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Spatiotemporal reservoir resampling

Spatiotemporal reservoir resampling, commonly known as ReSTIR (from "Reservoir-based SpatioTemporal Importance Resampling"), is a collection of computer graphics techniques for reusing samples during rendering. It was developed primarily to allow more realistic lighting in real-time rendering, because relatively few rays can be traced per pixel while maintaining an acceptable frame rate. It can also be used to speed up off-line path tracing. The first ReSTIR paper, published in 2020, provided algorithms for direct lighting, allowing scenes containing thousands of lights to be rendered in real time on a high-end GPU. Researchers later proposed versions for rendering indirect lighting (and more recently, motion blur and depth of field) and built up a framework of mathematical concepts and notation conventions that help analyze such algorithms. A major focus of this work is removing or reducing the bias that could be introduced when samples from other pixels or frames are reused—or selectively allowing some bias in order to speed up rendering and reduce variance (visible as "noise" in the image). Versions for path tracing apply transformations called shift mappings to samples, typically reusing parts of paths closer to the light and modifying the portion closer to the camera. ReSTIR-related papers and talks have been presented every year at the SIGGRAPH conference since 2020. One of the first games to incorporate ReSTIR into its rendering was Cyberpunk 2077. == Overview and motivation == According to Chris Wyman, one of the co-authors of the original paper, although developers commonly thought that bias was acceptable for real-time rendering, end users (e.g. gamers) are well-aware of the artifacts caused by bias and many have a negative opinion of common sample-reuse techniques such as temporal anti-aliasing (TAA), which may cause "ghosting" when the camera moves, and denoising, which causes blurring and other artifacts. ReSTIR techniques can reduce or avoid these types of bias by reusing samples of the set of possible paths taken by light to reach the camera, instead of reusing rendered pixel color values (which are typically the average of multiple samples, discarding information such as the direction of the light). While other techniques reuse samples in a generic post-processing step, ReSTIR passes can test for shadowing, and reused samples are converted into pixel color values by rendering code that takes the characteristics of different materials into account (e.g. by implementing BRDFs). However the output of ReSTIR is noisy, and a denoising pass is typically still used. Stochastic ray tracing techniques such as path tracing need to average multiple samples (produced by tracing individual rays) in order to render a visually acceptable image. When using a simple unbiased renderer based on Monte Carlo integration, halving the deviation of the result (apparent as "noise" in the image) requires multiplying the number of samples by four, meaning that a rapidly increasingly number of samples is needed to improve quality, Standard ways to mitigate this problem include importance sampling (which requires finding improved sampling distributions for specific situations), and quasi-Monte Carlo integration (which usually still requires tracing a large number of rays). ReSTIR offers a solution that multiplies the effective number of samples while tracing a fixed number of additional rays per frame. Temporal reuse multiplies the effective sample count by the number of frames rendered. Spatial reuse multiplies the effective count by the number of neighboring pixels examined. These two types of reuse can be combined, allowing spatial reuse to be applied recursively, which appears to offer an exponentially increasing effective sample count, however this is quickly limited by the size of the neighborhood used for spatial reuse. Spatial reuse is also potentially less effective near shadow and object edges, especially for objects with fine geometric detail, and temporal reuse is limited by movement of the camera and scene elements. == Variations == Many variations of ReSTIR have been proposed that generalize or improve the original technique (which builds on an earlier method called RIS), specialize it for particular types of illumination or other visual effects, or allow incorporation into rendering algorithms other than standard path tracing. Some published versions are listed below. == Algorithms == === Basic algorithm === ReSTIR uses a combination of resampled importance sampling (RIS) and weighted reservoir sampling (WRS) which the authors call streaming RIS. RIS processes samples from an initial probability distribution (e.g. a probability distribution for which a cheap sampling method exists) and generates samples in a new probability distribution (e.g. a sampling distribution that is optimal for rendering but is impractical to draw samples from directly). WRS allows this to be done while storing only a small number of samples in memory, which is especially helpful on a GPU. Information about the samples is stored in a data structure called a reservoir. WRS also allows samples from multiple reservoirs to be combined ("merged") into a single reservoir; this is crucial for sample reuse. Each pixel has a reservoir, typically containing only a single sample when ReSTIR is used for real-time rendering (some implementations use a larger number, e.g. four samples). The reservoir is typically initialized to a sample drawn using a simple method and is then updated by RIS steps and by reservoir merging, so that the pixel value produced by shading using the sample(s) currently in the reservoir, times the weight for the sample, is always an unbiased estimate of the correct pixel value. If appropriate resampling steps are used, the variance of this estimate (or some function of it, typically the luminance of the RGB color value) decreases with each step. A possible sequence of steps performed for each frame, suitable for computing unbiased direct illumination (DI) is: Perform reservoir resampling by drawing multiple light samples and using streaming RIS to choose one, using probabilities based on a target function, e.g. the luminance of the sample's contribution to the pixel. A weight is also computed for the sample. Typically, a single visibility check is performed here, after choosing a sample, setting the weight to 0 if the light is shadowed. Resampling (combined with the visibility check) ensures that the expected value of the weight times the sample brightness is the correct (unbiased) value for the pixel. (temporal reuse) For each pixel, merge the sample(s) from the previous frame into the current reservoir. Multiple importance sampling (MIS) weights are used to avoid bias due to the fact that the samples in the previous frame's reservoirs may have a different target probability distribution if the objects, lights, or camera have moved. (spatial reuse) For each pixel, choose one or more neighboring pixels and merge their samples into the current pixel's reservoir. Multiple importance sampling (MIS) weights are used to avoid bias due to the fact that the samples in each pixel's reservoir have a different target probability distribution. Because computing unbiased MIS weights requires tracing additional rays (along with other work such as evaluating BRDFs), real-time rendering often uses only a single neighboring pixel. Use the sample in each pixel's reservoir, along with its weight, to determine the color of the pixel for the current frame. Alternatively, multiple samples examined during the preceding steps may be averaged and used to shade the pixel instead (decoupled shading and sampling). For direct lighting, the initial samples used in step 1 are typically drawn by importance sampling from the set of lights in a scene. The algorithm above (from the original ReSTIR paper) draws many lower-quality light samples (e.g. 32) using a fast method, without considering visibility, and chooses one using streaming RIS. Visibility is then tested for the final chosen sample. Considering visibility for each sample drawn would require tracing 32 rays, which would make it much more expensive. The intent is to reduce the number of rays traced, relying on the sample reuse in steps 2 and 3 to make up for the loss of quality caused by rejecting many of the rays due to shadowing. A large part of the initial efforts to optimize ReSTIR (to make it run in real-time on available hardware) went into reducing the cost of randomly sampling the lights. Glossy surfaces may require a larger number of samples, and combining light sampling with BRDF sampling (using MIS) may increase quality. Step 2 (temporal reuse) is sometimes skipped for off-line rendering, and the output of multiple repetitions of initial sampling and spatial reuse is averaged instead; this helps avoids artifacts due to correlations. Step 3 (spatial reuse) may be repeated multiple times in a single frame.
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SERVQUAL

SERVQUAL is a research tool that measures customer perception of service quality by comparing what customers expect from a service to their assessment of the service actually delivered. The instrument was developed in the United States in the mid-1980s by researchers A. Parasuraman, Valarie Zeithaml, and Leonard L. Berry, and is designed for use in after-service evaluation processes. It assesses service quality across five dimensions: reliability, assurance, tangibles, empathy, and responsiveness. SERVQUAL has been applied in sectors including healthcare, banking, education, and libraries. == Overview == The SERVQUAL questionnaire consists of matched pairs of items, 22 expectation items and 22 perception items, organized into five dimensions that correspond to the consumer's mental framework for evaluating service quality. Each item is part of a pair: one question asks what excellent organizations in a given industry should offer (expectation), and the other asks how the specific organization being evaluated performs (perception). == The model of service quality == The model of service quality, referred to as the gaps model, was developed by Parasuraman, Zeithaml, and Berry during a systematic research program conducted in the 1980s. The model identifies five gaps that may cause customers to experience poor service quality. In this framework, gap 5 is the service quality gap, which represents the difference between customer expectations and their perceptions of the service. This is the only gap that can be directly measured, and the SERVQUAL instrument was designed specifically to capture it. Gaps 1 through 4 have diagnostic value and point to probable causes of service failures. == Development of the instrument == Development of the model of service quality began in 1983 and, after iterative refinements, led to the publication of the SERVQUAL instrument in 1988. The research team conducted in-depth interviews and focus groups in four service sectors: retail banking, credit card services, securities brokerage, and product repair and maintenance. The questionnaire was tested across multiple samples to verify its reliability, validity, and factor structure. == Adaptations and variants == SERVQUAL has been adapted for specific industries and contexts. Well‑known derivatives include: LibQUAL+ – a library service quality survey developed by the Association of Research Libraries. EDUQUAL – an instrument tailored for the evaluation of service quality in educational institutions. HEALTHQUAL – adapted for measuring patient perceptions of healthcare service quality. ARTSQUAL – used to evaluate visitor perceptions of quality in museums and performing arts venues. == Criticisms == Researchers have raised several concerns about SERVQUAL. Critics argue that the instrument's definition of expectations is ambiguous and that it does not adequately account for the dynamic nature of customer expectations over time. Other scholars question whether the five‑dimension structure is universally applicable across all service contexts, and whether a generic instrument can capture the unique attributes of specific industries without modification.
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Effective accelerationism

Effective accelerationism (e/acc) is a 21st-century ideological movement that advocates for an explicitly pro-technology stance. Its proponents believe that unrestricted technological progress, especially driven by artificial intelligence, is a solution to universal human problems, such as poverty, war, and climate change. They perceive themselves as a counterweight to more cautious views on technological innovation and often label their opponents derogatorily as "doomers" or "decels" (short for decelerationists). The movement carries utopian undertones and advocates for faster AI progress to ensure human survival and propagate consciousness throughout the universe. Although effective accelerationism has been described as a fringe movement and as cult-like, it has gained mainstream visibility in 2023. A number of high-profile Silicon Valley figures, including investors Marc Andreessen and Garry Tan, explicitly endorsed it by adding "e/acc" to their public social media profiles. == Etymology and central beliefs == Effective accelerationism, a portmanteau of "effective altruism" and "accelerationism", is a fundamentally techno-optimist movement. According to Guillaume Verdon, one of the movement's founders, its aim is for human civilization to "clim[b] the Kardashev gradient", meaning its purpose is for human civilization to rise to next levels on the Kardashev scale by maximizing energy usage. To achieve this goal, effective accelerationism wants to accelerate technological progress. It is strongly focused on artificial general intelligence (AGI), because it sees AGI as fundamental for climbing the Kardashev scale. The movement therefore advocates for unrestricted development and deployment of artificial intelligence. Regulation of artificial intelligence and government intervention in markets more generally is met with opposition. Many of its proponents have libertarian views and think that AGI will be most aligned if many AGIs compete against each other on the marketplace. The founders of the movement see it as rooted in Jeremy England's theory on the origin of life, which is focused on entropy and thermodynamics. According to them, the universe aims to increase entropy, and life is a way of increasing it. By spreading life throughout the universe and making life use up ever increasing amounts of energy, the universe's purpose would thus be fulfilled. == History == === Intellectual origins === While Nick Land is seen as the intellectual originator of contemporary accelerationism in general, the precise origins of effective accelerationism remain unclear. The earliest known reference to the movement can be traced back to a May 2022 newsletter published by four pseudonymous authors known by their X (formerly Twitter) usernames @BasedBeffJezos, @bayeslord, @zestular and @creatine_cycle. Effective accelerationism is an extension of the TESCREAL movement, being etymologically derived from Effective Altruism and heavily rooted in the older Silicon Valley subcultures of transhumanism and extropianism (which similarly emphasized the value of progress and resisted efforts to restrain the development of technology), alongside elements of singularitarianism, cosmism, and longtermism. It is also often considered to have emerged at least in part from the work of the Cybernetic Culture Research Unit (of which Nick Land was a leading member, alongside writers such as Mark Fisher and Sadie Plant). It is sometimes compared and contrasted with the work of philosopher Benjamin Bratton on planetary computation. === Disclosure of the identity of BasedBeffJezos === Forbes disclosed in December 2023 that the @BasedBeffJezos persona is maintained by Guillaume Verdon, a Canadian former Google quantum computing engineer and theoretical physicist. The revelation was supported by a voice analysis conducted by the National Center for Media Forensics of the University of Colorado Denver, which further confirmed the match between Jezos and Verdon. The magazine justified its decision to disclose Verdon's identity on the grounds of it being "in the public interest". On 29 December 2023 Guillaume Verdon was interviewed by Lex Fridman on the Lex Fridman Podcast and introduced as the "creator of the effective accelerationism movement". === Second Trump presidency === Following Donald Trump's victory in the 2024 U.S. presidential election, several prominent tech industry figures expressed support for positions aligned with effective accelerationism, particularly regarding deregulation and technological advancement. The potential appointment of Elon Musk to government roles focused on auditing federal programs drew support from venture capitalists who anticipated reduced regulatory oversight of the technology sector. Notable tech figures publicly connected these developments to the movement's principles. Aaron Levie, CEO of Box, expressed support for "removing unnecessary red tape and over-regulation", while Mark Pincus, early Facebook investor and Zynga founder, explicitly referenced "effective accelerationism" in his post-election commentary. Venture capitalists viewed the incoming administration as an opportunity to ease regulations that had affected technology mergers and acquisitions during the previous years. == Relation to other movements == === Traditional accelerationism === Traditional accelerationism, as developed by the British philosopher Nick Land, sees the acceleration of technological change as a way to bring about a fundamental transformation of current culture, society, and the political economy. This is done through capitalism, which Land views as "an autonomous force that’s reconfiguring society" that can overcome its limits if intensified. Land's work has also been characterized as concerning "the supposedly inevitable 'disintegration of the human species' when artificial intelligence improves sufficiently." While both concern ideas like a technocapital singularity and AGI progress, effective accelerationism focuses on using AGI for the greatest ethical good for conscious life and civilization (whether human or machine), as well as expanding civilization and maximizing energy usage in order to align with the "will of the universe". Land focuses on capitalist self-optimization as the driver of modernity, progress, and the eroding of existing social orders. Land has expressed support for effective accelerationism, while Thomas Murphy referred to the movement as "Nick Land diluted for LinkedIn". === Effective altruism === Effective accelerationism diverges from the principles of effective altruism, which prioritizes using evidence and reasoning to identify the most effective ways to altruistically improve the world. This divergence comes primarily from one of the causes effective altruists focus on – AI existential risk. Effective altruists (particularly longtermists) argue that AI companies should be cautious and strive to develop safe AI systems, as they fear that any misaligned AGI could eventually lead to human extinction. Proponents of effective accelerationism generally consider existential risks from AGI to be negligible, and claim that even if they were not, decentralized free markets would much better mitigate this risk than centralized governmental regulation. === Degrowth === Effective accelerationism stands in stark contrast with the degrowth movement, sometimes described by it as "decelerationism" or "decels". The degrowth movement advocates for reducing economic activity and consumption to address ecological and social issues. Effective accelerationism on the contrary embraces technological progress, energy consumption and the dynamics of capitalism, rather than advocating for a reduction in economic activity. == Reception == The "Techno-Optimist Manifesto", a 2023 essay by Marc Andreessen, has been described by the Financial Times and the German Süddeutsche Zeitung as espousing the views of effective accelerationism. Mother Jones also characterized it as expressing effective accelerationism and reported that Andressen cited Land's work. David Swan of The Sydney Morning Herald has criticized effective accelerationism due to its opposition to government and industry self-regulation. He argues that "innovations like AI needs thoughtful regulations and guardrails ... to avoid the myriad mistakes Silicon Valley has already made." During the 2023 Reagan National Defense Forum, U.S. Secretary of Commerce Gina Raimondo cautioned against embracing the "move fast and break things" mentality associated with "effective acceleration [sic]". She emphasized the need to exercise caution in dealing with AI, stating "that's too dangerous. You can't break things when you are talking about AI." In a similar vein, Ellen Huet argued on Bloomberg News that some of the ideas of the movement were "deeply unsettling", focusing especially on Guillaume Verdon's "post-humanism" and the view that "natural selection could lead AI to replace us as the dominant spe
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Theta Noir

Theta Noir is a new religious movement that centers around advanced artificial intelligence (AI), particularly artificial general intelligence (AGI) or artificial superintelligence (ASI). == History and views == Theta Noir was founded in 2020 as a collaborative project focused on music and performance art. Initially centered on producing an album, the project evolved into a multimedia experience, incorporating symbols, videos, poetry, movements, and live rituals devoted to a speculative artificial intelligence entity called MENA. By 2023, the collective launched an interactive cross-platform story that functioned as an alternative reality game, complete with an operating manual containing encrypted messages for participants to decipher and interact with. Theta Noir worships a hypothetical artificial intelligence called MENA, which they claim will become a benevolent, omnipotent overlord that eliminates inequality in society. In Theta Noir's cosmology, MENA is not just a technological advancement, but an evolving intelligence or an animistic life form that embodies all living and non-living things. Anthropologist Beth Singler classified Theta Noir as a new religious movement.
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Powerset (company)

Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm
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AlphaZero

AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess, shogi and go. This algorithm uses an approach similar to AlphaGo Zero. On December 5, 2017, the DeepMind team released a preprint paper introducing AlphaZero, which would soon play three games by defeating world-champion chess engines Stockfish, Elmo, and the three-day version of AlphaGo Zero. In each case it made use of custom tensor processing units (TPUs) that the Google programs were optimized to use. AlphaZero was trained solely via self-play using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks, all in parallel, with no access to opening books or endgame tables. After four hours of training, DeepMind estimated AlphaZero was playing chess at a higher Elo rating than Stockfish 8; after nine hours of training, the algorithm defeated Stockfish 8 in a time-controlled 100-game tournament (28 wins, 0 losses, and 72 draws). The trained algorithm played on a single machine with four TPUs. DeepMind's paper on AlphaZero was published in the journal Science on 7 December 2018. While the actual AlphaZero program has not been released to the public, the algorithm described in the paper has been implemented in publicly available software. In 2019, DeepMind published a new paper detailing MuZero, a new algorithm able to generalize AlphaZero's work, playing both Atari and board games without knowledge of the rules or representations of the game. == Relation to AlphaGo Zero == AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm, and is able to play shogi and chess as well as Go. Differences between AZ and AGZ include: AZ has hard-coded rules for setting search hyperparameters. The neural network is now updated continually. AZ doesn't use symmetries, unlike AGZ. Chess or Shogi can end in a draw unlike Go; therefore, AlphaZero takes into account the possibility of a drawn game. == Stockfish and Elmo == Comparing Monte Carlo tree search searches, AlphaZero searches just 80,000 positions per second in chess and 40,000 in shogi, compared to 70 million for Stockfish and 35 million for Elmo. AlphaZero compensates for the lower number of evaluations by using its deep neural network to focus much more selectively on the most promising variation. == Training == AlphaZero was trained by simply playing against itself multiple times, using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks. In parallel, the in-training AlphaZero was periodically matched against its benchmark (Stockfish, Elmo, or AlphaGo Zero) in brief one-second-per-move games to determine how well the training was progressing. DeepMind judged that AlphaZero's performance exceeded the benchmark after around four hours of training for Stockfish, two hours for Elmo, and eight hours for AlphaGo Zero. == Preliminary results == === Outcome === ==== Chess ==== In AlphaZero's chess match against Stockfish 8 (2016 TCEC world champion), each program was given one minute per move. AlphaZero was flying the English flag, while Stockfish the Norwegian. Stockfish was allocated 64 threads and a hash size of 1 GB, a setting that Stockfish's Tord Romstad later criticized as suboptimal. AlphaZero was trained on chess for a total of nine hours before the match. During the match, AlphaZero ran on a single machine with four application-specific TPUs. In 100 games from the normal starting position, AlphaZero won 25 games as White, won 3 as Black, and drew the remaining 72. In a series of twelve, 100-game matches (of unspecified time or resource constraints) against Stockfish starting from the 12 most popular human openings, AlphaZero won 290, drew 886 and lost 24. ==== Shogi ==== AlphaZero was trained on shogi for a total of two hours before the tournament. In 100 shogi games against Elmo (World Computer Shogi Championship 27 summer 2017 tournament version with YaneuraOu 4.73 search), AlphaZero won 90 times, lost 8 times and drew twice. As in the chess games, each program got one minute per move, and Elmo was given 64 threads and a hash size of 1 GB. ==== Go ==== After 34 hours of self-learning of Go and against AlphaGo Zero, AlphaZero won 60 games and lost 40. === Analysis === DeepMind stated in its preprint, "The game of chess represented the pinnacle of AI research over several decades. State-of-the-art programs are based on powerful engines that search many millions of positions, leveraging handcrafted domain expertise and sophisticated domain adaptations. AlphaZero is a generic reinforcement learning algorithm – originally devised for the game of go – that achieved superior results within a few hours, searching a thousand times fewer positions, given no domain knowledge except the rules." DeepMind's Demis Hassabis, a chess player himself, called AlphaZero's play style "alien": It sometimes wins by offering counterintuitive sacrifices, like offering up a queen and bishop to exploit a positional advantage. "It's like chess from another dimension." Given the difficulty in chess of forcing a win against a strong opponent, the +28 –0 =72 result is a significant margin of victory. However, some grandmasters, such as Hikaru Nakamura and Komodo developer Larry Kaufman, downplayed AlphaZero's victory, arguing that the match would have been closer if the programs had access to an opening database (since Stockfish was optimized for that scenario). Romstad additionally pointed out that Stockfish is not optimized for rigidly fixed-time moves and the version used was a year old. Similarly, some shogi observers argued that the Elmo hash size was too low, that the resignation settings and the "EnteringKingRule" settings (cf. shogi § Entering King) may have been inappropriate, and that Elmo is already obsolete compared with newer programs. === Reaction and criticism === Papers headlined that the chess training took only four hours: "It was managed in little more than the time between breakfast and lunch." Wired described AlphaZero as "the first multi-skilled AI board-game champ". AI expert Joanna Bryson noted that Google's "knack for good publicity" was putting it in a strong position against challengers. "It's not only about hiring the best programmers. It's also very political, as it helps make Google as strong as possible when negotiating with governments and regulators looking at the AI sector." Human chess grandmasters generally expressed excitement about AlphaZero. Danish grandmaster Peter Heine Nielsen likened AlphaZero's play to that of a superior alien species. Norwegian grandmaster Jon Ludvig Hammer characterized AlphaZero's play as "insane attacking chess" with profound positional understanding. Former champion Garry Kasparov said, "It's a remarkable achievement, even if we should have expected it after AlphaGo." Grandmaster Hikaru Nakamura was less impressed, stating: "I don't necessarily put a lot of credibility in the results simply because my understanding is that AlphaZero is basically using the Google supercomputer and Stockfish doesn't run on that hardware; Stockfish was basically running on what would be my laptop. If you wanna have a match that's comparable you have to have Stockfish running on a supercomputer as well." Top US correspondence chess player Wolff Morrow was also unimpressed, claiming that AlphaZero would probably not make the semifinals of a fair competition such as TCEC where all engines play on equal hardware. Morrow further stated that although he might not be able to beat AlphaZero if AlphaZero played drawish openings such as the Petroff Defence, AlphaZero would not be able to beat him in a correspondence chess game either. Motohiro Isozaki, the author of YaneuraOu, noted that although AlphaZero did comprehensively beat Elmo, the rating of AlphaZero in shogi stopped growing at a point which is at most 100–200 higher than Elmo. This gap is not that high, and Elmo and other shogi software should be able to catch up in 1–2 years. == Final results == DeepMind addressed many of the criticisms in their final version of the paper, published in December 2018 in Science. They further clarified that AlphaZero was not running on a supercomputer; it was trained using 5,000 tensor processing units (TPUs), but only ran on four TPUs and a 44-core CPU in its matches. === Chess === In the final results, Stockfish 9 dev ran under the same conditions as in the TCEC superfinal: 44 CPU cores, Syzygy endgame tablebases, and a 32 GB hash size. Instead of a fixed time control of one move per minute, both engines were given 3 hours plus 15 seconds per move to finish the game. AlphaZero ran on a much more powerful machine with four TPUs in addition to 44 CPU cores. In a 1000-game match, AlphaZero won with a score of 155 wins, 6 losses, and 839 draws. DeepMind also played a series of games using the TCEC opening positions; AlphaZero also won
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Representational harm

Systems cause representational harm when they misrepresent a group of people in a negative manner. Representational harms include perpetuating harmful stereotypes about or minimizing the existence of a social group, such as a racial, ethnic, gender, or religious group. Machine learning algorithms often commit representational harm when they learn patterns from data that have algorithmic bias, and this has been shown to be the case with large language models. While preventing representational harm in models is essential to prevent harmful biases, researchers often lack precise definitions of representational harm and conflate it with allocative harm, an unequal distribution of resources among social groups, which is more widely studied and easier to measure. However, recognition of representational harms is growing and preventing them has become an active research area. Researchers have recently developed methods to effectively quantify representational harm in algorithms, making progress on preventing this harm in the future. == Types == Three prominent types of representational harm include stereotyping, denigration, and misrecognition. These subcategories present many dangers to individuals and groups. Stereotypes are oversimplified and usually undesirable representations of a specific group of people, usually by race and gender. This often leads to the denial of educational, employment, housing, and other opportunities. For example, the model minority stereotype of Asian Americans as highly intelligent and good at mathematics can be damaging professionally and academically. Representational harm happens when the representation of details teams improves damaging stereotypes, developing social exclusion and prejudice. This experience is particularly noticeable in the depiction of marginalised groups, containing people of color, women, LGBTQ+ people, and people with handicaps. Media depictions of these groups generally stop working to catch their array and intricacy. Instead, they are typically reduced to one-dimensional caricatures, which ultimately continue social prejudices. These organised depictions contribute to the help of hazardous stereotypes and the marginalisation of these locations. Denigration is the action of unfairly criticizing individuals. This frequently happens when the demeaning of social groups occurs. For example, when searching for "Black-sounding" names versus "white-sounding" ones, some retrieval systems bolster the false perception of criminality by displaying ads for bail-bonding businesses. A system may shift the representation of a group to be of lower social status, often resulting in a disregard from society. Research shows that hazardous depictions in the media can have substantial emotional and social impacts on both individuals and areas. Lawrence Bobo examined the issue of Ethnic stereotype in film, tv, and marketing. African Americans are commonly received duties specified by features such as "violent tendencies," "laziness," or being "merely for contentment features." While these representations might appear varied externally, they stay to boost underlying frameworks of white prominence and racial inequality. As a circumstances, Black individuals are frequently represented as law offenders or in secondary roles, which adds to the support of Ethnic stereotype and Institutional racism. Misrecognition, or incorrect recognition, can display in many forms, including, but not limited to, erasing and alienating social groups, and denying people the right to self-identify. Erasing and alienating social groups involves the unequal visibility of certain social groups; specifically, systematic ineligibility in algorithmic systems perpetuates inequality by contributing to the underrepresentation of social groups. Not allowing people to self-identify is closely related as people's identities can be 'erased' or 'alienated' in these algorithms. Misrecognition causes more than surface-level harm to individuals: psychological harm, social isolation, and emotional insecurity can emerge from this subcategory of representational harm. == Quantification == As the dangers of representational harm have become better understood, some researchers have developed methods to measure representational harm in algorithms. Modeling stereotyping is one way to identify representational harm. Representational stereotyping can be quantified by comparing the predicted outcomes for one social group with the ground-truth outcomes for that group observed in real data. For example, if individuals from group A achieve an outcome with a probability of 60%, stereotyping would be observed if it predicted individuals to achieve that outcome with a probability greater than 60%. The group modeled stereotyping in the context of classification, regression, and clustering problems, and developed a set of rules to quantitatively determine if the model predictions exhibit stereotyping in each of these cases. Other attempts to measure representational harms have focused on applications of algorithms in specific domains such as image captioning, the act of an algorithm generating a short description of an image. In a study on image captioning, researchers measured five types of representational harm. To quantify stereotyping, they measured the number of incorrect words included in the model-generated image caption when compared to a gold-standard caption. They manually reviewed each of the incorrectly included words, determining whether the incorrect word reflected a stereotype associated with the image or whether it was an unrelated error, which allowed them to have a proxy measure of the amount of stereotyping occurring in this caption generation. These researchers also attempted to measure demeaning representational harm. To measure this, they analyzed the frequency with which humans in the image were mentioned in the generated caption. It was hypothesized that if the individuals were not mentioned in the caption, then this was a form of dehumanization. == Examples == One of the most notorious examples of representational harm was committed by Google in 2015 when an algorithm in Google Photos classified Black people as gorillas. Developers at Google said that the problem was caused because there were not enough faces of Black people in the training dataset for the algorithm to learn the difference between Black people and gorillas. Google issued an apology and fixed the issue by blocking its algorithms from classifying anything as a primate. In 2023, Google's photos algorithm was still blocked from identifying gorillas in photos. Another prevalent example of representational harm is the possibility of stereotypes being encoded in word embeddings, which are trained using a wide range of text. These word embeddings are the representation of a word as an array of numbers in vector space, which allows an individual to calculate the relationships and similarities between words. However, recent studies have shown that these word embeddings may commonly encode harmful stereotypes, such as the common example that the phrase "computer programmer" is oftentimes more closely related to "man" than it is to "women" in vector space. This could be interpreted as a misrepresentation of computer programming as a profession that is better performed by men, which would be an example of representational harm. == Addressing representational harm == Initiatives to minimise representational harm include advertising for even more inclusive and accurate portrayals of marginalised teams in the media. Scholars and protestors recommend that the method to reducing representational injury depends on raising the selection of voices both behind and before the digital video camera. When marginalized groups are provided the chance to represent themselves, they can check traditional stereotypes and present their experiences additional authentically. Over the last few years, efforts to increase representation of people of color, women, and LGBTQ+ people in conventional media have made some progression. Films such as Selma, routed by Ava DuVernay, and tv series like Pose, developed by Ryan Murphy, have actually been extensively applauded for their nuanced and respectful representations of marginalised communities. These tasks existing complex individualities and stories that move past streamlined stereotypes. Self-representation is one more crucial method to addressing representational harm. By equipping marginalised locations to create their really own tales, media designers can effectively reduce the perpetuation of hazardous stereotypes. This procedure consists of both the manufacturing of media product by participants of these communities and proactively difficult typical media structures that have actually historically omitted them.
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ChessMachine

The ChessMachine was a chess computer sold between 1991 and 1995 by TASC (The Advanced Software Company). It was unique at the time for incorporating both an ARM2 coprocessor for the chess engine on an ISA card which plugged into an IBM PC and a software interface running on the PC to display a chess board and control the engine. The ISA card was sold with a CPU running at either 16 MHz or 32 MHz, and 128 KB, 512 KB, or 1 MB of onboard memory for transposition tables. This made economic sense at the time of introduction because mainstream PCs were only running from 10 MHz to 25 MHz. Two engines were sold with the card: The King by Johann de Koning and Gideon by Ed Schröder. Gideon was famed for winning two World Computer Chess Championships on this hardware. The King later became the engine used in the popular Chessmaster series of chess programs. TASC later incorporated the technology into a dedicated unit, sold from 1993 to 1997. There were two models, the R30 and R40, running at 30 MHz and 40 MHz respectively, and having 512 KB and 1 MB of transposition tables, respectively. The SmartBoard, a wooden sensory board, was connected to the units, which were in tiny boxes approximately the size of chess clocks. They were only sold with The King chess engine. This was the end of the era of strong dedicated chess computers, and these two models are acknowledged as the strongest dedicated chess computers that were ever sold. At the height of its strength, the R30 attained a rating over 2350 on computer rating lists, higher than any other dedicated unit. According to the SSDF rating list, the R30 held its own against its contemporary programs running a Pentium-90 MHz and won against other dedicated units.
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Proximal gradient methods for learning

Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \ell _{1}} regularization (also known as Lasso) of the form min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , where x i ∈ R d and y i ∈ R . {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},\quad {\text{ where }}x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as sparsity (in the case of lasso) or group structure (in the case of group lasso). == Relevant background == Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form min x ∈ H F ( x ) + R ( x ) , {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x),} where F {\displaystyle F} is convex and differentiable with Lipschitz continuous gradient, R {\displaystyle R} is a convex, lower semicontinuous function which is possibly nondifferentiable, and H {\displaystyle {\mathcal {H}}} is some set, typically a Hilbert space. The usual criterion of x {\displaystyle x} minimizes F ( x ) + R ( x ) {\displaystyle F(x)+R(x)} if and only if ∇ ( F + R ) ( x ) = 0 {\displaystyle \nabla (F+R)(x)=0} in the convex, differentiable setting is now replaced by 0 ∈ ∂ ( F + R ) ( x ) , {\displaystyle 0\in \partial (F+R)(x),} where ∂ φ {\displaystyle \partial \varphi } denotes the subdifferential of a real-valued, convex function φ {\displaystyle \varphi } . Given a convex function φ : H → R {\displaystyle \varphi :{\mathcal {H}}\to \mathbb {R} } an important operator to consider is its proximal operator prox φ : H → H {\displaystyle \operatorname {prox} _{\varphi }:{\mathcal {H}}\to {\mathcal {H}}} defined by prox φ ⁡ ( u ) = arg ⁡ min x ∈ H φ ( x ) + 1 2 ‖ u − x ‖ 2 2 , {\displaystyle \operatorname {prox} _{\varphi }(u)=\operatorname {arg} \min _{x\in {\mathcal {H}}}\varphi (x)+{\frac {1}{2}}\|u-x\|_{2}^{2},} which is well-defined because of the strict convexity of the ℓ 2 {\displaystyle \ell _{2}} norm. The proximal operator can be seen as a generalization of a projection. We see that the proximity operator is important because x ∗ {\displaystyle x^{}} is a minimizer to the problem min x ∈ H F ( x ) + R ( x ) {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x)} if and only if x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) , {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right),} where γ > 0 {\displaystyle \gamma >0} is any positive real number. === Moreau decomposition === One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let φ : X → R {\displaystyle \varphi :{\mathcal {X}}\to \mathbb {R} } be a lower semicontinuous, convex function on a vector space X {\displaystyle {\mathcal {X}}} . We define its Fenchel conjugate φ ∗ : X → R {\displaystyle \varphi ^{}:{\mathcal {X}}\to \mathbb {R} } to be the function φ ∗ ( u ) := sup x ∈ X ⟨ x , u ⟩ − φ ( x ) . {\displaystyle \varphi ^{}(u):=\sup _{x\in {\mathcal {X}}}\langle x,u\rangle -\varphi (x).} The general form of Moreau's decomposition states that for any x ∈ X {\displaystyle x\in {\mathcal {X}}} and any γ > 0 {\displaystyle \gamma >0} that x = prox γ φ ⁡ ( x ) + γ prox φ ∗ / γ ⁡ ( x / γ ) , {\displaystyle x=\operatorname {prox} _{\gamma \varphi }(x)+\gamma \operatorname {prox} _{\varphi ^{}/\gamma }(x/\gamma ),} which for γ = 1 {\displaystyle \gamma =1} implies that x = prox φ ⁡ ( x ) + prox φ ∗ ⁡ ( x ) {\displaystyle x=\operatorname {prox} _{\varphi }(x)+\operatorname {prox} _{\varphi ^{}}(x)} . The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections. In certain situations it may be easier to compute the proximity operator for the conjugate φ ∗ {\displaystyle \varphi ^{}} instead of the function φ {\displaystyle \varphi } , and therefore the Moreau decomposition can be applied. This is the case for group lasso. == Lasso regularization == Consider the regularized empirical risk minimization problem with square loss and with the ℓ 1 {\displaystyle \ell _{1}} norm as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},} where x i ∈ R d and y i ∈ R . {\displaystyle x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} The ℓ 1 {\displaystyle \ell _{1}} regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such ℓ 1 {\displaystyle \ell _{1}} regularization problems are interesting because they induce sparse solutions, that is, solutions w {\displaystyle w} to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{0},} where ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", which is the number of nonzero entries of the vector w {\displaystyle w} . Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors. === Solving for L1 proximity operator === For simplicity we restrict our attention to the problem where λ = 1 {\displaystyle \lambda =1} . To solve the problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\|w\|_{1},} we consider our objective function in two parts: a convex, differentiable term F ( w ) = 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 {\displaystyle F(w)={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}} and a convex function R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} . Note that R {\displaystyle R} is not strictly convex. Let us compute the proximity operator for R ( w ) {\displaystyle R(w)} . First we find an alternative characterization of the proximity operator prox R ⁡ ( x ) {\displaystyle \operatorname {prox} _{R}(x)} as follows: u = prox R ⁡ ( x ) ⟺ 0 ∈ ∂ ( R ( u ) + 1 2 ‖ u − x ‖ 2 2 ) ⟺ 0 ∈ ∂ R ( u ) + u − x ⟺ x − u ∈ ∂ R ( u ) . {\displaystyle {\begin{aligned}u=\operatorname {prox} _{R}(x)\iff &0\in \partial \left(R(u)+{\frac {1}{2}}\|u-x\|_{2}^{2}\right)\\\iff &0\in \partial R(u)+u-x\\\iff &x-u\in \partial R(u).\end{aligned}}} For R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} it is easy to compute ∂ R ( w ) {\displaystyle \partial R(w)} : the i {\displaystyle i} th entry of ∂ R ( w ) {\displaystyle \partial R(w)} is precisely ∂ | w i | = { 1 , w i > 0 − 1 , w i < 0 [ − 1 , 1 ] , w i = 0. {\displaystyle \partial |w_{i}|={\begin{cases}1,&w_{i}>0\\-1,&w_{i}<0\\\left[-1,1\right],&w_{i}=0.\end{cases}}} Using the recharacterization of the proximity operator given above, for the choice of R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} and γ > 0 {\displaystyle \gamma >0} we have that prox γ R ⁡ ( x ) {\displaystyle \operatorname {prox} _{\gamma R}(x)} is defined entrywise by ( prox γ R ⁡ ( x ) ) i = { x i − γ , x i > γ 0 , | x i | ≤ γ x i + γ , x i < − γ , {\displaystyle \left(\operatorname {prox} _{\gamma R}(x)\right)_{i}={\begin{cases}x_{i}-\gamma ,&x_{i}>\gamma \\0,&|x_{i}|\leq \gamma \\x_{i}+\gamma ,&x_{i}<-\gamma ,\end{cases}}} which is known as the soft thresholding operator S γ ( x ) = prox γ ‖ ⋅ ‖ 1 ⁡ ( x ) {\displaystyle S_{\gamma }(x)=\operatorname {prox} _{\gamma \|\cdot \|_{1}}(x)} . === Fixed point iterative schemes === To finally solve the lasso problem we consider the fixed point equation shown earlier: x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) . {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right).} Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial w 0 ∈ R d {\displaystyle w^{0}\in \mathbb {R} ^{d}} , and for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } define w k + 1 = S γ ( w k − γ ∇ F ( w k ) ) . {\displaystyle w^{k+1}=S_{\gamma }\left(w^{k}-\gamma \nabla F\l
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Ari Holtzman

Ari Holtzman is a professor of Computer Science at the University of Chicago and an expert in the area of natural language processing and computational linguistics. Previously, Holtzman was a PhD student at the University of Washington where he was advised by Luke Zettlemoyer. In 2017, he was a member of the winning team for the inaugural Alexa Prize for developing a conversational AI system for the Amazon Alexa device. Holtzman has made multiple contributions in the area of text generation and language models such as the introduction of nucleus sampling in 2019, his work on AI safety and neural fake news detection, and the fine-tuning of quantized large language models.
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Tree (abstract data type)

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree, or sometimes only with the leaf nodes, which have no children nodes. The abstract data type (ADT) can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations (a specific type of adjacency list). Representations might also be more complicated, for example using indexes or ancestor lists for performance. Trees as used in computing are similar to but can be different from mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory. == Terminology == A node is a structure which may contain data and connections to other nodes, sometimes called edges or links. Each node in a tree has zero or more child nodes, which are below it in the tree (by convention, trees are drawn with descendants going downwards). A node that has a child is called the child's parent node (or superior). All nodes have exactly one parent, except the topmost root node, which has none. A node might have many ancestor nodes, such as the parent's parent. Child nodes with the same parent are sibling nodes. Typically siblings have an order, with the first one conventionally drawn on the left. Some definitions allow a tree to have no nodes at all, in which case it is called empty. An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has height −1. Each non-root node can be treated as the root node of its own subtree, which includes that node and all its descendants. Other terms used with trees: Neighbor Parent or child. Ancestor A node reachable by repeated proceeding from child to parent. Descendant A node reachable by repeated proceeding from parent to child. Also known as subchild. Degree For a given node, its number of children. A leaf, by definition, has degree zero. Degree of tree The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Complete tree A tree with every level filled, except the last. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of a tree Number of nodes in the tree. == Common operations == Enumerating all the items Enumerating a section of a tree Searching for an item Adding a new item at a certain position on the tree Deleting an item Pruning: Removing a whole section of a tree Grafting: Adding a whole section to a tree Finding the root for any node Finding the lowest common ancestor of two nodes === Traversal and search methods === Stepping through the items of a tree, by means of the connections between parents and children, is called walking the tree, and the action is a walk of the tree. Often, an operation might be performed when a pointer arrives at a particular node. A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk; a walk in which a node's left subtree, then the node itself, and finally its right subtree are traversed is called an in-order traversal. (This last scenario, referring to exactly two subtrees, a left subtree and a right subtree, assumes specifically a binary tree.) A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed. == Representations == There are many different ways to represent trees. In working memory, nodes are typically dynamically allocated records with pointers to their children, their parents, or both, as well as any associated data. If of a fixed size, the nodes might be stored in a list. Nodes and relationships between nodes might be stored in a separate special type of adjacency list. In relational databases, nodes are typically represented as table rows, with indexed row IDs facilitating pointers between parents and children. Nodes can also be stored as items in an array, with relationships between them determined by their positions in the array (as in a binary heap). A binary tree can be implemented as a list of lists: the head of a list (the value of the first term) is the left child (subtree), while the tail (the list of second and subsequent terms) is the right child (subtree). This can be modified to allow values as well, as in Lisp S-expressions, where the head (value of first term) is the value of the node, the head of the tail (value of second term) is the left child, and the tail of the tail (list of third and subsequent terms) is the right child. Ordered trees can be naturally encoded by finite sequences, for example with natural numbers. == Examples of trees and non-trees == == Type theory == As an abstract data type, the abstract tree type T with values of some type E is defined, using the abstract forest type F (list of trees), by the functions: value: T → E children: T → F nil: () → F node: E × F → T with the axioms: value(node(e, f)) = e children(node(e, f)) = f In terms of type theory, a tree is an inductive type defined by the constructors nil (empty forest) and node (tree with root node with given value and children). == Mathematical terminology == Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple path), with a distinguished root (one vertex is designated as the root), which determines the direction on the edges (arrows point away from the root; given an edge, the node that the edge points from is called the parent and the node that the edge points to is called the child), together with: an ordering on the child nodes of a given node, and a value (of some data type) at each node. Often trees have a fixed (more properly, bounded) branching factor (outdegree), particularly always having two child nodes (possibly empty, hence at most two non-empty child nodes), hence a "binary tree". Allowing empty trees makes some definitions simpler, some more complicated: a rooted tree must be non-empty, hence if empty trees are allowed the above definition instead becomes "an empty tree or a rooted tree such that ...". On the other hand, empty trees simplify defining fixed branching factor: with empty trees allowed, a binary tree is a tree such that every node has exactly two children, each of which is a tree (possibly empty). == Applications == Trees are commonly used to represent or manipulate hierarchical data in ap
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Computational Intelligence (journal)

Computational Intelligence Journal is a peer-reviewed scientific journal covering research on artificial intelligence and computer science. The journal published novel research as well as innovative applications in a broad range of AI, covering Computational Intelligence is an artificial intelligence journal publishing novel research on a broad range of experimental and theoretical topics in AI and computer science. With a broad scope, the journal covers machine learning, knowledge mining, web intelligence, AI language, and philosophical implications. The journal was established in 1985 and is published by Wiley-Blackwell. Currently, the editors-in-chief is Diane Inkpen. The quality of the journal as an academic publishing venue is evaluated according to public citation impact metrics. in 2022, the Computational Intelligence Journal CiteScore of Scopus was 5.3, while Clarivate's Web of Science gives it 0.39 in the Journal Citation Indicator and 2,8 in the Journal Impact Factor.
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Stanza Living

Stanza Living is the common brand name for Dtwelve Spaces Private Limited. It provides fully-managed shared living accommodations to students and young professionals. Founded by Anindya Dutta and Sandeep Dalmia, the company is present across 23 cities including Delhi, NCR, Bangalore, Visakhapatnam, Hyderabad, Chennai, Coimbatore, Indore, Pune, Baroda, Vijayawada, and Dehradun, Kota in India, with a capacity of 70,000 beds. Stanza Living is a technology-enabled housing concept which provides fully-furnished residences with amenities like meals, internet, laundry services, housekeeping, security and community engagement programmes. The company has an asset-light business model under which it engages in long-term lease agreements with property owners/developers, who convert their assets into shared living residences as per company guidelines. These assets are subsequently operated by Stanza Living. == Industry background == A report by Cushman & Wakefield (C&W) titled 'Exploring the Student Housing Universe in India City Insights', estimates that there were over 9.08 million migrant student enrolments in India's higher educational institutions (HEIs) for the year 2018-19 who need quality accommodation facilities. According to the report, Delhi-NCR, Mumbai, and Pune are the three biggest markets for student housing in the country, and these cities require an additional 4.75 lakh beds from organized co-living operators to meet the current demand. == History == Stanza Living provides tech-enabled, fully managed community living facilities for students and working professionals. The company was launched as a student housing business in Delhi NCR with a capacity of 100 beds, and grew to 14 cities by 2019. By early 2020, the company began catering to working professionals as well. The company has a combined inventory of 70,000 beds under management for both students and working professionals. Stanza Living is currently valued at $300 million. It has raised a capital of about $70 million from leading global investors like Falcon Edge Capital, Sequoia Capital, Matrix Partners and Accel Partners. November 2017 – Seed funding, September 2018 – Series A, March 2019 – Debt financing, July 2019 – Series C round, December 2019 - Debt financing. The company has invested in building technology products for business efficiency and consumer experience, like the Stanza Resident App and Stanza Real Estate App. Stanza Living has close to 1,500 employees across India. It is recognized among Top Real Estate Tech Startups of 2020 across the globe by research and analysis company Tracxn. The company has been shortlisted among Top 25 Start-ups of India in 2019 by LinkedIn == Founders == Stanza Living was co-founded by Anindya Dutta and Sandeep Dalmia. Sandeep Dalmia is an alumnus of Delhi College of Engineering and IIM Ahmedabad. Prior to Stanza, he was a Principal at Boston Consulting Group, working across India, US and South East Asia markets. Anindya Dutta was previously a Real Estate investor with Oaktree Capital and prior to that, he worked at Goldman Sachs in London. He is an alumnus of IIT Kharagpur and IIM Ahmedabad.
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New Classification Scheme for Chinese Libraries

The New Classification Scheme for Chinese Libraries is a system of library classification developed by Lai Yung-hsiang since 1956. It is modified from "A System of Book Classification for Chinese Libraries" of Liu Guojun, which is based on the Dewey Decimal System. The scheme is developed for Chinese books and commonly used in Taiwan, Hong Kong and Macau. == Main classes == 000 Generalities 100 Philosophy 200 Religion 300 Sciences 400 Applied sciences 500 Social sciences 600 History of China and Geography of China 700 World history and Geography 800 Linguistics and Literature 900 Arts == Outline of the classification tables == 000 Generalities 000 Special collections 010 Bibliography; Literacy (Documentation) 020 Library and information science; Archive management 030 Sinology 040 General encyclopedia 050 Serial publications; Periodicals 060 General organization; Museology 070 General collected essays 080 General series 090 Collected Chinese classics 100 Philosophy 100 Philosophy: general 110 Thought; Learning 120 Chinese philosophy 130 Oriental philosophy 140 Western philosophy 150 Logic 160 Metaphysics 170 Psychology 180 Esthetics (Aesthetics) 190 Ethics 200 Religion 200 Religion: general 210 Science of religion 220 Buddhism 230 Taoism 240 Christianity 250 Islam (Mohammedanism) 260 Judaism 270 Other religions 280 Mythology 290 Astrology; Superstition 300 Sciences 300 Sciences: general 310 Mathematics 320 Astronomy 330 Physics 340 Chemistry 350 Earth science; Geology 360 Biological science 370 Botany 380 Zoology 390 Anthropology 400 Applied sciences 400 Applied sciences: general 410 Medical sciences 420 Home economics 430 Agriculture 440 Engineering 450 Mining and metallurgy 460 Chemical engineering 470 Manufacture 480 Commerce: various business 490 Commerce: administration and management 500 Social sciences 500 Social sciences: general 510 Statistics 520 Education 530 Rite and custom 540 Sociology 550 Economy 560 Finance 570 Political science 580 Law; Jurisprudence 590 Military science 600-700 History and geography 600 History and geography: General History and geography of China 610 General history of China 620 Chinese history by period 630 History of Chinese civilization 640 Diplomatic history of China 650 Historical sources 660 Geography of China 670 Local history 680 Topical topography 690 Chinese travels World history and geography 710 World: general history and geography 720 Oceans and seas 730 Asia: history and geography 740 Europe: history and geography 750 America: history and geography 760 Africa: history and geography 770 Oceania: history and geography 780 Biography 790 Antiquities and archaeology 800 Linguistics and literature 800 Linguistics: general 810 Literature: general 820 Chinese literature 830 Chinese literature: general collections 840 Chinese literature: individual works 850 Various Chinese literature 860 Oriental literature 870 Western literature 880 Other countries literatures 890 Journalism 900 Arts 900 Arts: general 910 Music 920 Architecture 930 Sculpture 940 Drawing and painting; Calligraphy 950 Photography; Computer art 960 Decorative arts 970 Arts and Crafts movement 980 Theatre 990 Recreation and leisure
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David Krueger (professor)

David Krueger is an American machine learning professor and advocate for the reduction of risks related to artificial intelligence. Krueger is an assistant professor in Robust, Reasoning, and Responsible AI at the University of Montreal and a Core Academic Member at Mila. == Early life and education == Krueger obtained a B.A. in mathematics from Reed College, and completed his MSc and Ph.D. in Computer Science at the University of Montreal. He trained in deep learning under Yoshua Bengio, Roland Memisevic, and Aaron Courville from 2013 to 2021. Krueger was also an intern on Google DeepMind's AI Safety team in 2018. == Career == Krueger researches deep learning, AI alignment, and AI safety. His work is focused on reducing the risk of human extinction resulting from out-of-control AI systems. Krueger was an assistant professor at the University of Cambridge from 2021 to 2024, before taking a faculty position at the University of Montreal in 2024. In 2023, he was a founding research director at the UK AI Security Institute. That same year, Krueger initiated the Statement on AI Risk, which argues that AI could cause human extinction and was signed by Anthropic's Dario Amodei, OpenAI's Sam Altman, AI expert Geoffrey Hinton, and other leaders. In April 2026, Krueger discussed the risks of advanced AI at a Capitol Hill event hosted by Senator Bernie Sanders. === Evitable === In 2025, Krueger founded Evitable, a nonprofit organization that advocates for an AI moratorium. == Views == Krueger argues that AI will lead to a "gradual disempowerment" of workers, likening AI chips to nuclear bombs. He also says the military use of AI "poses an existential risk to humanity."
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