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  List of .NET libraries and frameworks

  This article contains a list of libraries that can be used in .NET languages. These languages require .NET Framework, Mono, or .NET, which provide a basis for software development, platform independence, language interoperability and extensive framework libraries. Standard Libraries (including the Base Class Library) are not included in this article. == Introduction == Apps created with .NET Framework or .NET run in a software environment known as the Common Language Runtime (CLR), an application virtual machine that provides services such as security, memory management, and exception handling. The framework includes a large class library called Framework Class Library (FCL). Thanks to the hosting virtual machine, different languages that are compliant with the .NET Common Language Infrastructure (CLI) can operate on the same kind of data structures. These languages can therefore use the FCL and other .NET libraries that are also written in one of the CLI compliant languages. When the source code of such languages are compiled, the compiler generates platform-independent code in the Common Intermediate Language (CIL, also referred to as bytecode), which is stored in CLI assemblies. When a .NET app runs, the just-in-time compiler (JIT) turns the CIL code into platform-specific machine code. To improve performance, .NET Framework also comes with the Native Image Generator (NGEN), which performs ahead-of-time compilation to machine code. This architecture provides language interoperability. Each language can use code written in other languages. Calls from one language to another are exactly the same as would be within a single programming language. If a library is written in one CLI language, it can be used in other CLI languages. Moreover, apps that consist only of pure .NET assemblies, can be transferred to any platform that contains an implementation of CLI and run on that platform. For example, apps written using .NET can run on Windows, macOS, and various versions of Linux. .NET apps or their libraries, however, may depend on native platform features, e.g. COM. As such, platform independence of .NET apps depends on the ability to transfer necessary native libraries to target platforms. In 2019, the Windows Forms and Windows Presentation Foundation portions of .NET Framework were made open source. === .NET implementations === There are four primary .NET implementations that are actively developed and maintained: .NET Framework: The original .NET implementation that has existed since 2002. While not yet discontinued, Microsoft does not plan on releasing its next major version, 5.0. Mono: A cross-platform implementation of .NET Framework by Ximian, introduced in 2004. It is free and open-source. It is now developed by Xamarin, a subsidiary of Microsoft. Universal Windows Platform (UWP): An implementation of .NET used for building UWP apps. It's designed to unify development for different targeted types of devices, including PCs, tablets, phablets, phones, and the Xbox. .NET: A cross-platform re-implementation of .NET Framework, introduced in 2016 and initially called .NET Core. It is free and open-source. .NET superseded .NET Framework with the release of .NET 5. Each implementation of .NET includes the following components: One or more runtime environments, e.g. Common Language Runtime (CLR) for .NET Framework and CoreCLR for .NET A class library The .NET Standard is a set of common APIs that are implemented in the Base Class Library of any .NET implementation. The class library of each implementation must implement the .NET Standard, but may also implement additional APIs. Traditionally, .NET apps targeted a certain version of a .NET implementation, e.g. .NET Framework 4.6. Starting with the .NET Standard, an app can target a version of the .NET Standard and then it could be used (without recompiling) by any implementation that supports that level of the standard. This enables portability across different .NET implementations. The following table lists the .NET implementations that adhere to the .NET Standard and the version number at which each implementation became compliant with a given version of .NET Standard. For example, according to this table, .NET Core 3.0 was the first version of .NET Core that adhered to .NET Standard 2.1. This means that any version of .NET Core bigger than 3.0 (e.g. .NET Core 3.1) also adheres to .NET Standard 2.1. == Web frameworks == === ASP.NET === First released in 2002, ASP.NET is an open-source server-side web application framework designed for web development to produce dynamic web pages. It is the successor to Microsoft's Active Server Pages (ASP) technology, built on the Common Language Runtime (CLR). === ASP.NET Core === ASP.NET was completely rewritten in 2016 as a modular web framework, together with other frameworks like Entity Framework. The re-written framework uses the new open-source .NET Compiler Platform (also known by its codename "Roslyn") and is cross platform. The programming models ASP.NET MVC, ASP.NET Web API, and ASP.NET Web Pages (a model using only Razor pages) were merged into a unified MVC 6. === Blazor === Blazor is a free and open-source web framework that enables developers to create Single-page Web apps using C# and HTML in ASP.NET Razor pages ("components"). Blazor is part of the ASP.NET Core framework. Blazor Server apps are hosted on a web server, while Blazor WebAssembly apps are downloaded to the client's web browser before running. In addition, a Blazor Hybrid framework is available with server-based and client-based application components. == Numerical libraries == === Open-source numerical libraries === ==== AForge.NET ==== This is a computer vision and artificial intelligence library. It implements a number of genetic, fuzzy logic and machine learning algorithms with several architectures of artificial neural networks with corresponding training algorithms. ==== ALGLIB ==== This is a cross-platform open source numerical analysis and data processing library. It consists of algorithm collections written in different programming languages (C++, C#, FreePascal, Delphi, VBA) and has dual licensing – commercial and GPL. ==== Math.NET Numerics ==== This library aims to provide methods and algorithms for numerical computations in science, engineering and everyday use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more. MIT/X11 license. ==== Meta.Numerics ==== This is a library for advanced scientific computation in the .NET Framework. ==== ML.NET ==== This is a free software machine learning library. The preview release of ML.NET included transforms for feature engineering like n-gram creation, and learners to handle binary classification, multi-class classification, and regression tasks. Additional ML tasks like anomaly detection and recommendation systems have since been added, and other approaches like deep learning will be included in future versions. === Proprietary numerical libraries === ==== ILNumerics.Net ==== This is a high performance, typesafe numerical array set of classes and functions for general math, FFT and linear algebra. The library, developed for .NET/Mono, aims to provide 32- and 64-bit script-like syntax in C#, 2D & 3D plot controls, and efficient memory management. It is released under GPLv3 or commercial license. ==== Measurement Studio ==== This is an integrated suite of UI controls and class libraries for use in developing test and measurement applications. The analysis class libraries provide various digital signal processing, signal filtering, signal generation, peak detection, and other general mathematical functionality. ==== NMath ==== This is a numerical component library for the .NET platform developed by CenterSpace Software. It includes signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package. == 3D graphics == === Open-source 3D graphics === ==== Open Toolkit (OpenTK) ==== This is a low-level C# binding for OpenGL, OpenGL ES and OpenAL. It runs on Windows, Linux, Mac OS X, BSD, Android and iOS. It can be used standalone or integrated into a GUI. ==== Windows Presentation Foundation (WPF) ==== This is a graphical subsystem for rendering user interfaces, developed by Microsoft. It also contains a 3D rendering engine. In addition, interactive 2D content can be overlaid on 3D surfaces natively. It only runs on Windows operating systems. === Proprietary 3D graphics === ==== Unity ==== This is a cross-platform game engine developed by Unity Technologies and used to develop video games for PC, consoles, mobile devices and websites. == Image processing == === AForge.NET === This is a computer vision and artificial intelligence library. It implements a number of image processing algorithms and filters. It is released under the LGPLv3 and partly GPLv3 license. Majority of the library is written in C# and th

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  Artificial intelligence

  Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in engineering, mathematics and computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines, chatbots, virtual assistants, autonomous vehicles, and play and analysis in strategy games (e.g., chess and Go). Since the 2020s, generative AI has become widely available to generate images, audio, and videos from text prompts. The traditional goals of AI research include learning, reasoning, knowledge representation, planning, natural language processing, and perception, as well as support for robotics. To reach these goals, AI researchers have used techniques including state space search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics. AI also draws upon psychology, linguistics, philosophy, neuroscience, and other fields. Some companies, such as OpenAI, Google DeepMind and Meta, aim to create artificial general intelligence (AGI) – AI that can complete virtually any cognitive task at least as well as a human. Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest increased substantially after 2012, when graphics processing units began being used to accelerate neural networks, and deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture. In the 2020s, an AI boom has coincided with advances in generative AI, which allowed for the creation and modification of media. In addition to AI safety and unintended consequences and harms from the use of AI, ethical concerns, AI's long-term effects, and potential existential risks have prompted discussions of AI regulation. == Goals == The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research. === Reasoning and problem-solving === Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions. By the late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics. Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments. Accurate and efficient reasoning is an unsolved problem. === Knowledge representation === Knowledge representation and knowledge engineering allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas. A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; situations, events, states, and time; causes and effects; knowledge about knowledge (what we know about what other people know); default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing); and many other aspects and domains of knowledge. Among the most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous); and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition, the problem of obtaining knowledge for AI applications. === Planning and decision-making === An "agent" is any entity (artificial or not) that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning, the agent has a specific goal. In automated decision-making, the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called the "utility") that measures how much the agent prefers it. For each possible action, it can calculate the "expected utility": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility. In classical planning, the agent knows exactly what the effect of any action will be. In most real-world problems, however, the agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. Alongside thorough testing and improvement based on previous decisions, having an explanation for why the agent took certain decisions is a way to build trust, especially when the decisions have to be relied upon. In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or experimental actions. The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be. A Markov decision process has a transition model that describes the probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration), be heuristic, or it can be learned. Game theory describes the rational behavior of multiple interacting agents and is used in AI programs that make decisions that involve other agents. === Learning === Machine learning is the study of programs that can improve their performance on a given task automatically. It has been a part of AI from the beginning. There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance. Supervised learning requires labeling the training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input). In reinforcement learning, the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good". Transfer learning is when the knowledge gained from one problem is applied to a new problem. Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning. Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization. === Natural language processing === Natural language processing (NLP) allows programs to read, write and communicate in human languages. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval and question answering. Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation unless

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  Inductive bias

  The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g., step-functions in decision trees instead of continuous functions in linear regression models). Learning involves searching a space of solutions for a solution that provides a good explanation of the data. However, in many cases, there may be multiple equally appropriate solutions. An inductive bias allows a learning algorithm to prioritize one solution (or interpretation) over another, independently of the observed data. In machine learning, the aim is to construct algorithms that are able to learn to predict a certain target output. To achieve this, the learning algorithm is presented some training examples that demonstrate the intended relation of input and output values. Then the learner is supposed to approximate the correct output, even for examples that have not been shown during training. Without any additional assumptions, this problem cannot be solved since unseen situations might have an arbitrary output value. The kind of necessary assumptions about the nature of the target function are subsumed in the phrase inductive bias. A classical example of an inductive bias is Occam's razor, assuming that the simplest consistent hypothesis about the target function is actually the best. Here, consistent means that the hypothesis of the learner yields correct outputs for all of the examples that have been given to the algorithm. Approaches to a more formal definition of inductive bias are based on mathematical logic. Here, the inductive bias is a logical formula that, together with the training data, logically entails the hypothesis generated by the learner. However, this strict formalism fails in many practical cases in which the inductive bias can only be given as a rough description (e.g., in the case of artificial neural networks), or not at all. == Types == The following is a list of common inductive biases in machine learning algorithms. Maximum conditional independence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditional independence. This is the bias used in the Naive Bayes classifier. Minimum cross-validation error: when trying to choose among hypotheses, select the hypothesis with the lowest cross-validation error. Although cross-validation may seem to be free of bias, the "no free lunch" theorems show that cross-validation must be biased, for example assuming that there is no information encoded in the ordering of the data. Maximum margin: when drawing a boundary between two classes, attempt to maximize the width of the boundary. This is the bias used in support vector machines. The assumption is that distinct classes tend to be separated by wide boundaries. Minimum description length: when forming a hypothesis, attempt to minimize the length of the description of the hypothesis. Minimum features: unless there is good evidence that a feature is useful, it should be deleted. This is the assumption behind feature selection algorithms. Nearest neighbors: assume that most of the cases in a small neighborhood in feature space belong to the same class. Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood. This is the bias used in the k-nearest neighbors algorithm. The assumption is that cases that are near each other tend to belong to the same class. == Shift of bias == Although most learning algorithms have a static bias, some algorithms are designed to shift their bias as they acquire more data. This does not avoid bias, since the bias shifting process itself must have a bias.

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  Apprenticeship learning

  In artificial intelligence, apprenticeship learning (or learning from demonstration or imitation learning) is the process of learning by observing an expert. It can be viewed as a form of supervised learning, where the training dataset consists of task executions by a demonstration teacher. == Mapping function approach == Mapping methods try to mimic the expert by forming a direct mapping either from states to actions, or from states to reward values. For example, in 2002 researchers used such an approach to teach an AIBO robot basic soccer skills. === Inverse reinforcement learning approach === Inverse reinforcement learning (IRL) is the process of deriving a reward function from observed behavior. While ordinary "reinforcement learning" involves using rewards and punishments to learn behavior, in IRL the direction is reversed, and a robot observes a person's behavior to figure out what goal that behavior seems to be trying to achieve. The IRL problem can be defined as: Given 1) measurements of an agent's behaviour over time, in a variety of circumstances; 2) measurements of the sensory inputs to that agent; 3) a model of the physical environment (including the agent's body): Determine the reward function that the agent is optimizing. IRL researcher Stuart J. Russell proposes that IRL might be used to observe humans and attempt to codify their complex "ethical values", in an effort to create "ethical robots" that might someday know "not to cook your cat" without needing to be explicitly told. The scenario can be modeled as a "cooperative inverse reinforcement learning game", where a "person" player and a "robot" player cooperate to secure the person's implicit goals, despite these goals not being explicitly known by either the person nor the robot. In 2017, OpenAI and DeepMind applied deep learning to the cooperative inverse reinforcement learning in simple domains such as Atari games and straightforward robot tasks such as backflips. The human role was limited to answering queries from the robot as to which of two different actions were preferred. The researchers found evidence that the techniques may be economically scalable to modern systems. Apprenticeship via inverse reinforcement learning (AIRP) was developed by in 2004 Pieter Abbeel, Professor in Berkeley's EECS department, and Andrew Ng, Associate Professor in Stanford University's Computer Science Department. AIRP deals with "Markov decision process where we are not explicitly given a reward function, but where instead we can observe an expert demonstrating the task that we want to learn to perform". AIRP has been used to model reward functions of highly dynamic scenarios where there is no obvious reward function intuitively. Take the task of driving for example, there are many different objectives working simultaneously - such as maintaining safe following distance, a good speed, not changing lanes too often, etc. This task, may seem easy at first glance, but a trivial reward function may not converge to the policy wanted. One domain where AIRP has been used extensively is helicopter control. While simple trajectories can be intuitively derived, complicated tasks like aerobatics for shows has been successful. These include aerobatic maneuvers like - in-place flips, in-place rolls, loops, hurricanes and even auto-rotation landings. This work was developed by Pieter Abbeel, Adam Coates, and Andrew Ng - "Autonomous Helicopter Aerobatics through Apprenticeship Learning" === System model approach === System models try to mimic the expert by modeling world dynamics. == Plan approach == The system learns rules to associate preconditions and postconditions with each action. In one 1994 demonstration, a humanoid learns a generalized plan from only two demonstrations of a repetitive ball collection task. == Example == Learning from demonstration is often explained from a perspective that the working Robot-control-system is available and the human-demonstrator is using it. And indeed, if the software works, the Human operator takes the robot-arm, makes a move with it, and the robot will reproduce the action later. For example, he teaches the robot-arm how to put a cup under a coffeemaker and press the start-button. In the replay phase, the robot is imitating this behavior 1:1. But that is not how the system works internally; it is only what the audience can observe. In reality, Learning from demonstration is much more complex. One of the first works on learning by robot apprentices (anthropomorphic robots learning by imitation) was Adrian Stoica's PhD thesis in 1995. In 1997, robotics expert Stefan Schaal was working on the Sarcos robot-arm. The goal was simple: solve the pendulum swingup task. The robot itself can execute a movement, and as a result, the pendulum is moving. The problem is, that it is unclear what actions will result into which movement. It is an Optimal control-problem which can be described with mathematical formulas but is hard to solve. The idea from Schaal was, not to use a Brute-force solver but record the movements of a human-demonstration. The angle of the pendulum is logged over three seconds at the y-axis. This results into a diagram which produces a pattern. In computer animation, the principle is called spline animation. That means, on the x-axis the time is given, for example 0.5 seconds, 1.0 seconds, 1.5 seconds, while on the y-axis is the variable given. In most cases it's the position of an object. In the inverted pendulum it is the angle. The overall task consists of two parts: recording the angle over time and reproducing the recorded motion. The reproducing step is surprisingly simple. As an input we know, in which time step which angle the pendulum must have. Bringing the system to a state is called “Tracking control” or PID control. That means, we have a trajectory over time, and must find control actions to map the system to this trajectory. Other authors call the principle “steering behavior”, because the aim is to bring a robot to a given line.

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  Inferential theory of learning

  Inferential Theory of Learning (ITL) is an area of machine learning which describes inferential processes performed by learning agents. ITL has been continuously developed by Ryszard S. Michalski, starting in the 1980s. The first known publication of ITL was in 1983. In the ITL learning process is viewed as a search (inference) through hypotheses space guided by a specific goal. The results of learning need to be stored. Stored information will later be used by the learner for future inferences. Inferences are split into multiple categories including conclusive, deduction, and induction. In order for an inference to be considered complete it was required that all categories must be taken into account. This is how the ITL varies from other machine learning theories like Computational Learning Theory and Statistical Learning Theory; which both use singular forms of inference. == Usage == The most relevant published usage of ITL was in scientific journal published in 2012 and used ITL as a way to describe how agent-based learning works. According to the journal "The Inferential Theory of Learning (ITL) provides an elegant way of describing learning processes by agents".

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  Perusall

  Perusall is a social web annotation tool intended for use by students at schools and universities. It allows users to annotate the margins of a text in a virtual group setting that is similar to social media—with upvoting, emojis, chat functionality, and notification. It also includes automatic AI grading. == History == Perusall began as a research project at Harvard University. It later became an educational product for students and teachers. As of 2024, Perusall states more than 5 million students have used the tool at over 5,000 educational institutions in 112 countries." == Functionality == Perusall integrates with learning management systems such as Moodle, Canvas and Blackboard to aid with collaborative annotation. The tool supports annotation of a range of media including text, images, equations, videos, PDFs and snapshots of webpages.

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  Actor-critic algorithm

  The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods, and value-based RL algorithms such as value iteration, Q-learning, SARSA, and TD learning. An AC algorithm consists of two main components: an "actor" that determines which actions to take according to a policy function, and a "critic" that evaluates those actions according to a value function. Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases. == Overview == The actor-critic methods can be understood as an improvement over pure policy gradient methods like REINFORCE via introducing a baseline. === Actor === The actor uses a policy function π ( a | s ) {\displaystyle \pi (a|s)} , while the critic estimates either the value function V ( s ) {\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or any combination thereof. The actor is a parameterized function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ | s ) {\displaystyle \pi _{\theta }(\cdot |s)} . If the action space is discrete, then ∑ a π θ ( a | s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a|s)=1} . If the action space is continuous, then ∫ a π θ ( a | s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a|s)da=1} . The goal of policy optimization is to improve the actor. That is, to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t r t ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}r_{t}\right]} where γ {\displaystyle \gamma } is the discount factor, r t {\displaystyle r_{t}} is the reward at step t {\displaystyle t} , and T {\displaystyle T} is the time-horizon (which can be infinite). The goal of policy gradient method is to optimize J ( θ ) {\displaystyle J(\theta )} by gradient ascent on the policy gradient ∇ J ( θ ) {\displaystyle \nabla J(\theta )} . As detailed on the policy gradient method page, there are many unbiased estimators of the policy gradient: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ j ≤ T ∇ θ ln ⁡ π θ ( A j | S j ) ⋅ Ψ j | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{0\leq j\leq T}\nabla _{\theta }\ln \pi _{\theta }(A_{j}|S_{j})\cdot \Psi _{j}{\Big |}S_{0}=s_{0}\right]} where Ψ j {\textstyle \Psi _{j}} is a linear sum of the following: ∑ 0 ≤ i ≤ T ( γ i R i ) {\textstyle \sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE algorithm. γ j ∑ j ≤ i ≤ T ( γ i − j R i ) − b ( S j ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})-b(S_{j})} : the REINFORCE with baseline algorithm. Here b {\displaystyle b} is an arbitrary function. γ j ( R j + γ V π θ ( S j + 1 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma V^{\pi _{\theta }}(S_{j+1})-V^{\pi _{\theta }}(S_{j})\right)} : TD(1) learning. γ j Q π θ ( S j , A j ) {\textstyle \gamma ^{j}Q^{\pi _{\theta }}(S_{j},A_{j})} . γ j A π θ ( S j , A j ) {\textstyle \gamma ^{j}A^{\pi _{\theta }}(S_{j},A_{j})} : Advantage Actor-Critic (A2C). γ j ( R j + γ R j + 1 + γ 2 V π θ ( S j + 2 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma R_{j+1}+\gamma ^{2}V^{\pi _{\theta }}(S_{j+2})-V^{\pi _{\theta }}(S_{j})\right)} : TD(2) learning. γ j ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(n) learning. γ j ∑ n = 1 ∞ λ n − 1 1 − λ ⋅ ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\sum _{n=1}^{\infty }{\frac {\lambda ^{n-1}}{1-\lambda }}\cdot \left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(λ) learning, also known as GAE (generalized advantage estimate). This is obtained by an exponentially decaying sum of the TD(n) learning terms. === Critic === In the unbiased estimators given above, certain functions such as V π θ , Q π θ , A π θ {\displaystyle V^{\pi _{\theta }},Q^{\pi _{\theta }},A^{\pi _{\theta }}} appear. These are approximated by the critic. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms. For example, if the critic is estimating the state-value function V π θ ( s ) {\displaystyle V^{\pi _{\theta }}(s)} , then it can be learned by any value function approximation method. Let the critic be a function approximator V ϕ ( s ) {\displaystyle V_{\phi }(s)} with parameters ϕ {\displaystyle \phi } . The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error: δ i = R i + γ V ϕ ( S i + 1 ) − V ϕ ( S i ) {\displaystyle \delta _{i}=R_{i}+\gamma V_{\phi }(S_{i+1})-V_{\phi }(S_{i})} The critic parameters are updated by gradient descent on the squared TD error: ϕ ← ϕ − α ∇ ϕ ( δ i ) 2 = ϕ + α δ i ∇ ϕ V ϕ ( S i ) {\displaystyle \phi \leftarrow \phi -\alpha \nabla _{\phi }(\delta _{i})^{2}=\phi +\alpha \delta _{i}\nabla _{\phi }V_{\phi }(S_{i})} where α {\displaystyle \alpha } is the learning rate. Note that the gradient is taken with respect to the ϕ {\displaystyle \phi } in V ϕ ( S i ) {\displaystyle V_{\phi }(S_{i})} only, since the ϕ {\displaystyle \phi } in γ V ϕ ( S i + 1 ) {\displaystyle \gamma V_{\phi }(S_{i+1})} constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly, if the critic is estimating the action-value function Q π θ {\displaystyle Q^{\pi _{\theta }}} , then it can be learned by Q-learning or SARSA. In SARSA, the critic maintains an estimate of the Q-function, parameterized by ϕ {\displaystyle \phi } , denoted as Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} . The temporal difference error is then calculated as δ i = R i + γ Q θ ( S i + 1 , A i + 1 ) − Q θ ( S i , A i ) {\displaystyle \delta _{i}=R_{i}+\gamma Q_{\theta }(S_{i+1},A_{i+1})-Q_{\theta }(S_{i},A_{i})} . The critic is then updated by θ ← θ + α δ i ∇ θ Q θ ( S i , A i ) {\displaystyle \theta \leftarrow \theta +\alpha \delta _{i}\nabla _{\theta }Q_{\theta }(S_{i},A_{i})} The advantage critic can be trained by training both a Q-function Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} and a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then let A ϕ ( s , a ) = Q ϕ ( s , a ) − V ϕ ( s ) {\displaystyle A_{\phi }(s,a)=Q_{\phi }(s,a)-V_{\phi }(s)} . Although, it is more common to train just a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then estimate the advantage by A ϕ ( S i , A i ) ≈ ∑ j ∈ 0 : n − 1 γ j R i + j + γ n V ϕ ( S i + n ) − V ϕ ( S i ) {\displaystyle A_{\phi }(S_{i},A_{i})\approx \sum _{j\in 0:n-1}\gamma ^{j}R_{i+j}+\gamma ^{n}V_{\phi }(S_{i+n})-V_{\phi }(S_{i})} Here, n {\displaystyle n} is a positive integer. The higher n {\displaystyle n} is, the more lower is the bias in the advantage estimation, but at the price of higher variance. The Generalized Advantage Estimation (GAE) introduces a hyperparameter λ {\displaystyle \lambda } that smoothly interpolates between Monte Carlo returns ( λ = 1 {\displaystyle \lambda =1} , high variance, no bias) and 1-step TD learning ( λ = 0 {\displaystyle \lambda =0} , low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with λ {\displaystyle \lambda } being the decay strength. == Variants == Asynchronous Advantage Actor-Critic (A3C): Parallel and asynchronous version of A2C. Soft Actor-Critic (SAC): Incorporates entropy maximization for improved exploration. Deep Deterministic Policy Gradient (DDPG): Specialized for continuous action spaces.

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  Data-driven model

  Data-driven models are a class of computational models that primarily rely on historical data collected throughout a system's or process' lifetime to establish relationships between input, internal, and output variables. Commonly found in numerous articles and publications, data-driven models have evolved from earlier statistical models, overcoming limitations posed by strict assumptions about probability distributions. These models have gained prominence across various fields, particularly in the era of big data, artificial intelligence, and machine learning, where they offer valuable insights and predictions based on the available data. == Background == These models have evolved from earlier statistical models, which were based on certain assumptions about probability distributions that often proved to be overly restrictive. The emergence of data-driven models in the 1950s and 1960s coincided with the development of digital computers, advancements in artificial intelligence research, and the introduction of new approaches in non-behavioural modelling, such as pattern recognition and automatic classification. == Key Concepts == Data-driven models encompass a wide range of techniques and methodologies that aim to intelligently process and analyse large datasets. Examples include fuzzy logic, fuzzy and rough sets for handling uncertainty, neural networks for approximating functions, global optimization and evolutionary computing, statistical learning theory, and Bayesian methods. These models have found applications in various fields, including economics, customer relations management, financial services, medicine, and the military, among others. Machine learning, a subfield of artificial intelligence, is closely related to data-driven modelling as it also focuses on using historical data to create models that can make predictions and identify patterns. In fact, many data-driven models incorporate machine learning techniques, such as regression, classification, and clustering algorithms, to process and analyse data. In recent years, the concept of data-driven models has gained considerable attention in the field of water resources, with numerous applications, academic courses, and scientific publications using the term as a generalization for models that rely on data rather than physics. This classification has been featured in various publications and has even spurred the development of hybrid models in the past decade. Hybrid models attempt to quantify the degree of physically based information used in hydrological models and determine whether the process of building the model is primarily driven by physics or purely data-based. As a result, data-driven models have become an essential topic of discussion and exploration within water resources management and research. The term "data-driven modelling" (DDM) refers to the overarching paradigm of using historical data in conjunction with advanced computational techniques, including machine learning and artificial intelligence, to create models that can reveal underlying trends, patterns, and, in some cases, make predictions Data-driven models can be built with or without detailed knowledge of the underlying processes governing the system behavior, which makes them particularly useful when such knowledge is missing or fragmented.

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  Multi-exposure HDR capture

  In photography and videography, multi-exposure HDR capture is a technique that creates high dynamic range (HDR) images (or extended dynamic range images) by taking and combining multiple exposures of the same subject matter at different exposures. Combining multiple images in this way results in an image with a greater dynamic range than what would be possible by taking one single image. The technique can also be used to capture video by taking and combining multiple exposures for each frame of the video. The term "HDR" is used frequently to refer to the process of creating HDR images from multiple exposures. Many smartphones have an automated HDR feature that relies on computational imaging techniques to capture and combine multiple exposures. A single image captured by a camera provides a finite range of luminosity inherent to the medium, whether it is a digital sensor or film. Outside this range, tonal information is lost and no features are visible; tones that exceed the range are "burned out" and appear pure white in the brighter areas, while tones that fall below the range are "crushed" and appear pure black in the darker areas. The ratio between the maximum and the minimum tonal values that can be captured in a single image is known as the dynamic range. In photography, dynamic range is measured in exposure value (EV) differences, also known as stops. The human eye's response to light is non-linear: halving the light level does not halve the perceived brightness of a space, it makes it look only slightly dimmer. For most illumination levels, the response is approximately logarithmic. Human eyes adapt fairly rapidly to changes in light levels. HDR can thus produce images that look more like what a human sees when looking at the subject. This technique can be applied to produce images that preserve local contrast for a natural rendering, or exaggerate local contrast for artistic effect. HDR is useful for recording many real-world scenes containing a wider range of brightness than can be captured directly, typically both bright, direct sunlight and deep shadows. Due to the limitations of printing and display contrast, the extended dynamic range of HDR images must be compressed to the range that can be displayed. The method of rendering a high dynamic range image to a standard monitor or printing device is called tone mapping; it reduces the overall contrast of an HDR image to permit display on devices or prints with lower dynamic range. == Benefits == One aim of HDR is to present a similar range of luminance to that experienced through the human visual system. The human eye, through non-linear response, adaptation of the iris, and other methods, adjusts constantly to a broad range of luminance present in the environment. The brain continuously interprets this information so that a viewer can see in a wide range of light conditions. Most cameras are limited to a much narrower range of exposure values within a single image, due to the dynamic range of the capturing medium. With a limited dynamic range, tonal differences can be captured only within a certain range of brightness. Outside of this range, no details can be distinguished: when the tone being captured exceeds the range in bright areas, these tones appear as pure white, and when the tone being captured does not meet the minimum threshold, these tones appear as pure black. Images captured with non-HDR cameras that have a limited exposure range (low dynamic range, LDR), may lose detail in highlights or shadows. Modern CMOS image sensors have improved dynamic range and can often capture a wider range of tones in a single exposure reducing the need to perform multi-exposure HDR. Color film negatives and slides consist of multiple film layers that respond to light differently. Original film (especially negatives versus transparencies or slides) feature a very high dynamic range (in the order of 8 for negatives and 4 to 4.5 for positive transparencies). Multi-exposure HDR is used in photography and also in extreme dynamic range applications such as welding or automotive work. In security cameras the term "wide dynamic range" is used instead of HDR. === Limitations === A fast-moving subject, or camera movement between the multiple exposures, will generate a "ghost" effect or a staggered-blur strobe effect due to the merged images not being identical. Unless the subject is static and the camera mounted on a tripod there may be a tradeoff between extended dynamic range and sharpness. Sudden changes in the lighting conditions (strobed LED light) can also interfere with the desired results, by producing one or more HDR layers that do have the luminosity expected by an automated HDR system, though one might still be able to produce a reasonable HDR image manually in software by rearranging the image layers to merge in order of their actual luminosity. Because of the nonlinearity of some sensors image artifacts can be common. Camera characteristics such as gamma curves, sensor resolution, noise, photometric calibration and color calibration affect resulting high-dynamic-range images. == Process == High-dynamic-range photographs are generally composites of multiple standard dynamic range images, often captured using exposure bracketing. Afterwards, photo manipulation software merges the input files into a single HDR image, which is then also tone mapped in accordance with the limitations of the planned output or display. === Capturing multiple images (exposure bracketing) === Any camera that allows manual exposure control can perform multi-exposure HDR image capture, although one equipped with automatic exposure bracketing (AEB) facilitates the process. Some cameras have an AEB feature that spans a far greater dynamic range than others, from ±0.6 in simpler cameras to ±18 EV in top professional cameras, as of 2020. The exposure value (EV) refers to the amount of light applied to the light-sensitive detector, whether film or digital sensor such as a CCD. An increase or decrease of one stop is defined as a doubling or halving of the amount of light captured. Revealing detail in the darkest of shadows requires an increased EV, while preserving detail in very bright situations requires very low EVs. EV is controlled using one of two photographic controls: varying either the size of the aperture or the exposure time. A set of images with multiple EVs intended for HDR processing should be captured only by altering the exposure time; altering the aperture size also would affect the depth of field and so the resultant multiple images would be quite different, preventing their final combination into a single HDR image. Multi-exposure HDR photography generally is limited to still scenes because any movement between successive images will impede or prevent success in combining them afterward. Also, because the photographer must capture three or more images to obtain the desired luminance range, taking such a full set of images takes extra time. Photographers have developed calculation methods and techniques to partially overcome these problems, but the use of a sturdy tripod is advised to minimize framing differences between exposures. === Merging the images into an HDR image === Tonal information and details from shadow areas can be recovered from images that are deliberately overexposed (i.e., with positive EV compared to the correct scene exposure), while similar tonal information from highlight areas can be recovered from images that are deliberately underexposed (negative EV). The process of selecting and extracting shadow and highlight information from these over/underexposed images and then combining them with image(s) that are exposed correctly for the overall scene is known as exposure fusion. Exposure fusion can be performed manually, relying on the HDR operator's judgment, experience, and training, but usually, fusion is performed automatically by software. === Storing === Information stored in high-dynamic-range images typically corresponds to the physical values of luminance or radiance that can be observed in the real world. This is different from traditional digital images, which represent colors as they should appear on a monitor or a paper print. Therefore, HDR image formats are often called scene-referred, in contrast to traditional digital images, which are device-referred or output-referred. Furthermore, traditional images are usually encoded for the human visual system (maximizing the visual information stored in the fixed number of bits), which is usually called gamma encoding or gamma correction. The values stored for HDR images are often gamma compressed using mathematical functions such as power laws logarithms, or floating point linear values, since fixed-point linear encodings are increasingly inefficient over higher dynamic ranges. HDR images often do not use fixed ranges per color channel, other than traditional images, to represent many more colors over a much wi

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  Description logic

  Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that

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  Moral outsourcing

  Moral outsourcing is the placing of responsibility for ethical decision-making onto external entities, often algorithms. The term is often used in discussions of computer science and algorithmic fairness, but it can apply to any situation in which one appeals to outside agents in order to absolve themselves of responsibility for their actions. In this context, moral outsourcing specifically refers to the tendency of society to blame technology, rather than its creators or users, for any harm it may cause. == Definition == The term "moral outsourcing" was first coined by Dr. Rumman Chowdhury, a data scientist concerned with the overlap between artificial intelligence and social issues. Chowdhury used the term to describe looming fears of a so-called “Fourth Industrial Revolution” following the rise of artificial intelligence. Moral outsourcing is often applied by technologists to shrink away from their part in building offensive products. In her TED Talk, Chowdhury gives the example of a creator excusing their work by saying they were simply doing their job. This is a case of moral outsourcing and not taking ownership for the consequences of creation. When it comes to AI, moral outsourcing allows for creators to decide when the machine is human and when it is a computer - shifting the blame and responsibility of moral plights off of the technologists and onto the technology. Conversations around AI and bias and its impacts require accountability to bring change. It is difficult to address these biased systems if their creators use moral outsourcing to avoid taking any responsibility for the issue. One example of moral outsourcing is the anger that is directed at machines for “taking jobs away from humans” rather than companies for employing that technology and jeopardizing jobs in the first place. The term "moral outsourcing" refers to the concept of outsourcing, or enlisting an external operation to complete specific work for another organization. In the case of moral outsourcing, the work of resolving moral dilemmas or making choices according to an ethical code is supposed to be conducted by another entity. == Real-world applications == In the medical field, AI is increasingly involved in decision-making processes about which patients to treat, and how to treat them. The responsibility of the doctor to make informed decisions about what is best for their patients is outsourced to an algorithm. Sympathy is also noted to be an important part of medical practice; an aspect that artificial intelligence, glaringly, is missing. This form of moral outsourcing is a major concern in the medical community. Another field of technology in which moral outsourcing is frequently brought up is autonomous vehicles. California Polytechnic State University professor Keith Abney proposed an example scenario: "Suppose we have some [troublemaking] teenagers, and they see an autonomous vehicle, they drive right at it. They know the autonomous vehicle will swerve off the road and go off a cliff, but should it?" The decision of whether to sacrifice the autonomous vehicle (and any passengers inside) or the vehicle coming at it will be written into the algorithms defining the car's behavior. In the case of moral outsourcing, the responsibility of any damage caused by an accident may be attributed to the autonomous vehicle itself, rather than the creators who wrote the protocol the vehicle will use to "decide" what to do. Moral outsourcing is also used to delegate the consequences of predictive policing algorithms to technology, rather than the creators or the police. There are many ethical concerns with predictive policing due to the fact that it results in the over-policing of low income and minority communities. In the context of moral outsourcing, the positive feedback loop of sending disproportionate police forces into minority communities is attributed to the algorithm and the data being fed into this system--rather than the users and creators of the predictive policing technology. == Outside of technology == === Religion === Moral outsourcing is also commonly seen in appeals to religion to justify discrimination or harm. In his book What It Means to be Moral, sociologist Phil Zuckerman contradicts the popular religious notion that morality comes from God. Religion is oftentimes cited as a foundation for a moral stance without any tangible relation between the religious beliefs and personal stance. In these cases, religious individuals will "outsource" their personal beliefs and opinions by claiming that they are a result of their religious identification. This is seen where religion is cited as a factor for political beliefs, medical beliefs, and in extreme cases an excuse for violence. === Manufacturing === Moral outsourcing can also be seen in the business world in terms of manufacturing goods and avoiding environmental responsibility. Some companies in the United States will move their production process to foreign countries with more relaxed environmental policies to avoid the pollution laws that exist in the US. A study by the Harvard Business Review found that "in countries with tight environmental regulation, companies have 29% lower domestic emissions on average. On the other hand, such a tightening in regulation results in 43% higher emissions abroad." The consequences of higher pollution rates are then attributed to the loose regulations in these countries, rather than on the companies themselves who purposefully moved into these areas to avoid strict pollution policy.

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  Random feature

  Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ⁡ ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⁡ ⟨ ω 1 , x ⟩ , sin ⁡ ⟨ ω 1 , x ⟩ , … , cos ⁡ ⟨ ω D , x ⟩ , sin ⁡ ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg ⁡ min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.

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  List of ARM Cortex-M development tools

  This is a list of development tools for 32-bit ARM Cortex-M-based microcontrollers, which consists of Cortex-M0, Cortex-M0+, Cortex-M1, Cortex-M3, Cortex-M4, Cortex-M7, Cortex-M23, Cortex-M33, Cortex-M35P, Cortex-M52, Cortex-M55, and Cortex-M85 cores. == Development toolchains == IDE, compiler, linker, debugger, flashing (in alphabetical order): Ac6 System Workbench for STM32 (based on Eclipse and the GNU GCC toolchain with direct support for all ST-provided evaluation boards, Eval, Discovery and Nucleo, debug with ST-LINK) ARM Development Studio 5 by ARM Ltd. Atmel Studio by Atmel (based on Visual Studio and GNU GCC Toolchain) Code Composer Studio by Texas Instruments CoIDE by CooCox (note - website dead since 2018) Crossware Development Suite for ARM by Crossware CrossWorks for ARM by Rowley Dave by Infineon. For XMC processors only. Includes project wizard, detailed register decoding and a code library still under development. DRT by SOMNIUM Technologies. Based on GCC toolchain and proprietary linker technology. Available as a plugin for Atmel Studio and an Eclipse-based IDE. EmBitz (formerly Em::Blocks) – free, fast (non-eclipse) IDE for ST-LINK (live data updates), OpenOCD, including GNU Tools for ARM and project wizards for ST, Atmel, EnergyMicro etc. Embeetle IDE - free, fast (non-eclipse) IDE. Works both on Linux and Windows. emIDE by emide – free Visual Studio Style IDE including GNU Tools for ARM GNU ARM Eclipse – A family of Eclipse CDT extensions and tools for GNU ARM development GNU Tools (aka GCC) for ARM Embedded Processors by ARM Ltd – free GCC for bare metal IAR Embedded Workbench for ARM by IAR Systems ICC by ImageCraft Keil MDK-ARM by Keil LPCXpresso by NXP (formerly Red Suite by Code Red Technologies) MikroC by mikroe – mikroC MULTI by Green Hills Software, for all Arm 7, 9, Cortex-M, Cortex-R, Cortex-A Ride and RKit for ARM by Raisonance SEGGER Embedded Studio for ARM by Segger. SEGGER Ozone by Segger. STM32CubeIDE by STMicroelectronics - Combines STCubeMX with TrueSTUDIO into a single Eclipse style package Sourcery CodeBench by Mentor Graphics TASKING VX-Toolset by Altium TrueSTUDIO by Atollic Visual Studio by Microsoft as IDE, with GNU Tools as compiler/linker – e.g. supported by VisualGDB VXM Design's Buildroot toolchain for Cortex. It integrates GNU toolchain, Nuttx, filesystem and debugger/flasher in one build. winIDEA/winIDEAOpen by iSYSTEM YAGARTO – free GCC (no longer supported) Code::Blocks (EPS edition) (debug with ST-LINK no GDB and no OpenOCD required) IDE for Arduino ARM boards Arduino – IDE for Atmel SAM3X (Arduino Due) Energia – Arduino IDE for Texas Instruments Tiva and CC3200 Notes: == Debugging tools == JTAG and/or SWD debug interface host adapters (in alphabetical order): Black Magic Probe by 1BitSquared. CMSIS-DAP by Mbed. Crossconnect by Rowley Associates. DSTREAM by ARM Holdings Green Hills Probe and SuperTrace Probe by Green Hills Software. iTAG by iSYSTEM. I-jet by IAR Systems. Jaguar by Crossware. J-Link by Segger Supports JTAG and SWD. Supports ARM7, ARM9, ARM11, Cortex-A, Cortex-M, Cortex-R, Renesas RX, Microchip PIC32. Eclipse plug-in available. Supports GDB, RDI, Ozone debuggers. J-Trace by Segger. Supports JTAG, SWD, and ETM trace on Cortex-M. JTAGjet by Signum. LPC-LINK by Embedded Artists (for NXP) This is only embedded on NXP LPCXpresso development boards. LPC-LINK 2 by NXP. This device can be reconfigured to support 3 different protocols: J-LINK by Segger, CMSIS-DAP by ARM, Redlink by Code Red. Multilink debug probes, Cyclone in-system programming/debugging interfaces, and a GDB Server plug-in for Eclipse-based ARM IDEs by PEmicro. OpenOCD open source GDB server supports a variety of JTAG probes OpenOCD Eclipse plug-in available in GNU ARM Eclipse Plug-ins. AK-OPENJTAG by Artekit (Open JTAG-compatible). AK-LINK by Artekit. PEEDI by RONETIX Debug Probe by Raspberry Pi. RLink by Raisonance. ST-LINK/V2 by STMicroelectronics The ST-LINK/V2 debugger embedded on STM32 Nucleo and Discovery development boards can be converted to SEGGER J-LINK protocol. TRACE32 Debugger and ETM/ITM Trace by Lauterbach. ULINK by Keil. Debugging tools and/or debugging plug-ins (in alphabetical order): Memfault Error Analysis for post mortem debugging Percepio Tracealyzer, RTOS trace visualizer (with Eclipse plugin). Segger SystemView, RTOS trace visualizer. == Real-time operating systems == Commonly referred to as RTOS: == C/C++ software libraries == The following are free C/C++ libraries: ARM Cortex libraries: Cortex Microcontroller Software Interface Standard (CMSIS) libopencm3 (formerly called libopenstm32) libmaple for STM32F1 chips LPCOpen for NXP LPC chips Alternate C standard libraries: Bionic libc, dietlibc, EGLIBC, glibc, klibc, musl, Newlib, uClibc FAT file system libraries: EFSL, FatFs, Petit FatFs Fixed-point math libraries: libfixmath, fixedptc, FPMLib Encryption libraries: Comparison of TLS implementations wolfSSL == Non-C/C++ computer languages and software libraries ==

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  Labeled data

  Labeled data is a group of samples that have been tagged with one or more labels. Labeling typically takes a set of unlabeled data and augments each piece of it with informative tags called judgments. For example, a data label might indicate whether a photo contains a horse or a cow, which words were uttered in an audio recording, what type of action is being performed in a video, what the topic of a news article is, what the overall sentiment of a tweet is, or whether a dot in an X-ray is a tumor. Labels can be obtained by having humans make judgments about a given piece of unlabeled data. Labeled data is significantly more expensive to obtain than the raw unlabeled data. The quality of labeled data directly influences the performance of supervised machine learning models in operation, as these models learn from the provided labels. == Crowdsourced labeled data == In 2006, Fei-Fei Li, the co-director of the Stanford Human-Centered AI Institute, initiated research to improve the artificial intelligence models and algorithms for image recognition by significantly enlarging the training data. The researchers downloaded millions of images from the World Wide Web and a team of undergraduates started to apply labels for objects to each image. In 2007, Li outsourced the data labeling work on Amazon Mechanical Turk, an online marketplace for digital piece work. The 3.2 million images that were labeled by more than 49,000 workers formed the basis for ImageNet, one of the largest hand-labeled database for outline of object recognition. == Automated data labelling == After obtaining a labeled dataset, machine learning models can be applied to the data so that new unlabeled data can be presented to the model and a likely label can be guessed or predicted for that piece of unlabeled data. == Challenges == === Data-driven bias === Algorithmic decision-making is subject to programmer-driven bias as well as data-driven bias. Training data that relies on bias labeled data will result in prejudices and omissions in a predictive model, despite the machine learning algorithm being legitimate. The labeled data used to train a specific machine learning algorithm needs to be a statistically representative sample to not bias the results. For example, in facial recognition systems underrepresented groups are subsequently often misclassified if the labeled data available to train has not been representative of the population,. In 2018, a study by Joy Buolamwini and Timnit Gebru demonstrated that two facial analysis datasets that have been used to train facial recognition algorithms, IJB-A and Adience, are composed of 79.6% and 86.2% lighter skinned humans respectively. === Human error and inconsistency === Human annotators are prone to errors and biases when labeling data. This can lead to inconsistent labels and affect the quality of the data set. The inconsistency can affect the machine learning model's ability to generalize well. === Domain expertise === Certain fields, such as legal document analysis or medical imaging, require annotators with specialized domain knowledge. Without the expertise, the annotations or labeled data may be inaccurate, negatively impacting the machine learning model's performance in a real-world scenario.

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  World model (artificial intelligence)

  A world model in artificial intelligence is a machine learning system that builds an internal representation of an environment. The model predicts how that environment changes over time in response to actions. Researchers design world models to help agents plan, reason, and act without constant real-world trial and error. World models differ from systems that merely classify or generate outputs. They simulate dynamics such as physics, object interactions, and causality. Early ideas date to the 1990s. Modern versions power robots, autonomous driving, and interactive video generation. == History == Jürgen Schmidhuber introduced the term world model in machine learning in 1990. He proposed recurrent neural networks that predict future states from observations and use those predictions to train agents. David Ha and Schmidhuber revived the concept in a 2018 paper. Their agents learned to drive virtual cars and play video games inside self-generated simulations. Yann LeCun advanced the idea in a 2022 position paper titled "A Path Towards Autonomous Machine Intelligence". He argued that intelligence requires predictive models of the world rather than pure pattern matching. LeCun proposed the joint embedding predictive architecture (JEPA) as a practical foundation. LeCun and collaborators developed several JEPA variants. V-JEPA 2 reached state-of-the-art performance on video understanding and physical reasoning at the time. It supports zero-shot robot control in unfamiliar environments. Introduced in March 2026, LeWorldModel trains stably end-to-end from raw pixels and uses two loss terms and avoids hand-crafted heuristics. LeCun founded Advanced Machine Intelligence Labs in 2026 to further develop world models. Google DeepMind introduced Genie in 2024. The model learned interactive environments from unlabeled internet videos. Genie 2 followed in late 2024 and added three-dimensional generation. The Genie series set benchmarks for general-purpose simulation. Genie 3 was introduced in August 2025. It produces photorealistic, real-time interactive worlds from text prompts which are displayed at 24 frames per second and explored in real time with text or image prompts. The model supports persistent three-dimensional worlds and real-time interaction. Waymo adopted Genie 3 in February 2026 and used it to create a specialized world model for autonomous driving simulation, called the Waymo World Model. It produces synchronized camera and lidar outputs and creates edge cases that real robotaxis rarely encounter. The edge cases were reported to be unusual by PCMag. General Intuition announced a $133.7 million seed round. World Labs raised $1 billion. AMI raised $1.03 billion. In April 2026, Alibaba announced Happy Oyster, its world model designed for real-time and “flowy” world model. It includes a directing mode for world building based on text and image prompts and a wandering mode for exploring the resulting world. It can generate 3-minute in-world video clips. Also in April, World Labs, co-founded by Li Fei Fei, unveiled Spark 2.0, an open-source 3D Gaussian splatting rendering engine that targets smartphone-class devices. In June 2026, Nvidia released Cosmos 3, a family of open-weight models. It combines previously independent physical reasoning, world simulation, and action generation. Cosmos 3 integrates can process and generate text, image, video, audio, and action sequences. The model employs a Mixture-of-Transformers" (MoT) approach. An autoregressive (AR) transformer handles reasoning and next-token prediction, while a diffusion transformer (DT) does multimodal generation. Encoders (ViT for vision, VAE for visual/audio, and domain-specific for actions) and generate a shared representation space using 3D multi-dimensional rotary position embedding (mRoPE) for spatial and temporal information. The family includes Cosmos3-Nano (16B parameters) for workstations; Cosmos3-Super (64B parameters) for research. == Architecture == World models process raw sensory data such as video frames or lidar scans. They compress this input into compact latent representations. The system then predicts future representations rather than pixel-by-pixel reconstructions. Many modern world models use joint embedding predictive architecture (JEPA). An encoder turns observations into embeddings. A predictor estimates one or a suite of embeddings from the current one and an action. In some cases a critic chooses one embedding as the best result. A regularizer keeps embeddings well-behaved. The model trains by minimizing prediction error in embedding space. This approach avoids the high cost of generating every detail. Some architectures add explicit components. A fast reactive path handles immediate responses. A slower deliberative path performs longer-horizon planning. Video prediction accuracy or robot success rates are key metrics, but do not always predict real-world performance. Generative world models such as Genie 3 combine these with a simulator. They accept text prompts or layouts and output consistent video, lidar, or three-dimensional scenes. World models often train with self-supervised learning. They use large unlabeled datasets of video or robot interactions. Self-supervised learning can speed learning. Reinforcement learning can fine-tune a model for specific tasks. == Applications == World models support robot learning. Agents train inside simulations and transfer skills to the physical world. This reduces the need for dangerous or expensive real-world trials. Autonomous vehicles use world models to test rare events. Waymo's system simulates tornadoes or unusual pedestrian behavior. Companies train planners without putting vehicles on public roads. Interactive entertainment benefits from world models. Genie 3 lets users generate playable environments from simple descriptions. Game studios prototype levels faster. Scientific simulation gains from these models. Researchers model physical systems or biological processes at scale. Planners in logistics or urban design test strategies inside accurate digital twins. == Comparison with large language models == Both world models and large language models (LLMs) use inferencing on their inputs to make predictions. LLMs operate on textual inputs. They predict the next token in text sequences. They excel at language-oriented tasks such as translation or summarization. However, they lack understanding of physics. World models operate on sensor inputs such as pixels. They predict state changes in that data in latent space. This design supports planning and causal reasoning. LLMs generate fluent text but often fail at consistent physical predictions. Their architecture employs transformers with refinements such as mixture of experts. World models divide an inferencing task into work performed by encoders, predictors, simulators, and other pieces. They typically handle multimodal inputs such as video, lidar, radar, and audio, guided by textual prompting. LLMs power chatbots and code assistants. World models drive embodied agents that act in dynamic environments, such as autonomous driving. The two may be combined in hybrid systems. For example, a LLM handles instructions, while a world model manages low-level control. World model proponents such as LeCun claim that because LLMs are trained only on text, they have no ability to predict anything beyond text, such as real-world events. == Benchmarks == World model benchmarks test physical understanding, long-term consistency, planning, and generalization from sensor data. Meta introduced three benchmarks for V-JEPA 2. IntPhys 2 measures a model's ability to detect physics violations. It presents pairs of videos that diverge when one breaks physical rules. Humans score near 100% accuracy. V-JEPA 2 achieves little better than random chance on many conditions. Minimal Video Pairs (MVPBench) tests physical understanding through multiple-choice questions based on short video clips. It probes object interactions and causality. Something-Something tests action recognition. Epic-Kitchens-100 tests human action anticipation. DeepMind benchmark: Interactive evaluation measures consistency over minutes of interaction, memory of off-screen objects, and response to user actions or text prompts. Waymo benchmark: Output generation quality: Metrics include realism, controllability (via text prompts), and usefulness for training planners in simulated worlds. However, pixel reconstruction error rate with episodic rewards often fails. Other: Epic-Kitchens-100 (often measured with Recall@5) Ego4D 50 Salads, Breakfast, etc. Potential benchmarks: Zero-shot transfer to robots Long-horizon planning Implausible prediction rate

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