KidDesk is an alternative desktop software application. The early childhood learning company Hatch Early Childhood created KidDesk; it subsequently went to Edmark, which was bought by IBM then sold to Riverdeep (now Houghton Mifflin Harcourt Learning Technology). KidDesk is compatible with Microsoft Windows 95 and newer, as well as Apple System 7 and newer. KidDesk can be set to start when the computer starts up, and can only be exited through password entry. Adults choose what programs are included for the child to use, what icon represented the desk, and customize the software programs available for use. == History == Edmark first started shipping KidDesk in 1992. In 1993, Edmark updated KidDesk with KidDesk Family Edition for Macintosh and DOS, adding more desk accessories and desk styles (Sometimes included as a free exclusive offer with the Early Learning House and Thinkin' Things Series). In 1995, KidDesk Family Edition was enhanced for Windows 95, and released one month after the new operating system shipped. In 1998, Edmark developed KidDesk Internet Safe. The Internet Safe edition was written for Windows 95, Windows 98, and Macintosh (including OS8). In 2008, HMH ported KidDesk Family Edition was to run on Windows Vista and in 2011 version 3.07 of KidDesk Family Edition was released as part of the 'Young Explorer' suite which is fully supported on Windows XP, Windows Vista and Windows 7. == Features == A picture editor incorporated into the desk. Used both in the Adult settings menu and in the desk itself. KidDesk users can edit their user logo with a pixel grid paint program. A calendar incorporated into the desk. This allows the user to set dates that the user finds important, and allows the date to be marked with a picture or text. A password exit feature. For security reasons, the adult can set a password so that KidDesk can only be exited if it is entered. As an extra security measure, the password exit function could only be accessed if the user pressed the ctrl + alt + A keyboard buttons simultaneously. A skin changer with several themes - farm, princess, sports, ocean, etc. These themes can be changed. The e-mail and voicemail features are customizable depending on the KidDesk installation. The ability to add websites that can be accessed on KidDesk, and the ability to block hyperlinks, JavaScript, data entry, etc., on said sites was an added for the 'Internet Safe' edition released in 1998. KidDesk Internet Safe edition is available in Spanish and Brazilian-Portuguese versions. == Reception == KidDesk was given a platinum award at the 1994 Oppenheim Toy Portfolio Awards. The judges praised the program's security features allowing "configur[ation] so that kids never have access to the possibly destructive DOS prompt", and concluded that "[i]f you and your kids share a computer, you need to install Kiddesk immediately!" === Awards === Since 1992, KidDesk has won 15 major awards.
Artisse AI
Artisse AI is a Hong Kong-based technology company founded by William Wu. The company developed a mobile photography application using generative artificial intelligence to transform selfies into high-quality, personalized images. The app allows users to visualize themselves in various scenarios, outfits, and hairstyles, and they can adjust lighting and ambiance to match their preferences. The app launched in 2023 across multiple markets, including the United States, United Kingdom, Japan, South Korea, Canada, and Australia. By January 2024, users had generated over 5 million images. That same month, the company secured $6.7 million in seed funding to support product development and marketing. == History == Artisse was originally founded in South Korea in 2022 by William Wu. The early concept was connected to a virtual idol initiative developed in collaboration with a K-pop agency, intended to support Wu's blockchain gaming business. The project later evolved into a standalone AI photography application. The current version of the Artisse app was developed following the company's relocation to Hong Kong in 2022. In January 2024, Artisse secured $6.7 million in seed funding, led by The London Fund. The investment was aimed at supporting product development, marketing, and user acquisition. Artisse uses an AI algorithm to create hyperrealistic images from uploaded photos. The app generates personalized images by combining generative AI technology, a global pool of licensed talent, and finished art services. The app works with individual users and businesses, offering professional-grade photos and advertisement images. According to the British newspaper Evening Standard the company has developed the world's first and most advanced AI photographer. It captures 15-30 photos of the user and generates 2D images, placing them in various outfits and locations worldwide. === Catheron Gaming === Artisse AI originated from Catheon Gaming, a blockchain gaming and entertainment company founded in 2021 by William Wu. Catheon Gaming published more than 30 Web3 titles in its first year, developed a blockchain game distribution platform, and offered advisory services to external developers. In 2022, HSBC and KPMG listed Catheon Gaming among the "Top 10 Emerging Giants" in the Asia–Pacific region, selected from a pool of more than 6,000 startups. In June 2023, Catheon Gaming was rebranded as Artisse Interactive, creating two divisions: Artisse Gaming, which continued blockchain and Web3 game development, and Artisse AI, which focused on generative photography technology. == Technology == Artisse uses a proprietary generative AI model combined with open-source imaging frameworks and diffusion models. Users are prompted to upload between 15 and 30 personal images, allowing the AI to train a personalized model in 30 to 40 minutes. After training, the app generates new images based on either textual or visual prompts, with options to adjust elements such as clothing, hairstyles, lighting, and backgrounds. To enhance realism, the app integrates augmented reality features and image refinement tools. The company has introduced features to address representation issues related to body shape and skin tone, although concerns persist about the ethical implications of altering personal traits. == Products == === Artisse mobile app === Available on iOS and Android platforms in 35 languages. Users initially receive 25 free images, after which the app adopts a subscription pricing model ranging from approximately $6 to $30 per month. By early 2024, the app reported around 4,000 paying subscribers out of more than 200,000 downloads. === Business and enterprise services === Artisse provides B2B solutions for creating marketing imagery and partners with agencies like Iconic Management to enable cost-effective virtual photoshoots. Additional features in development include virtual try-on capabilities and augmented reality integration for fashion retail. == Reception == Media coverage has noted the app's photorealistic image outputs with some sources highlighting its ease of use. However, concerns have been raised regarding image authenticity, algorithmic biases, and the potential impact on professional photography and modeling. Artisse has been widely covered by media outlets including TechCrunch, PetaPixel, Forbes Australia, and The Evening Standard. These publications discussed the app's integration of generative AI technology within the consumer photography space, its growing market influence, and its rapid adoption by users worldwide.
Coherent extrapolated volition
Coherent extrapolated volition (CEV) is a theoretical framework in the field of AI alignment describing an approach by which an artificial superintelligence (ASI) would act on a benevolent supposition of what humans would want if they were more knowledgeable, more rational, had more time to think, and had matured together as a society, as opposed to humanity's current individual or collective preferences. It was proposed by Eliezer Yudkowsky in 2004 as part of his work on friendly AI. == Concept == CEV proposes that an advanced AI system should derive its goals by extrapolating the idealized volition of humanity. This means aggregating and projecting human preferences into a coherent utility function that reflects what people would desire under ideal epistemic and moral conditions. The aim is to ensure that AI systems are aligned with humanity's true interests, rather than with transient or poorly informed preferences. In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted. == Debate == Yudkowsky and Nick Bostrom note that CEV has several interesting properties. It is designed to be humane and self-correcting, by capturing the source of human values instead of trying to list them. It avoids the difficulty of laying down an explicit, fixed list of rules. It encapsulates moral growth, preventing flawed current moral beliefs from getting locked in. It limits the influence that a small group of programmers can have on what the ASI would value, thus also reducing the incentives to build ASI first. And it keeps humanity in charge of its destiny. CEV also faces significant theoretical and practical challenges. Bostrom notes that CEV has "a number of free parameters that could be specified in various ways, yielding different versions of the proposal." One such parameter is the extrapolation base (whose extrapolated volition is taken into account). For example, whether it should include people with severe dementia, patients in a vegetative state, foetuses, or embryos. He also notes that if CEV's extrapolation base only includes humans, there is a risk that the result would be ungenerous toward other animals and digital minds. One possible solution would be to include a mechanism to expand CEV's extrapolation base. == Variants and alternatives == A proposed theoretical alternative to CEV is to rely on an artificial superintelligence's superior cognitive capabilities to figure out what is morally right, and let it act accordingly. It is also possible to combine both techniques, for instance with the ASI following CEV except when it is morally impermissible. In another review, a philosophical analysis explores CEV through the lens of social trust in autonomous systems. Drawing on Anthony Giddens' concept of "active trust", the author proposes an evolution of CEV into "Coherent, Extrapolated and Clustered Volition" (CECV). This formulation aims to better reflect the moral preferences of diverse cultural groups, thus offering a more pragmatic ethical framework for designing AI systems that earn public trust while accommodating societal diversity.
Operation Serenata de Amor
Operation Serenata de Amor is an artificial intelligence project designed to analyze public spending in Brazil. The project has been funded by a recurrent financing campaign since September 7, 2016, and came in the wake of major scandals of misappropriation of public funds in Brazil, such as the Mensalão scandal and what was revealed in the Operation Car Wash investigations. The analysis began with data from the National Congress then expanded to other types of budget and instances of government, such as the Federal Senate. The project is built through collaboration on GitHub and using a public group with more than 600 participants on Telegram. The name "Serenata de Amor," which means "serenade of love," was taken from a popular cashew cream bonbon produced by Chocolates Garoto in Brazil. == Modules == Throughout development of the project, new modules have been newly introduced in addition to the main repository: The main repository, serenata-de-amor, serves as the starting point for investigative work. Rosie is the robot programmed to identify public funds expenses with discrepancies, starting with CEAP (Quota for Exercise of Parliamentary Activity); it analyzes each of the reimbursements requested by the deputies and senators, indicating the reasons that lead it to believe they are suspicious. From Rosie was born whistleblower, which tweets under the name of @RosieDaSerenata, distributing the results found on social media. Jarbas (Github repository) is a data visualization tool which shows a complete list of reimbursements made available by the Chamber of Deputies and mined by Rosie. Toolbox is a Python installable package that supports the development of Serenata de Amor and Rosie. == History == Operation Serenata de Amor is an Artificial intelligence project for analysis of public expenditures. It was conceived in March 2016 by data scientist Irio Musskopf, sociologist Eduardo Cuducos and entrepreneur Felipe Cabral. The project was financed collectively in the Catarse platform, where it reached 131% of the collection goal paying 3 months of project development. Ana Schwendler, also a data scientist, Pedro Vilanova "Tonny", data journalist, Bruno Pazzim, software engineer, Filipe Linhares, a frontend engineer, Leandro Devegili, an entrepreneur and André Pinho took the first steps towards constructing the platform, such as collecting and structuring the first datasets. Jessica Temporal, data scientist and Yasodara Córdova "Yaso", researcher, Tatiana Balachova "Russa", UX designer, joined the project after the financing took place. The members created a recurring financing campaign, expanding the analysis of public spending to the Federal Senate. Donors make monthly payments ranging from 5 BRL to 200 BRL to maintain group activities. The monthly amount collected is around 10,000 BRL. == Results == In January 2017, concluding the period financed by the initial campaign, the group carried out an investigation into the suspicious activities found by the data analysis system. 629 complaints were made to the Ombudsman's Office of the Chamber of Deputies, questioning expenses of 216 federal deputies. In addition, the Facebook project page has more than 25,000 followers, and users frequently cite the operation as a benchmark in transparency in the Brazilian government. One of the examples of results obtained by the operation is the case of the Deputy who had to return about 700 BRL to the House after his expenses were analyzed by the platform. The platform was able to analyze more than 3 million notes, raising about 8,000 suspected cases in public spending. The community that supports the work of the team benefits from open source repositories, with licenses open for the collaboration. So much so that the two main data scientists of the project presented it at the CivicTechFest in Taipei, obtaining several mentions even in the international press. The technical leader presented the project in Poland during DevConf2017 in Kraków. It was also presented in the Google News Lab in 2017. It was presented by Yaso, when she was the Director of the initiative, at the MIT Media Lab/Berkman Klein Center Initiative for Artificial Intelligence ethics, and at the Artificial Intelligence and Inclusion Symposium, an initiative of the Global Network of Internet & Society Centers (NoC). It was also presented both by Irio and Yaso at the Digital Harvard Kennedy School, over a lunch seminar, where the transparency of the platform and the main solutions found were discussed, so that the code and data are always available to verify its suitability. This infographic provides information about the first results of Operation Serenata de Amor, a project that analyzes open data on public spending to find discrepancies. The project was presented by Yaso to the House Audit and Control Committee of the Chamber of Deputies in August 2017, and raised the interest of House officials who work with open data. The operation has been a source of inspiration for other civic projects that aim to work with similar goals, demonstrating the broader impact of artificial intelligence also in industry in Brazil. Participation of several team members in events throughout Brazil and abroad can be found on the Internet, such as presentation at OpenDataDay, held at Calango Hackerspace in the Federal District, Campus Party Bahia, Campus Party Brasilia, Friends of Tomorrow, XIII National Meeting of Internal Control, in the event USP Talks Hackfest against corruption in João Pessoa, the latter being also highlighted in the National Press.
Semantic folding
Semantic folding theory describes a procedure for encoding the semantics of natural language text in a semantically grounded binary representation. This approach provides a framework for modelling how language data is processed by the neocortex. == Theory == Semantic folding theory draws inspiration from Douglas R. Hofstadter's Analogy as the Core of Cognition which suggests that the brain makes sense of the world by identifying and applying analogies. The theory hypothesises that semantic data must therefore be introduced to the neocortex in such a form as to allow the application of a similarity measure and offers, as a solution, the sparse binary vector employing a two-dimensional topographic semantic space as a distributional reference frame. The theory builds on the computational theory of the human cortex known as hierarchical temporal memory (HTM), and positions itself as a complementary theory for the representation of language semantics. A particular strength claimed by this approach is that the resulting binary representation enables complex semantic operations to be performed simply and efficiently at the most basic computational level. == Two-dimensional semantic space == Analogous to the structure of the neocortex, Semantic Folding theory posits the implementation of a semantic space as a two-dimensional grid. This grid is populated by context-vectors in such a way as to place similar context-vectors closer to each other, for instance, by using competitive learning principles. This vector space model is presented in the theory as an equivalence to the well known word space model described in the information retrieval literature. Given a semantic space (implemented as described above) a word-vector can be obtained for any given word Y by employing the following algorithm: For each position X in the semantic map (where X represents cartesian coordinates) if the word Y is contained in the context-vector at position X then add 1 to the corresponding position in the word-vector for Y else add 0 to the corresponding position in the word-vector for Y The result of this process will be a word-vector containing all the contexts in which the word Y appears and will therefore be representative of the semantics of that word in the semantic space. It can be seen that the resulting word-vector is also in a sparse distributed representation (SDR) format [Schütze, 1993] & [Sahlgreen, 2006]. Some properties of word-SDRs that are of particular interest with respect to computational semantics are: high noise resistance: As a result of similar contexts being placed closer together in the underlying map, word-SDRs are highly tolerant of false or shifted "bits". boolean logic: It is possible to manipulate word-SDRs in a meaningful way using boolean (OR, AND, exclusive-OR) and/or arithmetical (SUBtract) functions . sub-sampling: Word-SDRs can be sub-sampled to a high degree without any appreciable loss of semantic information. topological two-dimensional representation: The SDR representation maintains the topological distribution of the underlying map therefore words with similar meanings will have similar word-vectors. This suggests that a variety of measures can be applied to the calculation of semantic similarity, from a simple overlap of vector elements, to a range of distance measures such as: Euclidean distance, Hamming distance, Jaccard distance, cosine similarity, Levenshtein distance, Sørensen-Dice index, etc. == Semantic spaces == Semantic spaces in the natural language domain aim to create representations of natural language that are capable of capturing meaning. The original motivation for semantic spaces stems from two core challenges of natural language: Vocabulary mismatch (the fact that the same meaning can be expressed in many ways) and ambiguity of natural language (the fact that the same term can have several meanings). The application of semantic spaces in natural language processing (NLP) aims at overcoming limitations of rule-based or model-based approaches operating on the keyword level. The main drawback with these approaches is their brittleness, and the large manual effort required to create either rule-based NLP systems or training corpora for model learning. Rule-based and machine learning-based models are fixed on the keyword level and break down if the vocabulary differs from that defined in the rules or from the training material used for the statistical models. Research in semantic spaces dates back more than 20 years. In 1996, two papers were published that raised a lot of attention around the general idea of creating semantic spaces: latent semantic analysis from Microsoft and Hyperspace Analogue to Language from the University of California. However, their adoption was limited by the large computational effort required to construct and use those semantic spaces. A breakthrough with regard to the accuracy of modelling associative relations between words (e.g. "spider-web", "lighter-cigarette", as opposed to synonymous relations such as "whale-dolphin", "astronaut-driver") was achieved by explicit semantic analysis (ESA) in 2007. ESA was a novel (non-machine learning) based approach that represented words in the form of vectors with 100,000 dimensions (where each dimension represents an Article in Wikipedia). However practical applications of the approach are limited due to the large number of required dimensions in the vectors. More recently, advances in neural networking techniques in combination with other new approaches (tensors) led to a host of new recent developments: Word2vec from Google and GloVe from Stanford University. Semantic folding represents a novel, biologically inspired approach to semantic spaces where each word is represented as a sparse binary vector with 16,000 dimensions (a semantic fingerprint) in a 2D semantic map (the semantic universe). Sparse binary representation are advantageous in terms of computational efficiency, and allow for the storage of very large numbers of possible patterns. == Visualization == The topological distribution over a two-dimensional grid (outlined above) lends itself to a bitmap type visualization of the semantics of any word or text, where each active semantic feature can be displayed as e.g. a pixel. As can be seen in the images shown here, this representation allows for a direct visual comparison of the semantics of two (or more) linguistic items. Image 1 clearly demonstrates that the two disparate terms "dog" and "car" have, as expected, very obviously different semantics. Image 2 shows that only one of the meaning contexts of "jaguar", that of "Jaguar" the car, overlaps with the meaning of Porsche (indicating partial similarity). Other meaning contexts of "jaguar" e.g. "jaguar" the animal clearly have different non-overlapping contexts. The visualization of semantic similarity using Semantic Folding bears a strong resemblance to the fMRI images produced in a research study conducted by A.G. Huth et al., where it is claimed that words are grouped in the brain by meaning. voxels, little volume segments of the brain, were found to follow a pattern were semantic information is represented along the boundary of the visual cortex with visual and linguistic categories represented on posterior and anterior side respectively.
Percept (artificial intelligence)
A percept is the input that an intelligent agent is perceiving at any given moment. It is essentially the same concept as a percept in psychology, except that it is being perceived not by the brain but by the agent. A percept is detected by a sensor, often a camera, processed accordingly, and acted upon by an actuator. Each percept is added to a "percept sequence", which is a complete history of each percept ever detected. The agent's action at any instant point may depend on the entire percept sequence up to that particular instant point. An intelligent agent chooses how to act not only based on the current percept, but the percept sequence. The next action is chosen by the agent function, which maps every percept to an action. For example, if a camera were to record a gesture, the agent would process the percepts, calculate the corresponding spatial vectors, examine its percept history, and use the agent program (the application of the agent function) to act accordingly. == Examples == Examples of percepts include inputs from touch sensors, cameras, infrared sensors, sonar, microphones, mice, and keyboards. A percept can also be a higher-level feature of the data, such as lines, depth, objects, faces, or gestures.
Tensor (machine learning)
In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .