AI Data Farms

AI Data Farms — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Film recorder

  A film recorder is a graphical output device for transferring images to photographic film from a digital source. In a typical film recorder, an image is passed from a host computer to a mechanism to expose film through a variety of methods, historically by direct photography of a high-resolution cathode-ray tube (CRT) display. The exposed film can then be developed using conventional developing techniques, and displayed with a slide or motion picture projector. The use of film recorders predates the current use of digital projectors, which eliminate the time and cost involved in the intermediate step of transferring computer images to film stock, instead directly displaying the image signal from a computer. Motion picture film scanners are the opposite of film recorders, copying content from film stock to a computer system. Film recorders can be thought of as modern versions of kinescopes. == Design == === Operation === All film recorders typically work in the same manner. The image is fed from a host computer as a raster stream over a digital interface. A film recorder exposes film through various mechanisms; flying spot (early recorders); photographing a high resolution video monitor; electron beam recorder (Sony HDVS); a CRT scanning dot (Celco); focused beam of light from a light valve technology (LVT) recorder; a scanning laser beam (Arrilaser); or recently, full-frame LCD array chips. For color image recording on a CRT film recorder, the red, green, and blue channels are sequentially displayed on a single gray scale CRT, and exposed to the same piece of film as a multiple exposure through a filter of the appropriate color. This approach yields better resolution and color quality than possible with a tri-phosphor color CRT. The three filters are usually mounted on a motor-driven wheel. The filter wheel, as well as the camera's shutter, aperture, and film motion mechanism are usually controlled by the recorder's electronics and/or the driving software. CRT film recorders are further divided into analog and digital types. The analog film recorder uses the native video signal from the computer, while the digital type uses a separate display board in the computer to produce a digital signal for a display in the recorder. Digital CRT recorders provide a higher resolution at a higher cost compared to analog recorders due to the additional specialized hardware. Typical resolutions for digital recorders were quoted as 2K and 4K, referring to 2048×1366 and 4096×2732 pixels, respectively, while analog recorders provided a resolution of 640×428 pixels in comparison. Higher-quality LVT film recorders use a focused beam of light to write the image directly onto a film loaded spinning drum, one pixel at a time. In one example, the light valve was a liquid-crystal shutter, the light beam was steered with a lens, and text was printed using a pre-cut optical mask. The LVT will record pixel beyond grain. Some machines can burn 120-res or 120 lines per millimeter. The LVT is basically a reverse drum scanner. The exposed film is developed and printed by regular photographic chemical processing. === Formats === Film recorders are available for a variety of film types and formats. The 35 mm negative film and transparencies are popular because they can be processed by any photo shop. Single-image 4×5 film and 8×10 are often used for high-quality, large format printing. Some models have detachable film holders to handle multiple formats with the same camera or with Polaroid backs to provide on-site review of output before exposing film. == Uses == Film recorders are used in digital printing to generate master negatives for offset and other bulk printing processes. For preview, archiving, and small-volume reproduction, film recorders have been rendered obsolete by modern printers that produce photographic-quality hardcopies directly on plain paper. They are also used to produce the master copies of movies that use computer animation or other special effects based on digital image processing. However, most cinemas nowadays use Digital Cinema Packages on hard drives instead of film stock. === Computer graphics === Film recorders were among the earliest computer graphics output devices; for example, the IBM 740 CRT Recorder was announced in 1954. Film recorders were also commonly used to produce slides for slide projectors; but this need is now largely met by video projectors that project images directly from a computer to a screen. The terms "slide" and "slide deck" are still commonly used in presentation programs. === Current uses === Currently, film recorders are primarily used in the motion picture film-out process for the ever increasing amount of digital intermediate work being done. Although significant advances in large venue video projection alleviates the need to output to film, there remains a deadlock between the motion picture studios and theater owners over who should pay for the cost of these very costly projection systems. This, combined with the increase in international and independent film production, will keep the demand for film recording steady for at least a decade. == Key manufacturers == Traditional film recorder manufacturers have all but vanished from the scene or have evolved their product lines to cater to the motion picture industry. Dicomed was one such early provider of digital color film recorders. Polaroid, Management Graphics, Inc, MacDonald-Detwiler, Information International, Inc., and Agfa were other producers of film recorders. Arri is the only current major manufacturer of film recorders. Kodak Lightning I film recorder. One of the first laser recorders. Needed an engineering staff to set up. Kodak Lightning II film recorder used both gas and diode laser to record on to film. The last LVT machines produced by Kodak / Durst-Dice stopped production in 2002. There are no LVT film recorders currently being produced. LVT Saturn 1010 uses a LED exposure (RGB) to 8"x10" film at 1000-3000ppi. LUX Laser Cinema Recorder from Autologic/Information International in Thousand Oaks, California. Sales end in March 2000. Used on the 1997 film “Titanic”. Arri produces the Arrilaser line of laser-based motion picture film recorders. MGI produced the Solitaire line of CRT-based motion picture film recorders. Matrix, originally ImaPRO, a branch of Agfa Division, produced the QCR line of CRT-based motion picture film recorders. CCG, formerly Agfa film recorders, has been a steady manufacturer of film recorders based in Germany. In 2004 CCG introduced Definity, a motion picture film recorder utilizing LCD technology. In 2010 CCG introduced the first full LED LCD film recorder as a new step in film recording. Cinevator was made by Cinevation AS, in Drammen, Norway. The Cinevator was a real-time digital film recorder. It could record IN, IP and prints with and without sound Oxberry produced the Model 3100 film recorder camera system, with interchangeable pin-registered movements (shuttles) for 35 mm (full frame/Silent, 1.33:1) and 16 mm (regular 16, "2R"), and others have adapted the Oxberry movements for CinemaScope, 1.85:1, 1.75:1, 1.66:1, as well as Academy/Sound (1.37:1) in 35 mm and Super-16 in 16 mm ("1R"). For instance, the "Solitaire" and numerous others employed the Oxberry 3100 camera system. == History == Before video tape recorders or VTRs were invented, TV shows were either broadcast live or recorded to film for later showing, using the kinescope process. In 1967, CBS Laboratories introduced the Electronic Video Recording format, which used video and telecined-to-video film sources, which were then recorded with an electron-beam recorder at CBS' EVR mastering plant at the time to 35mm film stock in a rank of 4 strips on the film, which was then slit down to 4 8.75 mm (0.344 in) film copies, for playback in an EVR player. All types of CRT recorders were (and still are) used for film recording. Some early examples used for computer-output recording were the 1954 IBM 740 CRT Recorder, and the 1962 Stromberg-Carlson SC-4020, the latter using a Charactron CRT for text and vector graphic output to either 16 mm motion picture film, 16 mm microfilm, or hard-copy paper output. Later 1970 and 80s-era recording to B&W (and color, with 3 separate exposures for red, green, and blue)) 16 mm film was done with an EBR (Electron Beam Recorder), the most prominent examples made by 3M), for both video and COM (Computer Output Microfilm) applications. Image Transform in Universal City, California used specially modified 3M EBR film recorders that could perform color film-out recording on 16 mm by exposing three 16 mm frames in a row (one red, one green and one blue). The film was then printed to color 16 mm or 35 mm film. The video fed to the recorder could either be NTSC, PAL or SECAM. Later, Image Transform used specially modified VTRs to record 24 frame for their "Image Vision" system. The modified 1 inch type B videotape VTRs would record

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  AppValley

  AppValley is an independent American digital distribution service operated and trademarked by AppValley LLC. It serves as an alternative app store for the iOS mobile operating system, which allows users to download applications that are not available on the App Store, most commonly tweaked "++" apps, jailbreak apps, and apps including paid apps on the app store. == Legality == AppValley is among several services that violate enterprise developer certificates from Apple. The terms under which these are granted make clear that they are for companies who wish to distribute apps to their employees. AppValley uses these certificates to distribute software directly to non-employees, thereby bypassing the AppStore. AppValley's conduct had implications in U.S. sanctioned markets like Iran, Iraq, North Korea, Cuba, and Venezuela, which have all been subject to commercial sanctions. Among the software offered by AppValley and other services is pirated software, including paid apps on the app store and premium versions of Instagram, Spotify, Pokémon Go, and others. For instance, AppValley distributes an ad-free version of the music streaming app Spotify even on the free tier. == History == The website was founded in May 2017, releasing late that month with a very basic version of the app. There were less than 100 apps available for download at this time. On Jan 19, 2018, a new version dubbed AppValley 2.0 was released bringing dark mode, more categories, a search, and a much faster interface. On February 14, 2019, a Chinese partner "Jason Wu" allegedly took control of the main Twitter account and domain, causing the original AppValley developers to migrate to the domain app-valley.vip and the Twitter account handle @App_Valley_vip. As of September 2024, the app-valley.vip domain now redirects to appvalley.signulous.com. Today, AppValley continues to offer an alternative to Apple's App Store where app developers can publish their applications. == Features == AppValley is a mobile app installer which can also support iOS version that can be installed and downloaded on the mobile or the devices of the people who wish to get access to many different applications available. AppValley also contains apps that have been modified or tweaked for user preferences, and allows the user to by pass national restrictions on the use of apps, without having to resort to jailbreaking. As of June 2, 2020, there are over 1300 apps available for download.

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  Open Syllabus Project

  The Open Syllabus Project (OSP) is an online open-source platform that catalogs and analyzes millions of college syllabi. Founded by researchers from the American Assembly at Columbia University, the OSP has amassed the most extensive collection of searchable syllabi. Since its beta launch in 2016, the OSP has collected over 7 million course syllabi from over 80 countries, primarily by scraping publicly accessible university websites. The project is directed by Joe Karaganis. == History == The OSP was formed by a group of data scientists, sociologists, and digital-humanities researchers at the American Assembly, a public-policy institute based at Columbia University. The OSP was partly funded by the Sloan Foundation and the Arcadia Fund. Joe Karaganis, former vice-president of the American Assembly, serves as the project director of the OSP. The project builds on prior attempts to archive syllabi, such as H-Net, MIT OpenCourseWare, and historian Dan Cohen's defunct Syllabus Finder website (Cohen now sits on the OSP's advisory board). The OSP became a non-profit and independent of the American Assembly in November 2019. In January 2016, the OSP launched a beta version of their "Syllabus Explorer," which they had collected data for since 2013. The Syllabus Explorer allows users to browse and search texts from over one million college course syllabi. The OSP launched a more comprehensive version 2.0 of the Syllabus Explorer in July 2019. The newer version includes an interactive visualization that displays texts as dots on a knowledge map. As of 2022, the OSP has collected over 7 million course syllabi. The Syllabus Explorer represents the "largest collection of searchable syllabi ever amassed." == Methodology == The OSP has collected syllabi data from over 80 countries dating to 2000. The syllabi stem from over 4,000 worldwide institutions. Most of the OSP's data originates from the United States. Canada, Australia, and the U.K also have large datasets. The OSP primarily collects syllabi by scraping publicly accessible university websites. The OSP also allows syllabi submissions from faculty, students, and administrators. The OSP developers use machine learning and natural language processing to extract metadata from such syllabi. Since only metadata is collected, no individual syllabus or personal identifying information is found in the OSP database. The OSP classifies the syllabi into 62 subject fields – corresponding to the U.S. Department of Education's Classification of Instructional Programs (CIP). Additionally, the OSP assigns each text a "teaching score" from 0–100. This score represents the text's percentile rank among citations in the total citation count and is a numerical indicator of the relative frequency of which a particular work is taught. The OSP also has data on which texts are most likely to be assigned together. The developers behind the OSP admit that the database is incomplete and likely contains "a fair number of errors." Karaganis estimates that 80–100 million syllabi exist in the United States alone. The OSP is unable to access syllabi behind private course-management software like Blackboard. == Notable findings == === Anthropology === Using data from the OSP, anthropologist Laurence Ralph uncovered that black anthropologists are "woefully under-represented in (if not erased from) most anthropology syllabi." Black authors wrote less than 1 percent of the top 1,000 assigned works. === Economics === The database indicates Greg Mankiw is the most frequently cited author for college economics courses. === English literature === The OSP found that Mary Shelley's Frankenstein was the most widely taught novel in college courses. Additionally, the majority of novels published after 1945 taught in English classes were historical fiction. === Female writers === The most read female writer on college campuses is Kate L. Turabian for her A Manual for Writers of Research Papers, Theses, and Dissertations . Turabian is followed by Diana Hacker, Toni Morrison, Jane Austen, and Virginia Woolf. === Film === The most assigned film according to the OSP is the 1929 Soviet documentary film, Man with a Movie Camera. English filmmaker Alfred Hitchcock is the most assigned director in college courses. === History === Historians George Brown Tindall and David Emory Shi's America: A Narrative History is the number one assigned textbook for history, followed by Anne Moody's memoir, Coming of Age in Mississippi. === Philosophy === The most assigned texts in the field of philosophy include Aristotle's Nicomachean Ethics, John Stuart Mill's Utilitarianism, and Plato's Republic. Plato's Republic was also the second most assigned text in universities in the English-speaking world (only behind Strunk and White's Elements of Style). === Physics === David Halliday's et al. Fundamentals of Physics is the number one ranked physics textbook in the OSP's database. === Political science === Data from the OSP indicates that the dominant political science texts are written almost exclusively by white men and scholars based in the West. In the top 200 most-frequently assigned works, 15 are authored by at least one woman. === Public administration === American president Woodrow Wilson's article "The Study of Administration" was the most frequently assigned text in public affairs and administration syllabi. == Reception == According to William Germano et al., the OSP is a "fascinating resource but is also prone to misrepresenting or at least distracting us from the most important business of a syllabus: communicating with students." Historian William Caferro remarks that the OSP is a "tacit experience of sharing, but a useful one." English professor Bart Beaty writes that, "Despite the many reservations about the completeness of its data, the OSP provides a rare opportunity for scholars to move beyond the anecdotal in discussions of canon-formation in teaching." Media theorist Elizabeth Losh opines that "big data approaches", like the OSP, may "raise troubling questions for instructors about informed consent, pedagogical privacy, and quantified metrics."

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  ISLRN

  The ISLRN or International Standard Language Resource Number is Persistent Unique Identifier for Language Resources. == Context == On November 18, 2013, 12 major organisations (see list below) from the fields Language Resources and Technologies, Computational Linguistics, and Digital Humanities held a cooperation meeting in Paris (France) and agreed to announce the establishment of the International Standard Language Resource Number (ISLRN), to be assigned to each Language Resource. Among the 12 organisations, 4 institutions constitute the ISLRN Steering Committee (ST) ADHO ACL Asian Federation of Natural Language Processing ST COCOSDA, International Committee for the Coordination & Standardisation of Speech Databases and Assessment Techniques ICCL (COLING) European Data Forum ELRA ST IAMT, International Association for Machine Translation Archived 2010-06-24 at the Wayback Machine ISCA LDC ST Oriental COCOSDA ST RMA, Language Resource Management Agency == Size and Content == The Joint Research Centre(JRC), the [European Commission]'s in-house science service, was the first organisation to adopt the ISLRN initiative and requested. 2500 resources and tools have already been allocated an ISLRN. These resources include written data (Annotated corpus, Annotated text, List of misspelled word, Terminological database, Treebank, Wordnet, etc.) and speech corpora (Synthesised Speech, Transcripts and Audiovisual Recordings, Conversational Speech, Folk Sayings, etc.) == Objectives == Providing Language Resources with unique names and identifiers using a standardized nomenclature ensures the identification of each Language Resources and streamlines the citation with proper references in activities within Human Language Technology as well as in documents and scientific publications. Such unique identifier also enhances the reproducibility, an essential feature of scientific work.

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  Pixelmator

  Pixelmator is a series of graphics editors developed by Apple for macOS, iOS, and iPadOS. Pixelmator apps leverage Apple-specific technologies such as CoreML and Metal. Pixelmator uses a proprietary format across their apps (.PXD), but supports editing a variety of file types including Photoshop, RAW, and WebP. == History == Pixelmator Team was founded in 2007 by Lithuanian brothers Saulius and Aidas Dailidė, and released Pixelmator (now Pixelmator Classic) 1.0 in September of the same year. The company resided in Vilnius, Lithuania. In November 2024, Pixelmator Team agreed to be acquired by Apple for an unknown monetary amount, which was completed on 11 February 2025, the company was later folded into Apple with its products coming under them fully. == Pixelmator Classic == Pixelmator Classic was the original version of Pixelmator released for Mac on 25 September 2007. It uses a palette-style interface with floating toolbars compared to Pixelmator Pro's single-window interface. It is no longer being updated and has been delisted from the Mac App Store. == Pixelmator iOS == Pixelmator for iOS launched on 23 October 2014 as an iPad-exclusive app with touch-optimized versions of Pixelmator's desktop features. In May 2015, Pixelmator for iOS 2.0 was released with support for the iPhone. Apple no longer updates Pixelmator for iOS as of 13 January 2026, shortly before the release of Pixelmator Pro for iPad. == Pixelmator Pro == Pixelmator Pro is an image, video, and vector editing software for macOS that launched on 29 November 2017. It was a paid upgrade for Pixelmator Classic users, featuring a redesigned interface, a graphics pipeline rewritten using Metal, Apple silicon support and a greater focus on ML/AI editing features. On 28 January 2026, Apple announced Apple Creator Studio, a subscription bundle for their professional software that contains Pixelmator Pro. They also brought Pixelmator Pro to iPad, shortly after discontinuing Pixelmator iOS. == Photomator == Photomator (formerly Pixelmator Photo) is a photo-oriented editing app which launched on iPad in 2019, on iOS in 2021, and macOS in 2022. After launching the macOS version, the app moved from a one-time purchase to a subscription; however, a lifetime license can still be purchased for $99. Photomator differentiates itself from other Pixelmator apps with features such as batch editing of full photoshoots and AI-powered color correction. Edits in Photomator are made on a single layer and are non-destructive.

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  DBGallery

  DBGallery, short for Database Gallery, is a cloud-based Software as a Service (SaaS) and on-prem webserver for teams of various sizes. DBGallery enables users to centrally store, manage, catalog, archive, and securely share image, video, and document files. It facilitates version control, detects duplicates, and offers an intuitive and advanced search functionality, making assets easily accessible to all users. It takes advantage of current AI technologies to automatically add significant metadata to images, facilitates custom-trained AI models, and offers bespoke AI features. Additionally, DBGallery provides team management tools, workflow management, an activity audit trail, and other collaborative features that foster a productive environment for both internal and external stakeholders. == History == DBGallery's first public release was December 2007. Since then each year has seen continuous enhancements. 2013 added support for additional non-English languages in its meta-data. 2014 added support for creating custom data fields for tagging and search. In 2015 included the ability to auto-tag images using Reverse Geocoding. 2018 added artificial intelligence (AI) image recognition as a further addition to auto-tagging. March 2020 added complete image collection management via the web (e.g. file and folder drag and drop), a new collection dashboard, custom data layouts, and an improved audit trail. 2021 saw user experience improvements provided by improved styling and performance enhancements. Version 12 was released in October 2021. It added the ability to upload unlimited file sizes and made significant performance improvements for very large collections. June 2022 saw the release of a global duplicate images search. In late 2022, DBGallery began offering significantly reduced cloud storage cost, at a third of its previous prices, which played into its recent high-volume/high-capacity capabilities and its clients' subsequent demand for additional storage. 2023 saw improvements in user and role management, introduced it's mobile app (PWA), and improved custom-trained object detection. Release 14.0 in the spring of 2024 had large sharing improvements and a new find related images feature. Winter 2025's v15 release introduced AI-generated image descriptions, image-to-text, and facial recognition.

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  Integrated writing environment

  An integrated writing environment (IWE) is software that provides comprehensive writing and knowledge management functionality for writers and information workers. IWEs enable writers and information workers to perform a variety of tasks related to the document in the IWE in a single environment. This provides a distraction-free workspace and streamlined writing experience. IWEs provide similar efficiency and functionality benefits to writers and information professionals that integrated development environments (IDEs) provide to software developers. == Overview == IWEs are designed to maximize productivity and help improve the quality of written work by integrating together tools that allow users to work effectively in a single application. The IWE features may include integrated content search, reversion management, outlining, note management, and reference management, as may be suitable for the target field of use. == List of IWEs == Celtx This IWE is intended for screenplay writers and has screenplay writing and management tools. Celtex provides tools for the pre-production work phase, story development, storyboarding, script breakdowns, production scheduling, and reports. Scrivener This IWE targets novel, research paper, and script writing. Scrivener provides tools to organize notes and research documents for easy access and referencing. After completing the writing, Scrivener allows the user to export the document to formats supported by common word processors, such as Microsoft Word. TeXstudio This IWE targets LaTeX documents and provides interactive spelling checker, code folding, and syntax highlighting.

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  ChatScript

  ChatScript is a combination Natural Language engine and dialog management system designed initially for creating chatbots, but is currently also used for various forms of NL processing. It is written in C++. The engine is an open source project at SourceForge. and GitHub. ChatScript was written by Bruce Wilcox and originally released in 2011, after Suzette (written in ChatScript) won the 2010 Loebner Prize, fooling one of four human judges. == Features == In general ChatScript aims to author extremely concisely, since the limiting scalability of hand-authored chatbots is how much/fast one can write the script. Because ChatScript is designed for interactive conversation, it automatically maintains user state across volleys. A volley is any number of sentences the user inputs at once and the chatbots response. The basic element of scripting is the rule. A rule consists of a type, a label (optional), a pattern, and an output. There are three types of rules. Gambits are something a chatbot might say when it has control of the conversation. Rejoinders are rules that respond to a user remark tied to what the chatbot just said. Responders are rules that respond to arbitrary user input which is not necessarily tied to what the chatbot just said. Patterns describe conditions under which a rule may fire. Patterns range from extremely simplistic to deeply complex (analogous to Regex but aimed for NL). Heavy use is typically made of concept sets, which are lists of words sharing a meaning. ChatScript contains some 2000 predefined concepts and scripters can easily write their own. Output of a rule intermixes literal words to be sent to the user along with common C-style programming code. Rules are bundled into collections called topics. Topics can have keywords, which allows the engine to automatically search the topic for relevant rules based on user input. == Example code == Words starting with ~ are concept sets. For example, ~fruit is the list of all known fruits. The simple pattern (~fruit) reacts if any fruit is mentioned immediately after the chatbot asks for favorite food. The slightly more complex pattern for the rule labelled WHATMUSIC requires all the words what, music, you and any word or phrase meaning to like, but they may occur in any order. Responders come in three types. ?: rules react to user questions. s: rules react to user statements. u: rules react to either. ChatScript code supports standard if-else, loops, user-defined functions and calls, and variable assignment and access. == Data == Some data in ChatScript is transient, meaning it will disappear at the end of the current volley. Other data is permanent, lasting forever until explicitly killed off. Data can be local to a single user or shared across all users at the bot level. Internally all data is represented as text and is automatically converted to a numeric form as needed. === Variables === User variables come in several kinds. Variables purely local to a topic or function are transient. Global variables can be declared as transient or permanent. A variable is generally declared merely by using it, and its type depends on its prefix ($, $$, $_). === Facts === In addition to variables, ChatScript supports facts – triples of data, which can also be transient or permanent. Functions can query for facts having particular values of some of the fields, making them act like an in-memory database. Fact retrieval is very quick and efficient the number of available in-memory facts is largely constrained to the available memory of the machine running the ChatScript engine. Facts can represent record structures and are how ChatScript represents JSON internally. Tables of information can be defined to generate appropriate facts. The above table links people to what they invented (1 per line) with Einstein getting a list of things he did. == External communication == ChatScript embeds the Curl library and can directly read and write facts in JSON to a website. == Server == A ChatScript engine can run in local or server mode. == Pos-tagging, parsing, and ontology == ChatScript comes with a copy of English WordNet embedded within, including its ontology, and creates and extends its own ontology via concept declarations. It has an English language pos-tagger and parser and supports integration with TreeTagger for pos-tagging a number of other languages (TreeTagger commercial license required). == Databases == In addition to an internal fact database, ChatScript supports PostgreSQL, MySQL, MSSQL and MongoDB both for access by scripts, but also as a central filesystem if desired so ChatScript can be scaled horizontally. A common use case is to use a centralized database to host the user files and multiple servers to scale the ChatScript engine. == JavaScript == ChatScript also embeds DukTape, ECMAScript E5/E5.1 compatibility, with some semantics updated from ES2015+. == Spelling Correction == ChatScript has built-in automatic spell checking, which can be augmented in script as both simple word replacements or context sensitive changes. With appropriate simple rules you can change perfect legal words into other words or delete them. E.g., if you have a concept of ~electronic_goods and don't want an input of Radio Shack (a store name) to be detected as an electronic good, you can get the input to change to Radio_Shack (a single word), or allow the words to remain but block the detection of the concept. This is particularly useful when combined with speech-to-text code that is imperfect, but you are familiar with common failings of it and can compensate for them in script. == Control flow == A chatbot's control flow is managed by the control script. This is merely another ordinary topic of rules, that invokes API functions of the engine. Thus control is fully configurable by the scripter (and functions exist to allow introspection into the engine). There are pre-processing control flow and post-processing control flow options available, for special processing.

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  List of data science software

  This is a list of data science software and platforms used in data science, which includes programming languages, programming environments, machine learning frameworks, data engineering tools, statistical software, data analysis, plotting, MLOps systems, and more. == Programming languages == == Development environments == These interactive notebooks, IDEs, and platforms provide specialised development environments. Apache Zeppelin Architect — Eclipse (software) CoCalc Dataiku Data Science Studio FreeMat GNU Octave Google Colab DataSpell Jupyter Notebook / JupyterLab Kaggle Notebooks MATLAB O-Matrix PyCharm RStudio SAS (software) and SAS Studio Spyder Visual Studio Code == Machine and deep learning software == The Machine learning / deep learning tools support development in those fields. == Data engineering == Examples of Data engineering tools. Apache Airflow Apache Flink Apache Hadoop Apache Kafka Apache NiFi Apache Spark Dask Data build tool (dbt) == Data mining == Examples of Data mining tools. === Free and open-source === === Proprietary === == Database management == === List of RDBMS === ==== Proprietary ==== == Data warehouses == Data warehouse environments include: Amazon Redshift Snowflake Google BigQuery Microsoft Azure Synapse Teradata Vertica == Data lakes == Data lake environments include: Apache Hadoop Cloudera Databricks Delta Lake Amazon S3 Google Cloud Storage Azure Data Lake == Algorithms == Apriori algorithm – frequent itemset mining and association rule learning in market basket analysis Backpropagation – algorithm for training artificial neural networks using gradient descent Decision Trees – tree-based algorithm for classification and regression Expectation–maximization algorithm – iterative procedure for maximum likelihood estimation with latent variables Gradient descent – iterative optimization algorithm for minimizing a loss function ID3 algorithm – used to generate a decision tree from a dataset K-Means – clustering algorithm based on minimizing within-cluster distances K-Nearest Neighbors (KNN) – instance-based learning and classification method Linear regression – estimation method for predicting a dependent variable based on independent variables Logistic regression – classification algorithm for predicting a binary outcome Naive Bayes – probabilistic classifier based on Bayes' theorem Ordinary least squares – estimation method for parameters in linear regression PageRank – graph-based algorithm for link analysis and search ranking Principal component analysis – technique to reduce high-dimensional data while preserving variance Q-learning – reinforcement learning algorithm for learning optimal actions Random forest – ensemble of decision trees for improved classification or regression Sequential minimal optimization – solver for training support vector machines Stochastic gradient descent – randomized variant of gradient descent for large-scale machine learning Support Vector Machines (SVM) – algorithm for finding a hyperplane to separate classes == Statistical software == === Open-source === === Public domain === CSPro Dataplot Epi Map X-13ARIMA-SEATS === Freeware === BV4.1 MINUIT WinBUGS Winpepi === Proprietary === == Data processing == Tools for Data processing and analysis: == Data and information visualization == Software for Data visualization: == Plotting software == Software for plotting data to support processing and visualise results. == Maps and geospatial visualization == ArcGIS Carto Epi Map GeoDA Google Earth Engine Leaflet Mapbox MountainsMap QGIS == Machine learning == MLOps and model deployment: BentoML Data Version Control (DVC) Kubeflow MLflow Seldon Core Streamlit TensorFlow Serving Weights & Biases == Data repositories == Kaggle – platform for data science competitions, datasets, and notebooks. OpenML – collaborative platform for sharing datasets, algorithms, and experiments. University of California, Irvine Machine Learning Repository Zenodo – open-access repository supported by CERN and the EU. == Educational data science software == Kaggle – online platform for data science education, competitions, datasets, and collaborative learning. KNIME – open-source data analytics platform used for teaching data science, machine learning, and workflow-based analysis. RapidMiner – used in academic research and education for data mining and machine learning. Statistics Online Computational Resource (SOCR) – online tools and instructional resources for statistics education. Tanagra (machine learning) – data mining software developed for research and teaching purposes. TinkerPlots – explore and analyze data through visual modeling.

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  NetMiner

  NetMiner is an all-in-one software platform for analyzing and visualizing complex network data, based on Social Network Analysis (SNA). Originally released in 2001, it supports research and education in a wide range of domains through interactive and visual data exploration. This tool allows researchers to explore their network data visually and interactively, and helps them to detect underlying patterns and structures of the network. It has also been recognized for its comprehensive features and user-friendly interface in comparative reviews of SNA software packages. == Features == === Integrated Data Environment === NetMiner supports unified management of diverse data types—including network (nodes and links), tabular, and unstructured text data—within a single platform. This enables users to perform the entire analysis workflow seamlessly without switching between tools. NetMiner also supports a wide range of analytical methods, allowing users to derive new insights by combining multiple approaches. Analytical results can be saved and reused across workflows(Add to Dataset) Graph and Network Analysis: Includes Centrality, Community Detection, Blockmodeling, and Similarity Measures. Machine learning: Provides algorithms for regression, classification, clustering, ensemble modeling and XAI(Explainable AI) Graph Neural Networks (GNNs): Supports models such as GraphSAGE, GCN, and GAT to learn from both node attributes and graph structure. Natural language processing (NLP): Uses pretrained deep learning models to analyze unstructured text, including named entity recognition and keyword extraction. Text mining and Text network analysis: Supports construction of word co-occurrence networks and topic modeling using LDA, BERTopic, enabling identification of thematic patterns and semantic structures in text data. Data Visualization: Offers advanced network visualization features, supporting multiple layout algorithms. Analytical outcomes such as centrality or community detection can be directly reflected in the network map via node size, color, and position, enhancing intuitive understanding. === AI Assistant === NetMiner integrates with external large language models such as OpenAI GPT and Google Gemini to interpret complex analysis results in natural language, summarize key findings, and suggest next steps for exploration. === Workflow and Usability === Designed to follow the structure of real-world data analysis workflows, NetMiner adopts a hierarchical data organization (Project → Workspace → Dataset → Data Item). Its web-based user interface improves clarity and reduces complexity. NetMiner 5 supports Windows 10 or higher and macOS 11 or later with M1 chip. Both academic and commercial licenses are available. == Extension == NetMiner Extension is small program to extend the functionality of NetMiner. In other words, it enables you to customize NetMiner according to your needs. By adding ‘NetMiner Extension’, you can expand your research. === Web Data Collection === NetMiner allows users to collect data from services such as YouTube, OpenAlex, Springer, and KCI via Open APIs. Collected data is automatically preprocessed and transformed to fit NetMiner’s internal structure, requiring no additional coding or external tools. SNS Data Collector: It collects social media data from YouTube, which has a large number of social media users worldwide. Biblio Data Collector: It collects the bibliographic data from Springer, OpenAlex, and KCI essential for research trend analysis. == File formats == === NetMiner data file format === .NMF === Importable/exportable formats === Plain text data: .TXT, .CSV Microsoft Excel data: .XLS, .XLSX Unstructured text data: .TXT, .CSV, .XLS(X) ※ NetMiner 4 only NetMiner 2 data: .NTF UCINet data: .DL, .DAT Pajek data: .NET, .VEC, .CLU, .PER StOCNET data file: .DAT Graph Modelling Language data: .GML(importing only) Related software UCINET Pajek Gephi StoCNET == Data structure == === Hierarchy of NetMiner data structure === NetMiner 5 supports not only graph data composed of nodes and links, but also tabular and unstructured data without fixed schema or identifiers. This enables users to easily import a wide variety of raw and unstructured data suitable for machine learning applications. Within a single workspace, users can manage node sets, link sets, and structured/unstructured data simultaneously. Multiple graph layers under a node set can be organized in a tree structure, allowing for intuitive understanding of the data currently being analyzed. == Release history == The first version of NetMiner was released on Dec 21, 2001. There have been five major updates from 2001. === NetMiner 5 === Released on June 9, 2025. NetMiner 5 retains the core features and no-code concept of NetMiner 4, but has evolved by integrating cutting-edge AI technologies. AI Assistant, Personal Analytics Tutor Support for Graph, Structured, and Unstructured Data Graph Analytics / Social Network Analysis Machine Learning(M/L) & XAI Graph Machine Learning(GML): Graph Neural Network Text Mining: Natural Language Processing(NLP), Text Network, Topic Modeling Data Visualization === NetMiner 4 (2011) === Latest version is 4.5.1. Introduced Python scripting, encrypted NMF format, semantic analysis tools (word cloud, topic modeling), and Extension - Data Collector. === NetMiner 3 (2007) === Enhanced scalability, integrated analysis-visualization modules, and DB import from Oracle, MS SQL. === NetMiner 2 (2003) === Improved statistical and network measures, visualization algorithms, and external data import modules.

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  Virtual assistant

  A virtual assistant (VA) is a software agent that can perform a range of tasks or services for a user based on user input, such as commands or questions, including verbal ones. Such technologies often incorporate chatbot capabilities to streamline task execution. The interaction may be via text, graphical interface, or voice, as some virtual assistants are able to interpret human speech and respond via synthesized voices. In many cases, users can ask their virtual assistants questions, control home automation devices and media playback, and manage other basic tasks such as email, to-do lists, and calendars – all with verbal commands. In recent years, prominent virtual assistants for direct consumer use have included Apple Siri, Amazon Alexa, Google Assistant (Gemini), Microsoft Copilot and Samsung Bixby. Also, companies in various industries often incorporate some kind of virtual assistant technology into their customer service or support. Into the 2020s, the emergence of artificial intelligence based chatbots, such as ChatGPT, has brought increased capability and interest to the field of virtual assistant products and services. == History == === Experimental decades: 1910s–1980s === Radio Rex was the first voice-activated toy, patented in 1916 and released in 1922. It was a wooden toy in the shape of a dog that would come out of its house when its name is called. In 1952, Bell Labs presented "Audrey", the Automatic Digit Recognition machine. It occupied a six-foot-high relay rack, consumed substantial power, had streams of cables and exhibited the myriad maintenance problems associated with complex vacuum-tube circuitry. It could recognize the fundamental units of speech, phonemes. It was limited to the accurate recognition of digits spoken by designated talkers. It could therefore be used for voice dialing, but in most cases, push-button dialing was cheaper and faster, rather than speaking the consecutive digits. Another early tool which was enabled to perform digital speech recognition was the IBM Shoebox voice-activated calculator, presented to the general public during the 1962 Seattle World's Fair after its initial market launch in 1961. This early computer, developed almost 20 years before the introduction of the first IBM Personal Computer in 1981, was able to recognize 16 spoken words and the digits 0 to 9. The first natural language processing computer program or the chatbot ELIZA was developed by MIT professor Joseph Weizenbaum in the 1960s. It was created to "demonstrate that the communication between man and machine was superficial". ELIZA used pattern matching and substitution methodology into scripted responses to simulate conversation, which gave an illusion of understanding on the part of the program. Weizenbaum's own secretary reportedly asked Weizenbaum to leave the room so that she and ELIZA could have a real conversation. Weizenbaum was surprised by this, later writing: "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people. This gave name to the ELIZA effect, the tendency to unconsciously assume computer behaviors are analogous to human behaviors; that is, anthropomorphisation, a phenomenon present in human interactions with virtual assistants. The next milestone in the development of voice recognition technology was achieved in the 1970s at the Carnegie Mellon University in Pittsburgh, Pennsylvania with substantial support of the United States Department of Defense and its DARPA agency, funded five years of a Speech Understanding Research program, aiming to reach a minimum vocabulary of 1,000 words. Companies and academia including IBM, Carnegie Mellon University (CMU) and Stanford Research Institute took part in the program. The result was "Harpy", it mastered about 1000 words, the vocabulary of a three-year-old and it could understand sentences. It could process speech that followed pre-programmed vocabulary, pronunciation, and grammar structures to determine which sequences of words made sense together, and thus reducing speech recognition errors. In 1986, Tangora was an upgrade of the Shoebox, it was a voice recognizing typewriter. Named after the world's fastest typist at the time, it had a vocabulary of 20,000 words and used prediction to decide the most likely result based on what was said in the past. IBM's approach was based on a hidden Markov model, which adds statistics to digital signal processing techniques. The method makes it possible to predict the most likely phonemes to follow a given phoneme. Still each speaker had to individually train the typewriter to recognize their voice, and pause between each word. In 1983, Gus Searcy invented the "Butler in a Box", an electronic voice home controller system. === Birth of smart virtual assistants: 1990s–2010s === In the 1990s, digital speech recognition technology became a feature of the personal computer with IBM, Philips and Lernout & Hauspie fighting for customers. Much later the market launch of the first smartphone IBM Simon in 1994 laid the foundation for smart virtual assistants as we know them today. In 1997, Dragon's NaturallySpeaking software could recognize and transcribe natural human speech without pauses between each word into a document at a rate of 100 words per minute. A version of Naturally Speaking is still available for download and it is still used today, for instance, by many doctors in the US and the UK to document their medical records. In 2001 Colloquis publicly launched SmarterChild, on platforms like AIM and MSN Messenger. While entirely text-based SmarterChild was able to play games, check the weather, look up facts, and converse with users to an extent. The first modern digital virtual assistant installed on a smartphone was Siri, which was introduced as a feature of the iPhone 4S on 4 October 2011. Apple Inc. developed Siri following the 2010 acquisition of Siri Inc., a spin-off of SRI International, which is a research institute financed by DARPA and the United States Department of Defense. Its aim was to aid in tasks such as sending a text message, making phone calls, checking the weather or setting up an alarm. Over time, it has developed to provide restaurant recommendations, search the internet, and provide driving directions. In November 2014, Amazon announced Alexa alongside the Echo. In 2016, Salesforce debuted Einstein, developed from a set of technologies underlying the Salesforce platform. Einstein was replaced by Agentforce, an agentic AI, in September 2024. In April 2017 Amazon released a service for building conversational interfaces for any type of virtual assistant or interface. === Large Language Models: 2020s-present === In the 2020s, artificial intelligence (AI) systems like ChatGPT have gained popularity for their ability to generate human-like responses to text-based conversations. In February 2020, Microsoft introduced its Turing Natural Language Generation (T-NLG), which was then the "largest language model ever published at 17 billion parameters." On November 30, 2022, ChatGPT was launched as a prototype and quickly garnered attention for its detailed responses and articulate answers across many domains of knowledge. The advent of ChatGPT and its introduction to the wider public increased interest and competition in the space. In February 2023, Google began introducing an experimental service called "Bard" which is based on its LaMDA program to generate text responses to questions asked based on information gathered from the web. While ChatGPT and other generalized chatbots based on the latest generative AI are capable of performing various tasks associated with virtual assistants, there are also more specialized forms of such technology that are designed to target more specific situations or needs. == Method of interaction == Virtual assistants work via: Text, including: online chat (especially in an instant messaging application or other application ), SMS text, e-mail or other text-based communication channel, for example Conversica's intelligent virtual assistants for business. Voice: for example with Amazon Alexa on Amazon Echo devices, Siri on an iPhone, Google Assistant on Google-enabled Android devices, or Bixby on Samsung devices. Images: some assistants, such as Google Assistant (which includes Google Lens) and Bixby on the Samsung Galaxy series, have the added capability of performing image processing to recognize objects in images. Many virtual assistants are accessible via multiple methods, offering versatility in how users can interact with them, whether through chat, voice commands, or other integrated technologies. Virtual assistants use natural language processing (NLP) to match user text or voice input to executable commands. Some continually learn using artificial intelligence techniques including machine learning and ambient intelligence. To activate a virtual assistant u

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  Text-to-image personalization

  Text-to-Image personalization is a task in deep learning for computer graphics that augments pre-trained text-to-image generative models. In this task, a generative model that was trained on large-scale data (usually a foundation model), is adapted such that it can generate images of novel, user-provided concepts. These concepts are typically unseen during training, and may represent specific objects (such as the user's pet) or more abstract categories (new artistic style or object relations). Text-to-Image personalization methods typically bind the novel (personal) concept to new words in the vocabulary of the model. These words can then be used in future prompts to invoke the concept for subject-driven generation, inpainting, style transfer and even to correct biases in the model. To do so, models either optimize word-embeddings, fine-tune the generative model itself, or employ a mixture of both approaches. == Technology == Text-to-Image personalization was first proposed during August 2022 by two concurrent works, Textual Inversion and DreamBooth. In both cases, a user provides a few images (typically 3–5) of a concept, like their own dog, together with a coarse descriptor of the concept class (like the word "dog"). The model then learns to represent the subject through a reconstruction based objective, where prompts referring to the subject are expected to reconstruct images from the training set. In Textual Inversion, the personalized concepts are introduced into the text-to-image model by adding new words to the vocabulary of the model. Typical text-to-image models represent words (and sometimes parts-of-words) as tokens, or indices in a predefined dictionary. During generation, an input prompt is converted into such tokens, each of which is converted into a ‘word-embedding’: a continuous vector representation which is learned for each token as part of the model's training. Textual Inversion proposes to optimize a new word-embedding vector for representing the novel concept. This new embedding vector can then be assigned to a user-chosen string, and invoked whenever the user's prompt contains this string. In DreamBooth, rather than optimizing a new word vector, the full generative model itself is fine-tuned. The user first selects an existing token, typically one which rarely appears in prompts. The subject itself is then represented by a string containing this token, followed by a coarse descriptor of the subject's class. A prompt describing the subject will then take the form: "A photo of " (e.g. "a photo of sks cat" when learning to represent a specific cat). The text-to-image model is then tuned so that prompts of this form will generate images of the subject. == Textual Inversion == The key idea in Textual Inversion is to add a new term to the vocabulary of the diffusion model that corresponds to the new (personalized) concept. Textual Inversion operates by inverting the concepts into new pseudo-words within the textual embedding space of a pre-trained text-to-image model. These pseudo-words can be injected into new scenes using simple natural language descriptions, allowing for simple and intuitive modifications. The method allows a user to leverage multi-modal information — using a text-driven interface for ease of editing, but providing visual cues when approaching the limits of natural language. The resulting model is extremely light-weight per concept: only 1K long, but succeeds to encode detailed visual properties of the concept. == Extensions == Several approaches were proposed to refine and improve over the original methods. These include the following. Low-rank Adaptation (LoRA) - an adapter-based technique for efficient finetuning of models. In the case of text-to-image models, LoRA is typically used to modify the cross-attention layers of a diffusion model. Perfusion - a low rank update method that also locks the activations of the key matrix in the diffusion model's cross attention layers to the concept's coarse class. Extended Textual Inversion - a technique that learns an individual word embedding for each layer in the diffusion model's denoising network. Encoder-based methods that use another neural network to quickly personalize a model == Challenges and limitations == Text-to-image personalization methods must contend with several challenges. At their core is the goal of achieving high-fidelity to the personal concept while maintaining high alignment between novel prompts containing the subject, and the generated images (typically referred to as ‘editability’). Another challenge that personalization methods must contend with is memory requirements. Initial implementations of personalization methods required more than 20 Gigabytes of GPU memory, and more recent approaches have reported requirements of more than 40 Gigabytes. However, optimizations such as Flash Attention have since reduced this requirement considerably. Approaches that tune the entire generative model may also create checkpoints that are several gigabytes in size, making it difficult to share or store many models. Embedding based approaches require only a few kilobytes, but typically struggle to preserve identity while maintaining editability. More recent approaches have proposed hybrid tuning goals which optimize both an embedding and a subset of network weights. These can reduce storage requirements to as little as 100 Kilobytes while achieving quality comparable to full tuning methods. Finally, optimization processes can be lengthy, requiring several minutes of tuning for each novel concept. Encoder and quick-tuning methods aim to reduce this to seconds or less.

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  Blanking (video)

  In analog video, blanking occurs between horizontal lines and between frames. In raster scan equipment, an image is built up by scanning an electron beam from left to right across a screen to produce a visible trace of one scan line, reducing the brightness of the beam to zero (horizontal blanking), moving it back as fast as possible to the left of the screen at a slightly lower position (the next scan line), restoring the brightness, and continuing until all the lines have been displayed and the beam is at the bottom right of the screen. Its intensity is then reduced to zero again (vertical blanking), and it is rapidly moved to the top left to start again, creating the next frame. In television, in particular, the vertical blanking interval is long to accommodate the slow equipment available at the time the standard was set. Fast modern electronics allows digital information to be encoded into the signal during the vertical blanking interval; it is not displayed on screen as the beam is blanked, but can be processed by appropriate circuitry.

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  Neural operators

  Neural operators are a class of deep learning architectures designed to learn maps between infinite-dimensional function spaces. Neural operators represent an extension of traditional artificial neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets. Neural operators directly learn operators between function spaces; they can receive input functions, and the output function can be evaluated at any discretization. The primary application of neural operators is in learning surrogate maps for the solution operators of partial differential equations (PDEs), which are critical tools in modeling the natural environment. Standard PDE solvers can be time-consuming and computationally intensive, especially for complex systems. Neural operators have demonstrated improved performance in solving PDEs compared to existing machine learning methodologies while being significantly faster than numerical solvers. Neural operators have also been applied to various scientific and engineering disciplines such as turbulent flow modeling, computational mechanics, graph-structured data, and the geosciences. In particular, they have been applied to learning stress-strain fields in materials, classifying complex data like spatial transcriptomics, predicting multiphase flow in porous media, and carbon dioxide migration simulations. Finally, the operator learning paradigm allows learning maps between function spaces, and is different from parallel ideas of learning maps from finite-dimensional spaces to function spaces, and subsumes these settings as special cases when limited to a fixed input resolution. == Operator learning == Understanding and mapping relationships between function spaces has many applications in engineering and the sciences. In particular, one can cast the problem of solving partial differential equations as identifying a map between function spaces, such as from an initial condition to a time-evolved state. In other PDEs this map takes an input coefficient function and outputs a solution function. Operator learning is a machine learning paradigm to learn solution operators mapping the input function to the output function . Using traditional machine learning methods, addressing this problem would involve discretizing the infinite-dimensional input and output function spaces into finite-dimensional grids and applying standard learning models, such as neural networks. This approach reduces the operator learning to finite-dimensional function learning and has some limitations, such as generalizing to discretizations beyond the grid used in training. The primary properties of neural operators that differentiate them from traditional neural networks is discretization invariance and discretization convergence. Unlike conventional neural networks, which are fixed on the discretization of training data, neural operators can adapt to various discretizations without re-training. This property improves the robustness and applicability of neural operators in different scenarios, providing consistent performance across different resolutions and grids. == Definition and formulation == Architecturally, neural operators are similar to feed-forward neural networks in the sense that they are composed of alternating linear maps and non-linearities. Since neural operators act on and output functions, neural operators have been instead formulated as a sequence of alternating linear integral operators on function spaces and point-wise non-linearities. Using an analogous architecture to finite-dimensional neural networks, similar universal approximation theorems have been proven for neural operators. In particular, it has been shown that neural operators can approximate any continuous operator on a compact set. Neural operators seek to approximate some operator G : A → U {\displaystyle {\mathcal {G}}:{\mathcal {A}}\to {\mathcal {U}}} between function spaces A {\displaystyle {\mathcal {A}}} and U {\displaystyle {\mathcal {U}}} by building a parametric map G ϕ : A → U {\displaystyle {\mathcal {G}}_{\phi }:{\mathcal {A}}\to {\mathcal {U}}} . Such parametric maps G ϕ {\displaystyle {\mathcal {G}}_{\phi }} can generally be defined in the form G ϕ := Q ∘ σ ( W T + K T + b T ) ∘ ⋯ ∘ σ ( W 1 + K 1 + b 1 ) ∘ P , {\displaystyle {\mathcal {G}}_{\phi }:={\mathcal {Q}}\circ \sigma (W_{T}+{\mathcal {K}}_{T}+b_{T})\circ \cdots \circ \sigma (W_{1}+{\mathcal {K}}_{1}+b_{1})\circ {\mathcal {P}},} where P , Q {\displaystyle {\mathcal {P}},{\mathcal {Q}}} are the lifting (lifting the codomain of the input function to a higher dimensional space) and projection (projecting the codomain of the intermediate function to the output dimension) operators, respectively. These operators act pointwise on functions and are typically parametrized as multilayer perceptrons. σ {\displaystyle \sigma } is a pointwise nonlinearity, such as a rectified linear unit (ReLU), or a Gaussian error linear unit (GeLU). Each layer t = 1 , … , T {\displaystyle t=1,\dots ,T} has a respective local operator W t {\displaystyle W_{t}} (usually parameterized by a pointwise neural network), a kernel integral operator K t {\displaystyle {\mathcal {K}}_{t}} , and a bias function b t {\displaystyle b_{t}} . Given some intermediate functional representation v t {\displaystyle v_{t}} with domain D {\displaystyle D} in the t {\displaystyle t} -th hidden layer, a kernel integral operator K ϕ {\displaystyle {\mathcal {K}}_{\phi }} is defined as ( K ϕ v t ) ( x ) := ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x):=\int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy,} where the kernel κ ϕ {\displaystyle \kappa _{\phi }} is a learnable implicit neural network, parametrized by ϕ {\displaystyle \phi } . In practice, one is often given the input function to the neural operator at a specific resolution. For instance, consider the setting where one is given the evaluation of v t {\displaystyle v_{t}} at n {\displaystyle n} points { y j } j n {\displaystyle \{y_{j}\}_{j}^{n}} . Borrowing from Nyström integral approximation methods such as Riemann sum integration and Gaussian quadrature, the above integral operation can be computed as follows: ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y ≈ ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j , {\displaystyle \int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy\approx \sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}},} where Δ y j {\displaystyle \Delta _{y_{j}}} is the sub-area volume or quadrature weight associated to the point y j {\displaystyle y_{j}} . Thus, a simplified layer can be computed as v t + 1 ( x ) ≈ σ ( ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j + W t ( v t ( y j ) ) + b t ( x ) ) . {\displaystyle v_{t+1}(x)\approx \sigma \left(\sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}}+W_{t}(v_{t}(y_{j}))+b_{t}(x)\right).} The above approximation, along with parametrizing κ ϕ {\displaystyle \kappa _{\phi }} as an implicit neural network, results in the graph neural operator (GNO). There have been various parameterizations of neural operators for different applications. These typically differ in their parameterization of κ {\displaystyle \kappa } . The most popular instantiation is the Fourier neural operator (FNO). FNO takes κ ϕ ( x , y , v t ( x ) , v t ( y ) ) := κ ϕ ( x − y ) {\displaystyle \kappa _{\phi }(x,y,v_{t}(x),v_{t}(y)):=\kappa _{\phi }(x-y)} and by applying the convolution theorem, arrives at the following parameterization of the kernel integral operator: ( K ϕ v t ) ( x ) = F − 1 ( R ϕ ⋅ ( F v t ) ) ( x ) , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x)={\mathcal {F}}^{-1}(R_{\phi }\cdot ({\mathcal {F}}v_{t}))(x),} where F {\displaystyle {\mathcal {F}}} represents the Fourier transform and R ϕ {\displaystyle R_{\phi }} represents the Fourier transform of some periodic function κ ϕ {\displaystyle \kappa _{\phi }} . That is, FNO parameterizes the kernel integration directly in Fourier space, using a prescribed number of Fourier modes. When the grid at which the input function is presented is uniform, the Fourier transform can be approximated using the discrete Fourier transform (DFT) with frequencies below some specified threshold. The discrete Fourier transform can be computed using a fast Fourier transform (FFT) implementation. == Training == Training neural operators is similar to the training process for a traditional neural network. Neural operators are typically trained in some Lp norm or Sobolev norm. In particular, for a dataset { ( a i , u i ) } i = 1 N {\displaystyle \{(a_{i},u_{i})\}_{i=1}^{N}} of size N {\displaystyle N} , neural operators minimize (a discretization of) L U ( { ( a i , u i ) } i = 1 N ) := ∑ i = 1 N ‖ u i − G θ ( a i ) ‖ U 2 {\displaystyle {\mathcal {L}}_{\mathca

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  Weak supervision

  Weak supervision (also known as semi-supervised learning) is a paradigm in machine learning, the relevance and notability of which increased with the advent of large language models due to the large amount of data required to train them. It is characterized by using a combination of a small amount of human-labeled data (exclusively used in more expensive and time-consuming supervised learning paradigm), followed by a large amount of unlabeled data (used exclusively in unsupervised learning paradigm). In other words, the desired output values are provided only for a subset of the training data. The remaining data is unlabeled or imprecisely labeled. Intuitively, it can be seen as an exam and labeled data as sample problems that the teacher solves for the class as an aid in solving another set of problems. In the transductive setting, these unsolved problems act as exam questions. In the inductive setting, they become practice problems of the sort that will make up the exam. == Problem == The acquisition of labeled data for a learning problem often requires a skilled human agent (e.g. to transcribe an audio segment) or a physical experiment (e.g. determining the 3D structure of a protein or determining whether there is oil at a particular location). The cost associated with the labeling process thus may render large, fully labeled training sets infeasible, whereas acquisition of unlabeled data is relatively inexpensive. In such situations, semi-supervised learning can be of great practical value. Semi-supervised learning is also of theoretical interest in machine learning and as a model for human learning. == Technique == More formally, semi-supervised learning assumes a set of l {\displaystyle l} independently identically distributed examples x 1 , … , x l ∈ X {\displaystyle x_{1},\dots ,x_{l}\in X} with corresponding labels y 1 , … , y l ∈ Y {\displaystyle y_{1},\dots ,y_{l}\in Y} and u {\displaystyle u} unlabeled examples x l + 1 , … , x l + u ∈ X {\displaystyle x_{l+1},\dots ,x_{l+u}\in X} are processed. Semi-supervised learning combines this information to surpass the classification performance that can be obtained either by discarding the unlabeled data and doing supervised learning or by discarding the labels and doing unsupervised learning. Semi-supervised learning may refer to either transductive learning or inductive learning. The goal of transductive learning is to infer the correct labels for the given unlabeled data x l + 1 , … , x l + u {\displaystyle x_{l+1},\dots ,x_{l+u}} only. The goal of inductive learning is to infer the correct mapping from X {\displaystyle X} to Y {\displaystyle Y} . It is unnecessary (and, according to Vapnik's principle, imprudent) to perform transductive learning by way of inferring a classification rule over the entire input space; however, in practice, algorithms formally designed for transduction or induction are often used interchangeably. == Assumptions == In order to make any use of unlabeled data, some relationship to the underlying distribution of data must exist. Semi-supervised learning algorithms make use of at least one of the following assumptions: === Continuity / smoothness assumption === Points that are close to each other are more likely to share a label. This is also generally assumed in supervised learning and yields a preference for geometrically simple decision boundaries. In the case of semi-supervised learning, the smoothness assumption additionally yields a preference for decision boundaries in low-density regions, so few points are close to each other but in different classes. === Cluster assumption === The data tend to form discrete clusters, and points in the same cluster are more likely to share a label (although data that shares a label may spread across multiple clusters). This is a special case of the smoothness assumption and gives rise to feature learning with clustering algorithms. === Manifold assumption === The data lie approximately on a manifold of much lower dimension than the input space. In this case learning the manifold using both the labeled and unlabeled data can avoid the curse of dimensionality. Then learning can proceed using distances and densities defined on the manifold. The manifold assumption is practical when high-dimensional data are generated by some process that may be hard to model directly, but which has only a few degrees of freedom. For instance, human voice is controlled by a few vocal folds, and images of various facial expressions are controlled by a few muscles. In these cases, it is better to consider distances and smoothness in the natural space of the generating problem, rather than in the space of all possible acoustic waves or images, respectively. == History == The heuristic approach of self-training (also known as self-learning or self-labeling) is historically the oldest approach to semi-supervised learning, with examples of applications starting in the 1960s. The transductive learning framework was formally introduced by Vladimir Vapnik in the 1970s. Interest in inductive learning using generative models also began in the 1970s. A probably approximately correct learning bound for semi-supervised learning of a Gaussian mixture was demonstrated by Ratsaby and Venkatesh in 1995. == Methods == === Generative models === Generative approaches to statistical learning first seek to estimate p ( x | y ) {\displaystyle p(x|y)} , the distribution of data points belonging to each class. The probability p ( y | x ) {\displaystyle p(y|x)} that a given point x {\displaystyle x} has label y {\displaystyle y} is then proportional to p ( x | y ) p ( y ) {\displaystyle p(x|y)p(y)} by Bayes' rule. Semi-supervised learning with generative models can be viewed either as an extension of supervised learning (classification plus information about p ( x ) {\displaystyle p(x)} ) or as an extension of unsupervised learning (clustering plus some labels). Generative models assume that the distributions take some particular form p ( x | y , θ ) {\displaystyle p(x|y,\theta )} parameterized by the vector θ {\displaystyle \theta } . If these assumptions are incorrect, the unlabeled data may actually decrease the accuracy of the solution relative to what would have been obtained from labeled data alone. However, if the assumptions are correct, then the unlabeled data necessarily improves performance. The unlabeled data are distributed according to a mixture of individual-class distributions. In order to learn the mixture distribution from the unlabeled data, it must be identifiable, that is, different parameters must yield different summed distributions. Gaussian mixture distributions are identifiable and commonly used for generative models. The parameterized joint distribution can be written as p ( x , y | θ ) = p ( y | θ ) p ( x | y , θ ) {\displaystyle p(x,y|\theta )=p(y|\theta )p(x|y,\theta )} by using the chain rule. Each parameter vector θ {\displaystyle \theta } is associated with a decision function f θ ( x ) = argmax y p ( y | x , θ ) {\displaystyle f_{\theta }(x)={\underset {y}{\operatorname {argmax} }}\ p(y|x,\theta )} . The parameter is then chosen based on fit to both the labeled and unlabeled data, weighted by λ {\displaystyle \lambda } : argmax Θ ( log ⁡ p ( { x i , y i } i = 1 l | θ ) + λ log ⁡ p ( { x i } i = l + 1 l + u | θ ) ) {\displaystyle {\underset {\Theta }{\operatorname {argmax} }}\left(\log p(\{x_{i},y_{i}\}_{i=1}^{l}|\theta )+\lambda \log p(\{x_{i}\}_{i=l+1}^{l+u}|\theta )\right)} === Low-density separation === Another major class of methods attempts to place boundaries in regions with few data points (labeled or unlabeled). One of the most commonly used algorithms is the transductive support vector machine, or TSVM (which, despite its name, may be used for inductive learning as well). Whereas support vector machines for supervised learning seek a decision boundary with maximal margin over the labeled data, the goal of TSVM is a labeling of the unlabeled data such that the decision boundary has maximal margin over all of the data. In addition to the standard hinge loss ( 1 − y f ( x ) ) + {\displaystyle (1-yf(x))_{+}} for labeled data, a loss function ( 1 − | f ( x ) | ) + {\displaystyle (1-|f(x)|)_{+}} is introduced over the unlabeled data by letting y = sign ⁡ f ( x ) {\displaystyle y=\operatorname {sign} {f(x)}} . TSVM then selects f ∗ ( x ) = h ∗ ( x ) + b {\displaystyle f^{}(x)=h^{}(x)+b} from a reproducing kernel Hilbert space H {\displaystyle {\mathcal {H}}} by minimizing the regularized empirical risk: f ∗ = argmin f ( ∑ i = 1 l ( 1 − y i f ( x i ) ) + + λ 1 ‖ h ‖ H 2 + λ 2 ∑ i = l + 1 l + u ( 1 − | f ( x i ) | ) + ) {\displaystyle f^{}={\underset {f}{\operatorname {argmin} }}\left(\displaystyle \sum _{i=1}^{l}(1-y_{i}f(x_{i}))_{+}+\lambda _{1}\|h\|_{\mathcal {H}}^{2}+\lambda _{2}\sum _{i=l+1}^{l+u}(1-|f(x_{i})|)_{+}\right)} An exact solution is intractable due to the non-convex term ( 1 − | f ( x ) | ) + {\displayst

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