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Google Books Ngram Viewer

The Google Books Ngram Viewer is an online search engine that charts the frequencies of any set of search strings using a yearly count of n-grams found in printed sources published between 1500 and 2022 in Google's text corpora in English, Chinese (simplified), French, German, Hebrew, Italian, Russian, or Spanish. There are also some specialized English corpora, such as American English, British English, and English Fiction. The program can search for a word or a phrase. The n-grams are matched with the text within the selected corpus, and if found in 40 or more books, are then displayed as a graph. The program supports searches for parts of speech and wildcards. It is routinely used in research. == History == The Ngram Viewer was created by Google software engineers Will Brockman and Jon Orwant , who teamed up with Harvard researchers Jean-Baptiste Michel and Erez Lieberman Aiden. The service was released on December 16, 2010. Before the release, it was difficult to quantify the rate of linguistic change because of the absence of a database that was designed for this purpose, said Steven Pinker, a well-known linguist who was one of the co-authors of the Science paper published on the same day. The Google Books Ngram Viewer was developed in the hope of opening a new window to quantitative research in the humanities field, and the database contained 500 billion words from 5.2 million books publicly available from the very beginning. The intended audience was scholarly, but the Google Books Ngram Viewer made it possible for anyone with a computer to see a graph that represents the diachronic change of the use of words and phrases with ease. Lieberman said in response to The New York Times that the developers aimed to provide even children with the ability to browse cultural trends throughout history. In the Science paper, Lieberman and his collaborators called the method of high-volume data analysis in digitized texts "culturomics". == Usage == Commas delimit user-entered search terms, where each comma-separated term is searched in the database as an n-gram (for example, "nursery school" is a 2-gram or bigram). The Ngram Viewer then returns a plotted line chart. Due to limitations on the size of the Ngram database, only matches found in at least 40 books are indexed. == Limitations == The data sets of the Ngram Viewer have been criticized for their reliance upon inaccurate optical character recognition (OCR) and for including large numbers of incorrectly dated and categorized texts. Because of these errors, and because they are uncontrolled for bias (such as the increasing amount of scientific literature, which causes other terms to appear to decline in popularity), care must be taken in using the corpora to study language or test theories. Furthermore, the data sets may not reflect general linguistic or cultural change and can only hint at such an effect because they do not involve any metadata like date published, author, length, or genre, to avoid any potential copyright infringements. Systemic errors like the confusion of s and f in pre-19th century texts (due to the use of ſ, the long s, which is similar in appearance to f) can cause systemic bias. Although the Google Books team claims that the results are reliable from 1800 onwards, poor OCR and insufficient data mean that frequencies given for languages such as Chinese may only be accurate from 1970 onward, with earlier parts of the corpus showing no results at all for common terms, and data for some years containing more than 50% noise. Guidelines for doing research with data from Google Ngram have been proposed that try to address some of the issues discussed above.
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Ugly duckling theorem

The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. == Mathematical formula == Suppose there are n things in the universe, and one wants to put them into classes or categories. One has no preconceived ideas or biases about what sorts of categories are "natural" or "normal" and what are not. So one has to consider all the possible classes that could be, all the possible ways of making a set out of the n objects. There are 2 n {\displaystyle 2^{n}} such ways, the size of the power set of n objects. One can use that to measure the similarity between two objects, and one would see how many sets they have in common. However, one cannot. Any two objects have exactly the same number of classes in common if we can form any possible class, namely 2 n − 1 {\displaystyle 2^{n-1}} (half the total number of classes there are). To see this is so, one may imagine each class is represented by an n-bit string (or binary encoded integer), with a zero for each element not in the class and a one for each element in the class. As one finds, there are 2 n {\displaystyle 2^{n}} such strings. As all possible choices of zeros and ones are there, any two bit-positions will agree exactly half the time. One may pick two elements and reorder the bits so they are the first two, and imagine the numbers sorted lexicographically. The first 2 n / 2 {\displaystyle 2^{n}/2} numbers will have bit #1 set to zero, and the second 2 n / 2 {\displaystyle 2^{n}/2} will have it set to one. Within each of those blocks, the top 2 n / 4 {\displaystyle 2^{n}/4} will have bit #2 set to zero and the other 2 n / 4 {\displaystyle 2^{n}/4} will have it as one, so they agree on two blocks of 2 n / 4 {\displaystyle 2^{n}/4} or on half of all the cases, no matter which two elements one picks. So if we have no preconceived bias about which categories are better, everything is then equally similar (or equally dissimilar). The number of predicates simultaneously satisfied by two non-identical elements is constant over all such pairs. Thus, some kind of inductive bias is needed to make judgements to prefer certain categories over others. === Boolean functions === Let x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} be a set of vectors of k {\displaystyle k} booleans each. The ugly duckling is the vector which is least like the others. Given the booleans, this can be computed using Hamming distance. However, the choice of boolean features to consider could have been somewhat arbitrary. Perhaps there were features derivable from the original features that were important for identifying the ugly duckling. The set of booleans in the vector can be extended with new features computed as boolean functions of the k {\displaystyle k} original features. The only canonical way to do this is to extend it with all possible Boolean functions. The resulting completed vectors have 2 k {\displaystyle 2^{k}} features. The ugly duckling theorem states that there is no ugly duckling because any two completed vectors will either be equal or differ in exactly half of the features. Proof. Let x and y be two vectors. If they are the same, then their completed vectors must also be the same because any Boolean function of x will agree with the same Boolean function of y. If x and y are different, then there exists a coordinate i {\displaystyle i} where the i {\displaystyle i} -th coordinate of x {\displaystyle x} differs from the i {\displaystyle i} -th coordinate of y {\displaystyle y} . Now the completed features contain every Boolean function on k {\displaystyle k} Boolean variables, with each one exactly once. Viewing these Boolean functions as polynomials in k {\displaystyle k} variables over GF(2), segregate the functions into pairs ( f , g ) {\displaystyle (f,g)} where f {\displaystyle f} contains the i {\displaystyle i} -th coordinate as a linear term and g {\displaystyle g} is f {\displaystyle f} without that linear term. Now, for every such pair ( f , g ) {\displaystyle (f,g)} , x {\displaystyle x} and y {\displaystyle y} will agree on exactly one of the two functions. If they agree on one, they must disagree on the other and vice versa. (This proof is believed to be due to Watanabe.) == Discussion == A possible way around the ugly duckling theorem would be to introduce a constraint on how similarity is measured by limiting the properties involved in classification, for instance, between A and B. However Medin et al. (1993) point out that this does not actually resolve the arbitrariness or bias problem since in what respects A is similar to B: "varies with the stimulus context and task, so that there is no unique answer, to the question of how similar is one object to another". For example, "a barberpole and a zebra would be more similar than a horse and a zebra if the feature striped had sufficient weight. Of course, if these feature weights were fixed, then these similarity relations would be constrained". Yet the property "striped" as a weight 'fix' or constraint is arbitrary itself, meaning: "unless one can specify such criteria, then the claim that categorization is based on attribute matching is almost entirely vacuous". Stamos (2003) remarked that some judgments of overall similarity are non-arbitrary in the sense they are useful: "Presumably, people's perceptual and conceptual processes have evolved that information that matters to human needs and goals can be roughly approximated by a similarity heuristic... If you are in the jungle and you see a tiger but you decide not to stereotype (perhaps because you believe that similarity is a false friend), then you will probably be eaten. In other words, in the biological world stereotyping based on veridical judgments of overall similarity statistically results in greater survival and reproductive success." Unless some properties are considered more salient, or 'weighted' more important than others, everything will appear equally similar, hence Watanabe (1986) wrote: "any objects, in so far as they are distinguishable, are equally similar". In a weaker setting that assumes infinitely many properties, Murphy and Medin (1985) give an example of two putative classified things, plums and lawnmowers: "Suppose that one is to list the attributes that plums and lawnmowers have in common in order to judge their similarity. It is easy to see that the list could be infinite: Both weigh less than 10,000 kg (and less than 10,001 kg), both did not exist 10,000,000 years ago (and 10,000,001 years ago), both cannot hear well, both can be dropped, both take up space, and so on. Likewise, the list of differences could be infinite… any two entities can be arbitrarily similar or dissimilar by changing the criterion of what counts as a relevant attribute." According to Woodward, the ugly duckling theorem is related to Schaffer's Conservation Law for Generalization Performance, which states that all algorithms for learning of boolean functions from input/output examples have the same overall generalization performance as random guessing. The latter result is generalized by Woodward to functions on countably infinite domains.
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Error level analysis

Error level analysis (ELA) is the analysis of compression artifacts in digital data with lossy compression such as JPEG. == Principles == When used, lossy compression is normally applied uniformly to a set of data, such as an image, resulting in a uniform level of compression artifacts. Alternatively, the data may consist of parts with different levels of compression artifacts. This difference may arise from the different parts having been repeatedly subjected to the same lossy compression a different number of times, or the different parts having been subjected to different kinds of lossy compression. A difference in the level of compression artifacts in different parts of the data may therefore indicate that the data has been edited. In the case of JPEG, even a composite with parts subjected to matching compressions will have a difference in the compression artifacts. In order to make the typically faint compression artifacts more readily visible, the data to be analyzed is subjected to an additional round of lossy compression, this time at a known, uniform level, and the result is subtracted from the original data under investigation. The resulting difference image is then inspected manually for any variation in the level of compression artifacts. In 2007, N. Krawetz denoted this method "error level analysis". Additionally, digital data formats such as JPEG sometimes include metadata describing the specific lossy compression used. If in such data the observed compression artifacts differ from those expected from the given metadata description, then the metadata may not describe the actual compressed data, and thus indicate that the data have been edited. == Limitations == By its nature, data without lossy compression, such as a PNG image, cannot be subjected to error level analysis. Consequently, since editing could have been performed on data without lossy compression with lossy compression applied uniformly to the edited, composite data, the presence of a uniform level of compression artifacts does not rule out editing of the data. Additionally, any non-uniform compression artifacts in a composite may be removed by subjecting the composite to repeated, uniform lossy compression. Also, if the image color space is reduced to 256 colors or less, for example, by conversion to GIF, then error level analysis will generate useless results. More significant, the actual interpretation of the level of compression artifacts in a given segment of the data is subjective, and the determination of whether editing has occurred is therefore not robust. == Controversy == In May 2013, Dr Neal Krawetz used error level analysis on the 2012 World Press Photo of the Year and concluded on his Hacker Factor blog that it was "a composite" with modifications that "fail to adhere to the acceptable journalism standards used by Reuters, Associated Press, Getty Images, National Press Photographer's Association, and other media outlets". The World Press Photo organizers responded by letting two independent experts analyze the image files of the winning photographer and subsequently confirmed the integrity of the files. One of the experts, Hany Farid, said about error level analysis that "It incorrectly labels altered images as original and incorrectly labels original images as altered with the same likelihood". Krawetz responded by clarifying that "It is up to the user to interpret the results. Any errors in identification rest solely on the viewer". In May 2015, the citizen journalism team Bellingcat wrote that error level analysis revealed that the Russian Ministry of Defense had edited satellite images related to the Malaysia Airlines Flight 17 disaster. In a reaction to this, image forensics expert Jens Kriese said about error level analysis: "The method is subjective and not based entirely on science", and that it is "a method used by hobbyists". On his Hacker Factor Blog, the inventor of error level analysis Neal Krawetz criticized both Bellingcat's use of error level analysis as "misinterpreting the results" but also on several points Jens Kriese's "ignorance" regarding error level analysis.
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Neural style transfer

Neural style transfer (NST) software algorithms are able to manipulate digital images, or videos, in order to adopt the appearance or visual style of another image. NST algorithms are characterized by their use of deep neural networks for the sake of image transformation. Common uses for NST are the creation of artificial artwork from photographs, for example by transferring the appearance of famous paintings to user-supplied photographs. Several notable mobile apps use NST techniques for this purpose, including DeepArt and Prisma. This method has been used by artists and designers around the globe to develop new artwork based on existent style(s). == History == NST is an example of image stylization, a problem studied for over two decades within the field of non-photorealistic rendering. The first two example-based style transfer algorithms were image analogies and image quilting. Both of these methods were based on patch-based texture synthesis algorithms. Given a training pair of images–a photo and an artwork depicting that photo–a transformation could be learned and then applied to create new artwork from a new photo, by analogy. If no training photo was available, it would need to be produced by processing the input artwork; image quilting did not require this processing step, though it was demonstrated on only one style. NST was first published in the paper "A Neural Algorithm of Artistic Style" by Leon Gatys et al., originally released to ArXiv 2015, and subsequently accepted by the peer-reviewed CVPR conference in 2016. The original paper used a VGG-19 architecture that has been pre-trained to perform object recognition using the ImageNet dataset. In 2017, Google AI introduced a method that allows a single deep convolutional style transfer network to learn multiple styles at the same time. This algorithm permits style interpolation in real-time, even when done on video media. == Mathematics == This section closely follows the original paper. === Overview === The idea of Neural Style Transfer (NST) is to take two images—a content image p → {\displaystyle {\vec {p}}} and a style image a → {\displaystyle {\vec {a}}} —and generate a third image x → {\displaystyle {\vec {x}}} that minimizes a weighted combination of two loss functions: a content loss L content ( p → , x → ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})} and a style loss L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})} . The total loss is a linear sum of the two: L NST ( p → , a → , x → ) = α L content ( p → , x → ) + β L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{NST}}({\vec {p}},{\vec {a}},{\vec {x}})=\alpha {\mathcal {L}}_{\text{content}}({\vec {p}},{\vec {x}})+\beta {\mathcal {L}}_{\text{style}}({\vec {a}},{\vec {x}})} By jointly minimizing the content and style losses, NST generates an image that blends the content of the content image with the style of the style image. Both the content loss and the style loss measures the similarity of two images. The content similarity is the weighted sum of squared-differences between the neural activations of a single convolutional neural network (CNN) on two images. The style similarity is the weighted sum of Gram matrices within each layer (see below for details). The original paper used a VGG-19 CNN, but the method works for any CNN. === Symbols === Let x → {\textstyle {\vec {x}}} be an image input to a CNN. Let F l ∈ R N l × M l {\textstyle F^{l}\in \mathbb {R} ^{N_{l}\times M_{l}}} be the matrix of filter responses in layer l {\textstyle l} to the image x → {\textstyle {\vec {x}}} , where: N l {\textstyle N_{l}} is the number of filters in layer l {\textstyle l} ; M l {\textstyle M_{l}} is the height times the width (i.e. number of pixels) of each filter in layer l {\textstyle l} ; F i j l ( x → ) {\textstyle F_{ij}^{l}({\vec {x}})} is the activation of the i th {\textstyle i^{\text{th}}} filter at position j {\textstyle j} in layer l {\textstyle l} . A given input image x → {\textstyle {\vec {x}}} is encoded in each layer of the CNN by the filter responses to that image, with higher layers encoding more global features, but losing details on local features. === Content loss === Let p → {\textstyle {\vec {p}}} be an original image. Let x → {\textstyle {\vec {x}}} be an image that is generated to match the content of p → {\textstyle {\vec {p}}} . Let P l {\textstyle P^{l}} be the matrix of filter responses in layer l {\textstyle l} to the image p → {\textstyle {\vec {p}}} . The content loss is defined as the squared-error loss between the feature representations of the generated image and the content image at a chosen layer l {\displaystyle l} of a CNN: L content ( p → , x → , l ) = 1 2 ∑ i , j ( A i j l ( x → ) − A i j l ( p → ) ) 2 {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)={\frac {1}{2}}\sum _{i,j}\left(A_{ij}^{l}({\vec {x}})-A_{ij}^{l}({\vec {p}})\right)^{2}} where A i j l ( x → ) {\displaystyle A_{ij}^{l}({\vec {x}})} and A i j l ( p → ) {\displaystyle A_{ij}^{l}({\vec {p}})} are the activations of the i th {\displaystyle i^{\text{th}}} filter at position j {\displaystyle j} in layer l {\displaystyle l} for the generated and content images, respectively. Minimizing this loss encourages the generated image to have similar content to the content image, as captured by the feature activations in the chosen layer. The total content loss is a linear sum of the content losses of each layer: L content ( p → , x → ) = ∑ l v l L content ( p → , x → , l ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})=\sum _{l}v_{l}{\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)} , where the v l {\displaystyle v_{l}} are positive real numbers chosen as hyperparameters. === Style loss === The style loss is based on the Gram matrices of the generated and style images, which capture the correlations between different filter responses at different layers of the CNN: L style ( a → , x → ) = ∑ l = 0 L w l E l , {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})=\sum _{l=0}^{L}w_{l}E_{l},} where E l = 1 4 N l 2 M l 2 ∑ i , j ( G i j l ( x → ) − G i j l ( a → ) ) 2 . {\displaystyle E_{l}={\frac {1}{4N_{l}^{2}M_{l}^{2}}}\sum _{i,j}\left(G_{ij}^{l}({\vec {x}})-G_{ij}^{l}({\vec {a}})\right)^{2}.} Here, G i j l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})} and G i j l ( a → ) {\displaystyle G_{ij}^{l}({\vec {a}})} are the entries of the Gram matrices for the generated and style images at layer l {\displaystyle l} . Explicitly, G i j l ( x → ) = ∑ k F i k l ( x → ) F j k l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})=\sum _{k}F_{ik}^{l}({\vec {x}})F_{jk}^{l}({\vec {x}})} Minimizing this loss encourages the generated image to have similar style characteristics to the style image, as captured by the correlations between feature responses in each layer. The idea is that activation pattern correlations between filters in a single layer captures the "style" on the order of the receptive fields at that layer. Similarly to the previous case, the w l {\displaystyle w_{l}} are positive real numbers chosen as hyperparameters. === Hyperparameters === In the original paper, they used a particular choice of hyperparameters. The style loss is computed by w l = 0.2 {\displaystyle w_{l}=0.2} for the outputs of layers conv1_1, conv2_1, conv3_1, conv4_1, conv5_1 in the VGG-19 network, and zero otherwise. The content loss is computed by w l = 1 {\displaystyle w_{l}=1} for conv4_2, and zero otherwise. The ratio α / β ∈ [ 5 , 50 ] × 10 − 4 {\displaystyle \alpha /\beta \in [5,50]\times 10^{-4}} . === Training === Image x → {\displaystyle {\vec {x}}} is initially approximated by adding a small amount of white noise to input image p → {\displaystyle {\vec {p}}} and feeding it through the CNN. Then we successively backpropagate this loss through the network with the CNN weights fixed in order to update the pixels of x → {\displaystyle {\vec {x}}} . After several thousand epochs of training, an x → {\displaystyle {\vec {x}}} (hopefully) emerges that matches the style of a → {\displaystyle {\vec {a}}} and the content of p → {\displaystyle {\vec {p}}} . As of 2017, when implemented on a GPU, it takes a few minutes to converge. == Extensions == In some practical implementations, it is noted that the resulting image has too much high-frequency artifact, which can be suppressed by adding the total variation to the total loss. Compared to VGGNet, AlexNet does not work well for neural style transfer. NST has also been extended to videos. Subsequent work improved the speed of NST for images by using special-purpose normalizations. In a paper by Fei-Fei Li et al. adopted a different regularized loss metric and accelerated method for training to produce results in real-time (three orders of magnitude faster than Gatys). Their idea was to use not the pixel-based loss defined above but rather a 'perceptual loss' measuring t
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GEPIR

GEPIR (Global Electronic Party Information Registry) was a distributed database operated and owned by GS1 that contains basic information on over 1,000,000 companies in over 100 countries. The database could be searched by Global Trade Item Number (GTIN) code (including Universal Product Code (UPC) and EAN-13 codes), container Code (Serial Shipping Container Code (SSCC)), location number (Global Location Number (GLN)), and (in some countries) the company name. A SOAP webservice existed for API access. As of end December 2023, GEPIR was replaced by a service called Verified by GS1. While it operated, GEPIR had more than 1 million members in more than 100 countries. In 2013, all GS1 111 member organisations joined GEPIR. == Access == GEPIR was accessible for free in almost all countries but the number of request per day was limited (from 20 to 30). Since October 2013, GS1 France restricts access to GEPIR to companies (registration with SIREN code was required to use it). A premium access service had been created by GS1 France in January 2010 which allows companies to use GS1 web and SOAP interface without any limit. == System architecture == GEPIR was a lookup service coordinated by the GS1 GO that provided all end users with the ability to look up information about GS1 Identification Keys. Depending on the service, systems were provided by GS1 Member Organisations (MOs) or 3rd party service providers, or both. Where a GS1 MO did not choose to provide the service directly to its end users, the GS1 Global Office provided the service for that geography. Some services involved a technical component deployed by the GS1 Global Office that coordinates the systems provided by GS1 MOs and/or 3rd party service providers. The GEPIR service was provided by systems deployed by GS1 MOs, with the GS1 GO providing a central point of coordination to federate the local systems. The GS1 GO also provides the MO-level service for MOs that could not or did not wish to deploy their own system.
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Scale-space axioms

In image processing and computer vision, a scale space framework can be used to represent an image as a family of gradually smoothed images. This framework is very general and a variety of scale space representations exist. A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision. == Scale space axioms for the linear scale-space representation == The linear scale space representation L ( x , y , t ) = ( T t f ) ( x , y ) = g ( x , y , t ) ∗ f ( x , y ) {\displaystyle L(x,y,t)=(T_{t}f)(x,y)=g(x,y,t)f(x,y)} of signal f ( x , y ) {\displaystyle f(x,y)} obtained by smoothing with the Gaussian kernel g ( x , y , t ) {\displaystyle g(x,y,t)} satisfies a number of properties 'scale-space axioms' that make it a special form of multi-scale representation: linearity T t ( a f + b h ) = a T t f + b T t h {\displaystyle T_{t}(af+bh)=aT_{t}f+bT_{t}h} where f {\displaystyle f} and h {\displaystyle h} are signals while a {\displaystyle a} and b {\displaystyle b} are constants, shift invariance T t S ( Δ x , Δ y ) f = S ( Δ x , Δ y ) T t f {\displaystyle T_{t}S_{(\Delta x,\Delta _{y})}f=S_{(\Delta x,\Delta _{y})}T_{t}f} where S ( Δ x , Δ y ) {\displaystyle S_{(\Delta x,\Delta _{y})}} denotes the shift (translation) operator ( S ( Δ x , Δ y ) f ) ( x , y ) = f ( x − Δ x , y − Δ y ) {\displaystyle (S_{(\Delta x,\Delta _{y})}f)(x,y)=f(x-\Delta x,y-\Delta y)} semi-group structure g ( x , y , t 1 ) ∗ g ( x , y , t 2 ) = g ( x , y , t 1 + t 2 ) {\displaystyle g(x,y,t_{1})g(x,y,t_{2})=g(x,y,t_{1}+t_{2})} with the associated cascade smoothing property L ( x , y , t 2 ) = g ( x , y , t 2 − t 1 ) ∗ L ( x , y , t 1 ) {\displaystyle L(x,y,t_{2})=g(x,y,t_{2}-t_{1})L(x,y,t_{1})} existence of an infinitesimal generator A {\displaystyle A} ∂ t L ( x , y , t ) = ( A L ) ( x , y , t ) {\displaystyle \partial _{t}L(x,y,t)=(AL)(x,y,t)} non-creation of local extrema (zero-crossings) in one dimension, non-enhancement of local extrema in any number of dimensions ∂ t L ( x , y , t ) ≤ 0 {\displaystyle \partial _{t}L(x,y,t)\leq 0} at spatial maxima and ∂ t L ( x , y , t ) ≥ 0 {\displaystyle \partial _{t}L(x,y,t)\geq 0} at spatial minima, rotational symmetry g ( x , y , t ) = h ( x 2 + y 2 , t ) {\displaystyle g(x,y,t)=h(x^{2}+y^{2},t)} for some function h {\displaystyle h} , scale invariance g ^ ( ω x , ω y , t ) = h ^ ( ω x φ ( t ) , ω x φ ( t ) ) {\displaystyle {\hat {g}}(\omega _{x},\omega _{y},t)={\hat {h}}({\frac {\omega _{x}}{\varphi (t)}},{\frac {\omega _{x}}{\varphi (t)}})} for some functions φ {\displaystyle \varphi } and h ^ {\displaystyle {\hat {h}}} where g ^ {\displaystyle {\hat {g}}} denotes the Fourier transform of g {\displaystyle g} , positivity g ( x , y , t ) ≥ 0 {\displaystyle g(x,y,t)\geq 0} , normalization ∫ x = − ∞ ∞ ∫ y = − ∞ ∞ g ( x , y , t ) d x d y = 1 {\displaystyle \int _{x=-\infty }^{\infty }\int _{y=-\infty }^{\infty }g(x,y,t)\,dx\,dy=1} . In fact, it can be shown that the Gaussian kernel is a unique choice given several different combinations of subsets of these scale-space axioms: most of the axioms (linearity, shift-invariance, semigroup) correspond to scaling being a semigroup of shift-invariant linear operator, which is satisfied by a number of families integral transforms, while "non-creation of local extrema" for one-dimensional signals or "non-enhancement of local extrema" for higher-dimensional signals are the crucial axioms which relate scale-spaces to smoothing (formally, parabolic partial differential equations), and hence select for the Gaussian. The Gaussian kernel is also separable in Cartesian coordinates, i.e. g ( x , y , t ) = g ( x , t ) g ( y , t ) {\displaystyle g(x,y,t)=g(x,t)\,g(y,t)} . Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities, including image deformations caused by viewing variations, approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. In this theory, rotational symmetry is not imposed as a necessary scale-space axiom and is instead replaced by requirements of affine and/or Galilean covariance. The generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. In the computer vision, image processing and signal processing literature there are many other multi-scale approaches, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; please see the article on related multi-scale approaches. There has also been work on discrete scale-space concepts that carry the scale-space properties over to the discrete domain; see the article on scale space implementation for examples and references.
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Mistral Vibe

Mistral Vibe or Vibe (Le Chat until May 2026), is a chatbot that uses generative artificial intelligence developed in France by Mistral AI. Mistral Vibe is available in iOS and Android. Its services are operated on a freemium model. == History == In February 2024, Mistral AI released Le Chat. In January 2025, Mistral AI made a content deal with Agence France-Presse (AFP) that lets Le Chat query AFP's entire archive dating back to 1983. On 6 February 2025, a mobile app for Le Chat was released for iOS and Android, and a subscription tier, Pro, was introduced at a cost of $14.99 per month. In July 2025, Mistral AI released Voxtral, an open-source language model that understands and generates audio. Mistral introduced a voice mode for chatting that uses Voxtral, and projects, which allows grouping chats and files. In September 2025, Le Chat introduced the capability to remember previous conversations. In May 2026, Mistral AI announced the rebrand from Le Chat to Mistral Vibe and new features were introduced at the same time.
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Outline of natural language processing

Natural language processing is computer activity in which computers are entailed to analyze, understand, alter, or generate natural language. This includes the automation of any or all linguistic forms, activities, or methods of communication, such as conversation, correspondence, reading, written composition, dictation, publishing, translation, lip reading, and so on. Natural-language processing is also the name of the branch of computer science, artificial intelligence, and linguistics concerned with enabling computers to engage in communication using natural language(s) in all forms, including but not limited to speech, print, writing, and signing. The following outline is provided as an overview of and topical guide to natural-language processing: == Natural-language processing == Natural-language processing can be described as all of the following: A field of science – systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. An applied science – field that applies human knowledge to build or design useful things. A field of computer science – scientific and practical approach to computation and its applications. A branch of artificial intelligence – intelligence of machines and robots and the branch of computer science that aims to create it. A subfield of computational linguistics – interdisciplinary field dealing with the statistical or rule-based modeling of natural language from a computational perspective. An application of engineering – science, skill, and profession of acquiring and applying scientific, economic, social, and practical knowledge, in order to design and also build structures, machines, devices, systems, materials and processes. An application of software engineering – application of a systematic, disciplined, quantifiable approach to the design, development, operation, and maintenance of software, and the study of these approaches; that is, the application of engineering to software. A subfield of computer programming – process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages (such as Java, C++, C#, Python, etc.). The purpose of programming is to create a set of instructions that computers use to perform specific operations or to exhibit desired behaviors. A subfield of artificial intelligence programming – A type of system – set of interacting or interdependent components forming an integrated whole or a set of elements (often called 'components' ) and relationships which are different from relationships of the set or its elements to other elements or sets. A system that includes software – software is a collection of computer programs and related data that provides the instructions for telling a computer what to do and how to do it. Software refers to one or more computer programs and data held in the storage of the computer. In other words, software is a set of programs, procedures, algorithms and its documentation concerned with the operation of a data processing system. A type of technology – making, modification, usage, and knowledge of tools, machines, techniques, crafts, systems, methods of organization, in order to solve a problem, improve a preexisting solution to a problem, achieve a goal, handle an applied input/output relation or perform a specific function. It can also refer to the collection of such tools, machinery, modifications, arrangements and procedures. Technologies significantly affect human as well as other animal species' ability to control and adapt to their natural environments. A form of computer technology – computers and their application. NLP makes use of computers, image scanners, microphones, and many types of software programs. Language technology – consists of natural-language processing (NLP) and computational linguistics (CL) on the one hand, and speech technology on the other. It also includes many application oriented aspects of these. It is often called human language technology (HLT). == Prerequisite technologies == The following technologies make natural-language processing possible: Communication – the activity of a source sending a message to a receiver Language – Speech – Writing – Computing – Computers – Computer programming – Information extraction – User interface – Software – Text editing – program used to edit plain text files Word processing – piece of software used for composing, editing, formatting, printing documents Input devices – pieces of hardware for sending data to a computer to be processed Computer keyboard – typewriter style input device whose input is converted into various data depending on the circumstances Image scanners – == Subfields of natural-language processing == Information extraction (IE) – field concerned in general with the extraction of semantic information from text. This covers tasks such as named-entity recognition, coreference resolution, relationship extraction, etc. Ontology engineering – field that studies the methods and methodologies for building ontologies, which are formal representations of a set of concepts within a domain and the relationships between those concepts. Speech processing – field that covers speech recognition, text-to-speech and related tasks. Statistical natural-language processing – Statistical semantics – a subfield of computational semantics that establishes semantic relations between words to examine their contexts. Distributional semantics – a subfield of statistical semantics that examines the semantic relationship of words across a corpora or in large samples of data. == Related fields == Natural-language processing contributes to, and makes use of (the theories, tools, and methodologies from), the following fields: Automated reasoning – area of computer science and mathematical logic dedicated to understanding various aspects of reasoning, and producing software which allows computers to reason completely, or nearly completely, automatically. A sub-field of artificial intelligence, automatic reasoning is also grounded in theoretical computer science and philosophy of mind. Linguistics – scientific study of human language. Natural-language processing requires understanding of the structure and application of language, and therefore it draws heavily from linguistics. Applied linguistics – interdisciplinary field of study that identifies, investigates, and offers solutions to language-related real-life problems. Some of the academic fields related to applied linguistics are education, linguistics, psychology, computer science, anthropology, and sociology. Some of the subfields of applied linguistics relevant to natural-language processing are: Bilingualism / Multilingualism – Computer-mediated communication (CMC) – any communicative transaction that occurs through the use of two or more networked computers. Research on CMC focuses largely on the social effects of different computer-supported communication technologies. Many recent studies involve Internet-based social networking supported by social software. Contrastive linguistics – practice-oriented linguistic approach that seeks to describe the differences and similarities between a pair of languages. Conversation analysis (CA) – approach to the study of social interaction, embracing both verbal and non-verbal conduct, in situations of everyday life. Turn-taking is one aspect of language use that is studied by CA. Discourse analysis – various approaches to analyzing written, vocal, or sign language use or any significant semiotic event. Forensic linguistics – application of linguistic knowledge, methods and insights to the forensic context of law, language, crime investigation, trial, and judicial procedure. Interlinguistics – study of improving communications between people of different first languages with the use of ethnic and auxiliary languages (lingua franca). For instance by use of intentional international auxiliary languages, such as Esperanto or Interlingua, or spontaneous interlanguages known as pidgin languages. Language assessment – assessment of first, second or other language in the school, college, or university context; assessment of language use in the workplace; and assessment of language in the immigration, citizenship, and asylum contexts. The assessment may include analyses of listening, speaking, reading, writing or cultural understanding, with respect to understanding how the language works theoretically and the ability to use the language practically. Language pedagogy – science and art of language education, including approaches and methods of language teaching and study. Natural-language processing is used in programs designed to teach language, including first- and second-language training. Language planning – Language policy – Lexicography – Literacies – Pragmatics – Second-language acquisition – Stylistics – Translation – Comp
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SAP StreamWork

SAP StreamWork is an enterprise collaboration tool from SAP SE released in March 2010, and discontinued in December 2015. StreamWork allowed real-time collaboration like Google Wave, but focused on business activities such as analyzing data, planning meetings, and making decisions. It incorporated technology from Box.net and Evernote to allow users to connect to online files and documents, and document-reader technology from Scribd allowed users to view documents directly within its environment. StreamWork supported the OpenSocial set of application programming interfaces (APIs), allowing it to connect to tools built by third-party developers, such as Google Docs. A version of StreamWork intended for large enterprises used a virtual appliance based on Novell's SUSE Linux Enterprise to connect it to business systems, including those from SAP.
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Rhetorical structure theory

Rhetorical structure theory (RST) is a theory of text organization that describes relations that hold between parts of text. It was originally developed by William Mann, Sandra Thompson, Christian M. I. M. Matthiessen and others at the University of Southern California's Information Sciences Institute (ISI) and defined in a 1988 paper. The theory was developed as part of studies of computer-based text generation. Natural language processing researchers later began using RST in automatic summarization and other applications. It explains coherence by postulating a hierarchical, connected structure of texts, which are labeled using a small, predefined inventory of relation types - for example, one part of a text may provide an elaboration on another part, provide background or specify a cause for another. In the 2000s, following the release of the first large-scale dataset implementing the theory, the RST Discourse Treebank (RST-DT), Daniel Marcu demonstrated the feasibility of practical applications of RST to discourse parsing and summarization at ISI. Originally limited to written text, subsequent work in the 2010s expanded RST to spoken language analysis, and the framework has been applied to a variety of languages including Farsi, German, Mandarin Chinese, Russian and Spanish. Following the introduction of Transformers, LLMs have been applied to automatic RST parsing, with results approaching human performance on parsing text in English. == Rhetorical relations == Rhetorical relations, also called coherence or discourse relations, are paratactic (coordinate) or hypotactic (subordinate) relations that hold across two or more text spans. The logical arrangement of relations in a text contributes to its coherence by connecting different propositions in a relational structure. RST using rhetorical relations provides a systematic way for an analyst to analyze the underlying intention of a text. The analysis is usually built by reading the text and constructing a tree using the relations. The following example is a title and summary, appearing at the top of an article in Scientific American magazine (adapted from Ramachandran and Anstis, 1986). The original text, broken into numbered units, is: [Title:] The Perception of Apparent Motion [Abstract:] When the motion of an intermittently seen object is ambiguous the visual system resolves confusion by applying some tricks that reflect a built-in knowledge of properties of the physical world. In the figure, the numbers 1-5 show the corresponding units from the text above. Unit 5 provides an "elaboration" on unit 4, and therefore constitutes a less prominent satellite of unit 4, which acts as a nucleus for the relation. Units 4-5 form a relation "Means", explaining the means by which the visual system resolves confusion. Unit 3 is the Central Discourse Unit (CDU) of the text, since all units point to it directly or indirectly. Similarly units 1 and 2 form "preparation" and "circumstance" relations relative to their nuclei. Groups of units which serve as a satellite or nucleus together are called complex discourse units, and always span a set of adjacent EDUs. == Nuclearity in discourse == RST establishes two different types of units. Nuclei are considered as the most important parts of text whereas satellites contribute to the nuclei and are secondary. Nucleus contains basic information and satellite contains additional information about nucleus. The satellite is often incomprehensible without nucleus, whereas a text where satellites have been deleted can be understood to a certain extent. == Hierarchy in the analysis == RST relations are applied recursively in a text, until all units in that text are constituents in an RST relation. The result of such analyses is that RST structure are typically represented as trees, with one top level relation that encompasses other relations at lower levels. == Why RST? == From linguistic point of view, RST proposes a different view of text organization than most linguistic theories. RST points to a tight relation between relations and coherence in text From a computational point of view, it provides a characterization of text relations that has been implemented in different systems and for applications as text generation and summarization. == In design rationale == Computer scientists Ana Cristina Bicharra Garcia and Clarisse Sieckenius de Souz have used RST as the basis of a design rationale system called ADD+. In ADD+, RST is used as the basis for the rhetorical organization of a knowledge base, in a way comparable to other knowledge representation systems such as issue-based information system (IBIS). Similarly, RST has been used in representation schemes for argumentation.
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Computational photography

Computational photography refers to digital image capture and processing techniques that use digital computation instead of optical processes. Computational photography can improve the capabilities of a camera, or introduce features that were not possible at all with film-based photography, or reduce the cost or size of camera elements. Examples of computational photography include in-camera computation of digital panoramas, high-dynamic-range images, and light field cameras. Light field cameras use novel optical elements to capture three-dimensional scene information, which can then be used to produce 3D images, enhanced depth-of-field, and selective de-focusing (or "post focus"). Enhanced depth-of-field reduces the need for mechanical focusing systems. All of these features use computational imaging techniques. The definition of computational photography has evolved to cover a number of subject areas in computer graphics, computer vision, and applied optics. These areas are given below, organized according to a taxonomy proposed by Shree K. Nayar. Within each area is a list of techniques, and for each technique, one or two representative papers or books are cited. Deliberately omitted from the taxonomy are image processing (see also digital image processing) techniques applied to traditionally captured images to produce better images. Examples of such techniques are image scaling, dynamic range compression (i.e. tone mapping), color management, image completion (a.k.a. inpainting or hole filling), image compression, digital watermarking, and artistic image effects. Also omitted are techniques that produce range data, volume data, 3D models, 4D light fields, 4D, 6D, or 8D BRDFs, or other high-dimensional image-based representations. Epsilon photography is a sub-field of computational photography. == Effect on photography == Photos taken using computational photography can allow amateurs to produce photographs rivalling the quality of professional photographers, but as of 2019 do not outperform the use of professional-level equipment. == Computational illumination == This is controlling photographic illumination in a structured fashion, then processing the captured images, to create new images. The applications include image-based relighting, image enhancement, image deblurring, geometry/material recovery and so forth. High-dynamic-range imaging uses differently exposed pictures of the same scene to extend dynamic range. Other examples include processing and merging differently illuminated images of the same subject matter ("lightspace"). == Computational optics == This is a capture of optically coded images, followed by computational decoding to produce new images. Coded aperture imaging was mainly applied in astronomy and X-ray imaging to boost the image quality. Instead of a single pin-hole, a pinhole pattern is applied in imaging, and deconvolution is performed to recover the image. In coded exposure imaging, the on/off state of the shutter is coded to modify the kernel of motion blur. In this way, motion deblurring becomes a well-conditioned problem. Similarly, in a lens based coded aperture, the aperture can be modified by inserting a broadband mask. Thus, out of focus deblurring becomes a well-conditioned problem. The coded aperture can also improve the quality in light field acquisition using Hadamard transform optics. Coded aperture patterns can also be designed using color filters, in order to apply different codes at different wavelengths. This allows for increase the amount of light that reaches the camera sensor, compared to binary masks. == Computational imaging == Computational imaging is a set of imaging techniques that combine data acquisition and data processing to create the image of an object through indirect means to yield enhanced resolution, additional information such as optical phase or 3D reconstruction. The information is often recorded without using a conventional optical microscope configuration or with limited datasets. Computational imaging allows going beyond physical limitations of optical systems, such as numerical aperture, or even obliterates the need for optical elements. For parts of the optical spectrum where imaging elements such as objectives are difficult to manufacture or image sensors cannot be miniaturized, computational imaging provides useful alternatives, in fields such as X-ray and THz radiations. === Common techniques === Among common computational imaging techniques are lensless imaging, computational speckle imaging , ptychography and Fourier ptychography. Computational imaging technique often draws on compressive sensing or phase retrieval techniques, where the angular spectrum of the object is reconstructed. Other techniques are related to the field of computational imaging, such as digital holography, computer vision and inverse problems such as tomography. == Computational processing == This is the processing of non-optically-coded images to produce new images. == Computational sensors == These are detectors that combine sensing and processing, typically in hardware, like the oversampled binary image sensor. == Early work in computer vision == Although computational photography is a currently popular buzzword in computer graphics, many of its techniques first appeared in the computer vision literature, either under other names or within papers aimed at 3D shape analysis. == Art history == Computational photography, as an art form, has been practiced by capturing differently exposed pictures of the same subject matter and combining them. This was the inspiration for the development of the wearable computer in the 1970s and early 1980s. Computational photography was inspired by the work of Charles Wyckoff, and thus computational photography datasets (e.g. differently exposed pictures of the same subject matter that are taken in order to make a single composite image) are sometimes referred to as Wyckoff Sets, in his honor. Early work in this area (joint estimation of image projection and exposure value) was undertaken by Mann and Candoccia. Charles Wyckoff devoted much of his life to creating special kinds of 3-layer photographic films that captured different exposures of the same subject matter. A picture of a nuclear explosion, taken on Wyckoff's film, appeared on the cover of Life Magazine and showed the dynamic range from the dark outer areas to the inner core.
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ByLock

ByLock was a smartphone application that allowed users to communicate via a private, encrypted connection. It was launched in March 2014 on Google Play, Apple App Store The app was downloaded over 600,000 times from its launch in April 2014 until March 2016, when it was permanently shut down. The Turkish National Intelligence Organization (Turkish: Millî İstihbarat Teşkilatı, MİT) stated that the app was downloaded mainly in Turkey and the users were “Fetullahist Terror Organisation (FETÖ) which was formerly known as “Gülen movement” members. == Gülen Movement controversy == In Turkey, possession of the app is deemed evidence of membership in the Gülen Movement, which was allegedly connected to the failed Turkish coup d'état attempt in July 2016. Users of ByLock were deemed terrorists in Turkish courts. According to Deutsche Welle, of the 215,000 former ByLock users, an estimated 23,000 have been detained by Turkish authorities. Some believe that the MİT and other Turkish authorities manipulated the ByLock database in order to arrest suspected members of the Gülen Movement. Tuncay Beşikçi, a computer forensic expert in Turkey, emphasized that "the demands to investigate and analyze ByLock data from independent institutions are refused by the Turkish courts. But it is not normal". Tuncay Beşikçi believes that this application is precisely one of the channels for Gülen molecules to communicate and can also monitor the activities of other members of the organization. He also stated that the developers behind the Mor Beyin app, deliberately set a plan in motion that would put thousands of innocent people in prison as a cover for the Gülen movement. In December 2017, Turkish authorities revealed that almost half the people who had been prosecuted for having ByLock on their smartphones would have their legal cases reviewed, as they could have been redirected to the app without their knowledge. Following the failed coup attempt on 15 July 2016, the use of the ByLock messaging application by members of the Gülen Movement was the sole evidence in investigations and prosecutions to justify arrests and convictions for "membership in an armed terrorist organization." However, these decisions have been considered human rights violations by the European Court of Human Rights (ECHR), the United Nations Human Rights Committee, and the UN Working Group on Arbitrary Detention. Some of the relevant decisions include the following: === Decisions of the European Court of Human Rights === On 20 July 2021, in the case of Tekin Akgün v. Turkey, the European Court of Human Rights (ECHR) ruled that the use of the ByLock messaging application, unless supported by other evidence, does not create a reasonable suspicion of a crime. Based on this reasoning, the court found that the detention order violated Article 5 of the European Convention on Human Rights, which protects the right to liberty and security. In the Yüksel Yalçınkaya v. Turkey decision on 26 September 2023, the European Court of Human Rights (ECHR) examined an appeal against a conviction based on the use of ByLock. The Court ruled that the failure to provide an opportunity to challenge the authenticity of the ByLock data violated the right to a fair trial (Article 6 of the ECHR). The Court also stated that the mere use of ByLock could not be considered sufficient evidence for membership in an armed terrorist organization. It further noted that local courts had established an automatic presumption of guilt based solely on ByLock use, creating a broad and unpredictable interpretation of the law, making it nearly impossible for the accused to exonerate themselves. Therefore, the Court concluded that the conviction based on the use of ByLock violated the principle of no punishment without law (Article 7 of the ECHR). On 22 July 2025, in the Demirhan and 238 Others case, the European Court of Human Rights (ECHR) consolidated the applications of 239 individuals who had been convicted of "membership in an armed terrorist organization" based on their use of ByLock, as determined by 239 separate courts in Turkey. The Court ruled that the convictions violated the right to a fair trial under Article 6 and the principle of no punishment without law under Article 7 of the European Convention on Human Rights (ECHR). The ruling stated that the Turkish courts' "categorical approach" to the use of ByLock lacked legal foundation. In this context, it was emphasized that anyone who had used ByLock could not be convicted of membership in an armed terrorist organization based solely on this reasoning. The ruling also stated that, due to the large number of similar applications, the issue was "systemic in nature" and it called for a national solution to be developed by Turkey. While the Court did not order compensation for the 239 applicants, it emphasized that reopening the trial to ensure the enforcement of the violation ruling was the most appropriate remedy. This ruling, which confirms the violation finding in the Yüksel Yalçınkaya case of 26 September 2023, is considered a continuation of the ECHR's case law concerning trials based on ByLock evidence. === Decisions of the United Nations Human Rights Committee and Working Group === In the İsmet Özçelik and Turgay Karaman v. Turkey decision, dated 28 May 2019 (Application No. 2980/2017), the UN Human Rights Committee ruled that the use of ByLock and allegations of depositing money into Bank Asya could not justify the applicants' arrests. In the Mestan Yayman v. Turkey decision (Opinion No. 42/2018 – 21 August 2018) by the UN Human Rights Council Working Group on Arbitrary Detention, it was stated that using a public messaging application like ByLock cannot be considered criminal evidence, and that the use of such an application falls under the scope of freedom of thought and expression. The dozens of decisions later issued by the UN Human Rights Council Working Group are of the same nature.
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Art Recognition

Art Recognition is a Swiss technology company headquartered in Adliswil, within the Zurich metropolitan area, Switzerland. Art Recognition specializes in the application of artificial intelligence (AI) for art authentication and the detection of art forgeries. == Overview == Art Recognition was established in 2019 by Dr. Carina Popovici and Christiane Hoppe-Oehl. Art Recognition employs a combination of machine learning techniques, computer vision algorithms, and deep neural networks to assess the authenticity of artworks. The company's technology undergoes a process of data collection, dataset preparation, and training. === Academic partnerships and grants === Art Recognition has established a relationship with Innosuisse, a Swiss innovation agency, to expand its research and development initiatives. It has also formed a strategic collaboration with Nils Büttner, an art historian and professor at the State Academy of Fine Arts Stuttgart (ABK Stuttgart). === Notable developments === In May 2024, Art Recognition played a key role in identifying counterfeit artworks, including alleged Monets and Renoirs, being sold on eBay. Germann Auction in November 2024 became the first auction house to successfully conduct a sale of artwork authenticated entirely by artificial intelligence. As of January 2025, Art Recognition has appointed art crime expert and Pulitzer Prize finalist Noah Charney as an advisor. === Recognition and debates === The company was featured on the front page of The Wall Street Journal for its involvement in the authentication case of the Flaget Madonna, believed to have been partly painted by Raphael. A broadcast by the Swiss public television SRF covered how the algorithm can be used to detect art forgeries with high accuracy. The technology developed by Art Recognition has been recognized for its role in providing a technology-based art authentication solution, compared to traditional methods. == Controversial cases == Art Recognition's AI algorithm has been applied to several high-profile and controversial artworks, sparking significant interest and debate in the art world. Samson and Delilah at the National Gallery in London: The National Gallery's "Samson and Delilah", traditionally attributed to the artist Rubens, has also been examined using Art Recognition's AI, which has assessed the painting as non-authentic. De Brecy Tondo Madonna. A research team from Bradford University and the University of Nottingham initially attributed the painting to Raphael, employing an AI face recognition software, while the AI developed at Art Recognition returned a negative result. The Bradford group's AI was trained on 49 images, whereas Art Recognition employed a larger dataset of over 100 images. Lucian Freud Painting Controversy: Featured in The New Yorker, a painting attributed to Lucian Freud became a subject of dispute. Art Recognition's AI analysis played a big role in examining the painting's authenticity. Titian at Kunsthaus Zürich: A painting attributed to Titian, housed at Kunsthaus Zürich, has been a topic of debate among art experts. The application of Art Recognition's technology offered a new perspective. Following this debate, Kunsthaus Zürich has announced plans to initiate a comprehensive project aimed at resolving the authenticity questions surrounding the painting. Art Recognition has contributed to the authentication debate surrounding The Polish Rider, a painting traditionally attributed to Rembrandt but subject to scholarly debate.
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Chinchilla (language model)

Chinchilla is a family of large language models (LLMs) developed by the research team at Google DeepMind, presented in March 2022. == Models == It is named "chinchilla" because it is a further development over a previous model family named Gopher. Both model families were trained in order to investigate the scaling laws of large language models. It claimed to outperform GPT-3. It considerably simplifies downstream utilization because it requires much less computer power for inference and fine-tuning. Based on the training of previously employed language models, it has been determined that if one doubles the model size, one must also have twice the number of training tokens. This hypothesis has been used to train Chinchilla by DeepMind. Similar to Gopher in terms of cost, Chinchilla has 70B parameters and four times as much data. Chinchilla has an average accuracy of 67.5% on the Measuring Massive Multitask Language Understanding (MMLU) benchmark, which is 7% higher than Gopher's performance. Chinchilla was still in the testing phase as of January 12, 2023. Chinchilla contributes to developing an effective training paradigm for large autoregressive language models with limited compute resources. The Chinchilla team recommends that the number of training tokens is twice for every model size doubling, meaning that using larger, higher-quality training datasets can lead to better results on downstream tasks. It has been used for the Flamingo vision-language model. == Architecture == Both the Gopher family and Chinchilla family are families of transformer models. In particular, they are essentially the same as GPT-2, with different sizes and minor modifications. Gopher family uses RMSNorm instead of LayerNorm; relative positional encoding rather than absolute positional encoding. The Chinchilla family is the same as the Gopher family, but trained with AdamW instead of Adam optimizer. The Gopher family contains six models of increasing size, from 44 million parameters to 280 billion parameters. They refer to the largest one as "Gopher" by default. Similar naming conventions apply for the Chinchilla family. Table 1 of shows the entire Gopher family: Table 4 of compares the 70-billion-parameter Chinchilla with Gopher 280B.
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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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