or it could simply be between 0 and 1 (using a sigmoid function) if one only wanted to know if it made money or not. This output allows filtering out trades that are likely to lead to losses. One could stop at this point or use the outputs of the secondary model as inputs to a position sizing algorithm (M3) which could further enhance strategy performance metrics by translating the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 3: Optimizing position sizes === ==== Position sizing methods (M3) ==== Various algorithms have been proposed for transforming predicted probabilities into trade sizes: All-or-nothing: Allocate 100% of capital if the probability exceeds a predefined threshold (e.g., 0.5); otherwise, do not trade. Model confidence: Use the probability score directly as the fraction of capital allocated. Linear scaling: Rescale the model's probabilities using min-max normalization based on the training data. Normal CDF (NCDF): Use a normal cumulative distribution function applied to a z-statistic derived from the predicted probability. Empirical CDF (ECDF): Rank probabilities based on their percentile in the training data to ensure relative allocation. Sigmoid Optimal Position Sizing (SOPS): Applies a smooth non-linear sigmoid transformation optimized to maximize risk-adjusted returns (Sharpe ratio). ==== Model calibration ==== Each machine learning algorithm used in meta-labeling tends to produce outputs with different characteristic distributions; for example, some are approximately normally distributed, whereas others exhibit a pronounced U-shape, concentrating probabilities near the extremes. Due to these varying distributions, simply summing the outputs of different models can inadvertently lead to uneven weighting of signals, biasing trade decisions. To address this, model calibration techniques are essential to adjust the predicted probabilities towards frequentist probabilities, ensuring that model outputs reflect true likelihoods more accurately. Two common calibration techniques are: Platt scaling (Sigmoid scaling): Suitable for correcting S-shaped calibration plots typically produced by models such as support vector machines (SVMs). Isotonic regression: Fits a non-decreasing step function to probabilities and is effective particularly with larger datasets, though it can sometimes lead to overfitting. Transforming predictions to frequentist probabilities is crucial as it provides probabilistic outputs that are directly interpretable as the actual likelihood of an event occurring. Such calibration significantly enhances the effectiveness of fixed position sizing methods, reducing maximum drawdowns and increasing risk-adjusted returns. However, calibration has less impact on position sizing methods that directly estimate parameters from the training data, such as ECDF and SOPS, suggesting that calibration is a critical step mainly for fixed methods that rely heavily on raw model outputs. =

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  Apertus (LLM)

  Apertus is a public large language model, developed by the Swiss AI Initiative (a collaboration between EPFL, ETH Zurich, and the Swiss National Supercomputing Centre). It was released on September 2, 2025, under the free and open-source Apache 2.0 license. Designed initially for business and research use cases around the world, Apertus was trained on over 1800 languages, and comes in 8 billion or 70 billion parameter versions and is available on Hugging Face for download. The model was developed aiming to adhere to European copyright law, and is one of the first examples of AI as a public good in the vein of AI Sovereignty. It is also the first large model to comply with the European Union's Artificial Intelligence Act. At its launch, the model creators emphasized multilinguality, transparency, and auditability as priorities in contrast to commercial frontier model. While international reception was largely positive, the first iteration was significantly behind the capabilities of frontier models and needs adaptation for many use cases with chatbots being a secondary but not a primary use case. As of late 2025, it was considered the largest and most capable fully open model. The capability of future models will depend in part on how much more funding can be secured.

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  Hard sigmoid

  In artificial intelligence, especially computer vision and artificial neural networks, a hard sigmoid is non-smooth function used in place of a sigmoid function. These retain the basic shape of a sigmoid, rising from 0 to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of computation is more important than precision. == Examples == The most extreme examples are the sign function or Heaviside step function, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0. Other examples include the Theano library, which provides two approximations: ultra_fast_sigmoid, which is a multi-part piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1).

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  Quantum natural language processing

  Quantum natural language processing (QNLP) is the application of quantum computing to natural language processing (NLP). It computes word embeddings as parameterised quantum circuits that can solve NLP tasks faster than any classical computer. It is inspired by categorical quantum mechanics and the DisCoCat framework, making use of string diagrams to translate from grammatical structure to quantum processes. == Theory == The first quantum algorithm for natural language processing used the DisCoCat framework and Grover's algorithm to show a quadratic quantum speedup for a text classification task. It was later shown that quantum language processing is BQP-Complete, i.e. quantum language models are more expressive than their classical counterpart, unless quantum mechanics can be efficiently simulated by classical computers. These two theoretical results assume fault-tolerant quantum computation and a QRAM, i.e. an efficient way to load classical data on a quantum computer. Thus, they are not applicable to the noisy intermediate-scale quantum (NISQ) computers available today. == Experiments == The algorithm of Zeng and Coecke was adapted to the constraints of NISQ computers and implemented on IBM quantum computers to solve binary classification tasks. Instead of loading classical word vectors onto a quantum memory, the word vectors are computed directly as the parameters of quantum circuits. These parameters are optimised using methods from quantum machine learning to solve data-driven tasks such as question answering, machine translation and even algorithmic music composition.

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  Color balance

  In photography and image processing, color balance is the global adjustment of the intensities of the colors (typically red, green, and blue primary colors). An important goal of this adjustment is to render specific colors – particularly neutral colors like white or grey – correctly. Hence, the general method is sometimes called gray balance, neutral balance, or white balance. Color balance changes the overall mixture of colors in an image and is used for color correction. Generalized versions of color balance are used to correct colors other than neutrals or to deliberately change them for effect. White balance is one of the most common kinds of balancing, and is when colors are adjusted to make a white object (such as a piece of paper or a wall) appear white and not a shade of any other colour. Image data acquired by sensors – either film or electronic image sensors – must be transformed from the acquired values to new values that are appropriate for color reproduction or display. Several aspects of the acquisition and display process make such color correction essential – including that the acquisition sensors do not match the sensors in the human eye, that the properties of the display medium must be accounted for, and that the ambient viewing conditions of the acquisition differ from the display viewing conditions. The color balance operations in popular image editing applications usually operate directly on the red, green, and blue channel pixel values, without respect to any color sensing or reproduction model. In film photography, color balance is typically achieved by using color correction filters over the lights or on the camera lens. == Generalized color balance == Sometimes the adjustment to keep neutrals neutral is called white balance, and the phrase color balance refers to the adjustment that in addition makes other colors in a displayed image appear to have the same general appearance as the colors in an original scene. It is particularly important that neutral (gray, neutral, white) colors in a scene appear neutral in the reproduction. === Psychological color balance === Humans relate to flesh tones more critically than other colors. Trees, grass and sky can all be off without concern, but if human flesh tones are 'off' then the human subject can look sick or dead. To address this critical color balance issue, the tri-color primaries themselves are formulated to not balance as a true neutral color. The purpose of this color primary imbalance is to more faithfully reproduce the flesh tones through the entire brightness range. == Illuminant estimation and adaptation == Most digital cameras have means to select color correction based on the type of scene lighting, using either manual lighting selection, automatic white balance, or custom white balance. The algorithms for these processes perform generalized chromatic adaptation. Many methods exist for color balancing. Setting a button on a camera is a way for the user to indicate to the processor the nature of the scene lighting. Another option on some cameras is a button which one may press when the camera is pointed at a gray card or other neutral colored object. This captures an image of the ambient light, which enables a digital camera to set the correct color balance for that light. There is a large literature on how one might estimate the ambient lighting from the camera data and then use this information to transform the image data. A variety of algorithms have been proposed, and the quality of these has been debated. A few examples and examination of the references therein will lead the reader to many others. Examples are Retinex, an artificial neural network or a Bayesian method. == Chromatic colors == Color balancing an image affects not only the neutrals, but other colors as well. An image that is not color balanced is said to have a color cast, as everything in the image appears to have been shifted towards one color. Color balancing may be thought in terms of removing this color cast. Color balance is also related to color constancy. Algorithms and techniques used to attain color constancy are frequently used for color balancing, as well. Color constancy is, in turn, related to chromatic adaptation. Conceptually, color balancing consists of two steps: first, determining the illuminant under which an image was captured; and second, scaling the components (e.g., R, G, and B) of the image or otherwise transforming the components so they conform to the viewing illuminant. Viggiano found that white balancing in the camera's native RGB color model tended to produce less color inconstancy (i.e., less distortion of the colors) than in monitor RGB for over 4000 hypothetical sets of camera sensitivities. This difference typically amounted to a factor of more than two in favor of camera RGB. This means that it is advantageous to get color balance right at the time an image is captured, rather than edit later on a monitor. If one must color balance later, balancing the raw image data will tend to produce less distortion of chromatic colors than balancing in monitor RGB. == Mathematics of color balance == Color balancing is sometimes performed on a three-component image (e.g., RGB) using a 3x3 matrix. This type of transformation is appropriate if the image was captured using the wrong white balance setting on a digital camera, or through a color filter. Changing the color balance of an image can improve classifier results on a trained ML model. === Scaling monitor R, G, and B === In principle, one wants to scale all relative luminances in an image so that objects which are believed to be neutral appear so. If, say, a surface with R = 240 {\displaystyle R=240} was believed to be a white object, and if 255 is the count which corresponds to white, one could multiply all red values by 255/240. Doing analogously for green and blue would result, at least in theory, in a color balanced image. In this type of transformation the 3x3 matrix is a diagonal matrix. [ R G B ] = [ 255 / R w ′ 0 0 0 255 / G w ′ 0 0 0 255 / B w ′ ] [ R ′ G ′ B ′ ] {\displaystyle \left[{\begin{array}{c}R\\G\\B\end{array}}\right]=\left[{\begin{array}{ccc}255/R'_{w}&0&0\\0&255/G'_{w}&0\\0&0&255/B'_{w}\end{array}}\right]\left[{\begin{array}{c}R'\\G'\\B'\end{array}}\right]} where R {\displaystyle R} , G {\displaystyle G} , and B {\displaystyle B} are the color balanced red, green, and blue components of a pixel in the image; R ′ {\displaystyle R'} , G ′ {\displaystyle G'} , and B ′ {\displaystyle B'} are the red, green, and blue components of the image before color balancing, and R w ′ {\displaystyle R'_{w}} , G w ′ {\displaystyle G'_{w}} , and B w ′ {\displaystyle B'_{w}} are the red, green, and blue components of a pixel which is believed to be a white surface in the image before color balancing. This is a simple scaling of the red, green, and blue channels, and is why color balance tools in Photoshop have a white eyedropper tool. It has been demonstrated that performing the white balancing in the phosphor set assumed by sRGB tends to produce large errors in chromatic colors, even though it can render the neutral surfaces perfectly neutral. === Scaling X, Y, Z === If the image may be transformed into CIE XYZ tristimulus values, the color balancing may be performed there. This has been termed a "wrong von Kries" transformation. Although it has been demonstrated to offer usually poorer results than balancing in monitor RGB, it is mentioned here as a bridge to other things. Mathematically, one computes: [ X Y Z ] = [ X w / X w ′ 0 0 0 Y w / Y w ′ 0 0 0 Z w / Z w ′ ] [ X ′ Y ′ Z ′ ] {\displaystyle \left[{\begin{array}{c}X\\Y\\Z\end{array}}\right]=\left[{\begin{array}{ccc}X_{w}/X'_{w}&0&0\\0&Y_{w}/Y'_{w}&0\\0&0&Z_{w}/Z'_{w}\end{array}}\right]\left[{\begin{array}{c}X'\\Y'\\Z'\end{array}}\right]} where X {\displaystyle X} , Y {\displaystyle Y} , and Z {\displaystyle Z} are the color-balanced tristimulus values; X w {\displaystyle X_{w}} , Y w {\displaystyle Y_{w}} , and Z w {\displaystyle Z_{w}} are the tristimulus values of the viewing illuminant (the white point to which the image is being transformed to conform to); X w ′ {\displaystyle X'_{w}} , Y w ′ {\displaystyle Y'_{w}} , and Z w ′ {\displaystyle Z'_{w}} are the tristimulus values of an object believed to be white in the un-color-balanced image, and X ′ {\displaystyle X'} , Y ′ {\displaystyle Y'} , and Z ′ {\displaystyle Z'} are the tristimulus values of a pixel in the un-color-balanced image. If the tristimulus values of the monitor primaries are in a matrix P {\displaystyle \mathbf {P} } so that: [ X Y Z ] = P [ L R L G L B ] {\displaystyle \left[{\begin{array}{c}X\\Y\\Z\end{array}}\right]=\mathbf {P} \left[{\begin{array}{c}L_{R}\\L_{G}\\L_{B}\end{array}}\right]} where L R {\displaystyle L_{R}} , L G {\displaystyle L_{G}} , and L B {\displaystyle L_{B}} are the un-gamma corrected monitor RGB, one may use: [ L R L G L B ] = P − 1 [ X w / X w ′ 0 0

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  Superquadrics

  In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ⁡ ( sin ⁡ ω ) | sin ⁡ ω | m g ( ω , m ) = sgn ⁡ ( cos ⁡ ω ) | cos ⁡ ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ⁡ ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin ⁡ θ cos ⁡ φ y = y 0 + r sin ⁡ θ sin ⁡ φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos ⁡ θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:

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  Textual entailment

  In natural language processing, textual entailment (TE), also known as natural language inference (NLI), is a directional relation between text fragments. The relation holds whenever the truth of one text fragment follows from another text. == Definition == In the TE framework, the entailing and entailed texts are termed text (t) and hypothesis (h), respectively. Textual entailment is not the same as pure logical entailment – it has a more relaxed definition: "t entails h" (t ⇒ h) if, typically, a human reading t would infer that h is most likely true. (Alternatively: t ⇒ h if and only if, typically, a human reading t would be justified in inferring the proposition expressed by h from the proposition expressed by t.) The relation is directional because even if "t entails h", the reverse "h entails t" is much less certain. Determining whether this relationship holds is an informal task, one which sometimes overlaps with the formal tasks of formal semantics (satisfying a strict condition will usually imply satisfaction of a less strict conditioned); additionally, textual entailment partially subsumes word entailment. == Examples == Textual entailment can be illustrated with examples of three different relations: An example of a positive TE (text entails hypothesis) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man has good consequences. An example of a negative TE (text contradicts hypothesis) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man has no consequences. An example of a non-TE (text does not entail nor contradict) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man will make you a better person. == Ambiguity of natural language == A characteristic of natural language is that there are many different ways to state what one wants to say: several meanings can be contained in a single text and the same meaning can be expressed by different texts. This variability of semantic expression can be seen as the dual problem of language ambiguity. Together, they result in a many-to-many mapping between language expressions and meanings. The task of paraphrasing involves recognizing when two texts have the same meaning and creating a similar or shorter text that conveys almost the same information. Textual entailment is similar but weakens the relationship to be unidirectional. Mathematical solutions to establish textual entailment can be based on the directional property of this relation, by making a comparison between some directional similarities of the texts involved. == Approaches == Textual entailment measures natural language understanding as it asks for a semantic interpretation of the text, and due to its generality remains an active area of research. Many approaches and refinements of approaches have been considered, such as word embedding, logical models, graphical models, rule systems, contextual focusing, and machine learning. Practical or large-scale solutions avoid these complex methods and instead use only surface syntax or lexical relationships, but are correspondingly less accurate. As of 2005, state-of-the-art systems are far from human performance; a study found humans to agree on the dataset 95.25% of the time. Algorithms from 2016 had not yet achieved 90%. == Applications == Many natural language processing applications, like question answering, information extraction, summarization, multi-document summarization, and evaluation of machine translation systems, need to recognize that a particular target meaning can be inferred from different text variants. Typically entailment is used as part of a larger system, for example in a prediction system to filter out trivial or obvious predictions. Textual entailment also has applications in adversarial stylometry, which has the objective of removing textual style without changing the overall meaning of communication. == Datasets == Some of available English NLI datasets include: SNLI MultiNLI SciTail SICK MedNLI QA-NLI In addition, there are several non-English NLI datasets, as follows: XNLI DACCORD, RTE3-FR, SICK-FR for French FarsTail for Farsi OCNLI for Chinese SICK-NL for Dutch IndoNLI for Indonesian

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  Cuboid (computer vision)

  In computer vision, the term cuboid is used to describe a small spatiotemporal volume extracted for purposes of behavior recognition. The cuboid is regarded as a basic geometric primitive type and is used to depict three-dimensional objects within a three dimensional representation of a flat, two dimensional image. == Production == Cuboids can be produced from both two-dimensional and three-dimensional images. One method used to produce cuboids utilizes scene understanding (SUN) primitive databases, which are collections of pictures that already contain cuboids. By sorting through SUN primitive databases with machine learning tools, computers observe the conditions in which cuboids are produced in images from SUN primitive databases and can learn to produce cuboids from other images. RGB-D images, which are RGB images that also record the depth of each pixel, are occasionally used to produce cuboids because computers no longer need to determine the depth of an object, as they typically do because depth is already recorded. Cuboid production is sensitive to changes in color and illumination, blockage, and background clutter. This means that it is difficult for computers to produce cuboids of objects that are multicolored, irregularly illuminated, or partially covered, or if there are many objects in the background. This is partially due to the fact that algorithms for producing cuboids are still relatively simple. == Usage == Cuboids are created for point cloud-based three-dimensional maps and can be utilized in various situations such as augmented reality, the automated control of cars, drones, and robots, and object detection. Cuboids allow for software to identify a scene through geometric descriptions in an “object-agnostic” fashion. Interest points, locations within images that are identified by a computer as essential to identifying the image, created from two-dimensional images can be used with cuboids for image matching, identifying a room or scene, and instance recognition. Interest points created from three dimensional images can be used with cuboids to recognize activities. This is possible because interest points aid software to focus on only the most important aspects of the images. RGB-D images and SLAM systems are used together in RGB-D SLAM systems, which are employed by Computer-aided design systems to generate point cloud-based three-dimensional maps. Most industrial multi-axis machining tools use computer-aided manufacturing and subsequently work in cuboid work spaces.

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  Artifact (app)

  Artifact was a personalized social news aggregator app that uses recommender systems to suggest articles. Launched in January 2023 by Nokto, Inc., a company founded by co-founders of Instagram Kevin Systrom and Mike Krieger, the app is available for iOS and Android. The app's name is a portmanteau of the words "articles", "artificial intelligence", and "fact". The app shut down in January 2024 as a result of low interest. == History == Nokto, Inc. was established on March 3, 2022, as a foreign stock company in California, with its headquarters in San Francisco. The company's main product, Artifact, is the first new product launched by Krieger and Systrom since their 2018 resignation from Instagram after conflicts with parent company Meta, which acquired Instagram in 2012. Artifact launched on January 31, 2023, after the team had been working on it for over a year, offering the option to sign up for a waiting list for its private beta, which grew to about 160,000 people, and then launching in open beta on February 22, 2023. With a team of seven employees in San Francisco, the app was free throughout its lifetime, with the founders explaining at the time that different business models - such as advertising or subscription fees - could be explored in the future. In January 2024, cofounder Kevin Systrom announced that the app would be shutting down after concluding that "the market opportunity isn’t big enough to warrant continued investment in this way." In April 2024, it was announced Artifact had been acquired by Yahoo, who intended to use the service's technology in an upgraded Yahoo! News app. == Features == Frequently described as "TikTok for text" and a competitor to Twitter, Artifact was a news aggregator that used machine learning to make personalized recommendations based on topics, news sources, and authors that the reader is interested in. In addition to reading articles, the app offered the ability to like articles, leave comments, or listen to an audio version of an article read by AI-generated voices, including a simulation of the voices of Snoop Dogg or Gwyneth Paltrow. AI also would rewrite clickbait headlines that users flagged. Artifact later expanded to a social network where users could post links, images and text to their profile, which could be liked or commented on by other users. Similar to other social news websites like Reddit, reader accounts had profiles with reputation scores.

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  Colloquis

  Colloquis, previously known as ActiveBuddy and Conversagent, was a company that created conversation-based interactive agents originally distributed via instant messaging platforms. The company had offices in New York, New York, and Sunnyvale, California. == History == Founded in 2000, the company was the brainchild of Robert Hoffer, Timothy Kay, and Peter Levitan. The idea for interactive agents (also known as Internet bots) came from the team's vision to add functionality to increasingly popular instant messaging services. The original implementation took shape as a word-based adventure game but quickly grew to include a wide range of database applications, including access to news, weather, stock information, movie times, Yellow Pages listings, and detailed sports data, as well as a variety of tools (calculators, translator, etc.). These various applications were bundled into one entity and launched as SmarterChild in 2001. SmarterChild acted as a showcase for the quick data access and possibilities for fun conversation that the company planned to turn into customized, niche-specific products. The rapid success of SmarterChild led to targeted promotional products for Radiohead, Austin Powers, The Sporting News, and others. ActiveBuddy sought to strengthen its hold on the interactive agent market for the future by filing for, and receiving, a controversial patent on their creation in 2002. The company also released the BuddyScript SDK, a free developer kit that allow programmers to design and launch their own interactive agents using ActiveBuddy's proprietary scripting language, in 2002. Ultimately, however, the decline in ad spending in 2001 and 2002 led to a shift in corporate strategy towards business focused Automated Service Agents, building products for clients including Cingular, Comcast and Cox Communications. The company subsequently changed its name from ActiveBuddy to Conversagent in 2003, and then again to Colloquis in 2006. Colloquis was purchased by Microsoft in October 2006.

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  Ayoba

  Ayoba is an African communication platform developed in South Africa. It is owned by Progressive Tech Holdings in Mauritius and managed by SIMFY Africa. Launched on May 4, 2019, as of April 2024, it has over 35 million active users. == History == Ayoba was first published on Google Play in February 2019. Its first marketing campaign and brand launch took place in Cameroon on May 4, 2019. In June 2019, the platform introduced its first eight channels. In November 2019, the platform reached one million active users, which increased to two million by June 2020. Subsequently, ayoba expanded its services, including the launch of games for Android in February 2020, Momo (Mobile Money) in Cameroon in May 2020, and MicroApps in May 2020. It also launched music and voice and video calling features in 12 territories in August 2020. The first version of ayoba for iOS was released in September 2020. In December of the same year, games and Messaging 2.0 were launched on the platform. In November 2020, it won Best Mobile Application at the African Digital Awards. In 2021, it won OTT Brand of the Year at the Marketing World Awards in Ghana. In December 2022, it received Top Innovative Technology and Telecom Product of the Year at the National Communications Awards in December 2022. In June 2023 ayoba partnered with BoomPlay and as of April 2024, it had 35 million monthly active users. Ayoba has partnered with Jumia Ghana to offer exclusive deals to users. Ayoba users can get a 10% discount on selected Jumia purchases through the app, with no data charges for MTN users. This partnership aims to make online shopping more affordable and accessible by integrating Jumia's offers into the ayoba app. Ayoba supports over 35 million users across Africa and provides services in 22 languages. To access the deals, users can download the ayoba app from the Google Play Store, iOS Store, or the official website. == Platform features == Chat, Call and Share: ayoba enables instant messaging, voice notes, picture sharing, and file sharing with contacts, even if they do not have the app installed. The app supports voice and video calls on both Android and iOS, as well as group chats, help channel and SMS continuity (non ayoba users receive messages as SMS, their responses appear in the ayoba app). Music: ayoba offers a free music player with daily updates on international and African music. Users can find playlists for different genres. Games: ayoba provides a selection of interactive games, including action, adventure, and children's games available on both Android and iOS. Mobile Money Transfers: In certain territories, ayoba supports mobile money transfers using MTN Mobile Money (MoMo) for transactions within the app. MicroApps: ayoba features individual MicroApps within the platform that offer content and services, including streaming channels, podcasts, and specialized apps. The availability of these apps may vary by country. == Operations == ayoba primarily focuses on the following territories: Nigeria, Cameroon, South Africa, Ghana, Côte d'Ivoire, Uganda, Republic of Congo, Benin, Zambia, Tanzania, Kenya, Senegal, Togo, Guinea Bissau, Guinea Conakry, Sudan, South Sudan, and Liberia. The company operates from its offices in Cape Town and Johannesburg, South Africa. David Gillaranz served as the CEO from 2019 to 2021, and Burak Akinci has been the CEO since 2021.

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  Language Computer Corporation

  Language Computer Corporation (LCC) is a natural language processing research company based in Richardson, Texas. The company develops a variety of natural language processing products, including software for question answering, information extraction, and automatic summarization. Since its founding in 1995, the low-profile company has landed significant United States Government contracts, with $8,353,476 in contracts in 2006-2008. While the company has focused primarily on the government software market, LCC has also used its technology to spin off three start-up companies. The first spin-off, known as Lymba Corporation, markets the PowerAnswer question answering product originally developed at LCC. In 2010, LCC's CEO, Andrew Hickl, co-founded two start-ups which made use of the company's technology. These included Swingly, an automatic question answering start-up, and Extractiv, an information extraction service that was founded in partnership with Houston, Texas-based 80legs.

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  Webmail

  Webmail (or web-based email) is an email service that can be accessed using a standard web browser. It contrasts with email service accessible through a specialised email client software. Additionally, many internet service providers (ISP) provide webmail as part of their internet service package. Similarly, some web hosting providers also provide webmail as a part of their hosting package. As with any web application, webmail's main advantage over the use of a desktop email client is the ability to send and receive email anywhere from a web browser. == History == === Early implementations === The first Web Mail implementation was developed at CERN in 1993 by Phillip Hallam-Baker as a test of the HTTP protocol stack, but was not developed further. In the next two years, however, several people produced working webmail applications. In Europe, there were three implementations, Søren Vejrum's "WWW Mail", Luca Manunza's "WebMail", and Remy Wetzels' "WebMail". Søren Vejrum's "WWW Mail" was written when he was studying and working at the Copenhagen Business School in Denmark, and was released on February 28, 1995. Luca Manunza's "WebMail" was written while he was working at CRS4 in Sardinia, from an idea of Gianluigi Zanetti, with the first source release on March 30, 1995. Remy Wetzels' "WebMail" was written while he was studying at the Eindhoven University of Technology in the Netherlands for the DSE and was released early January 1995. In the United States, Matt Mankins wrote "Webex", and Bill Fitler, while at Lotus cc:Mail, began working on an implementation which he demonstrated publicly at Lotusphere on January 24, 1995. Customers who saw the cc:Mail demonstration were very enthusiastic, one recalling that they were "like an angry mob. People were yelling, 'We want this now!'". Matt Mankins, under the supervision of Dr. Burt Rosenberg at the University of Miami, released his "Webex" application source code in a post to comp.mail.misc on August 8, 1995, although it had been in use as the primary email application at the School of Architecture where Mankins worked for some months prior. Bill Fitler's webmail implementation was further developed as a commercial product, which Lotus announced and released in the fall of 1995 as cc:Mail for the World Wide Web 1.0; thereby providing an alternative means of accessing a cc:Mail message store (the usual means being a cc:Mail desktop application that operated either via dialup or within the confines of a local area network). Early commercialization of webmail was also achieved when "Webex" began to be sold by Mankins' company, DotShop, Inc., at the end of 1995. Within DotShop, "Webex" changed its name to "EMUmail"; which would be sold to companies like UPS and Rackspace until its sale to Accurev in 2001. EMUmail was one of the first applications to feature a free version that included embedded advertising, as well as a licensed version that did not. Hotmail and Four11's RocketMail both launched in 1996 as free services and immediately became very popular. === Widespread deployment === As the 1990s progressed, and into the 2000s, it became more common for the general public to have access to webmail because: many Internet service providers (such as EarthLink) and web hosting providers (such as Verio) began bundling webmail into their service offerings (often in parallel with POP/SMTP services); many other enterprises (such as universities and large corporations) also started offering webmail as a way for their user communities to access their email (either locally managed or outsourced); webmail service providers (such as Hotmail and RocketMail) emerged in 1996 as a free service to the general public, and rapidly gained in popularity. In some cases, webmail application software is developed in-house by the organizations running and managing the application, and in some cases it is obtained from software companies that develop and sell such applications, usually as part of an integrated mail server package (an early example being Netscape Messaging Server). The market for webmail application software has continued into the 2010s. == Rendering and compatibility == Email users may find the use of both a webmail client and a desktop client using the POP3 protocol presents some difficulties. For example, email messages that are downloaded by the desktop client and are removed from the server will no longer be available on the webmail client. The user is limited to previewing messages using the web client before they are downloaded by the desktop email client. However, one may choose to leave the emails on the server, in which case this problem does not occur. The use of both a webmail client and a desktop client using the IMAP4 protocol allows the contents of the mailbox to be consistently displayed in both the webmail and desktop clients and any action the user performs on messages in one interface will be reflected when the email is accessed via the other interface. There are significant differences in rendering capabilities for many popular webmail services such as Gmail, Outlook.com and Yahoo! Mail. Due to the varying treatment of HTML tags, such as