Apertus is a public large language model, developed by the Swiss AI Initiative (a collaboration between EPFL, ETH Zurich, and the Swiss National Supercomputing Centre). It was released on September 2, 2025, under the free and open-source Apache 2.0 license. Designed initially for business and research use cases around the world, Apertus was trained on over 1800 languages, and comes in 8 billion or 70 billion parameter versions and is available on Hugging Face for download. The model was developed aiming to adhere to European copyright law, and is one of the first examples of AI as a public good in the vein of AI Sovereignty. It is also the first large model to comply with the European Union's Artificial Intelligence Act. At its launch, the model creators emphasized multilinguality, transparency, and auditability as priorities in contrast to commercial frontier model. While international reception was largely positive, the first iteration was significantly behind the capabilities of frontier models and needs adaptation for many use cases with chatbots being a secondary but not a primary use case. As of late 2025, it was considered the largest and most capable fully open model. The capability of future models will depend in part on how much more funding can be secured.
Gibberlink
GibberLink is an acoustic data transmission project, with an open-source client available on GitHub, in which two conversational AI agents switch from speaking to one another in a Human-listenable language (such as English) to their own unique language that consists of a sound-level protocol after confirming they are both AI agents. The project was created by Anton Pidkuiko and Boris Starkov. == Reception == The project won the global top prize at the ElevenLabs Worldwide Hackathon. It has also been cited as raising questions around AI ethics and oversight. On February 23, 2025, a YouTube video of two independent conversational ElevenLabs AI agents being prompted to chat about booking a hotel (one as a caller, one as a receptionist) received coverage for going viral. In this video, both agents are prompted to switch to ggwave data-over-sound protocol when they identify the other side as AI, and keep speaking in English otherwise.
Blackboard system
A blackboard system is an artificial intelligence approach based on the blackboard architectural model, where a common knowledge base, the "blackboard", is iteratively updated by a diverse group of specialist knowledge sources, starting with a problem specification and ending with a solution. Each knowledge source updates the blackboard with a partial solution when its internal constraints match the blackboard state. In this way, the specialists work together to solve the problem. The blackboard model was originally designed as a way to handle complex, ill-defined problems, where the solution is the sum of its parts. == Metaphor == The following scenario provides a simple metaphor that gives some insight into how a blackboard functions: A group of specialists are seated in a room with a large blackboard. They work as a team to brainstorm a solution to a problem, using the blackboard as the workplace for cooperatively developing the solution. The session begins when the problem specifications are written onto the blackboard. The specialists all watch the blackboard, looking for an opportunity to apply their expertise to the developing solution. When someone writes something on the blackboard that allows another specialist to apply their expertise, the second specialist records their contribution on the blackboard, hopefully enabling other specialists to then apply their expertise. This process of adding contributions to the blackboard continues until the problem has been solved. == Components == A blackboard-system application consists of three major components The software specialist modules, which are called knowledge sources (KSs). Like the human experts at a blackboard, each knowledge source provides specific expertise needed by the application. The blackboard, a shared repository of problems, partial solutions, suggestions, and contributed information. The blackboard can be thought of as a dynamic "library" of contributions to the current problem that have been recently "published" by other knowledge sources. The control shell, which controls the flow of problem-solving activity in the system. Just as the eager human specialists need a moderator to prevent them from trampling each other in a mad dash to grab the chalk, KSs need a mechanism to organize their use in the most effective and coherent fashion. In a blackboard system, this is provided by the control shell. === Learnable Task Modeling Language === A blackboard system is the central space in a multi-agent system. It's used for describing the world as a communication platform for agents. To realize a blackboard in a computer program, a machine readable notation is needed in which facts can be stored. One attempt in doing so is a SQL database, another option is the Learnable Task Modeling Language (LTML). The syntax of the LTML planning language is similar to PDDL, but adds extra features like control structures and OWL-S models. LTML was developed in 2007 as part of a much larger project called POIROT (Plan Order Induction by Reasoning from One Trial), which is a Learning from demonstrations framework for process mining. In POIROT, Plan traces and hypotheses are stored in the LTML syntax for creating semantic web services. Here is a small example: A human user is executing a workflow in a computer game. The user presses some buttons and interacts with the game engine. While the user interacts with the game, a plan trace is created. That means the user's actions are stored in a logfile. The logfile gets transformed into a machine readable notation which is enriched by semantic attributes. The result is a textfile in the LTML syntax which is put on the blackboard. Agents (software programs in the blackboard system) are able to parse the LTML syntax. == Implementations == We start by discussing two well known early blackboard systems, BB1 and GBB, below and then discuss more recent implementations and applications. The BB1 blackboard architecture was originally inspired by studies of how humans plan to perform multiple tasks in a trip, used task-planning as a simplified example of tactical planning for the Office of Naval Research. Hayes-Roth & Hayes-Roth found that human planning was more closely modeled as an opportunistic process, in contrast to the primarily top-down planners used at the time: While not incompatible with successive-refinement models, our view of planning is somewhat different. We share the assumption that planning processes operate in a two-dimensional planning space defined on time and abstraction dimensions. However, we assume that people's planning activity is largely opportunistic. That is, at each point in the process, the planner's current decisions and observations suggest various opportunities for plan development. The planner's subsequent decisions follow up on selected opportunities. Sometimes, these decision-sequences follow an orderly path and produce a neat top-down expansion as described above. However, some decisions and observations might also suggest less orderly opportunities for plan development. A key innovation of BB1 was that it applied this opportunistic planning model to its own control, using the same blackboard model of incremental, opportunistic, problem-solving that was applied to solve domain problems. Meta-level reasoning with control knowledge sources could then monitor whether planning and problem-solving were proceeding as expected or stalled. If stalled, BB1 could switch from one strategy to another as conditions – such as the goals being considered or the time remaining – changed. BB1 was applied in multiple domains: construction site planning, inferring 3-D protein structures from X-ray crystallography, intelligent tutoring systems, and real-time patient monitoring. BB1 also allowed domain-general language frameworks to be designed for wide classes of problems. For example, the ACCORD language framework defined a particular approach to solving configuration problems. The problem-solving approach was to incrementally assemble a solution by adding objects and constraints, one at a time. Actions in the ACCORD language framework appear as short English-like commands or sentences for specifying preferred actions, events to trigger KSes, preconditions to run a KS action, and obviation conditions to discard a KS action that is no longer relevant. GBB focused on efficiency, in contrast to BB1, which focused more on sophisticated reasoning and opportunistic planning. GBB improves efficiency by allowing blackboards to be multi-dimensional, where dimensions can be either ordered or not, and then by increasing the efficiency of pattern matching. GBB1, one of GBB's control shells implements BB1's style of control while adding efficiency improvements. Other well-known of early academic blackboard systems are the Hearsay II speech recognition system and Douglas Hofstadter's Copycat and Numbo projects. Some more recent examples of deployed real-world applications include: The PLAN component of the Mission Control System for RADARSAT-1, an Earth observation satellite developed by Canada to monitor environmental changes and Earth's natural resources. The GTXImage CAD software by GTX Corporation was developed in the early 1990s using a set of rulebases and neural networks as specialists operating on a blackboard system. Adobe Acrobat Capture (now discontinued), as it used a blackboard system to decompose and recognize image pages to understand the objects, text, and fonts on the page. This function is currently built into the retail version of Adobe Acrobat as "OCR Text Recognition". Details of a similar OCR blackboard for Farsi text are in the public domain. Blackboard systems are used routinely in many military C4ISTAR systems for detecting and tracking objects. Another example of current use is in Game AI, where they are considered a standard AI tool to help with adding AI to video games. == Recent developments == Blackboard-like systems have been constructed within modern Bayesian machine learning settings, using agents to add and remove Bayesian network nodes. In these 'Bayesian Blackboard' systems, the heuristics can acquire more rigorous probabilistic meanings as proposal and acceptances in Metropolis Hastings sampling though the space of possible structures. Conversely, using these mappings, existing Metropolis-Hastings samplers over structural spaces may now thus be viewed as forms of blackboard systems even when not named as such by the authors. Such samplers are commonly found in musical transcription algorithms for example. Blackboard systems have also been used to build large-scale intelligent systems for the annotation of media content, automating parts of traditional social science research. In this domain, the problem of integrating various AI algorithms into a single intelligent system arises spontaneously, with blackboards providing a way for a collection of distributed, modular natural language processing algorithm
Terminator (franchise)
Terminator is an American media franchise created by James Cameron and Gale Anne Hurd. It is considered to be of the cyberpunk subgenre of science fiction. The franchise primarily focuses on the events leading to a future post-apocalyptic war between a synthetic intelligence known as Skynet, and a surviving resistance of humans led by John Connor. In this future, Skynet uses an arsenal of cyborgs known as Terminators, designed to mimic humans and infiltrate the resistance. Much of the franchise takes place in time periods prior to the Skynet takeover, with both humans and Terminators using time travel to attempt to alter the past and change the outcome of the future. A prominent Terminator model throughout the films is the T-800, commonly known as "the Terminator", with instances of this model portrayed by Arnold Schwarzenegger. The franchise began with the 1984 film The Terminator, written and directed by Cameron, with Hurd as producer. They would return for the 1991 sequel Terminator 2: Judgment Day (or T2). Both films were critical and commercial successes. Terminator 3: Rise of the Machines (or T3) was released in 2003 to positive reviews, followed by Terminator Salvation in 2009 to more negative reviews. Salvation was intended as the first in a new trilogy, which was later scrapped after the film rights were sold. Cameron was consulted for the 2015 film Terminator Genisys, a reboot branching off from the timeline of the original film. It was negatively received and performed poorly at the box-office. Cameron had a larger role as a producer of the 2019 film Terminator: Dark Fate, a direct sequel to T2 that ignores the three preceding films. As with Salvation, both Genisys and Dark Fate were planned as first installments of new trilogies, with the plans scrapped each time due to the films' poor box-office performances. Outside of the theatrical films, Cameron co-directed T2-3D: Battle Across Time, a 1996 theme park film-based attraction. It was produced as the original sequel to T2 and reunited its main cast. A television series, Terminator: The Sarah Connor Chronicles, was developed without Cameron's involvement and aired for two seasons in 2008 and 2009. It was also produced as a T2 sequel, taking place in an alternate timeline that ignores the third film and subsequent events. Terminator Zero, an anime series, premiered in August 2024. The franchise has also inspired several lines of comic books since 1988, and numerous video games since 1991. By 2010, the franchise had generated $3 billion in revenue. == Themes and setting == The central theme of the franchise is the battle for survival between the nearly-extinct human race and the world-spanning, synthetic intelligence that is Skynet. Skynet is positioned in the first film, The Terminator (1984), as a U.S. strategic "Global Digital Defense Network" computer system by Cyberdyne Systems which becomes self-aware. Shortly after activation, Skynet seemingly perceives all humans as a threat to its existence and formulates a plan to systematically wipe out humanity itself. The system initiates a nuclear first strike against Russia, thereby ensuring a devastating second strike and a nuclear holocaust which wipes out much of humanity in the resulting nuclear war. In the post-apocalyptic aftermath, Skynet later builds up its own autonomous machine-based military capability which includes the Terminators used against individual human targets and thereafter proceeds to wage a persistent total war against the surviving elements of humanity, some of whom have militarily organized themselves into a Resistance. At some point in this future, Skynet develops the capability of time travel and both it and the Resistance seek to use this technology in order to win the war; either by altering or accelerating past events or by preventing the apocalyptic timeline. === Judgment Day === In the franchise, Judgment Day (a reference to the biblical Day of Judgment) is the date on which Skynet becomes self-aware, in which case its creators panic and attempt to deactivate the network. As a result, Skynet perceives humanity as a threat and attempts to exterminate them. Skynet launches an all-out nuclear attack on Russia in order to provoke a nuclear counter-strike against the United States, knowing this will eliminate its human enemies. Due to time travel and the consequent ability to change the future, several differing dates are given for Judgment Day. In Terminator 2: Judgment Day (1991), Sarah Connor states that Judgment Day will occur on August 29, 1997. However, this date is delayed following the attack on Cyberdyne Systems in the same film. Judgment Day has various different dates in different timelines of the subsequent films, as well as the television series, creating a multiverse of temporal phenomena. In Terminator 3: Rise of the Machines (2003) and Terminator Salvation (2009), Judgment Day was postponed to July 2003. In Terminator: The Sarah Connor Chronicles (2008–2009), the attack on Cyberdyne Systems in the second film delayed Judgment Day to April 21, 2011. In Terminator Genisys (2015), the fifth film in the franchise, Judgment Day was postponed to an unspecified day in October 2017, attributed to altered events in both the future and the past. Sarah and Kyle Reese travel through time to the year 2017 and seemingly defeat Skynet, but the system core, contained inside a subterranean blast shelter, survives unknown to them, thus further delaying, rather than preventing, Judgment Day. In Terminator: Dark Fate (2019), the direct sequel to Terminator 2: Judgment Day, a date is not given for the new Judgment Day though it is named as such by Grace. Since Grace is a ten-year-old in 2020 and shown as a teenager in the post-Judgment Day world in flash-forwards throughout the film, Judgment Day occurs sometime in the early 2020s in this timeline. == Franchise rights == Before the first film was created, director James Cameron sold the rights for $1 to Gale Anne Hurd, his future wife, who produced the film, under the strict provision that he be allowed to direct it. Hemdale Film Corporation also became a 50-percent owner of the franchise rights, until its share was sold in 1990 to Carolco Pictures, a company founded by Andrew G. Vajna and Mario Kassar. Terminator 2: Judgment Day was released a year later. Carolco filed for bankruptcy in 1995 and its library was subsequently acquired by StudioCanal, which continues to own the franchise today. However, the rights to future Terminator films were ultimately put up for auction. By that time, Cameron had become interested in making a Terminator 3 film. The rights were ultimately auctioned to Vajna in 1997, for $8 million. Vajna and Kassar spent another $8 million to purchase Hurd's half of the rights in 1998, becoming the full owners of the franchise. Hurd was initially opposed to the sale of the rights, while Cameron had lost interest in the franchise and a third film. After the 2003 release of Terminator 3: Rise of the Machines, the franchise rights were sold in 2007 for about $25 million to The Halcyon Company, which produced Terminator Salvation in 2009. Later that year, the company faced legal issues and filed for bankruptcy, putting the franchise rights up for sale. The rights were valued at about $70 million. In 2010, the rights were sold for $29.5 million to Pacificor, a hedge fund that was Halcyon's largest creditor. In 2012, the rights were sold to Megan Ellison and her production company Annapurna Pictures for less than $20 million, a lower price than what was previously offered. The low price was because of the possibility of Cameron regaining the rights in 2019, as a result of new North American copyright laws. Megan's brother David Ellison and Skydance Productions produced Terminator Genisys in 2015. Cameron worked together with David Ellison to produce the 2019 film Terminator: Dark Fate. As the film neared its release, Hurd filed to terminate a copyright grant made 35 years earlier. Under this move, Hurd would again become a 50-percent owner of the rights with Cameron and Skydance could lose the rights to make any additional Terminator films beginning in November 2020, unless a new deal is worked out. Skydance responded that it had a deal in place with Cameron and that it "controls the rights to the Terminator franchise for the foreseeable future". == Films == === The Terminator (1984) === The Terminator is a 1984 science fiction action film released by Orion Pictures, co-written and directed by James Cameron and starring Arnold Schwarzenegger, Linda Hamilton and Michael Biehn. It is the first work in the Terminator franchise. In the film, robots take over the world in the near future, directed by the artificial intelligence Skynet. With its sole mission to completely annihilate humanity, it develops android assassins called Terminators that outwardly appear human. A man named John Connor starts the Tech-Com resistance to fight the machi
Generative adversarial network
A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative artificial intelligence. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss. Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, fully supervised learning, and reinforcement learning. The core idea of a GAN is based on the "indirect" training through the discriminator, another neural network that can tell how "realistic" the input seems, which itself is also being updated dynamically. This means that the generator is not trained to minimize the distance to a specific image, but rather to fool the discriminator. This enables the model to learn in an unsupervised manner. GANs are similar to mimicry in evolutionary biology, with an evolutionary arms race between both networks. == Definition == === Mathematical === The original GAN is defined as the following game: Each probability space ( Ω , μ ref ) {\displaystyle (\Omega ,\mu _{\text{ref}})} defines a GAN game. There are 2 players: generator and discriminator. The generator's strategy set is P ( Ω ) {\displaystyle {\mathcal {P}}(\Omega )} , the set of all probability measures μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , where P [ 0 , 1 ] {\displaystyle {\mathcal {P}}[0,1]} is the set of probability measures on [ 0 , 1 ] {\displaystyle [0,1]} . The GAN game is a zero-sum game, with objective function L ( μ G , μ D ) := E x ∼ μ ref , y ∼ μ D ( x ) [ ln y ] + E x ∼ μ G , y ∼ μ D ( x ) [ ln ( 1 − y ) ] . {\displaystyle L(\mu _{G},\mu _{D}):=\operatorname {E} _{x\sim \mu _{\text{ref}},y\sim \mu _{D}(x)}[\ln y]+\operatorname {E} _{x\sim \mu _{G},y\sim \mu _{D}(x)}[\ln(1-y)].} The generator aims to minimize the objective, and the discriminator aims to maximize the objective. The generator's task is to approach μ G ≈ μ ref {\displaystyle \mu _{G}\approx \mu _{\text{ref}}} , that is, to match its own output distribution as closely as possible to the reference distribution. The discriminator's task is to output a value close to 1 when the input appears to be from the reference distribution, and to output a value close to 0 when the input looks like it came from the generator distribution. === In practice === The generative network generates candidates while the discriminative network evaluates them. This creates a contest based on data distributions, where the generator learns to map from a latent space to the true data distribution, aiming to produce candidates that the discriminator cannot distinguish from real data. The discriminator's goal is to correctly identify these candidates, but as the generator improves, its task becomes more challenging, increasing the discriminator's error rate. A known dataset serves as the initial training data for the discriminator. Training involves presenting it with samples from the training dataset until it achieves acceptable accuracy. The generator is trained based on whether it succeeds in fooling the discriminator. Typically, the generator is seeded with randomized input that is sampled from a predefined latent space (e.g. a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the generator produces better samples, while the discriminator becomes more skilled at flagging synthetic samples. When used for image generation, the generator is typically a deconvolutional neural network, and the discriminator is a convolutional neural network. === Relation to other statistical machine learning methods === GANs are implicit generative models, which means that they do not explicitly model the likelihood function nor provide a means for finding the latent variable corresponding to a given sample, unlike alternatives such as flow-based generative model. Compared to fully visible belief networks such as WaveNet and PixelRNN and autoregressive models in general, GANs can generate one complete sample in one pass, rather than multiple passes through the network. Compared to Boltzmann machines and linear ICA, there is no restriction on the type of function used by the network. Since neural networks are universal approximators, GANs are asymptotically consistent. Variational autoencoders might be universal approximators, but it is not proven as of 2017. == Mathematical properties == === Measure-theoretic considerations === This section provides some of the mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra. As a result, a more rigorous definition of the GAN game would make the following changes:Each probability space ( Ω , B , μ ref ) {\displaystyle (\Omega ,{\mathcal {B}},\mu _{\text{ref}})} defines a GAN game. The generator's strategy set is P ( Ω , B ) {\displaystyle {\mathcal {P}}(\Omega ,{\mathcal {B}})} , the set of all probability measures μ G {\displaystyle \mu _{G}} on the measure-space ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's strategy set is the set of Markov kernels μ D : ( Ω , B ) → P ( [ 0 , 1 ] , B ( [ 0 , 1 ] ) ) {\displaystyle \mu _{D}:(\Omega ,{\mathcal {B}})\to {\mathcal {P}}([0,1],{\mathcal {B}}([0,1]))} , where B ( [ 0 , 1 ] ) {\displaystyle {\mathcal {B}}([0,1])} is the Borel σ-algebra on [ 0 , 1 ] {\displaystyle [0,1]} .Since issues of measurability never arise in practice, these will not concern us further. === Choice of the strategy set === In the most generic version of the GAN game described above, the strategy set for the discriminator contains all Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , and the strategy set for the generator contains arbitrary probability distributions μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . However, as shown below, the optimal discriminator strategy against any μ G {\displaystyle \mu _{G}} is deterministic, so there is no loss of generality in restricting the discriminator's strategies to deterministic functions D : Ω → [ 0 , 1 ] {\displaystyle D:\Omega \to [0,1]} . In most applications, D {\displaystyle D} is a deep neural network function. As for the generator, while μ G {\displaystyle \mu _{G}} could theoretically be any computable probability distribution, in practice, it is usually implemented as a pushforward: μ G = μ Z ∘ G − 1 {\displaystyle \mu _{G}=\mu _{Z}\circ G^{-1}} . That is, start with a random variable z ∼ μ Z {\displaystyle z\sim \mu _{Z}} , where μ Z {\displaystyle \mu _{Z}} is a probability distribution that is easy to compute (such as the uniform distribution, or the Gaussian distribution), then define a function G : Ω Z → Ω {\displaystyle G:\Omega _{Z}\to \Omega } . Then the distribution μ G {\displaystyle \mu _{G}} is the distribution of G ( z ) {\displaystyle G(z)} . Consequently, the generator's strategy is usually defined as just G {\displaystyle G} , leaving z ∼ μ Z {\displaystyle z\sim \mu _{Z}} implicit. In this formalism, the GAN game objective is L ( G , D ) := E x ∼ μ ref [ ln D ( x ) ] + E z ∼ μ Z [ ln ( 1 − D ( G ( z ) ) ) ] . {\displaystyle L(G,D):=\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln D(x)]+\operatorname {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z)))].} === Generative reparametrization === The GAN architecture has two main components. One is casting optimization into a game, of form min G max D L ( G , D ) {\displaystyle \min _{G}\max _{D}L(G,D)} , which is different from the usual kind of optimization, of form min θ L ( θ ) {\displaystyle \min _{\theta }L(\theta )} . The other is the decomposition of μ G {\displaystyle \mu _{G}} into μ Z ∘ G − 1 {\displaystyle \mu _{Z}\circ G^{-1}} , which can be understood as a reparametrization trick. To see its significance, one must compare GAN with previous methods for learning generative models, which were plagued with "intractable probabilistic computations that arise in maximum likelihood estimation and related strategies". At the same time, Kingma and Welling and Rezende et al. developed the same idea of reparametrization into a general stochastic backpropagation method. Among its first applications was the variational autoencoder. === Move order and st
Visualization (graphics)
Visualization (or visualisation in Commonwealth English; see spelling differences), also known as graphics visualization, is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of humanity. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering purposes that actively involve scientific requirements. Visualization today has ever-expanding applications in science, education, engineering (e.g., product visualization), interactive multimedia, medicine, etc. Typical of a visualization application is the field of computer graphics. The invention of computer graphics (and 3D computer graphics) may be the most important development in visualization since the invention of central perspective in the Renaissance period. The development of animation also helped advance visualization. == Overview == The use of visualization to present information is not a new phenomenon. It has been used in maps, scientific drawings, and data plots for over a thousand years. Examples from cartography include Ptolemy's Geographia (2nd century AD), a map of China (1137 AD), and Minard's map (1861) of Napoleon's invasion of Russia a century and a half ago. Most of the concepts learned in devising these images carry over in a straightforward manner to computer visualization. Edward Tufte has written three critically acclaimed books that explain many of these principles. Computer graphics has from its beginning been used to study scientific problems. However, in its early days the lack of graphics power often limited its usefulness. The recent emphasis on visualization started in 1987 with the publication of Visualization in Scientific Computing, a special issue of Computer Graphics. Since then, there have been several conferences and workshops, co-sponsored by the IEEE Computer Society and ACM SIGGRAPH, devoted to the general topic, and special areas in the field, for example volume visualization. Most people are familiar with the digital animations produced to present meteorological data during weather reports on television, though few can distinguish between those models of reality and the satellite photos that are also shown on such programs. TV also offers scientific visualizations when it shows computer drawn and animated reconstructions of road or airplane accidents. Some of the most popular examples of scientific visualizations are computer-generated images that show real spacecraft in action, out in the void far beyond Earth, or on other planets. Dynamic forms of visualization, such as educational animation or timelines, have the potential to enhance learning about systems that change over time. Apart from the distinction between interactive visualizations and animation, the most useful categorization is probably between abstract and model-based scientific visualizations. The abstract visualizations show completely conceptual constructs in 2D or 3D. These generated shapes are completely arbitrary. The model-based visualizations either place overlays of data on real or digitally constructed images of reality or make a digital construction of a real object directly from the scientific data. Scientific visualization is usually done with specialized software, though there are a few exceptions, noted below. Some of these specialized programs have been released as open source software, having very often its origins in universities, within an academic environment where sharing software tools and giving access to the source code is common. There are also many proprietary software packages of scientific visualization tools. Models and frameworks for building visualizations include the data flow models popularized by systems such as AVS, IRIS Explorer, and VTK toolkit, and data state models in spreadsheet systems such as the Spreadsheet for Visualization and Spreadsheet for Images. == Applications == === Scientific visualization === As a subject in computer science, scientific visualization is the use of interactive, sensory representations, typically visual, of abstract data to reinforce cognition, hypothesis building, and reasoning. Scientific visualization is the transformation, selection, or representation of data from simulations or experiments, with an implicit or explicit geometric structure, to allow the exploration, analysis, and understanding of the data. Scientific visualization focuses and emphasizes the representation of higher order data using primarily graphics and animation techniques. It is a very important part of visualization and maybe the first one, as the visualization of experiments and phenomena is as old as science itself. Traditional areas of scientific visualization are flow visualization, medical visualization, astrophysical visualization, and chemical visualization. There are several different techniques to visualize scientific data, with isosurface reconstruction and direct volume rendering being the more common. === Data and information visualization === Data visualization is a related subcategory of visualization dealing with statistical graphics and geospatial data (as in thematic cartography) that is abstracted in schematic form. Information visualization concentrates on the use of computer-supported tools to explore large amount of abstract data. The term "information visualization" was originally coined by the User Interface Research Group at Xerox PARC and included Jock Mackinlay. Practical application of information visualization in computer programs involves selecting, transforming, and representing abstract data in a form that facilitates human interaction for exploration and understanding. Important aspects of information visualization are dynamics of visual representation and the interactivity. Strong techniques enable the user to modify the visualization in real-time, thus affording unparalleled perception of patterns and structural relations in the abstract data in question. === Educational visualization === Educational visualization is using a simulation to create an image of something so it can be taught about. This is very useful when teaching about a topic that is difficult to otherwise see, for example, atomic structure, because atoms are far too small to be studied easily without expensive and difficult to use scientific equipment. === Knowledge visualization === The use of visual representations to transfer knowledge between at least two persons aims to improve the transfer of knowledge by using computer and non-computer-based visualization methods complementarily. Thus properly designed visualization is an important part of not only data analysis but knowledge transfer process, too. Knowledge transfer may be significantly improved using hybrid designs as it enhances information density but may decrease clarity as well. For example, visualization of a 3D scalar field may be implemented using iso-surfaces for field distribution and textures for the gradient of the field. Examples of such visual formats are sketches, diagrams, images, objects, interactive visualizations, information visualization applications, and imaginary visualizations as in stories. While information visualization concentrates on the use of computer-supported tools to derive new insights, knowledge visualization focuses on transferring insights and creating new knowledge in groups. Beyond the mere transfer of facts, knowledge visualization aims to further transfer insights, experiences, attitudes, values, expectations, perspectives, opinions, and estimates in different fields by using various complementary visualizations. See also: picture dictionary, visual dictionary === Product visualization === Product visualization involves visualization software technology for the viewing and manipulation of 3D models, technical drawing and other related documentation of manufactured components and large assemblies of products. It is a key part of product lifecycle management. Product visualization software typically provides high levels of photorealism so that a product can be viewed before it is actually manufactured. This supports functions ranging from design and styling to sales and marketing. Technical visualization is an important aspect of product development. Originally technical drawings were made by hand, but with the rise of advanced computer graphics the drawing board has been replaced by computer-aided design (CAD). CAD-drawings and models have several advantages over hand-made drawings such as the possibility of 3-D modeling, rapid prototyping, and simulation. 3D product visualization promises more interactive experiences for online shoppers, but also challenges retailers to overcome hurdles in the production of 3D content, as large-scale 3D content production can be extremel
Thompson sampling
Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.