Artificial intelligence in Wikimedia projects

Some editors of Wikimedia projects use artificial intelligence (AI) and machine learning programs to edit existing articles or create new ones. Some applications of artificial intelligence, like using large language models (LLMs) to create new articles from scratch, have been more controversial than others for the Wikipedia community. In August 2025, English Wikipedia adopted a policy that allowed editors to nominate suspected LLM-generated articles for speedy deletion. This was followed by a March 2026 decision to prohibit the use of LLMs to generate or rewrite article content, with exceptions for copyediting one's own writing and machine translation from another language's Wikipedia. Wikipedia has also been a significant source of training data for some of the earliest artificial intelligence projects. This has received mixed reactions including concern about companies not citing Wikipedia when relying on it to answer a question as well as Wikipedia's increased costs from data scraping. == AI usage == === Earliest use of automated tools, machine learning and AI === Since 2002, bots have been allowed to run on Wikipedia but must be approved and supervised by a human. A bot created in 2002, rambot, transformed census data into short new articles about towns in the United States; the vast majority of town, city, and county articles were started by it. Fighting vandalism has been a major focus of machine learning and AI bots and tools. The 2007 ClueBot relied on simple heuristics to identify likely vandalism, while its 2010 successor, ClueBot NG, uses machine learning through an artificial neural network. Machine translation software has also been used by Wikimedia contributors for a number of years. Aaron Halfaker's Objective Revision Evaluation Service (ORES) project was launched in late 2015 as an artificial intelligence service for grading the quality of Wikipedia edits. === Generative AI and LLMs === In 2022, the public release of ChatGPT inspired more experimentation with AI and writing Wikipedia articles. A debate was sparked about whether and to what extent such large language models are suitable for such purposes in light of their tendency to generate plausible-sounding misinformation, including fake references; to generate prose that is not encyclopedic in tone; and to reproduce biases. An early experiment on December 6, 2022 by a Wikipedia contributor named Pharos occurred when he created the article "Artwork title" using ChatGPT for the initial draft. Another editor who experimented with this early version of ChatGPT said that ChatGPT's overview of "Weaponized incompetence" was decent, but that the citations were fabricated. Since 2023, work has been done to draft an English Wikipedia policy regarding ChatGPT and similar LLMs, at times recommending that users who are unfamiliar with LLMs should avoid using them due to the aforementioned risks, as well as noting the potential for libel or copyright infringement. In early 2023, the Wiki Education Foundation reported that some experienced editors found AI to be useful in starting drafts or creating new articles. It said that ChatGPT "knows" what Wikipedia articles look like and can easily generate one that is written in the style of Wikipedia, but warned that ChatGPT had a tendency to use promotional language, among other issues. In 2023, a ban on AI was deemed "too harsh" by the community given the productivity benefits it offered editors. In 2023, members of the English Wikipedia community created a WikiProject named AI Cleanup to assist in the removal of poor quality AI content from Wikipedia. Miguel García, a former Wikimedia member from Spain, said in 2024 that when ChatGPT was originally launched, the number of AI-generated articles on the site peaked. He added that the rate of AI articles has now stabilized due to the community's efforts to combat it. He said that majority of the articles that have no sources are deleted instantly or are nominated for deletion. In October 2024, a study by Princeton University found that about 5% of 3,000 newly created articles (created in August 2024) on English Wikipedia were created using AI. The study said that some of the AI articles were on innocuous topics and that AI had likely only been used to assist in writing. For some other articles, AI had been used to promote businesses or political interests. In October 2024, Ilyas Lebleu, founder of WikiProject AI Cleanup, said that they and their fellow editors noticed a pattern of unnatural writing that could be connected to ChatGPT. They added that AI is able to mass-produce content that sounds real while being completely fake, leading to the creation of hoax articles on Wikipedia that they were tasked to delete. In June 2025, the Wikimedia Foundation started testing a "Simple Article Summaries" feature which would provide AI-generated summaries of Wikipedia articles, similar to Google Search's AI Overviews. The decision was met with immediate and harsh criticism from some Wikipedia editors, who called the feature a "ghastly idea" and a "PR hype stunt." They criticized a perceived loss of trust in the site due to AI's tendency to hallucinate and questioned the necessity of the feature. The criticism led the Wikimedia Foundation to halt the rollout of Simple Article Summaries that same month while still expressing interest in integrating generative AI more into Wikipedia. The project hints at tensions within the community and with the Foundation over when to use AI.In August 2025, the English Wikipedia community created a policy that allowed users to nominate suspected AI-generated articles for speedy deletion. Editors might recognize AI-generated articles because they use citations that are not related to the subject of the article or fabricated citations or the wording has particular quirks. If an article uses language that reads like an LLM response to a user, such as "Here is your Wikipedia article on" or "Up to my last training update", the article is typically tagged for speedy deletion. Other signs of AI use include excessive use of em dashes, overuse of the word "moreover", promotional material in articles that describes something as "breathtaking" and formatting issues like using curly quotation marks instead of straight versions. During the discussion on implementing the speedy deletion policy, one user, who is an article reviewer, said that he is "flooded non-stop with horrendous drafts" created using AI. Other users said that AI articles have a large amount of "lies and fake references" and that it takes a significant amount of time to fix the issues. English Wikipedia created a guide on how to spot signs of AI-generated writing in August 2025, titled "Signs of AI writing". In January 2026, the Wiki Education Foundation continued to caution against copying and pasting outputs from generative AI into Wikipedia and to avoid it for creating new articles explaining that the text often failed verification with the sources provided. The foundation created a training module that encourages editors to use AI for identifying gaps in articles, finding access to sources and finding relevant sources. In March 2026, the English Wikipedia community prohibited the use of AI to add content to articles, with exceptions for copy editing and machine translation from another language's Wikipedia. The English Wikipedia community holds the position that LLMs often violate core content policies. == Using Wikipedia for artificial intelligence == A 2017 paper described Wikipedia as the mother lode for human-generated text available for machine learning. In the development of the Google's Perspective API that identifies toxic comments in online forums, a dataset containing hundreds of thousands of Wikipedia talk page comments with human-labelled toxicity levels was used. As of 2023, subsets of the Wikipedia corpus were considered one of the largest well-curated data sets available for AI training, used to train every LLM to-date according to Stephen Harrison. This use of Wikipedia was divisive as of 2023. The Wikimedia Foundation and many of its projects supporters worry that attribution to Wikipedia articles is missing in many large-language models like ChatGPT (as well as AI like Siri and Alexa). While Wikipedia's licensing policy lets anyone use its texts, including in modified forms, it does have the condition that credit is given, implying that using its contents in answers by AI models without clarifying the sourcing may violate its terms of use. The Foundation expressed concern that without attribution, people will not visit the site as much or be as motivated to donate to support the project if they do not know when they are benefiting from it. They also noticed an 8% decrease in visitors to Wikipedia in 2025 which they attributed both to the increased popularity of generative AI and social media. In 2025, the Wikimedia Foundation has cited absorbing increased costs associated with scra

Super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j

Global Artificial Intelligence Summit & Awards

The Global Artificial Intelligence Summit & Awards (GAISA) is an international conference on Artificial Intelligence organized annually by AICRA. Since its inception in 2019, GAISA has been held at various locations each year. The 5th Edition of GAISA will be Scheduled on April 11-12, 2024, at Bharat Mandapam. GAISA 2025 features a distinguished lineup of speakers, including leading experts, researchers, and executives from top global tech companies. These thought leaders are at the forefront of AI innovation, with deep expertise in areas such as machine learning, robotics, and ethical AI. Their diverse backgrounds span academia, industry, and entrepreneurship, offering unique insights into how AI is reshaping sectors like healthcare, finance, transportation, and more. Attendees can expect thought-provoking discussions on the future of AI, its societal impact, and the transformative potential of emerging technologies in solving complex global challenges Few Speakers are listed below:- Shri Nitin Gadkari, Rao Inderjit Singh, Piyush Goyal, Admiral R Hari Kumar PVSM, AVSM, ADC, Samir V Kamat, Narayan Tatu Rane, Prof. K. Vijay Raghavan and many others. == History == The conference was launched first in 2019 as Vigyan Bhawan New Delhi by AICRA with an objective of discussion and exploring artificial intelligence in engrossed sectors.

AI Snake Oil

AI Snake Oil: What Artificial Intelligence Can Do, What It Can't, and How to Tell the Difference is a 2024 non-fiction book written by scholars Arvind Narayanan and Sayash Kapoor. It is a critique of the tech industry's overly inflated promises and capabilities of artificial intelligence (AI) as well as a debunking of the flawed science fueling AI hype while attempting to outline both the potential positives and negatives that come with different modes of the technology. == Contents == === Publication === The book was published in September 2024 by the Princeton University Press. AI Snake Oil consists of 360 pages and features eight chapters, and sections for acknowledgements, references, and an index. An updated edition with a new preface and epilogue by the authors was published in September 2025. The authors use the term "AI snake oil" derived from the U.S. idiom for a fraudulent remedy, to describe overhyped AI systems. === Chapter one: Introduction === Narayanan and Kapoor argue that many individuals do not yet have the literacy to detect functioning aspects of AI compared to potential snake oil, which they identify as "AI that does not and cannot work as advertised". Some of the major examples utilized by the authors include Allstate's 2013 use of predictive AI, as well as the concern surrounding actors and AI attempting to replicate or use their likeness. Important discussions regarding discrimination are brought up and explored in the first chapter, including the false arrests of six Black individuals due to errors with AI facial recognition tools. The chapter concludes with a comparison to the Industrial Revolution, where Narayanan and Kapoor highlight the extensive human labour that is necessary for artificial intelligence technologies to function. === Chapter two: How Predictive AI Goes Wrong === Chapter two focuses on predictive artificial intelligence, and criticizes the overestimation of the capabilities of the technology. === Chapter three: Why Can't AI Predict the Future? === Chapter three works to inform the reader about the history of early computational prediction attempts, with examples from companies like Simulatics. === Chapter four: The Long Road to Generative AI === The fourth chapter goes in more in-depth in explorations of generative AI. Generative AI software examples include ChatGPT, Midjourney, and DALL-E. The section begins with a positive example of generative AI. As the chapter progresses, the authors begin to provide examples of harm produced by generative AI, including the suicide of a Belgian man after connecting with Chai, a generative chatbot. Issues of deepfakes and preservation of artistic property are also discussed. The use of generative AI to create non-consensual pornographic deepfake content is discussed in relation to female celebrities. === Chapter five: Is Advanced AI an Existential Threat? === The fifth chapter draws attention the AGI, or Artificial General Intelligence. The authors describe AGI as "AI that can perform most or economically relevant tasks as effectively as any human". They summarize that many contributors to the field of artificial intelligence believe AGI to be an impending threat that demands attention. However, they argue that the perceived threat of AGI would only exist if the technology continually functioned reliably. In order to better illustrate the hype surrounding AGI, Narayanan and Kapoor use the Ladder of Generality, which is described as a visual tool in which "each rung represents a way of computing that is more flexible, and more general, than the previous one". They note that we are not yet aware of the next rungs on the ladder, or if the ladder will eventually result in a dead end. The rungs that have been identified so far are as follows: (0, or floor) special purpose hardware, (1) programmable computers, (2) stored program computers, (3) machine learning, (4) deep learning, (5) pretrained models, and, finally, (6) instruction-tuned models. The potential for future rungs and what those rungs might be are currently undetermined. The chapter also discusses the ELIZA effect, which Lawrence Switzky discusses in his article "ELIZA Effects". Switzky attributes the coined term ELIZA Effect to Sherry Turke, who defined it as "our more general tendency to treat responsive computer programs as more intelligent than they really are". === Chapter six: Why Can't AI Fix Social Media? === The sixth chapter focuses on content moderation, why it is important, and how it has been and could be affected by artificial automation. The first issue raised in regard to AI-driven content moderation is the inability for computers and machines to understand context and nuance, resulting in potential for discriminatory moderation and shadow banning. While they note that there are issues with automating content moderation, Narayanan and Kapoor also highlight the psychological impact on human content moderators and their labour. They indicate the hidden labour behind moderation, which is often outsourced to less developed countries, where labourers sort through potentially traumatizing content for pay. However, the discussion focuses more heavily on why automated moderation can be problematic, including discriminatory algorithms and lack of nuance. To balance their argument, issues of discrimination and bias are also discussed in relation the human content moderators. To automate moderation, there are two types of AI used, which are fingerprint matching and machine learning. === Chapter seven: Why Do Myths about AI Persist? === The seventh chapter outlines possible factors that contribute to hype surrounding AI. Narayanan and Kapoor explain how companies often promote their new AI models without properly disclosing how the model works, and what it is learning from. They attribute hype to several different groups, including journalists, researchers, and companies. They explain the impact of companies and the misplaced hype that they spread can be attributed to greed and a desire to grow corporate funds. For journalists, one of the stated sources of hype, they argue that news media has a tendency to prioritize financial incentives over validity and quality of writing. As well, Narayanan and Kapoor point out the emergence of company statement regurgitation in news media, leading to clickbait. Hype from researchers is potentially linked to lack of reproducibility in studies as well as leakage, which occurs when AI models are tested on their training data. === Chapter eight: Where do we go from here? === The final chapter, chapter eight, turns its attention to the future. The authors express their ideas and predictions for how the technology will evolve and be utilized in the upcoming years. == Authors == Author Narayanan is a computer science professor at Princeton University. Kapoor is a doctoral candidate at the same university, and both scholars are located at the Center for Information Technology at Princeton. In 2023, Narayanan and Kapoor appeared on the TIME100 Artificial Intelligence list, which features influential figures in the field. == Reception == Nature, a science and technology peer-reviewed journal, released an article highlighting the top "10 essential reads from the past year", listing Arvind Narayanan and Sayash Kapoor's AI Snake Oil. The article states the that text is "one of the best on this controversial subject". Elizabeth Quill, in her review of the text in Science News, writes that the authors "squarely achieve their stated goal: to empower people to distinguish AI that works well from AI snake oil". Joshua Rothman of The New Yorker writes that "compared with many technologists, Narayanan, Kapoor, and Vallor [Shannon Vallor, University of Edinburgh], are deeply skeptical about today's A.I. technology and what it can achieve. Perhaps they shouldn't be". Rothman argues, following an interview with prominent computer scientist Geoffrey Hinton of University of Toronto, that the potential for AI to replicate complexity is already here and continues to be heavily funded, enhancing the prospective capabilities of the technology. However, he does praise the author's ability to address questions regarding the existential human experience. Alexya Martinez discusses the text in a book review for Journalism and Mass Communication Quarterly, critiquing AI Snake Oil for its extensive focus on the West. Martinez writes that Narayanan and Kapoor "do not fully explore how AI impacts other countries", and suggests more focus on countries outside of the United States to enhance their argument.

Darwin among the Machines

"Darwin among the Machines" is a letter to the editor published in The Press newspaper on 13 June 1863 in Christchurch, New Zealand. The title, which was chosen by the author, references the work of Charles Darwin. Written by Samuel Butler but signed Cellarius, the letter raised the possibility that machines were a kind of "mechanical life" undergoing constant evolution, and that eventually machines might supplant humans as the dominant species. == Book of the Machines == Butler developed this and subsequent articles into The Book of the Machines, three chapters of Erewhon, published anonymously in 1872. The Erewhonian society Butler envisioned had long ago undergone a revolution that destroyed most mechanical inventions. The narrator of the story finds a book that details the reasons for this revolution, which he translates for the reader. Despite the initial popularity of Erewhon, Butler commented in the preface to the second edition that reviewers had "in some cases been inclined to treat the chapters on Machines as an attempt to reduce Mr. Darwin's theory to an absurdity." He protested that "few things would be more distasteful to me than any attempt to laugh at Mr. Darwin", but also added "I am surprised, however, that the book at which such an example of the specious misuse of analogy would seem most naturally levelled should have occurred to no reviewer; neither shall I mention the name of the book here, though I should fancy that the hint given will suffice", which may suggest that the chapter on Machines was in fact a satire intended to illustrate the "specious misuse of analogy", even if the target was not Darwin; Butler, fearing that he had offended Darwin, wrote him a letter explaining that the actual target was Joseph Butler's 1736 The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature. The Victorian scholar Herbert Sussman has suggested that although Butler's exploration of machine evolution was intended to be whimsical, he may also have been genuinely interested in the notion that living organisms are a type of mechanism and was exploring this notion with his writings on machines, while the philosopher Louis Flaccus called it "a mixture of fun, satire, and thoughtful speculation." == Evolution of Global Intelligence == George Dyson applies Butler's original premise to the artificial life and intelligence of Alan Turing in Darwin Among the Machines: The Evolution of Global Intelligence (1998) ISBN 0-7382-0030-1, to suggest that the internet is a living, sentient being. Dyson's main claim is that the evolution of a conscious mind from today's technology is inevitable. It is not clear whether this will be a single mind or multiple minds, how smart that mind would be, and even if we will be able to communicate with it. He also clearly suggests that there are forms of intelligence on Earth that we are currently unable to understand. From the book: "What mind, if any, will become apprehensive of the great coiling of ideas now under way is not a meaningless question, but it is still too early in the game to expect an answer that is meaningful to us."

Sample complexity

The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl

International Conference on Automated Planning and Scheduling

The International Conference on Automated Planning and Scheduling (ICAPS) is a leading international academic conference in automated planning and scheduling held annually for researchers and practitioners in planning and scheduling. ICAPS is supported by the National Science Foundation, the journal Artificial Intelligence, and other supporters. == The IPC and PDDL == ICAPS conducts the International Planning Competition (IPC), a competition scheduled every few years that empirically evaluates state-of-the-art planning systems on a collection of benchmark problems. The Planning Domain Definition Language (PDDL) was developed mainly to make the 1998/2000 International Planning Competition possible, and then evolved with each competition. PDDL is an attempt to standardize Artificial Intelligence (AI) planning languages. PDDL was first developed by Drew McDermott and his colleagues in 1998, inspired by STRIPS, ADL, and other sources. == History == The ICAPS conferences began in 2003 as a merge of two bi-annual conferences, the International Conference on Artificial Intelligence Planning and Scheduling (AIPS) and the European Conference on Planning (ECP). == List of events ==