AI Content Creator Course Review

AI Content Creator Course Review — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Object Data Management Group

  The Object Data Management Group (ODMG) was conceived in the summer of 1991 at a breakfast with object database vendors that was organized by Rick Cattell of Sun Microsystems. In 1998, the ODMG changed its name from the Object Database Management Group to reflect the expansion of its efforts to include specifications for both object database and object–relational mapping products. The primary goal of the ODMG was to put forward a set of specifications that allowed a developer to write portable applications for object database and object–relational mapping products. In order to do that, the data schema, programming language bindings, and data manipulation and query languages needed to be portable. Between 1993 and 2001, the ODMG published five revisions to its specification. The last revision was ODMG version 3.0, after which the group disbanded. == Major components of the ODMG 3.0 specification == Object Model. This was based on the Object Management Group's Object Model. The OMG core model was designed to be a common denominator for object request brokers, object database systems, object programming languages, etc. The ODMG designed a profile by adding components to the OMG core object model. Object Specification Languages. The ODMG Object Definition Language (ODL) was used to define the object types that conform to the ODMG Object Model. The ODMG Object Interchange Format (OIF) was used to dump and load the current state to or from a file or set of files. Object Query Language (OQL). The ODMG OQL was a declarative (nonprocedural) language for query and updating. It used SQL as a basis, where possible, though OQL supports more powerful object-oriented capabilities. C++ Language Binding. This defined a C++ binding of the ODMG ODL and a C++ Object Manipulation Language (OML). The C++ ODL was expressed as a library that provides classes and functions to implement the concepts defined in the ODMG Object Model. The C++ OML syntax and semantics are those of standard C++ in the context of the standard class library. The C++ binding also provided a mechanism to invoke OQL. Smalltalk Language Binding. This defined the mapping between the ODMG ODL and Smalltalk, which was based on the OMG Smalltalk binding for the OMG Interface Definition Language (IDL). The Smalltalk binding also provided a mechanism to invoke OQL. Java Language Binding. This defined the binding between the ODMG ODL and the Java programming language as defined by the Java 2 Platform. The Java binding also provided a mechanism to invoke OQL. == Status == ODMG 3.0 was published in book form in 2000.[1] By 2001, most of the major object database and object-relational mapping vendors claimed conformance to the ODMG Java Language Binding. Compliance to the other components of the specification was mixed.[2] In 2001, the ODMG Java Language Binding was submitted to the Java Community Process as a basis for the Java Data Objects specification. The ODMG member companies then decided to concentrate their efforts on the Java Data Objects specification. As a result, the ODMG disbanded in 2001. In 2004, the Object Management Group (OMG) was granted the right to revise the ODMG 3.0 specification as an OMG specification by the copyright holder, Morgan Kaufmann Publishers. In February 2006, the OMG announced the formation of the Object Database Technology Working Group (ODBT WG) and plans to work on the 4th generation of an object database standard. == ODMG Compliant DBMS == Orient ODBMS: http://www.OrienTechnologies.com Objectivity/DB C++, Java and Smalltalk interfaces.

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  Lighthill report

  Artificial Intelligence: A General Survey, commonly known as the Lighthill report, is a scholarly article by James Lighthill, published in Artificial Intelligence: a paper symposium in 1973. It was compiled by Lighthill for the British Science Research Council as an evaluation of academic research in the field of artificial intelligence (AI). The report gave a very pessimistic prognosis for many core aspects of research in this field, stating that "In no part of the field have the discoveries made so far produced the major impact that was then promised". It "formed the basis for the decision by the British government to end support for AI research in most British universities", contributing to an AI winter in the United Kingdom. == Publication history == It was commissioned by the SRC in 1972 for Lighthill to "make a personal review of the subject [of AI]". Lighthill completed the report in July. The SRC discussed the report in September, and decided to publish it, together with some alternative points of view by Stuart Sutherland, Roger Needham, Christopher Longuet-Higgins, and Donald Michie. The SRC's decision to invite the report was partly a reaction to high levels of discord within the University of Edinburgh's Department of Artificial Intelligence, one of the earliest and biggest centres for AI research in the UK. On May 9, 1973, Lighthill debated several leading AI researchers (Donald Michie, John McCarthy, Richard Gregory) at the Royal Institution in London concerning the report. == Content == While the report was supportive of research into the simulation of neurophysiological and psychological processes, it was "highly critical of basic research in foundational areas such as robotics and language processing". The report stated that AI researchers had failed to address the issue of combinatorial explosion when solving problems within real-world domains. That is, the report states that whilst AI techniques may have worked within the scope of small problem domains, the techniques would not scale up well to solve more realistic problems. The report represents a pessimistic view of AI that began after early excitement in the field. The report divides AI research into three categories: Advanced Automation ("A"): applications of AI, such as optical character recognition, mechanical component design and manufacture, missile perception and guidance, etc. Computer-based Central Nervous System research ("C"): building computational models of human brains (neurobiology) and behavior (psychology). Bridge, or Building Robots ("B"): research that combines categories A and C. This category is intentionally vague. Projects in category A had had some success, but only in restricted domains where a large quantity of detailed knowledge was used in designing the program. This was disappointing to researchers who hoped for generic methods. Due to the issue of the combinatorial explosion, the amount of detailed knowledge required by the program quickly grew too large to be entered by hand, thus restricting projects to restricted domains. Projects in category C had had some measure of success. Artificial neural networks were successfully used to model neurobiological data. SHRDLU demonstrated that human use of language, even in fine details, depends on the semantics or knowledge, and is not purely syntactical. This was influential in psycholinguistics. Attempts to extend SHRDLU to larger domains of discourse was considered impractical, again due to the issue of the combinatorial explosion. Projects in category B were held to be failures. One important project, that of "programming and building a robot that would mimic human ability in a combination of eye-hand co-ordination and common-sense problem solving", was considered entirely disappointing. Similarly, chess playing programs were no better than human amateurs. Due to the combinatorial explosion, the run-time of general algorithms quickly grew impractical, requiring detailed problem-specific heuristics. The report stated that it was expected that within the next 25 years, category A would simply become applied technologies engineering, C would integrate with psychology and neurobiology, while category B would be abandoned.

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  Frame (artificial intelligence)

  Frames are an artificial intelligence data structure used to divide knowledge into substructures by representing "stereotyped situations". They were proposed by Marvin Minsky in his 1974 article "A Framework for Representing Knowledge". Frames are the primary data structure used in artificial intelligence frame languages; they are stored as ontologies of sets. Frames are also an extensive part of knowledge representation and reasoning schemes. They were originally derived from semantic networks and are therefore part of structure-based knowledge representations. According to Russell and Norvig's Artificial Intelligence: A Modern Approach, structural representations assemble "facts about particular object and event types and [arrange] the types into a large taxonomic hierarchy analogous to a biological taxonomy". == Frame structure == The frame contains information on how to use the frame, what to expect next, and what to do when these expectations are not met. Some information in the frame is generally unchanged while other information, stored in "terminals", usually change. Terminals can be considered as variables. Top-level frames carry information, that is always true about the problem in hand, however, terminals do not have to be true. Their value might change with the new information encountered. Different frames may share the same terminals. Each piece of information about a particular frame is held in a slot. The information can contain: Facts or Data Values (called facets) Procedures (also called procedural attachments) IF-NEEDED: deferred evaluation IF-ADDED: updates linked information Default Values For Data For Procedures Other Frames or Subframes == Features and advantages == A frame's terminals are already filled with default values, which is based on how the human mind works. For example, when a person is told "a boy kicks a ball", most people will visualize a particular ball (such as a familiar soccer ball) rather than imagining some abstract ball with no attributes. One particular strength of frame-based knowledge representations is that, unlike semantic networks, they allow for exceptions in particular instances. This gives frames a degree of flexibility that allows representations to reflect real-world phenomena more accurately. Like semantic networks, frames can be queried using spreading activation. Following the rules of inheritance, any value given to a slot that is inherited by subframes will be updated (IF-ADDED) to the corresponding slots in the subframes and any new instances of a particular frame will feature that new value as the default. Because frames are based on structures, it is possible to generate a semantic network given a set of frames even though it lacks explicit arcs. References to Noam Chomsky and his generative grammar of 1950 are generally missing from Minsky's work. The simplified structures of frames allow for easy analogical reasoning, a much prized feature in any intelligent agent. The procedural attachments provided by frames also allow a degree of flexibility that makes for a more realistic representation and gives a natural affordance for programming applications. == Example == Worth noticing here is the easy analogical reasoning (comparison) that can be done between a boy and a monkey just by having similarly named slots. Also notice that Alex, an instance of a boy, inherits default values like "Sex" from the more general parent object Boy, but the boy may also have different instance values in the form of exceptions such as the number of legs. == Frame language == A frame language is a technology used for knowledge representation in artificial intelligence. They are similar to class hierarchies in object-oriented languages although their fundamental design goals are different. Frames are focused on explicit and intuitive representation of knowledge whereas objects focus on encapsulation and information hiding. Frames originated in AI research and objects primarily in software engineering. However, in practice, the techniques and capabilities of frame and object-oriented languages overlap significantly. === Example === A simple example of concepts modeled in a frame language is the Friend of A Friend (FOAF) ontology defined as part of the Semantic Web as a foundation for social networking and calendar systems. The primary frame in this simple example is a Person. Example slots are the person's email, home page, phone, etc. The interests of each person can be represented by additional frames describing the space of business and entertainment domains. The slot knows links each person with other persons. Default values for a person's interests can be inferred by the web of people they are friends of. === Implementations === The earliest frame-based languages were custom developed for specific research projects and were not packaged as tools to be re-used by other researchers. Just as with expert system inference engines, researchers soon realized the benefits of extracting part of the core infrastructure and developing general-purpose frame languages that were not coupled to specific applications. One of the first general-purpose frame languages was KRL. One of the most influential early frame languages was KL-ONE. KL-ONE spawned several subsequent Frame languages. One of the most widely used successors to KL-ONE was the Loom language developed by Robert MacGregor at the Information Sciences Institute. In the 1980s, Artificial Intelligence generated a great deal of interest in the business world fueled by expert systems. This led to the development of many commercial products for the development of knowledge-based systems. These early products were usually developed in Lisp and integrated constructs such as IF-THEN rules for logical reasoning with Frame hierarchies for representing data. One of the most well known of these early Lisp knowledge-base tools was the Knowledge Engineering Environment (KEE) from Intellicorp. KEE provided a full Frame language with multiple inheritance, slots, triggers, default values, and a rule engine that supported backward and forward chaining. As with most early commercial versions of AI software KEE was originally deployed in Lisp on Lisp machine platforms but was eventually ported to PCs and Unix workstations. The research agenda of the Semantic Web spawned a renewed interest in automatic classification and frame languages. An example is the Web Ontology Language (OWL) standard for describing information on the Internet. OWL is a standard to provide a semantic layer on top of the Internet. The goal is that rather than searching the web using keywords as most search engines (e.g. Google) do today, the web can be organized by concepts organized in an ontology, like a directory structure. The name of the OWL language itself provides a good example of the value of a Semantic Web. If one were to search for "OWL" using the Internet today most of the pages retrieved would be on the bird Owl rather than the standard OWL. With a Semantic Web it would be possible to specify the concept "Web Ontology Language" and the user would not need to worry about the various possible acronyms or synonyms as part of the search. Likewise, the user would not need to worry about homonyms crowding the search results with irrelevant data such as information about birds of prey as in this simple example. In addition to OWL, various standards and technologies that are relevant to the Semantic Web and were influenced by Frame languages include OIL and DAML. The Protege Open Source software tool from Stanford University provides an ontology editing capability that is built on OWL and has the full capabilities of a classifier. However it ceased to explicitly support frames as of version 3.5 (which is maintained for those preferring frame orientation), with the current version being 5.6.8 as of 2025. The justification for moving from explicit frames being that OWL DL is more expressive and "industry standard". === Comparison of frames and objects === Frame languages have a significant overlap with object-oriented languages. The terminologies and goals of the two communities were different but as they moved from the academic world and labs to the commercial world developers tended to not care about philosophical issues and focused primarily on specific capabilities, taking the best from either camp regardless of where the idea began. What both paradigms have in common is a desire to reduce the distance between concepts in the real world and their implementation in software. As such both paradigms arrived at the idea of representing the primary software objects in taxonomies starting with very general types and progressing to more specific types. The following table illustrates the correlation between standard terminology from the object-oriented and frame language communities: The primary difference between the two paradigms was in the degree that encapsulation was considered a majo

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  ComfyUI

  ComfyUI is an open source, node-based program that allows users to generate images from a series of text prompts. It uses free diffusion models such as Stable Diffusion as the base model for its image capabilities combined with other tools such as ControlNet and LCM Low-rank adaptation with each tool being represented by a node in the program. == History == ComfyUI was released on GitHub in January 2023. According to comfyanonymous, the creator, a major goal of the project was to improve on existing software designs in terms of the user interface. The creator had been involved with Stability AI but by 3 June 2024 that involvement had ended and an organization called Comfy Org had been created along with the core developers. In July 2024, Nvidia announced support for ComfyUI within its RTX Remix modding software. In August 2024, support was added for the Flux diffusion model developed by Black Forest Labs, and Comfy Org joined the Open Model Initiative created by the Linux Foundation. As of Sept 2025, the project has 89.2k stars on GitHub. ComfyUI is one of the most popular user interfaces for Stable Diffusion, along with Automatic1111. == Features == ComfyUI's main feature is that it is node based. Each node has a function such as "load a model" or "write a prompt". The nodes are connected to form a control-flow graph called a workflow. When a prompt is queued, a highlighted frame appears around the currently executing node, starting from "load checkpoint" and ending with the final image and its save location. Workflows commonly consist of tens of nodes, forming a complex directed acyclic graph. Node types include loading a model, specifying prompts, samplers, schedulers, VAE decoders, face restoration and upscaling models, LoRAs, embeddings, and ControlNets. Several samplers are supported, such as Euler, Euler_a, dpmpp_2m_sde and dpmpp_3m_sde. Workflows can be saved to a file, allowing users to re-use node workflows and share them with other users. The file format for the workflows is in JSON and can be embedded in the generated images. Users have also created custom extensions to the base system which are exposed as new nodes, such as the extension for AnimateDiff, which aims to create videos. ComfyUI has been described as more complex compared to other diffusion UIs such as Automatic1111. A default node group is also included with the program. As of December 2024, 1,674 nodes were supported. ComfyUI Supports multiple text-to-image models including, Stable Diffusion, Flux and Tencent's Hunyuan-DiT, as well as custom models from Civitai like Pony. == LLMVision extension compromise == In June 2024, a hacker group called "Nullbulge" compromised an extension of ComfyUI to add malicious code to it. The compromised extension, called ComfyUI_LLMVISION, was used for integrating the interface with AI language models GPT-4 and Claude 3, and was hosted on GitHub. Nullbulge hosted a list of hundreds of ComfyUI users' login details across multiple services on its website, while users of the extension reported receiving numerous login notifications. vpnMentor conducted security research on the extension and claimed it could "steal crypto wallets, screenshot the user’s screen, expose device information and IP addresses, and steal files that contain certain keywords or extensions". Nullbulge's website claims they targeted users who committed "one of our sins", which included AI-art generation, art theft, promoting cryptocurrency, and any other kind of theft from artists such as from Patreon. They claimed that they were "a collective of individuals who believe in the importance of protecting artists' rights and ensuring fair compensation for their work" and that they believed that "AI-generated artwork is detrimental to the creative industry and should be discouraged".

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  Kubity

  Kubity is a cloud-based 3D communication tool that works on desktop computers, the web, smartphones, tablets, augmented reality gear, and virtual reality glasses. Kubity is powered by several proprietary 3D processing engines including "Paragone" and "Etna" that prepare the 3D file for transfer over mobile devices. Kubity has practical applications for architecture, interior design, engineering, product design, film, and video games among others. The majority of its users create 3D models using SketchUp or Autodesk Revit software. Kubity products include the Kubity web app and Kubity Go (a mobile application for iOS and Android). Kubity is compatible across many platforms, devices and operating systems including: iOS, Android, Firefox, Chrome, Windows, MacOS, and Linux. == History == Kubity was created by SPK Technology (ex Kubity S.A.S.), a Paris-based software company specializing in automatic 3D data optimization and visualization. Founded in 2012 by a group of software engineers and an urban projects developer, they united around a simple idea: create a way for anyone, anywhere to simply and intuitively explore 3D models on smartphones and computers. In order to bring architects, engineers and designers together with their clients around a 3D model, it was essential to develop an interactive platform that supported multiple desktop and mobile devices for instantaneous and fluid 3D navigation. With specifications in place, 15 engineers fused together several technologies: 3D design, data compression, decimation and rendering optimization, web and mobile transfer, and virtual reality headset integration. In January 2014, the first public Kubity prototype (1.0 Amethyst) was launched to a small group of beta testers with a plug-in that allowed users to import 3D models from SketchUp to their browser. A global release was announced in April 2014 at the SketchUp Basecamp in Vail, Colorado. In May 2015, Kubity launched a web application that worked using WebGL technology (2.0 Citrine). For the first time, users were able to drag and drop any SketchUp file in a web browser without having to install a plug-in. In December 2015, Kubity launched a mobile application on the App Store for iPhone, iPod, and iPad as well as on Google Play for Android devices (3.0 Druzy). In November 2016, Kubity launched support for Oculus Rift and HTC Vive (4.0 Emerald). Beginning in November 2017, Kubity launched a full suite rollout of mobile applications over six months that included Kubity AR for augmented reality, Kubity VR for virtual reality, and Kubity Mirror for remote presentations and screen mirroring (5.0 Feldspar). In September 2018, a one-click plugin for SketchUp and Revit (Kubity PRO), along with a mobile-first revamp of Kubity Go was launched, allowing PRO-to-Go device pairing for automatic mobile sync (6.0 Gypsum). In early 2019, the Kubity Go application was updated to include fully integrated AR, VR, and screen mirroring functionalities, killing off the dedicated companion apps Kubity AR, Kubity VR and Kubity Mirror in the process (7.0 Heliotrope). In January 2020, support for the Kubity PRO plugin for SketchUp and Revit was migrated to a SketchUp-only web app. == Technology == Kubity is powered by a proprietary 3D crystallization engine known as "Paragone"; a technology developed by SPK Technology. Paragone takes constrained information from a 3D file and runs it through the "BlockWave" algorithm (US Patent 10,482.629), also developed by SPK Technology. BlockWave is a multiphase optimization algorithm that combines 3D design, data compression, decimation and rendering optimization, web and mobile transfer, and mixed reality headset integration to create a crystallized universal format of the original file. One phase of the BlockWave algorithm is based on the quadric-based polygonal surface simplification algorithm, performed using predefined heuristics, and is associated with a plurality of simplified versions of the 3D model, each version being associated with a predefined level of detail adapted to the user specific end device. BlockWave extracts data content, geometry and textures, then sets quadrics for each top of the original 3D model, and identifies pairs of adjacent tops linked by vertices. The algorithm uses a local collapsing operator and a top-plan error metric to obtain a fixed number of faces or a maximum defined error; 3D meshing is simplified by replacing two points with one, then deleting the degrading faces and updating adjacent relations. Once decimation is completed, texture optimization is set using texture target parameters allowing maximized GPU memory to improve computing time. With texture encoding completed, the crystallized universal 3D file can now be easily opened on any user-specific end device and played across most digital devices with real-time rendering. == Features == === 3D Crystallization === A user converts (or crystallizes) a 3D file by exporting it with the Kubity web app. Crystallization adds features like AR/VR and cinematic fly-through tour as well as assigns the model a dedicated QR code. === Automatic Mobile Sync === When a 3D model is exported, it is automatically synced to Kubity Go on the user's mobile device. From there, it can be accessed, explored, and shared with others with or without an internet connection. === Security and Management === User models can be managed all in one place on Kubity Go or in a browser from their account. Models can be renamed, password-protected, shared, and played. === Augmented Reality === Developed using Apple ARKit and Google ARCore technology, Kubity Go's augmented reality feature maps the environment in a room detecting horizontal planes like tables and floors to track and place 3D objects. By blending digital objects and information with the environment, Kubity allows users to interact with 3D models in true augmented reality. Built-in communication features allows users to instantly share 3D models with anyone over text, email, social media, or direct device-to-device with a QR Code. Platform Support AR supports devices running iOS11 including: iPhone SE, iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, iPhone 8, iPhone X, all iPad Pro models, and iPad (2017). AR for Android requires Android 7.0 or later and access to the Google Play Store. === Virtual Reality === VR allows users to explore SketchUp models and Revit projects on-the-go right from a mobile device using Oculus Go, Google Cardboard, Samsung Gear VR, or the glasses-free Magic Window feature. Kubity's virtual reality feature is compatible with Oculus Go, Google Cardboard viewers and other cardboard compatible devices including clip-on style VR glasses like Homido Mini, as well as the mobile virtual reality headset, Samsung Gear VR. Samsung Gear VR supports: Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+, Samsung Galaxy Note 5, Galaxy S7, Galaxy S7 Edge, Galaxy S8, Galaxy S8+, Samsung Galaxy Note Fan Edition, Samsung Galaxy Note 8, Samsung Galaxy A8/A8+ (2018), and Samsung Galaxy S9/Galaxy S9+. === Screen Mirroring === Screen mirroring allows a user to sync the sender device to a receiver on a webpage, then control from the sender device to give a remote presentation of the 3D model. Devices are easily synced by entering a six-digit number displayed on the receiving computer. == Platform support == On iOS, the Kubity application is compatible with devices running on the version 9.0 or higher. On Android, Kubity is compatible with devices running on the version 4.4 “Kit Kat” or higher. The web version of Kubity applications currently support web browsers compatible with WebGL2 : Mozilla Firefox and Google Chrome. AR is compatible with devices running iOS11 including: iPhone SE, iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, iPhone 8, iPhone X, all iPad Pro models, and iPad (2017), and Android devices. Requires Android 7.0 or later and access to the Google Play Store. VR is compatible with Google Cardboard viewers and other cardboard compatible devices including clip-on style VR glasses like Homido Mini, as well as the Samsung Gear VR and Oculus Go. Samsung Gear VR supports: Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+, Samsung Galaxy Note 5, Galaxy S7, Galaxy S7 Edge, Galaxy S8, Galaxy S8+, Samsung Galaxy Note Fan Edition, Samsung Galaxy Note 8, Samsung Galaxy A8/A8+ (2018) and Samsung Galaxy S9/Galaxy S9+.

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  Knowledge space

  In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne, and remain in extensive use in the education theory. Modern applications include two computerized tutoring systems, ALEKS and the defunct RATH. Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered. Not all concepts are interchangeable; some require other concepts as prerequisites. Conversely, competency at one skill may ease the acquisition of another through similarity. A knowledge space marks out which collections of skills are feasible: they can be learned without mastering any other skills. Under reasonable assumptions, the collection of feasible competencies forms the mathematical structure known as an antimatroid. Researchers and educators usually explore the structure of a discipline's knowledge space as a latent class model. == Motivation == Knowledge Space Theory attempts to address shortcomings of standardized testing when used in educational psychometry. Common tests, such as the SAT and ACT, compress a student's knowledge into a very small range of ordinal ranks, in the process effacing the conceptual dependencies between questions. Consequently, the tests cannot distinguish between true understanding and guesses, nor can they identify a student's particular weaknesses, only the general proportion of skills mastered. The goal of knowledge space theory is to provide a language by which exams can communicate What the student can do and What the student is ready to learn. == Model structure == Knowledge Space Theory-based models presume that an educational subject S can be modeled as a finite set Q of concepts, skills, or topics. Each feasible state of knowledge about S is then a subset of Q; the set of all such feasible states is K. The precise term for the information (Q, K) depends on the extent to which K satisfies certain axioms: A knowledge structure assumes that K contains the empty set (a student may know nothing about S) and Q itself (a student may have fully mastered S). A knowledge space is a knowledge structure that is closed under set union: if, for each topic, there is an expert in a class on that topic, then it is possible, with enough time and effort, for each student in the class to become an expert on all those topics simultaneously. A quasi-ordinal knowledge space is a knowledge space that is also closed under set intersection: if student a knows topics A and B; and student c knows topics B and C; then it is possible for another student b to know only topic B. A well-graded knowledge space or learning space is a knowledge space satisfying the following axiom: If S∈K, then there exists x∈S such that S\{x}∈K In educational terms, any feasible body of knowledge can be learned one concept at a time. === Prerequisite partial order === The more contentful axioms associated with quasi-ordinal and well-graded knowledge spaces each imply that the knowledge space forms a well-understood (and heavily studied) mathematical structure: A quasi-ordinal knowledge space can be associated with a distributive lattice under set union and set intersection. The name "quasi-ordinal" arises from Birkhoff's representation theorem, which explains that distributive lattices uniquely correspond to partial orders. A well-graded knowledge space is an antimatroid, a type of mathematical structure that describes certain problems solvable with a greedy algorithm. In either case, the mathematical structure implies that set inclusion defines partial order on K, interpretable as an educational prerequirement: if a(⪯)b in this partial order, then a must be learned before b. === Inner and outer fringe === The prerequisite partial order does not uniquely identify a curriculum; some concepts may lead to a variety of other possible topics. But the covering relation associated with the prerequisite partial does control curricular structure: if students know a before a lesson and b immediately after, then b must cover a in the partial order. In such a circumstance, the new topics covered between a and b constitute the outer fringe of a ("what the student was ready to learn") and the inner fringe of b ("what the student just learned"). == Construction of knowledge spaces == In practice, there exist several methods to construct knowledge spaces. The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions. Another method is to construct the knowledge space by explorative data analysis (for example by item tree analysis) from data. A third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain.

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  Simple Knowledge Organization System

  Simple Knowledge Organization System (SKOS) is a W3C recommendation designed for representation of thesauri, classification schemes, taxonomies, subject-heading systems, or any other type of structured controlled vocabulary. SKOS is part of the Semantic Web family of standards built upon RDF and RDFS, and its main objective is to enable easy publication and use of such vocabularies as linked data. == History == === DESIRE II project (1997–2000) === The most direct ancestor to SKOS was the RDF Thesaurus work undertaken in the second phase of the EU DESIRE project . Motivated by the need to improve the user interface and usability of multi-service browsing and searching, a basic RDF vocabulary for Thesauri was produced. As noted later in the SWAD-Europe workplan, the DESIRE work was adopted and further developed in the SOSIG and LIMBER projects. A version of the DESIRE/SOSIG implementation was described in W3C's QL'98 workshop, motivating early work on RDF rule and query languages: A Query and Inference Service for RDF. === LIMBER (1999–2001) === SKOS built upon the output of the Language Independent Metadata Browsing of European Resources (LIMBER) project funded by the European Community, and part of the Information Society Technologies programme. In the LIMBER project CCLRC further developed an RDF thesaurus interchange format which was demonstrated on the European Language Social Science Thesaurus (ELSST) at the UK Data Archive as a multilingual version of the English language Humanities and Social Science Electronic Thesaurus (HASSET) which was planned to be used by the Council of European Social Science Data Archives CESSDA. === SWAD-Europe (2002–2004) === SKOS as a distinct initiative began in the SWAD-Europe project, bringing together partners from both DESIRE, SOSIG (ILRT) and LIMBER (CCLRC) who had worked with earlier versions of the schema. It was developed in the Thesaurus Activity Work Package, in the Semantic Web Advanced Development for Europe (SWAD-Europe) project. SWAD-Europe was funded by the European Community, and part of the Information Society Technologies programme. The project was designed to support W3C's Semantic Web Activity through research, demonstrators and outreach efforts conducted by the five project partners, ERCIM, the ILRT at Bristol University, HP Labs, CCLRC and Stilo. The first release of SKOS Core and SKOS Mapping were published at the end of 2003, along with other deliverables on RDF encoding of multilingual thesauri and thesaurus mapping. === Semantic web activity (2004–2005) === Following the termination of SWAD-Europe, SKOS effort was supported by the W3C Semantic Web Activity in the framework of the Best Practice and Deployment Working Group. During this period, focus was put both on consolidation of SKOS Core, and development of practical guidelines for porting and publishing thesauri for the Semantic Web. === Development as W3C Recommendation (2006–2009) === The SKOS main published documents — the SKOS Core Guide, the SKOS Core Vocabulary Specification, and the Quick Guide to Publishing a Thesaurus on the Semantic Web — were developed through the W3C Working Draft process. Principal editors of SKOS were Alistair Miles, initially Dan Brickley, and Sean Bechhofer. The Semantic Web Deployment Working Group, chartered for two years (May 2006 – April 2008), put in its charter to push SKOS forward on the W3C Recommendation track. The roadmap projected SKOS as a Candidate Recommendation by the end of 2007, and as a Proposed Recommendation in the first quarter of 2008. The main issues to solve were determining its precise scope of use, and its articulation with other RDF languages and standards used in libraries (such as Dublin Core). === Formal release (2009) === On August 18, 2009, W3C released the new standard that builds a bridge between the world of knowledge organization systems – including thesauri, classifications, subject headings, taxonomies, and folksonomies – and the linked data community, bringing benefits to both. Libraries, museums, newspapers, government portals, enterprises, social networking applications, and other communities that manage large collections of books, historical artifacts, news reports, business glossaries, blog entries, and other items can now use SKOS to leverage the power of linked data. === Historical view of components === SKOS was originally designed as a modular and extensible family of languages, organized as SKOS Core, SKOS Mapping, and SKOS Extensions, and a Metamodel. The entire specification is now complete within the namespace http://www.w3.org/2004/02/skos/core#. == Overview == In addition to the reference itself, the SKOS Primer (a W3C Working Group Note) summarizes the Simple Knowledge Organization System. The SKOS defines the classes and properties sufficient to represent the common features found in a standard thesaurus. It is based on a concept-centric view of the vocabulary, where primitive objects are not terms, but abstract notions represented by terms. Each SKOS concept is defined as an RDF resource. Each concept can have RDF properties attached, including: one or more preferred index terms (at most one in each natural language) alternative terms or synonyms definitions and notes, with specification of their language Concepts can be organized in hierarchies using broader-narrower relationships, or linked by non-hierarchical (associative) relationships. Concepts can be gathered in concept schemes, to provide consistent and structured sets of concepts, representing whole or part of a controlled vocabulary. === Element categories === The principal element categories of SKOS are concepts, labels, notations, documentation, semantic relations, mapping properties, and collections. The associated elements are listed in the table below. === Concepts === The SKOS vocabulary is based on concepts. Concepts are the units of thought—ideas, meanings, or objects and events (instances or categories)—which underlie many knowledge organization systems. As such, concepts exist in the mind as abstract entities which are independent of the terms used to label them. In SKOS, a Concept (based on the OWL Class) is used to represent items in a knowledge organization system (terms, ideas, meanings, etc.) or such a system's conceptual or organizational structure. A ConceptScheme is analogous to a vocabulary, thesaurus, or other way of organizing concepts. SKOS does not constrain a concept to be within a particular scheme, nor does it provide any way to declare a complete scheme—there is no way to say the scheme consists only of certain members. A topConcept is (one of) the upper concept(s) in a hierarchical scheme. === Labels and notations === Each SKOS label is a string of Unicode characters, optionally with language tags, that are associated with a concept. The prefLabel is the preferred human-readable string (maximum one per language tag), while altLabel can be used for alternative strings, and hiddenLabel can be used for strings that are useful to associate, but not meant for humans to read. A SKOS notation is similar to a label, but this literal string has a datatype, like integer, float, or date; the datatype can even be made up (see 6.5.1 Notations, Typed Literals and Datatypes in the SKOS Reference). The notation is useful for classification codes and other strings not recognizable as words. === Documentation === The Documentation or Note properties provide basic information about SKOS concepts. All the properties are considered a type of skos:note; they just provide more specific kinds of information. The property definition, for example, should contain a full description of the subject resource. More specific note types can be defined in a SKOS extension, if desired. A query for skos:note ? will obtain all the notes about , including definitions, examples, and scope, history and change, and editorial documentation. Any of these SKOS Documentation properties can refer to several object types: a literal (e.g., a string); a resource node that has its own properties; or a reference to another document, for example using a URI. This enables the documentation to have its own metadata, like creator and creation date. Specific guidance on SKOS documentation properties can be found in the SKOS Primer Documentary Notes. === Semantic relations === SKOS semantic relations are intended to provide ways to declare relationships between concepts within a concept scheme. While there are no restrictions precluding their use with two concepts from separate schemes, this is discouraged because it is likely to overstate what can be known about the two schemes, and perhaps link them inappropriately. The property related simply makes an association relationship between two concepts; no hierarchy or generality relation is implied. The properties broader and narrower are used to assert a direct hierarchical link between two concepts. The meaning may be unexpected; the relat

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  Semantic parameterization

  Semantic parameterization is a conceptual modeling process for expressing natural language descriptions of a domain in first-order predicate logic. The process yields a formalization of natural language sentences in Description Logic to answer the who, what and where questions in the Inquiry-Cycle Model (ICM) developed by Colin Potts and his colleagues at the Georgia Institute of Technology. The parameterization process complements the Knowledge Acquisition and autOmated Specification (KAOS) method, which formalizes answers to the when, why and how ICM questions in Temporal Logic, to complete the ICM formalization. The artifacts used in the parameterization process include a dictionary that aligns the domain lexicon with unique concepts, distinguishing between synonyms and polysemes, and several natural language patterns that aid in mapping common domain descriptions to formal specifications. == Relationship to other theories == Semantic Parameterization defines a meta-model consisting of eight roles that are domain-independent and reusable. Seven of these roles correspond to Jeffrey Gruber's thematic relations and case roles in Charles Fillmore's case grammar: The Inquiry-Cycle Model (ICM) was introduced to drive elicitation between engineers and stakeholders in requirements engineering. The ICM consists of who, what, where, why, how and when questions. All but the when questions, which require a Temporal Logic to represent such phenomena, have been aligned with the meta-model in semantic parameterization using Description Logic (DL). == Introduction with Example == The semantic parameterization process is based on Description Logic, wherein the TBox is composed of words in a dictionary, including nouns, verbs, and adjectives, and the ABox is partitioned into two sets of assertions: 1) those assertions that come from words in the natural language statement, called the grounding, and 2) those assertions that are inferred by the (human) modeler, called the meta-model. Consider the following unstructured natural language statement (UNLS) (see Breaux et al. for an extended discussion): UNLS1.0 The customer1,1 must not share2,2 the access-code3,3 of the customer1,1 with someone4,4 who is not the provider5,4. The modeler first identifies intensional and extensional polysemes and synonyms, denoted by the subscripts: the first subscript uniquely refers to the intensional index, i.e., the same first index in two or more words refer to the same concept in the TBox; the second subscript uniquely refers to the extensional index, i.e., two same second index in two or more words refer to the same individual in the ABox. This indexing step aligns words in the statement and concepts in the dictionary. Next, the modeler identifies concepts from the dictionary to compose the meta-model. The following table illustrates the complete DL expression that results from applying semantic parameterization.

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  Sentence embedding

  In natural language processing, a sentence embedding is a representation of a sentence as a vector of numbers which encodes meaningful semantic information. State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated [CLS] token prepended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the [CLS] token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's [CLS] token embeddings through the usage of a siamese neural network architecture on the SNLI dataset. Other approaches are loosely based on the idea of distributional semantics applied to sentences. Skip-Thought trains an encoder-decoder structure for the task of neighboring sentences predictions; this has been shown to achieve worse performance than approaches such as InferSent or SBERT. An alternative direction is to aggregate word embeddings, such as those returned by Word2vec, into sentence embeddings. The most straightforward approach is to simply compute the average of word vectors, known as continuous bag-of-words (CBOW). However, more elaborate solutions based on word vector quantization have also been proposed. One such approach is the vector of locally aggregated word embeddings (VLAWE), which demonstrated performance improvements in downstream text classification tasks. == Applications == In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating embeddings for chunks of documents and storing (document chunk, embedding) tuples. Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also known formally as retrieval-augmented generation. Though not as predominant as BERTScore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a Large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. By using the cosine-similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid-search algorithm can be utilized to automate hyperparameter optimization. == Evaluation == A way of testing sentence encodings is to apply them on Sentences Involving Compositional Knowledge (SICK) corpus for both entailment (SICK-E) and relatedness (SICK-R). In the best results are obtained using a BiLSTM network trained on the Stanford Natural Language Inference (SNLI) Corpus. The Pearson correlation coefficient for SICK-R is 0.885 and the result for SICK-E is 86.3. A slight improvement over previous scores is presented in: SICK-R: 0.888 and SICK-E: 87.8 using a concatenation of bidirectional Gated recurrent unit.

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  Leading the Future

  Leading the Future is an American super PAC network focused on lobbying for policies friendly to the artificial intelligence industry. It was launched in 2025 with over $100 million from industry stakeholders including Andreessen Horowitz, OpenAI President Greg Brockman and Palantir co-founder Joe Lonsdale. The launch was preceded by talks between Collin McCune, head of government affairs at Andreessen Horowitz, and Chris Lehane, chief global affairs officer at OpenAI. Among the members of the network are the American Mission PAC, which supported Chris Gober, and the Think Big PAC, which targeted Alex Bores. Leading the Future is affiliated with the nonprofit Build American AI, which Axios describes as a dark money advocacy "offshoot" operating alongside the super PAC. NBC News states that the network’s efforts are modeled after the pro-cryptocurrency group Fairshake. Leading the Future is led by Zac Moffatt and Josh Vlasto, the latter of whom previously served as an advisor to Fairshake. In response to the creation of Leading the Future, former members of Congress Brad Carson and Chris Stewart co-founded the super PAC network Public First, aiming to counter the group’s influence. In April 2026, an investigation by Model Republic linked Leading the Future to The Wire By Acutus, an automated news website that allegedly used AI agents posing as human journalists to solicit interviews. The site's content was found to closely mirror the PAC's deregulatory policy goals while targeting researchers and advocates skeptical of rapid AI development. In May 2026, Wired revealed that Build American AI used a "dark money" campaign to pay TikTok and Instagram influencers $5,000 per video to promote scripted narratives framing Chinese AI as a "national security threat." According to internal documents and staff at the marketing agency managing the project, the campaign's explicit goal was to "subtly shift public debate" toward the deregulation of AI industries while intentionally avoiding technical discussions regarding AI quality or safety. During the 2026 primary season Leading the Future went on to endorse several candidates in both Democratic and Republican races with several of them going on to win.

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  Historical Thesaurus of English

  The Historical Thesaurus of English (HTE) is the largest thesaurus in the world. It is called a historical thesaurus as it arranges the whole vocabulary of English, from the earliest written records in Old English to the present, according to the first documented occurrence of a word in the entire history of the English language. The HTE was conceived and begun in 1965 by the English Language & Linguistics department of the University of Glasgow, who have ever since continued to compile the thesaurus. From the 1980s onwards the project was moved from paper-based records to a computer database. Today, the HTE is available to the public online, but a print version, the Historical Thesaurus of the Oxford English Dictionary (HTOED), was published in 2009. == Main project: The Historical Thesaurus of English (HTE) == The Historical Thesaurus of English (HTE) is a complete database of all the words in the Oxford English Dictionary and other dictionaries (including Old English), arranged by semantic field and date. In this way, the HTE arranges the whole vocabulary of English, from the earliest written records in Old English to the present, alongside dates of use. It is the first historical thesaurus to be compiled for any of the world's languages and contains 800,000 meanings for 600,000 words, within 230,000 categories. As the HTE website states, "in addition to providing hitherto unavailable information for linguistic and textual scholars, the Historical Thesaurus online is a rich resource for students of social and cultural history, showing how concepts developed through the words that refer to them." === Structure === The work is divided into three main sections: the External World, the Mind, and Society. These are broken down into successively narrower domains. The text eventually discriminates more than 236,000 categories. The second order categories are: === History === The ambitious project was announced at a 1965 meeting of the Philological Society by its originator, Michael Samuels. Work on the HTE started in the same year. In 2017, the University of Glasgow was awarded the Queen's Anniversary Prize for Higher Education for the HTE. A second edition of the online HTE is currently in progress and is expected to be launched in late 2020. Work is released on the freely-available HTE website when available. == Print edition: Historical Thesaurus of the Oxford English Dictionary (HTOED) == On 22 October 2009, after 44 years of work, version 1.0 of the HTE was published by Oxford University Press in a two-volume slipcased set as the Historical Thesaurus of the Oxford English Dictionary (HTOED). The two hardcover volumes together total nearly 4,500 pages.

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  Rnn (software)

  rnn is an open-source machine learning framework that implements recurrent neural network architectures, such as LSTM and GRU, natively in the R programming language, that has been downloaded over 100,000 times (from the RStudio servers alone). The rnn package is distributed through the Comprehensive R Archive Network under the open-source GPL v3 license. == Workflow == The below example from the rnn documentation show how to train a recurrent neural network to solve the problem of bit-by-bit binary addition. == sigmoid == The sigmoid functions and derivatives used in the package were originally included in the package, from version 0.8.0 onwards, these were released in a separate R package sigmoid, with the intention to enable more general use. The sigmoid package is a dependency of the rnn package and therefore automatically installed with it. == Reception == With the release of version 0.3.0 in April 2016 the use in production and research environments became more widespread. The package was reviewed several months later on the R blog The Beginner Programmer as "R provides a simple and very user friendly package named rnn for working with recurrent neural networks.", which further increased usage. The book Neural Networks in R by Balaji Venkateswaran and Giuseppe Ciaburro uses rnn to demonstrate recurrent neural networks to R users. It is also used in the r-exercises.com course "Neural network exercises". The RStudio CRAN mirror download logs show that the package is downloaded on average about 2,000 per month from those servers , with a total of over 100,000 downloads since the first release, according to RDocumentation.org, this puts the package in the 15th percentile of most popular R packages .

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  Residual neural network

  A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu

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  Johns Hopkins Beast

  The Johns Hopkins Beast was a mobile automaton, an early pre-robot, built in the 1960s at the Johns Hopkins University Applied Physics Laboratory. The machine had a rudimentary intelligence and the ability to survive on its own. As it wandered through the white halls of the laboratory, it would seek black wall outlets. When it found one it would plug in and recharge. The robot was cybernetic. It did not use a computer. Its control circuitry consisted of dozens of transistors controlling analog voltages. It used photocell optics and sonar to navigate. The 2N404 transistors were used to create NOR logic gates that implemented the Boolean logic to tell it what to do when a specific sensor was activated. The 2N404 transistors were also used to create timing gates to tell it how long to do something. 2N1040 Power transistors were used to control the power to the motion treads, the boom, and the charging mechanism. The original sensors in Mod I were physical touch only. The wall socket was detected by physical switches on the arm that followed the wall. Once detected, two electrical prongs were extended until they entered the wall socket and made the electrical connection to charge the vehicle. The stairway, doors, and pipes on the hall wall were also detected by physical switches and recognized by appropriate logic. The sonar guidance system was developed for Mod I and improved for Mod II. It used two ultrasonic transducers to determine distance, location within the halls, and obstructions in its path. This provided "The Beast" with bat-like guidance. At this point, it could detect obstructions in the hallway, such as people. Once an obstruction was detected, the Beast would slow down and then decide whether to stop or divert around the obstruction. It could also ultrasonically recognize the stairway and doorways to take appropriate action. An optical guidance system was added to Mod II. This provided, among other capabilities, the ability to optically identify the black wall sockets that contrasted with the white wall. The Hopkins Beast Autonomous Robot Mod II link below was written by Dr. Ronald McConnell, at that time a co-op student and one of the designers for Mod II.

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  GPT-5.3-Codex

  GPT-5.3-Codex (Generative Pre-trained Transformer 5.3 Codex) is a large language model (LLM) announced and released by OpenAI on February 5, 2026. It is made as a competitor to Claude's Opus 4.6, focusing on code generation, speed and the ability to search repositories, run terminal commands and at the same time, debug code. In technical benchmarks, it is reported that GPT-5.3 Codex is 25% faster than Opus 4.6. GPT-5.3 Codex is available in the Codex app and on the web; access via API is also planned. According to OpenAI, GPT-5.3-Codex is the company's "first model that was instrumental in creating itself." On February 12, 2026, GPT-5.3-Codex-Spark was released in a research preview, which is a smaller version of GPT-5.3-Codex which supports text-only input. As of February 2026, GPT-5.3-Codex is only available for ChatGPT Pro ($200/month) subscribers.

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