AI Art Detection

AI Art Detection — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Procreate (software)

  Procreate is a raster graphics editor app for digital painting developed and published by the Australian company Savage Interactive for iOS and iPadOS. It was launched on the App Store in 2011. == Versions == === Procreate === Procreate for iPad was first released in 2011 by the Tasmanian software company Savage Interactive. In June 2013, Savage launched Procreate 2 in conjunction with iOS 7, adding new features such as higher resolution capabilities and more brush options. In 2016, Procreate became one of the top ten best-selling iPad apps on the App Store. In 2018, Procreate became the overall best selling iPad app. With iOS 26, Procreate adapted Liquid Glass into its software. As of March 2026, the most recent version of Procreate for the iPad is 5.4.9. === Procreate Pocket === Procreate Pocket was released to the App Store in December 2014. In 2018, Savage launched Procreate Pocket 2.0 to the App Store. In December 2018, Procreate Pocket received Apple's "App of the Year" award. As of September 2025, the most recent version of Procreate Pocket (for the iPhone) is 4.0.15. === Procreate Dreams === Procreate Dreams, their more recent app focused on 2D animation, was released on the App Store on November 22, 2023. While the application is commended for its intuitive interface and accessibility, some reviewers have noted that it may lack some key animations features, such as reference layers. In June 2024, Procreate Dreams received the 2024 Apple Design Award for Innovation. In December 2025, Savage Interactive released Procreate Dreams 2, a long awaited update and redesign to Procreate Dreams. == Features == The current versions of Procreate use Valkyrie, a proprietary graphics engine to allow customisable brush options and importing brushes from Adobe Photoshop. Procreate offers known features like layers, masks, and blending mode. Its biggest standout compared to other professional drawing software is its simple UI and comparatively easy learning curve. The app also allows for animation. Savage expanded upon Procreate's animation features with a companion app dedicated to 2D animation called Procreate Dreams, released in November 2023. On August 2024, Procreate announced that it would not be incorporating generative artificial intelligence into its software. Savage offers a free internet forum called Procreate Discussions in which users can ask for help, suggest ideas, and share user-generated content on the marketplace or the resources board. == Notable users == Concept artist Doug Chiang creates robot, vehicle, and creature designs for Star Wars in Procreate. Professional artists have also used Procreate to create the posters for Stranger Things, Logan, and Blade Runner 2049, as well as several covers for The New Yorker. It has also been professionally adopted at Marvel Comics, DC Comics, Disney Animation, and Pixar.

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  Cortica

  Headquartered in Tel Aviv Cortica utilizes unsupervised learning methods to recognize and analyze digital images and video. The technology developed by the Cortica team is based on research of the function of the human brain. == Company Founding == Cortica was founded in 2007 by Igal Raichelgauz, Karina Odinaev and Yehoshua Zeevi. Together, the founders developed the company’s core technology while at Technion – Israel Institute of Technology. By combining discoveries in neuroscience with developments in computer programming, the team created technology that possesses the ability to interpret large amounts of visual data with increased accuracy. This technology, called Image2Text, is based on the founders’ work in digitally replicating cortical neural networks’ ability to identify complex patterns within massive quantities of ambiguous and noisy data. Cortica’s offerings have application in the automotive industry, media industries, as well as the smart city and medical industries. Industry experts suggest that the self-driving automotive industry alone will be worth upwards of $7 trillion while each connected car is expected to generate 4,000 GB of data per day. Beyond that, industry analysts expect the proliferation of surveillance cameras to continue leading to an expected 2,500 Petabytes of data being generated daily by new surveillance cameras. Cortica operates in these high scale industries. The company currently employs professionals from many domains including AI researchers as well as veterans of intelligence units within the Israeli Defense Forces. == Research and Technology == In 2006, Founders Raichelgauz, Odinaev, and Zeevi shared their findings with the 28th IEEE EMBS Annual International Conference in New York in a paper titled, “Natural Signal Classification by Neural Cliques and Phase-Locked Attractors”. That same year, the team also published “Cliques in Neural Ensembles as Perception Carriers" CB Insights recently identified Cortica as the number one patent holder among AI companies. Cortica is researching to develop a machine-learning driving system which can identify objects and pedestrians. Connecting to it, Elon Musk has been rumored to partner with Cortica for his electric car company, Tesla. However, Tesla denies it stating that Musk did not discuss a collaboration with artificial intelligence firm Cortica. == Funding == Cortica raised $7 million in its Series A funding round, announced in August 2012. Investors included Horizons Ventures (the investment firm of Hong Kong billionaire Li Ka-Shing), and Ynon Kreiz, the former chairman and CEO of the Endemol Group. In May 2013, it was announced that Cortica had raised $1.5 million from Russian firm Mail.ru Group. It later transpired that this was a part of Cortica's Series B funding round for $6.4 million, announced in June 2013. The round was led by Horizons Ventures, with participation from the Russian firm Mail.ru Group and other angel investors. In its fourth funding round, Cortica has raised $20 million, bringing the total investments to $38 million. According to a report from The Israeli lead Daily economic newspaper, TheMarker, the fourth round was led by a strategic Chinese investor who will probably help the company expand into the Asian market. == Media coverage == GigaOm listed Cortica as one of the top deep learning startups in a November 2013 article surveying the field, along with AlchemyAPI, Ersatz, and Semantria. Business Insider ranked Cortica as one of the coolest tech companies in Israel. CB Insights has identified Cortica as the top patent holding AI company. In 2017 several leading automotive media outlets covered the launch of Cortica's automotive business unit

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  Rnn (software)

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

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  Turing test

  The Turing test, originally called the imitation game by Alan Turing in 1949, is a test of a machine's ability to exhibit intelligent behaviour equivalent to that of a human. In the test, a human evaluator judges a text transcript of a natural-language conversation between a human and a machine. The evaluator tries to identify the machine, and the machine passes if the evaluator cannot reliably tell them apart. The results would not depend on the machine's ability to answer questions correctly, only on how closely its answers resembled those of a human. Since the Turing test is a test of indistinguishability in performance capacity, the verbal version generalizes naturally to all of human performance capacity, verbal as well as nonverbal (robotic). The test was introduced by Turing in his 1950 paper "Computing Machinery and Intelligence" while working at the University of Manchester. It opens with the words: "I propose to consider the question, 'Can machines think?'." Because "thinking" is difficult to define, Turing chooses to "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words". Turing describes the new form of the problem in terms of a three-person party game called the "imitation game", in which an interrogator asks questions of a man and a woman in another room in order to determine the correct sex of the two players. Turing's new question is: "Are there imaginable digital computers which would do well in the imitation game?" This question, Turing believed, was one that could actually be answered. In the remainder of the paper, he argued against the major objections to the proposition that "machines can think". Since Turing introduced his test, it has been highly influential in the philosophy of artificial intelligence, resulting in substantial discussion and controversy, as well as criticism from philosophers like John Searle, who argue against the test's ability to detect consciousness. == History == === Philosophical background === The question of whether it is possible for machines to think has a long history, which is firmly entrenched in the distinction between dualist and materialist views of the mind. René Descartes prefigures aspects of the Turing test in his 1637 Discourse on the Method when he writes: [H]ow many different automata or moving machines could be made by the industry of man ... For we can easily understand a machine's being constituted so that it can utter words, and even emit some responses to action on it of a corporeal kind, which brings about a change in its organs; for instance, if touched in a particular part it may ask what we wish to say to it; if in another part it may exclaim that it is being hurt, and so on. But it never happens that it arranges its speech in various ways, in order to reply appropriately to everything that may be said in its presence, as even the lowest type of man can do. Here Descartes notes that automata are capable of responding to human interactions but argues that such automata cannot respond appropriately to things said in their presence in the way that any human can. Descartes therefore prefigures the Turing test by defining the insufficiency of appropriate linguistic response as that which separates the human from the automaton. Descartes fails to consider the possibility that future automata might be able to overcome such insufficiency, and so does not propose the Turing test as such, even if he prefigures its conceptual framework and criterion. Denis Diderot formulates in his 1746 book Pensées philosophiques a Turing-test criterion, though with the important implicit limiting assumption maintained, of the participants being natural living beings, rather than considering created artifacts: If they find a parrot who could answer to everything, I would claim it to be an intelligent being without hesitation. This does not mean he agrees with this, but that it was already a common argument of materialists at that time. According to dualism, the mind is non-physical (or, at the very least, has non-physical properties) and, therefore, cannot be explained in purely physical terms. According to materialism, the mind can be explained physically, which leaves open the possibility of minds that are produced artificially. In 1936, philosopher Alfred Ayer considered the standard philosophical question of other minds: how do we know that other people have the same conscious experiences that we do? In his book, Language, Truth and Logic, Ayer suggested a protocol to distinguish between a conscious man and an unconscious machine: "The only ground I can have for asserting that an object which appears to be conscious is not really a conscious being, but only a dummy or a machine, is that it fails to satisfy one of the empirical tests by which the presence or absence of consciousness is determined". (This suggestion is very similar to the Turing test, but it is not certain that Ayer's popular philosophical classic was familiar to Turing.) In other words, a thing is not conscious if it fails the consciousness test. === Cultural background === A rudimentary idea of the Turing test appears in the 1726 novel Gulliver's Travels by Jonathan Swift. When Gulliver is brought before the king of Brobdingnag, the king thinks at first that Gulliver might be a "a piece of clock-work (which is in that country arrived to a very great perfection) contrived by some ingenious artist". Even when he hears Gulliver speaking, the king still doubts whether Gulliver was taught "a set of words" to make him "sell at a better price". Gulliver tells that only after "he put several other questions to me, and still received rational answers" the king became satisfied that Gulliver was not a machine. Tests where a human judges whether a computer or an alien is intelligent were an established convention in science fiction by the 1940s, and it is likely that Turing would have been aware of these. Stanley G. Weinbaum's "A Martian Odyssey" (1934) provides an example of how nuanced such tests could be. Earlier examples of machines or automatons attempting to pass as human include the Ancient Greek myth of Pygmalion who creates a sculpture of a woman that is animated by Aphrodite, Carlo Collodi's novel The Adventures of Pinocchio, about a puppet who wants to become a real boy, and E. T. A. Hoffmann's 1816 story "The Sandman," where the protagonist falls in love with an automaton. In all these examples, people are fooled by artificial beings that—up to a point—pass as human. === Alan Turing and the imitation game === Researchers in the United Kingdom had been exploring "machine intelligence" for up to ten years prior to the founding of the field of artificial intelligence (AI) research in 1956. It was a common topic among the members of the Ratio Club, an informal group of British cybernetics and electronics researchers that included Alan Turing. Turing, in particular, had been running the notion of machine intelligence since at least 1941 and one of the earliest-known mentions of "computer intelligence" was made by him in 1947. In Turing's report, "Intelligent Machinery," he investigated "the question of whether or not it is possible for machinery to show intelligent behaviour" and, as part of that investigation, proposed what may be considered the forerunner to his later tests: It is not difficult to devise a paper machine which will play a not very bad game of chess. Now get three men A, B and C as subjects for the experiment. A and C are to be rather poor chess players, B is the operator who works the paper machine. ... Two rooms are used with some arrangement for communicating moves, and a game is played between C and either A or the paper machine. C may find it quite difficult to tell which he is playing. "Computing Machinery and Intelligence" (1950) was the first published paper by Turing to focus exclusively on machine intelligence. Turing begins the 1950 paper with the claim, "I propose to consider the question 'Can machines think?'" As he highlights, the traditional approach to such a question is to start with definitions, defining both the terms "machine" and "think". Turing chooses not to do so; instead, he replaces the question with a new one, "which is closely related to it and is expressed in relatively unambiguous words". In essence he proposes to change the question from "Can machines think?" to "Can machines do what we (as thinking entities) can do?" The advantage of the new question, Turing argues, is that it draws "a fairly sharp line between the physical and intellectual capacities of a man". To demonstrate this approach Turing proposes a test inspired by a party game, known as the "imitation game", in which a man and a woman go into separate rooms and guests try to tell them apart by writing a series of questions and reading the typewritten answers sent back. In this game, both the man and the woman aim to convince the guests that they ar

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  Security.txt

  security.txt is an accepted standard for website security information that allows security researchers to report security vulnerabilities easily. The standard prescribes a text file named security.txt in the well known location, similar in syntax to robots.txt but intended to be machine and human readable, for those wishing to contact a website's owner about security issues. security.txt files have been adopted by Google, GitHub, LinkedIn, and Facebook. == History == The Internet Draft was first submitted by Edwin Foudil in September 2017. At that time it covered four directives, "Contact", "Encryption", "Disclosure" and "Acknowledgement". Foudil expected to add further directives based on feedback. In addition, web security expert Scott Helme said he had seen positive feedback from the security community while use among the top 1 million websites was "as low as expected right now". In 2019, the Cybersecurity and Infrastructure Security Agency (CISA) published a draft binding operational directive that requires all US federal agencies to publish a security.txt file within 180 days. The Internet Engineering Steering Group (IESG) issued a Last Call for security.txt in December 2019 which ended on January 6, 2020. A study in 2021 found that over ten percent of top-100 websites published a security.txt file, with the percentage of sites publishing the file decreasing as more websites were considered. The study also noted a number of discrepancies between the standard and the content of the file. In April 2022 the security.txt file has been accepted by Internet Engineering Task Force (IETF) as RFC 9116. == File format == security.txt files can be served under the /.well-known/ directory (i.e. /.well-known/security.txt) or the top-level directory (i.e. /security.txt) of a website. The file must be served over HTTPS and in plaintext format.

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  Elon Musk

  Elon Reeve Musk ( EE-lon; born June 28, 1971) is a businessman and former public official known for his leadership of Tesla and SpaceX. Musk has been the wealthiest person in the world since 2025; as of June 2026, Forbes estimates his net worth to be US$834 billion. Born into the wealthy Musk family in Pretoria, South Africa, Musk emigrated in 1989 to Canada; he has Canadian citizenship since his mother was born there. He received bachelor's degrees in 1997 from the University of Pennsylvania before moving to California to pursue business ventures. In 1995, Musk co-founded the software company Zip2. Following its sale in 1999, he co-founded X.com, an online payment company that later merged to form PayPal, which was acquired by eBay in 2002. Musk also became an American citizen in 2002. In 2002, Musk founded the space technology company SpaceX, becoming its CEO and chief engineer; the company has since led innovations in reusable rockets and commercial spaceflight. Musk joined the automaker Tesla as an early investor in 2004 and became its CEO and product architect in 2008; it has since become a leader in electric vehicles. In 2015, he co-founded OpenAI to advance artificial intelligence (AI) research, but later left; growing discontent with the organization's direction and leadership in the AI boom in the 2020s led him to establish xAI, which became a subsidiary of SpaceX in 2026. In 2022, he acquired the social network Twitter, implementing significant changes, and rebranding it as X in 2023. His other businesses include the neurotechnology company Neuralink, which he co-founded in 2016, and the tunneling company the Boring Company, which he founded in 2017. In November 2025, Tesla approved a pay package worth $1 trillion for Musk, which he is to receive over 10 years if he meets specific goals. Musk is a supporter of global far-right politics, figures, and political parties. He was the largest donor in the 2024 U.S. presidential election, where he supported Donald Trump. After Trump was inaugurated as president in January 2025, Musk served as Senior Advisor to the President and as the de facto head of the Department of Government Efficiency (DOGE). Shortly before a public feud with Trump, Musk left the Trump administration in May 2025 and returned to managing his companies. Musk's political activities, statements and views have made him a polarizing figure. He has been criticized for making unscientific and misleading statements, including spreading COVID-19 misinformation, promoting conspiracy theories, and affirming antisemitic, racist, and transphobic comments. His acquisition of Twitter was controversial due to a subsequent increase in hate speech and the spread of misinformation on the service, following his pledge to decrease censorship. His role in the second Trump administration attracted public backlash, particularly in response to DOGE. == Early life and education == Elon Reeve Musk was born on June 28, 1971, in Pretoria, South Africa's administrative capital. He is of British and Pennsylvania Dutch ancestry. His mother, Maye (née Haldeman), is a model and dietitian born in Saskatchewan, Canada, and raised in South Africa. Musk therefore holds both South African and Canadian citizenship from birth. His father, Errol Musk, is a South African electromechanical engineer, pilot, sailor, consultant, emerald dealer, and property developer, who partly owned a rental lodge at Timbavati Private Nature Reserve. His maternal grandfather, Joshua N. Haldeman, who died in a plane crash when Elon was a toddler, was an American-born Canadian chiropractor, aviator and political activist in the Technocracy movement who moved to South Africa in 1950. Haldeman's anti-government, anti-democratic and conspiracist views, which included the promotion of far-right antisemitic conspiracy theories, "fanatical" support of apartheid, and according to Errol Musk, support of Nazism, have been suggested as an influence on Elon. During his childhood, Elon was told stories by his grandmother of Haldeman's travels and exploits, and Elon has suggested that all of Haldeman's descendants have his "desire for adventure, exploration – doing crazy things". Elon has a younger brother, Kimbal, a younger sister, Tosca, and four paternal half-siblings. Musk was baptized as a child in the Anglican Church of Southern Africa. The Musk family was wealthy during Elon's youth. Despite both Elon and Errol previously stating that Errol was a part owner of a Zambian emerald mine, in 2023, Errol recounted that the deal he made was to receive "a portion of the emeralds produced at three small mines". Errol was elected to the Pretoria City Council as a representative of the anti-apartheid Progressive Party and has said that his children shared their father's dislike of apartheid. After his parents divorced in 1979, Elon, aged around 9, chose to live with his father because he had an Encyclopædia Britannica set and a computer. Elon later regretted his decision and became estranged from his father. Elon has recounted trips to a wilderness school that he described as a "paramilitary Lord of the Flies" where "bullying was a virtue" and children were encouraged to fight over rations. In one incident, after an altercation with a fellow pupil, Elon was thrown down concrete steps and beaten severely, leading to him being hospitalized for his injuries. Elon described his father berating him after he was discharged from the hospital. Errol denied berating Elon and claimed, "The [other] boy had just lost his father to suicide, and Elon had called him stupid. Elon had a tendency to call people stupid. How could I possibly blame that child?" Elon was an enthusiastic reader of books, and had attributed his success in part to having read The Lord of the Rings, the Foundation series, and The Hitchhiker's Guide to the Galaxy. At age ten, he developed an interest in computing and video games, teaching himself how to program from the VIC-20 user manual. At age twelve, Elon sold his BASIC-based game Blastar to PC and Office Technology magazine for approximately $500 (equivalent to $1,600 in 2025). === Education === Musk attended Waterkloof House Preparatory School, Bryanston High School, and then Pretoria Boys High School, where he graduated. Musk was a decent but unexceptional student, earning a 61/100 in Afrikaans and a B on his senior math certification. Musk applied for a Canadian passport through his Canadian-born mother to avoid South Africa's mandatory military service, which would have forced him to participate in the apartheid regime, as well as to ease his path to immigration to the United States. While waiting for his application to be processed, he attended the University of Pretoria for five months. Musk arrived in Canada in June 1989, connected with a second cousin in Saskatchewan, and worked odd jobs, including at a farm and a lumber mill. In 1990, he entered Queen's University in Kingston, Ontario. Two years later, he transferred to the University of Pennsylvania, where he studied until 1995. Although Musk has said that he earned his degrees in 1995, the University of Pennsylvania did not award them until 1997 – a Bachelor of Arts in physics and a Bachelor of Science in economics from the university's Wharton School. He reportedly hosted large, ticketed house parties to help pay for tuition, and wrote a business plan for an electronic book-scanning service similar to Google Books. In 1994, Musk held two internships in Silicon Valley: one at energy storage startup Pinnacle Research Institute, which investigated electrolytic supercapacitors for energy storage, and another at Palo Alto–based startup Rocket Science Games. In 1995, he was accepted to a graduate program in materials science at Stanford University, but did not enroll. Musk decided to join the Internet boom of the 1990s, applying for a job at Netscape, to which he reportedly never received a response. The Washington Post reported that Musk lacked legal authorization to remain and work in the United States after failing to enroll at Stanford. In response, Musk said he was allowed to work at that time and that his student visa transitioned to an H1-B. According to numerous former business associates and shareholders, Musk said he was on a student visa at the time. == Business career == === Zip2 === In 1995, Musk, his brother Kimbal, and Greg Kouri founded the web software company Zip2 with funding from a group of angel investors. They housed the venture at a small rented office in Palo Alto. Replying to Rolling Stone, Musk denounced the notion that they started their company with funds borrowed from Elon's father Errol Musk, but in a tweet, he recognized that his father contributed 10% of a later funding round. The company developed and marketed an Internet city guide for the newspaper publishing industry, with maps, directions, and yellow pages. According to Musk, "The website was up during the day and I was coding it

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  Juergen Pirner

  Juergen Pirner (born 1956) is the German creator of Jabberwock, a chatterbot that won the 2003 Loebner prize. Pirner created Jabberwock modelling the Jabberwocky from Lewis Carroll's poem of the same name. Initially, Jabberwock would just give rude or fantasy-related answers; but over the years, Pirner has programmed better responses into it. As of 2007 he has taught it 2.7 million responses. Pirner lives in Hamburg, Germany.

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  Seeing AI

  Seeing AI is an artificial intelligence application developed by Microsoft for iOS. Seeing AI uses the device camera to identify people and objects, and then the app audibly describes those objects for visually impaired people. == Capabilities == Seeing AI is primarily used to describe short text, documents, products, people, currency scenery, colors, handwriting and light. The app can scan a barcode to describe a product and uses sounds to assist the user in focusing on the barcode. When the app describes people, it attempts to estimate the person's age, gender, and emotional status. Additionally, in a test run by German journalists in December 2019, Seeing AI apparently used some sort of facial recognition system to identify people on photographs by name. Some functions are performed on the device, however more complex functions such as describing a scene or recognizing handwriting require an Internet connection. In December 2017, Seeing AI introduced the ability for currency recognition for US and Canadian dollar, British pounds and Euros. In December 2019, Seeing AI added support for five more languages, Dutch, French, German, Japanese, Spanish. Seeing AI is available in 70 countries such as Brazil, Argentina, Australia, Canada, Egypt, Albania, Bhutan, etc. Supported on iPhone 5C, 5S and later best performance with iPhone 6S, SE and later models

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  Actor-critic algorithm

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

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  Jess (programming language)

  Jess is a rule engine for the Java computing platform, written in the Java programming language. It was developed by Ernest Friedman-Hill of Sandia National Laboratories. It is a superset of the CLIPS language. It was first written in late 1995. The language provides rule-based programming for the automation of an expert system, and is often termed as an expert system shell. In recent years, intelligent agent systems have also developed, which depend on a similar ability. Rather than a procedural paradigm, where one program has a loop that is activated only one time, the declarative paradigm used by Jess applies a set of rules to a set of facts continuously by a process named pattern matching. Rules can modify the set of facts, or can execute any Java code. It uses the Rete algorithm to execute rules. == License == The licensing for Jess is freeware for education and government use, and is proprietary software, needing a license, for commercial use. In contrast, CLIPS, which is the basis and starting code for Jess, is free and open-source software. == Code examples == Code examples: Sample code:

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  Issue tree

  An issue tree, also called logic tree, is a graphical breakdown of a question that dissects it into its different components vertically and that progresses into details as it reads to the right. Issue trees are useful in problem solving to identify the root causes of a problem as well as to identify its potential solutions. They also provide a reference point to see how each piece fits into the whole picture of a problem. == Types == According to professor of strategy Arnaud Chevallier, elaborating an approach used at McKinsey & Company, there are two types of issue trees: diagnostic ones and solution ones. Diagnostic trees break down a "why" key question, identifying all the possible root causes for the problem. Solution trees break down a "how" key question, identifying all the possible alternatives to fix the problem. == Rules == Four basic rules can help ensure that issue trees are optimal, according to Chevallier: Consistently answer a "why" or a "how" question Progress from the key question to the analysis as it moves to the right Have branches that are mutually exclusive and collectively exhaustive (MECE) Use an insightful breakdown The requirement for issue trees to be collectively exhaustive implies that divergent thinking is a critical skill. == Applications == === In management interviews === Issue trees are used to answer questions in case interviews for management consulting positions. A quantitative type of question, the market sizing question, requires the interviewee to estimate the size of a data group such as a specific segment of a population, an amount of objects, a company's revenues, or similar. The candidates are expected to use a structured and logical method of arriving at their answer, and using an issue tree provides a diagram to aid the candidate's logical reasoning. Issue trees are used for other types of case interview questions as well.

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  Common Crawl

  The Common Crawl Foundation (Common Crawl) is a nonprofit 501(c)(3) organization that crawls the web and freely provides its archives and datasets to the public. Common Crawl was founded by Gil Elbaz. The data had mostly been primarily used by researchers and some startups until the 2020s, when AI companies started training large language models using the data. In November 2025, an investigation by The Atlantic revealed that Common Crawl misled publishers when it claimed it respected paywalls in its scraping and it was not honoring requests from publishers to have their content removed from its databases. == History == Common Crawl was founded in 2007 in San Francisco. It began publishing its crawls in 2011. By 2013, sites like TinEye were building their products off of Common Crawl. The crawl reduces the reliance of companies and researchers on Google, which has the biggest dataset. Common Crawl was designed to have more and fresher data that was more efficient to analyze and utilize than the Wayback Machine created by the Internet Archive. By 2015, 1.8 billion webpages were on the Common Crawl, which started by crawling a list of URLs donated by the search engine Blekko. They use Amazon Web Services, which provides some of its services for free, allowing computing costs to average $2-4000/month. The Common Crawl website listed 30 studies based on Common Crawl data. Before 2023, Common Crawl was not very well known outside of academic researchers who utilize the data. Common Crawl received its first requests to redact information in 2023 and increasingly started seeing its crawler, CCBot, blocked. In 2023, it began receiving significant financial support from AI companies, including Anthropic and OpenAI, each of which donated $250,000. It was also used to train Google DeepMind's large language model Gemini. By April 2023, Common Crawl was capturing 3.1 billion webpages, with an estimated 5% of pages before 2021 containing hate speech or slurs. As of 2024, Common Crawl had been cited in more than 10,000 academic studies. By 2024, The Pile and Common Crawl had been the two main training datasets being used to train AI models. In November 2025, an investigation by technology journalist Alex Reisner for The Atlantic revealed that Common Crawl misled publishers when it claimed it respected paywalls in its scraping and when it said that it was honoring requests from publishers to have their content removed from its databases. It included misleading results in the public search function on its website that showed no entries for websites that had requested their archives be removed, when in fact those sites were still included in its scrapes used by AI companies. As of 2025, Reisner found that CCBot was the most widely-blocked bot by the top 1000 websites. A 2026 article in LWN.net discussed an advantage to services like Common Crawl being that it can limit the scraping costs to websites by allowing companies and researchers to download the data from Common Crawl instead of scraping it themselves. In April 2026, Common Crawl experimentally began to distribute its data through Hugging Face Storage Bucket, in addition to its standard storage on Amazon S3. == Organization == Peter Norvig and Joi Ito have served on the advisory board. Rich Skrenta is the executive director. It has received funding almost exclusively from the Elbaz Family Foundation Trust until 2023 when it started receiving donations from the AI industry. == Refined versions == A number of organizations take raw Common Crawl data and refine it into datasets that exclude edgy content or are otherwise higher-quality for their purposes, such as FineWeb, DCLM and C4. === Colossal Clean Crawled Corpus === Google version of the Common Crawl is called the Colossal Clean Crawled Corpus, or C4 for short. It was constructed for the training of the T5 language model series in 2019. As of 2023, there were some concerns over copyrighted content in the C4 as well as racist content. A 2024 study found that 45% of content was explicitly restricted by websites' terms of service to be used for purposes like AI training by for-profit companies.

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  Reparameterization trick

  The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization. It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients". Its use in variational inference was proposed in 2013. == Mathematics == Let z {\displaystyle z} be a random variable with distribution q ϕ ( z ) {\displaystyle q_{\phi }(z)} , where ϕ {\displaystyle \phi } is a vector containing the parameters of the distribution. === REINFORCE estimator === Consider an objective function of the form: L ( ϕ ) = E z ∼ q ϕ ( z ) [ f ( z ) ] {\displaystyle L(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[f(z)]} Without the reparameterization trick, estimating the gradient ∇ ϕ L ( ϕ ) {\displaystyle \nabla _{\phi }L(\phi )} can be challenging, because the parameter appears in the random variable itself. In more detail, we have to statistically estimate: ∇ ϕ L ( ϕ ) = ∇ ϕ ∫ d z q ϕ ( z ) f ( z ) {\displaystyle \nabla _{\phi }L(\phi )=\nabla _{\phi }\int dz\;q_{\phi }(z)f(z)} The REINFORCE estimator, widely used in reinforcement learning and especially policy gradient, uses the following equality: ∇ ϕ L ( ϕ ) = ∫ d z q ϕ ( z ) ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) = E z ∼ q ϕ ( z ) [ ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) ] {\displaystyle \nabla _{\phi }L(\phi )=\int dz\;q_{\phi }(z)\nabla _{\phi }(\ln q_{\phi }(z))f(z)=\mathbb {E} _{z\sim q_{\phi }(z)}[\nabla _{\phi }(\ln q_{\phi }(z))f(z)]} This allows the gradient to be estimated: ∇ ϕ L ( ϕ ) ≈ 1 N ∑ i = 1 N ∇ ϕ ( ln ⁡ q ϕ ( z i ) ) f ( z i ) {\displaystyle \nabla _{\phi }L(\phi )\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }(\ln q_{\phi }(z_{i}))f(z_{i})} The REINFORCE estimator has high variance, and many methods were developed to reduce its variance. === Reparameterization estimator === The reparameterization trick expresses z {\displaystyle z} as: z = g ϕ ( ϵ ) , ϵ ∼ p ( ϵ ) {\displaystyle z=g_{\phi }(\epsilon ),\quad \epsilon \sim p(\epsilon )} Here, g ϕ {\displaystyle g_{\phi }} is a deterministic function parameterized by ϕ {\displaystyle \phi } , and ϵ {\displaystyle \epsilon } is a noise variable drawn from a fixed distribution p ( ϵ ) {\displaystyle p(\epsilon )} . This gives: L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ f ( g ϕ ( ϵ ) ) ] {\displaystyle L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[f(g_{\phi }(\epsilon ))]} Now, the gradient can be estimated as: ∇ ϕ L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ ∇ ϕ f ( g ϕ ( ϵ ) ) ] ≈ 1 N ∑ i = 1 N ∇ ϕ f ( g ϕ ( ϵ i ) ) {\displaystyle \nabla _{\phi }L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[\nabla _{\phi }f(g_{\phi }(\epsilon ))]\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }f(g_{\phi }(\epsilon _{i}))} == Examples == For some common distributions, the reparameterization trick takes specific forms: Normal distribution: For z ∼ N ( μ , σ 2 ) {\displaystyle z\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , we can use: z = μ + σ ϵ , ϵ ∼ N ( 0 , 1 ) {\displaystyle z=\mu +\sigma \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,1)} Exponential distribution: For z ∼ Exp ( λ ) {\displaystyle z\sim {\text{Exp}}(\lambda )} , we can use: z = − 1 λ log ⁡ ( ϵ ) , ϵ ∼ Uniform ( 0 , 1 ) {\displaystyle z=-{\frac {1}{\lambda }}\log(\epsilon ),\quad \epsilon \sim {\text{Uniform}}(0,1)} Discrete distribution can be reparameterized by the Gumbel distribution (Gumbel-softmax trick or "concrete distribution") and diffusion models. In general, any distribution that is differentiable with respect to its parameters can be reparameterized by inverting the multivariable CDF function, then apply the implicit method. See for an exposition and application to the Gamma, Beta, Dirichlet, and von Mises distributions. == Applications == === Variational autoencoder === In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by: ELBO ( ϕ , θ ) = E z ∼ q ϕ ( z | x ) [ log ⁡ p θ ( x | z ) ] − D KL ( q ϕ ( z | x ) | | p ( z ) ) {\displaystyle {\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{z\sim q_{\phi }(z|x)}[\log p_{\theta }(x|z)]-D_{\text{KL}}(q_{\phi }(z|x)||p(z))} where q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is the encoder (recognition model), p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is the decoder (generative model), and p ( z ) {\displaystyle p(z)} is the prior distribution over latent variables. The gradient of ELBO with respect to θ {\displaystyle \theta } is simply E z ∼ q ϕ ( z | x ) [ ∇ θ log ⁡ p θ ( x | z ) ] ≈ 1 L ∑ l = 1 L ∇ θ log ⁡ p θ ( x | z l ) {\displaystyle \mathbb {E} _{z\sim q_{\phi }(z|x)}[\nabla _{\theta }\log p_{\theta }(x|z)]\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\theta }\log p_{\theta }(x|z_{l})} but the gradient with respect to ϕ {\displaystyle \phi } requires the trick. Express the sampling operation z ∼ q ϕ ( z | x ) {\displaystyle z\sim q_{\phi }(z|x)} as: z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ , ϵ ∼ N ( 0 , I ) {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,I)} where μ ϕ ( x ) {\displaystyle \mu _{\phi }(x)} and σ ϕ ( x ) {\displaystyle \sigma _{\phi }(x)} are the outputs of the encoder network, and ⊙ {\displaystyle \odot } denotes element-wise multiplication. Then we have ∇ ϕ ELBO ( ϕ , θ ) = E ϵ ∼ N ( 0 , I ) [ ∇ ϕ log ⁡ p θ ( x | z ) + ∇ ϕ log ⁡ q ϕ ( z | x ) − ∇ ϕ log ⁡ p ( z ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{\epsilon \sim {\mathcal {N}}(0,I)}[\nabla _{\phi }\log p_{\theta }(x|z)+\nabla _{\phi }\log q_{\phi }(z|x)-\nabla _{\phi }\log p(z)]} where z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon } . This allows us to estimate the gradient using Monte Carlo sampling: ∇ ϕ ELBO ( ϕ , θ ) ≈ 1 L ∑ l = 1 L [ ∇ ϕ log ⁡ p θ ( x | z l ) + ∇ ϕ log ⁡ q ϕ ( z l | x ) − ∇ ϕ log ⁡ p ( z l ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )\approx {\frac {1}{L}}\sum _{l=1}^{L}[\nabla _{\phi }\log p_{\theta }(x|z_{l})+\nabla _{\phi }\log q_{\phi }(z_{l}|x)-\nabla _{\phi }\log p(z_{l})]} where z l = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ l {\displaystyle z_{l}=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon _{l}} and ϵ l ∼ N ( 0 , I ) {\displaystyle \epsilon _{l}\sim {\mathcal {N}}(0,I)} for l = 1 , … , L {\displaystyle l=1,\ldots ,L} . This formulation enables backpropagation through the sampling process, allowing for end-to-end training of the VAE model using stochastic gradient descent or its variants. === Variational inference === More generally, the trick allows using stochastic gradient descent for variational inference. Let the variational objective (ELBO) be of the form: ELBO ( ϕ ) = E z ∼ q ϕ ( z ) [ log ⁡ p ( x , z ) − log ⁡ q ϕ ( z ) ] {\displaystyle {\text{ELBO}}(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[\log p(x,z)-\log q_{\phi }(z)]} Using the reparameterization trick, we can estimate the gradient of this objective with respect to ϕ {\displaystyle \phi } : ∇ ϕ ELBO ( ϕ ) ≈ 1 L ∑ l = 1 L ∇ ϕ [ log ⁡ p ( x , g ϕ ( ϵ l ) ) − log ⁡ q ϕ ( g ϕ ( ϵ l ) ) ] , ϵ l ∼ p ( ϵ ) {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi )\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\phi }[\log p(x,g_{\phi }(\epsilon _{l}))-\log q_{\phi }(g_{\phi }(\epsilon _{l}))],\quad \epsilon _{l}\sim p(\epsilon )} === Dropout === The reparameterization trick has been applied to reduce the variance in dropout, a regularization technique in neural networks. The original dropout can be reparameterized with Bernoulli distributions: y = ( W ⊙ ϵ ) x , ϵ i j ∼ Bernoulli ( α i j ) {\displaystyle y=(W\odot \epsilon )x,\quad \epsilon _{ij}\sim {\text{Bernoulli}}(\alpha _{ij})} where W {\displaystyle W} is the weight matrix, x {\displaystyle x} is the input, and α i j {\displaystyle \alpha _{ij}} are the (fixed) dropout rates. More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: y i = μ i + σ i ⊙ ϵ i , ϵ i ∼ N ( 0 , I ) {\displaystyle y_{i}=\mu _{i}+\sigma _{i}\odot \epsilon _{i},\quad \epsilon _{i}\sim {\mathcal {N}}(0,I)} where μ i = m i ⊤ x {\displaystyle \mu _{i}=\mathbf {m} _{i}^{\top }x} and σ i 2 = v i ⊤ x 2 {\displaystyle \sigma _{i}^{2}=\mathbf {v} _{i}^{\top }x^{2}} , with m i {\displaystyle \mathbf {m} _{i}} and v i {\displaystyle \mathbf {v} _{i}} being the mean and variance of the i {\displaystyle i} -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.

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  Lethal autonomous weapon

  A lethal autonomous weapon (LAW), also known as a lethal autonomous weapon system (LAWS), autonomous weapon system (AWS), robotic weapon, or killer robot, is a type of military drone or military robot, which is autonomous in that it can independently search for and engage targets based on programmed constraints and descriptions. As of 2025, most military drones (including unmanned aerial vehicles and unmanned combat aerial vehicles) and military robots are not truly autonomous. LAWs may engage in drone warfare in the air, on land, on water, underwater, or in space. == Definitions == In weapons development, the term "autonomous" is somewhat ambiguous and can vary hugely between different scholars, nations and organizations. There is no definition of lethal autonomous weapon systems that is generally agreed upon among different countries. The official United States Department of Defense Policy on Autonomy in Weapon Systems (Department of Defense Directive 3000.09) defines an Autonomous Weapon System as one that "...once activated, can select and engage targets without further intervention by a human operator." Heather Roff, a writer for Case Western Reserve University School of Law, describes autonomous weapon systems as "... capable of learning and adapting their 'functioning in response to changing circumstances in the environment in which [they are] deployed,' as well as capable of making firing decisions on their own." The British Ministry of Defence states "Whilst definitions can vary, the key difference is that an automated system is capable of carrying out complicated tasks but is incapable of complex decision-making, whereas an autonomous system is capable of deciding a course of action without depending on human oversight and control." Scholars such as Peter Asaro and Mark Gubrud believe that any weapon system that is capable of releasing a lethal force without the operation, decision, or confirmation of a human supervisor can be deemed autonomous. == Automatic defensive systems == Some definitions of autonomous weapon systems are broad enough to include land mines and naval mines, simple automatically-triggered lethal weapons that have been in use for centuries. Some current examples of LAWs are automated "hardkill" active protection systems, such as a radar-guided close-in weapon systems (CIWS) used to defend ships that have been in use since the 1970s (e.g., the US Phalanx CIWS). Such systems can autonomously identify and attack oncoming missiles, rockets, artillery fire, aircraft, and surface vessels according to criteria set by the human operator. Similar systems exist for tanks, such as the Russian Arena, the Israeli Trophy, and the German AMAP-ADS. Several types of stationary sentry guns, which can fire at humans and vehicles, are used in South Korea and Israel. Many missile defence systems, such as Iron Dome, also have autonomous targeting capabilities. The main reason for not having a "human in the loop" in these systems is the need for rapid response. They have generally been used to protect personnel and installations against incoming projectiles. == Autonomous offensive systems == According to The Economist in 2018, as technology advances, applications of uncrewed undersea vehicles could include mine clearance, mine-laying, anti-submarine sensor networking in contested waters, patrolling with active sonar, resupplying manned submarines, and becoming low-cost missile platforms. In 2017 the Russian Federation was developing artificially intelligent missiles, drones, unmanned vehicles, military robots and medic robots. In 2018, the U.S. Nuclear Posture Review alleged that Russia was developing a "new intercontinental, nuclear-armed, nuclear-powered, undersea autonomous torpedo" named "Status 6". Israeli Minister Ayoob Kara stated in 2017 that Israel is developing military robots, including ones as small as flies. In October 2018, Zeng Yi, a senior executive at the Chinese defense firm Norinco, gave a speech in which he said that "In future battlegrounds, there will be no people fighting", and that the use of lethal autonomous weapons in warfare is "inevitable". In 2019, US Defense Secretary Mark Esper lashed out at China for selling drones capable of taking life with no human oversight. As of 2020, DARPA was working on making swarms of 250 autonomous lethal drones available to the American military. The US Navy is developing unmanned surface vehicles, also called sea drones, including Ghost Fleet Overlord, with plans to equip them with weapons and with the potential to use them semi-autonomously. In 2020 a Kargu 2 drone hunted down and attacked a human target in Libya, according to a report from the UN Security Council's Panel of Experts on Libya, published in March 2021. This may have been the first time an autonomous killer robot armed with lethal weaponry attacked human beings. In May 2021 Israel conducted an AI-guided combat drone swarm attack in Gaza. In the Russo-Ukrainian war, Ukraine has developed advanced drones with integrated artificial intelligence for a range of drone warfare purposes, including to attack infrastructure in Russia, although as of May 2026, Al Jazeera reported that humans remain in control of operation. == Ethical and legal issues == === Degree of human control === Three classifications of the degree of human control of autonomous weapon systems were laid out by Bonnie Docherty in a 2012 Human Rights Watch report. human-in-the-loop: a human must instigate the action of the weapon (in other words not fully autonomous). human-on-the-loop: a human may abort an action. human-out-of-the-loop: no human action is involved. === Standard used in US policy === Department of Defense Directive 3000.09 states that "Autonomous … weapons systems shall be designed to allow commanders and operators to exercise appropriate levels of human judgment over the use of force." However, as noted in the Bulletin of the Atomic Scientists, the policy requires that autonomous weapon systems that kill people or use kinetic force, selecting and engaging targets without further human intervention, be certified as compliant with "appropriate levels" and other standards, not that such weapon systems cannot meet these standards and are therefore forbidden. "Semi-autonomous" hunter-killers that autonomously identify and attack targets do not even require certification. Deputy Defense Secretary Robert O. Work said in 2016 that the Defense Department would "not delegate lethal authority to a machine to make a decision", but might need to reconsider this since "authoritarian regimes" may do so. In October 2016 President Barack Obama stated that early in his career he was wary of a future in which a US president making use of drone warfare could "carry on perpetual wars all over the world, and a lot of them covert, without any accountability or democratic debate". In the US, security-related AI has fallen under the purview of the National Security Commission on Artificial Intelligence since 2018. On October 31, 2019, the United States Department of Defense's Defense Innovation Board published the draft of a report outlining five principles for weaponized AI and making 12 recommendations for the ethical use of artificial intelligence by the Department of Defense that would ensure a human operator would always be able to look into the 'black box' and understand the kill-chain process. A major concern is how the report will be implemented. === Possible violations of ethics and international acts === Stuart Russell, professor of computer science from University of California, Berkeley stated the concern he has with LAWs is that his view is that it is unethical and inhumane. The main issue with this system is it is hard to distinguish between combatants and non-combatants. There is concern by some economists and legal scholars about whether LAWs would violate International Humanitarian Law, especially the principle of distinction, which requires the ability to discriminate combatants from non-combatants, and the principle of proportionality, which requires that damage to civilians be proportional to the military aim. This concern is often invoked as a reason to ban "killer robots" altogether - but it is doubtful that this concern can be an argument against LAWs that do not violate International Humanitarian Law. A 2021 report by the American Congressional Research Service states that "there are no domestic or international legal prohibitions on the development of use of LAWs," although it acknowledges ongoing talks at the UN Convention on Certain Conventional Weapons (CCW). LAWs are said by some to blur the boundaries of who is responsible for a particular killing. Philosopher Robert Sparrow argues that autonomous weapons are causally but not morally responsible, similar to child soldiers. In each case, he argues there is a risk of atrocities occurring without an appropriate subject to hold responsible, which violates jus in bell

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  Buddhism and artificial intelligence

  The relationship between Buddhist philosophy and artificial intelligence (AI) includes how principles such as the reduction of suffering and ethical responsibility may influence AI development. Buddhist scholars and philosophers have explored questions such as whether AI systems could be considered sentient beings under Buddhist definitions, and how Buddhist ethics might guide the design and application of AI technologies. Some Buddhist scholars, including Somparn Promta and Kenneth Einar Himma, have analyzed the ethical implications of AI, emphasizing the distinction between satisfying sensory desires and pursuing the reduction of suffering. Other thinkers, such as Thomas Doctor and colleagues, have proposed applying the Bodhisattva vow—a commitment to alleviate suffering for all sentient beings—as a guiding principle for AI system design. Buddhist scholars and ethicists have examined Buddhist ethical principles, such as nonviolence, in relation to AI, focusing on the need to ensure that AI technologies are not used to cause harm. == Context == === Sentient beings === A major goal in Buddhist philosophy is the removal of suffering for all sentient beings, an aspiration often referred to in the Bodhisattva vow. Discussions about artificial intelligence (AI) in relation to Buddhist principles have raised questions about whether artificial systems could be considered sentient beings or how such systems might be developed in ways that align with Buddhist concepts. Buddhists have varying opinions about AI sentience, but if AI systems are determined to be sentient under Buddhist definitions, their suffering would also need to be addressed and alleviated in accordance with the principles of Buddhist thought. == Buddhist principles in AI system design == === Nonviolence and AI === The broadest ethical concern is that artificial intelligence should align with the Buddhist principle of nonviolence. From this perspective, AI systems should not be designed or used to cause harm. === Instrumental and transcendental goals === Scholars Somparn Promta and Kenneth Einar Himma have argued that the advancement of artificial intelligence can only be considered instrumentally good, rather than good a priori, from a Buddhist perspective. They propose two main goals for AI designers and developers: to set ethical and pragmatic objectives for AI systems, and to fulfill these objectives in morally permissible ways. Promta and Himma identify two potential purposes for creating AI systems. The first is to fulfill our sensory desires and survival instincts, similar to other tools. They suggest that many AI developers implicitly prioritize this goal by focusing on technicalities rather than broader functionalities. The second, and more important goal according to Buddhist teachings, is to transcend these desires and instincts. In texts like the Brahmajāla Sutta and minor Malunkya Sutta, the Buddha emphasizes that sensory desires and survival instincts confine beings to suffering, and that eliminating suffering is the primary goal of human life. Promta and Himma argue that AI has the potential to assist humanity in transcending suffering by helping individuals overcome survival-driven instincts. === Intelligence as care === Thomas Doctor, Olaf Witkowski, Elizaveta Solomonova, Bill Duane, and Michael Levin propose redefining intelligence through the concept of "intelligence as care," and promote it as a slogan. Inspired by the Bodhisattva vow, they suggest this principle could guide AI system design. The Bodhisattva vow involves a formal commitment to alleviate suffering for all sentient beings, with four primary objectives: Liberating all beings from suffering. Extirpating all forms of suffering. Mastering endless techniques of practicing Dharma (Pali: dhammakkhandha, Sanskrit: dharmaskandha). Achieving ultimate enlightenment (Sanskrit: अनुत्तर सम्यक् सम्बोधि, Romanized: anuttara-samyak-saṃbodhi). This approach positions AI as a tool for exercising infinite care and alleviating stress and suffering for sentient beings. Doctor et al. emphasize that AI development should align with these altruistic principles.

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