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  • Pronunciation assessment

    Pronunciation assessment

    Automatic pronunciation assessment uses computer speech recognition to determine how accurately speech has been pronounced, instead of relying on a human instructor or proctor. It is also called speech verification, pronunciation evaluation, and pronunciation scoring. This technology is used to grade speech quality, for language testing, for computer-aided pronunciation teaching (CAPT) in computer-assisted language learning (CALL), for speaking skill remediation, and for accent reduction. Pronunciation assessment is different from dictation or automatic transcription, because instead of determining unknown speech, it verifies learners' pronunciation of known word(s), often from prior transcription of the same utterance; ideally scoring the intelligibility of the learners' speech. Sometimes pronunciation assessment evaluates the prosody of the learners' speech, such as intonation, pitch, tempo, rhythm, and syllable and word stress, although those are usually not essential for being understood in most languages. Pronunciation assessment is also used in reading tutoring, for example in products from Google, Microsoft, and Amira Learning. Automatic pronunciation assessment can also be used to help diagnose and treat speech disorders such as apraxia. == Intelligibility == Intelligibility refers to how well a learner's utterance is understood by a listener, rather than how much it sounds like a native speaker. This is separate from measures of fluency, such as so-called "Goodness of Pronunciation" (GoP) scores, which estimate how closely an utterance aligns with those of native speakers. Intelligibility is widely regarded as the most important communicative goal in pronunciation teaching and assessment. For example, in the Common European Framework of Reference for Languages (CEFR) assessment criteria for "overall phonological control", intelligibility outweighs formally correct pronunciation at all levels. Studies in applied linguistics have shown that accent reduction does not always increase intelligibility because listeners can often comprehend heavily accented speech without difficulty. Pronunciation assessment systems often rely on acoustic methods such as GoP which compare learner speech to reference models to produce phoneme-level scores, which are in turn aggregated to produce word and phrase scores. While these methods are effective for identifying deviations from native speakers' utterances, they do not effectively measure how understandable speech is to human listeners. Intelligibility is influenced by broader linguistic and contextual factors such as stress placement, speech rate, and coarticulation, which are not represented in purely segmental scores. The earliest work on pronunciation assessment avoided measuring genuine listener intelligibility, a shortcoming corrected in 2011 at the Toyohashi University of Technology, and included in the Versant high-stakes English fluency assessment from Pearson and mobile apps from 17zuoye Education & Technology, but still missing in 2023 products from Google Search, Microsoft, Educational Testing Service, Speechace, and ELSA. Assessing authentic listener intelligibility is essential for avoiding inaccuracies from accent bias, especially in high-stakes assessments; from words with multiple correct pronunciations; and from phoneme coding errors in machine-readable pronunciation dictionaries. In 2022, researchers found that some newer speech-to-text systems, based on end-to-end reinforcement learning to map audio signals directly into words, produce word and phrase confidence scores (from 10-25ms audio frame logit aggregation) closely correlated with genuine listener intelligibility. Others have been able to assess intelligibility using Levenshtein or dynamic time warping distance measures from Wav2Vec2 representation of good speech. Further work through 2025 has focused specifically on measuring intelligibility. A 2025 study of 42 pronunciation and speech coaching apps (32 mobile and 10 web) found that none offered intelligibility assessment. Instead, most provided only segmental and accent-focused scoring. About two-thirds of the apps provided some form of specific pronunciation feedback, usually with phonetic transcriptions, but accompanied by visual cues (such as animations of the vocal tract or the lips and tongue from the front) in only about 5% of the apps. Less than a third provided feedback on learner perception of exemplar speech. == Evaluation == Although there are as yet no industry-standard benchmarks for evaluating pronunciation assessment accuracy, researchers occasionally release evaluation speech corpuses for others to use for improving assessment quality. Such evaluation databases often emphasize formally unaccented pronunciation to the exclusion of genuine intelligibility evident from blinded listener transcriptions. As of mid-2025, state of the art approaches for automatically transcribing phonemes typically achieve an error rate of about 10% from known good speech. The International Speech Communication Association (ISCA) 2025 Workshop on Speech and Language Technology in Education (SLaTE) administered a Speak & Improve Challenge: Spoken Language Assessment and Feedback, introducing benchmarks for evaluating pronunciation assessment and remediation systems across languages, accents, and learner populations. The challenge emphasized cross-lingual generalization and alignment with human intelligibility judgments, for more robust and interpretable assessment systems. Ethical issues in pronunciation assessment are present in both human and automatic methods. Authentic validity, fairness, and mitigating bias in evaluation are all crucial. Diverse speech data should be included in automatic pronunciation assessment models. Combining human judgments, especially blinded transcriptions from a wide diversity of listeners, with automated feedback can improve accuracy and fairness. Second language learners benefit substantially from their use of widely available speech recognition systems for dictation, virtual assistants, and AI chatbots. In such systems, users naturally try to correct their own errors evident in speech recognition results that they notice. Such use improves their grammar and vocabulary development along with their pronunciation skills. The extent to which explicit pronunciation assessment and remediation approaches improve on such self-directed interactions remains an open question. Similarly, automatic dictation results have been shown to reflect intelligibility about as well as human scorers. == Recent developments == During 2021–22, a smartphone-based CAPT system was used to sense articulation through both audible and inaudible signals, providing feedback at the phoneme level. Some promising areas for improvement which were being developed in 2024 include articulatory feature extraction and transfer learning to suppress unnecessary corrections. Other interesting advances under development include "augmented reality" interfaces for mobile devices using optical character recognition to provide pronunciation training on text found in user environments. In 2024, audio multimodal large language models were first described as assessing pronunciation. That work has been carried forward by other researchers in 2025 who report positive results. Subsequently, researchers demonstrated pronunciation scoring by providing a language model with textual descriptions of speech, including the speech-to-text transcript, phoneme sequences, pauses, and phoneme sequence matching; this approach can achieve performance similar to multimodal LLMs that analyze raw audio while avoiding their higher computational cost. In 2025, the Duolingo English Test authors published a description of their pronunciation assessment method, purportedly built to measure intelligibility rather than accent imitation. While achieving a correlation of 0.82 with expert human ratings, very close to inter-rater agreement and outperforming alternative methods, the method is nonetheless based on experts' scores along the six-point CEFR common reference levels scale, instead of actual blinded listener transcriptions. Further promising work in 2025 includes assessment feedback aligning learner speech to synthetic utterances using interpretable features, identifying continuous spans of words for remediation feedback; synthesizing corrected speech matching learners' self-perceived voices, which they prefer and imitate more accurately as corrections; and streaming such interactions. On January 21, 2026, Educational Testing Service's TOEFL iBT high-stakes English language test, required by US university admissions and employers from English as a foreign language applicants more often than all other internet-based tests combined, changed its speaking assessments. While official rubrics claim that the new scoring will be based primarily on intelligibility, the new test's technical description indicates that it ju

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  • Cellular neural network

    Cellular neural network

    In computer science and machine learning, Cellular Neural Networks (CNN) or Cellular Nonlinear Networks (CNN) are a parallel computing paradigm similar to neural networks, with the difference that communication is allowed between neighbouring units only. Typical applications include image processing, analyzing 3D surfaces, solving partial differential equations, reducing non-visual problems to geometric maps, modelling biological vision and other sensory-motor organs. CNN is not to be confused with convolutional neural networks (also colloquially called CNN). == CNN architecture == Due to their number and variety of architectures, it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as neurons or cells. Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of Continuous-Time CNN (CT-CNN) processors, but can be discrete, as in the case of Discrete-Time CNN (DT-CNN) processors. Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically real-valued, but can be complex or even quaternion, i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells. === Chua-Yang CNN === In the original Chua-Yang CNN (CY-CNN) processor, the state of the cell was a weighted sum of the inputs and the output was a piecewise linear function. However, like the original perceptron-based neural networks, the functions it could perform were limited: specifically, it was incapable of modeling non-linear functions, such as XOR. More complex functions are realizable via Non-Linear CNN (NL-CNN) processors. Cells are defined in a normed gridded space like two-dimensional Euclidean geometry. However, the cells are not limited to two-dimensional spaces; they can be defined in an arbitrary number of dimensions and can be square, triangle, hexagonal, or any other spatially invariant arrangement. Topologically, cells can be arranged on an infinite plane or on a toroidal space. Cell interconnect is local, meaning that all connections between cells are within a specified radius (with distance measured topologically). Connections can also be time-delayed to allow for processing in the temporal domain. Most CNN architectures have cells with the same relative interconnects, but there are applications that require a spatially variant topology, i.e. Multiple-Neighborhood-Size CNN (MNS-CNN) processors. Also, Multiple-Layer CNN (ML-CNN) processors, where all cells on the same layer are identical, can be used to extend the capability of CNN processors. The definition of a system is a collection of independent, interacting entities forming an integrated whole, whose behavior is distinct and qualitatively greater than its entities. Although connections are local, information exchange can happen globally through diffusion. In this sense, CNN processors are systems because their dynamics are derived from the interaction between the processing units and not within processing units. As a result, they exhibit emergent and collective behavior. Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor. When the coupling laws are modeled by fuzzy logic, it is a fuzzy CNN. When these laws are modeled by computational verb logic, it becomes a computational verb CNN. Both fuzzy and verb CNNs are useful for modelling social networks when the local couplings are achieved by linguistic terms. == History == The idea of CNN processors was introduced by Leon Chua and Lin Yang in 1988. In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). Leon Chua is still active in CNN research and publishes many of his articles in the International Journal of Bifurcation and Chaos, of which he is an editor. Both IEEE Transactions on Circuits and Systems and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors. In 1993, Tamas Roska and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world. The multi-national effort was funded by the Office of Naval Research, the National Science Foundation, and the Hungarian Academy of Sciences, and researched by the Hungarian Academy of Sciences and the University of California. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology. === Literature === Two references are considered invaluable since they manage to organize the vast amount of CNN literature into a coherent framework: An overview by Valerio Cimagalli and Marco Balsi. The paper provides a concise intro to definitions, CNN types, dynamics, implementations, and applications. "Cellular Neural Networks and Visual Computing Foundations and Applications", written by Leon Chua and Tamas Roska, which provides examples and exercises. The book covers many different aspects of CNN processors and can serve as a textbook for a Masters or Ph.D. course. Other resources include The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature. The proceedings are available online, via IEEE Xplore, for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006. There was also a workshop held in Santiago de Composetela, Spain. Topics included theory, design, applications, algorithms, physical implementations and programming and training methods. For an understanding of the analog semiconductor based CNN technology, AnaLogic Computers has their product line, in addition to the published articles available on their homepage and their publication list. They also have information on other CNN technologies such as optical computing. Many of the commonly used functions have already been implemented using CNN processors. A good reference point for some of these can be found in image processing libraries for CNN based visual computers such as Analogic’s CNN-based systems. == Related processing architectures == CNN processors could be thought of as a hybrid between artificial neural network (ANN) and Continuous Automata (CA). === Artificial Neural Networks === The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, dynamical systems, and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. However, in CNN processors, connections are made locally, whereas in ANN, connections are global. For example, neurons in one layer are fully connected to another layer in a feed-forward NN and all the neurons are fully interconnected in Hopfield networks. In ANNs, the weights of interconnections contain information on the processing system’s previous state or feedback. But in CNN processors, the weights are used to determine the dynamics of the system. Furthermore, due to the high inter-connectivity of ANNs, they tend not exploit locality in either the data set or the processing and as a result, they usually are highly redundant systems that allow for robust, fault-tolerant behavior without catastrophic errors. A cross between an ANN and a CNN processor is a Ratio Memory CNN (RMCNN). In RMCNN processors, the cell interconnect is local and topologically invariant, but the weights are used to store

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  • GuideGeek

    GuideGeek

    GuideGeek is an AI-powered travel assistant that was launched by travel publisher Matador Network in April 2023 and is accessed by users through Instagram, WhatsApp and Facebook Messenger to plan itineraries or provide travel tips and recommendations. It uses generative artificial intelligence technology from OpenAI. Matador Network is a San Francisco-based digital media company and online travel publication with millions of monthly visitors and social media followers. == Features == Users message GuideGeek questions about travel and receive customized answers and itineraries that are pulled from ChatGPT in addition to over 1,000 additional travel-specific integrations such as live flight, hotel and vacation rental data. Travelers can specify their budget and needs to generate custom itineraries. GuideGeek is not an app and does not require the user to download anything, instead relying on messaging apps such as Instagram to connect users with the AI. GuideGeek is free to use, doesn't include ads, and doesn't sell user data. Matador Network has a team of staff members monitoring conversations to correct them if the AI makes a false statement; for example, one user incorrectly inputted “Crete Freeze” instead of “Crete, Greece”, and the AI made up a fictional soft serve company. Using a technique known as reinforcement learning from human feedback (RLHF), the accuracy of GuideGeek increased to 98%, according to Matador Network CEO, Ross Borden. == Destination partnerships == Matador Network is monetizing GuideGeek via white-label partnerships with tourism bureaus and destination marketing organizations (DMOs). As of March 2024, it had over a dozen such clients. Estes Park, Colorado, was one of the first DMOs to partner with Matador for a custom version of GuideGeek called “Rocky Mountain Roamer.” For Discover Greece, Matador created Pythia, a custom AI named after the high priestess of the Temple of Apollo at Delphi. As Borden explained to Travel + Leisure, “Visitors to the Discover Greece website will find Pythia in the bottom right corner, and they can converse with the AI like a friend who knows everything about Greece.” Other DMOs who have partnerships with GuideGeek include the Aruba Tourism Authority, Visit Reno Tahoe, Illinois Office of Tourism, and Tourism Richmond. == Awards == In recognition of GuideGeek, Fast Company named Matador Network to its 2024 list of Most Innovative Companies. Following growth driven by the launch of GuideGeek, Matador Network was ranked on the 2024 Inc. 5000 list of fastest-growing private companies in America. The 2024 Skift IDEA Awards recognized Matador Network as a finalist in the category of Best Use of AI for GuideGeek's customized AI for the travel industry. == Michael Motamedi experiment == Travel influencer and chef Michael Motamedi traveled the world with his wife Vanessa Salas and their 2-year-old daughter on a six-month trip (which was later extended to a full year) led by GuideGeek. The family started off in Morocco before heading to Spain and continuing east. The experiment became the basis of a web series called “No Fixed Address.” Motamedi used GuideGeek's AI to select countries the family visited, where they ate, and what sites they saw. Motamedi and Salas first tested out the technology in April 2023 while using the chatbot to plan a date night in Mexico City. GuideGeek provided speakeasy and drink recommendations as well as local history facts.

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  • AlphaGo

    AlphaGo

    AlphaGo is a computer program that plays the board game Go. It was developed by the London-based DeepMind Technologies, an acquired subsidiary of Google. Subsequent versions of AlphaGo became increasingly powerful, including a version that competed under the name Master. After retiring from competitive play, AlphaGo Master was succeeded by an even more powerful version known as AlphaGo Zero, which was completely self-taught without learning from human games. AlphaGo Zero was then generalized into a program known as AlphaZero, which played additional games, including chess and shogi. AlphaZero has in turn been succeeded by a program known as MuZero which learns without being taught the rules. AlphaGo and its successors use a Monte Carlo tree search algorithm to find its moves based on knowledge previously acquired by machine learning, specifically by an artificial neural network (a deep learning method) by extensive training, both from human and computer play. A neural network is trained to identify the best moves and the winning percentages of these moves. This neural network improves the strength of the tree search, resulting in stronger move selection in the next iteration. In October 2015, in a match against Fan Hui, the original AlphaGo became the first computer Go program to beat a human professional Go player without handicap on a full-sized 19×19 board. In March 2016, it beat Lee Sedol in a five-game match, the first time a computer Go program has beaten a 9-dan professional without handicap. Although it lost to Lee Sedol in the fourth game, Lee resigned in the final game, giving a final score of 4 games to 1 in favour of AlphaGo. In recognition of the victory, AlphaGo was awarded an honorary 9-dan by the Korea Baduk Association. The lead up and the challenge match with Lee Sedol were documented in a documentary film also titled AlphaGo, directed by Greg Kohs. The win by AlphaGo was chosen by Science as one of the Breakthrough of the Year runners-up on 22 December 2016. At the 2017 Future of Go Summit, the Master version of AlphaGo beat Ke Jie, the number one ranked player in the world at the time, in a three-game match, after which AlphaGo was awarded professional 9-dan by the Chinese Weiqi Association. After the match between AlphaGo and Ke Jie, DeepMind retired AlphaGo, while continuing AI research in other areas. The self-taught AlphaGo Zero achieved a 100–0 victory against the early competitive version of AlphaGo, and its successor AlphaZero was perceived as the world's top player in Go by the end of the 2010s. == History == Go is considered much more difficult for computers to win than other games such as chess, because its strategic and aesthetic nature makes it hard to directly construct an evaluation function, and its much larger branching factor makes it prohibitively difficult to use traditional AI methods such as alpha–beta pruning, tree traversal and heuristic search. Almost two decades after IBM's computer Deep Blue beat world chess champion Garry Kasparov in the 1997 match, the strongest Go programs using artificial intelligence techniques only reached about amateur 5-dan level, and still could not beat a professional Go player without a handicap. In 2012, the software program Zen, running on a four PC cluster, beat Masaki Takemiya (9p) twice at five- and four-stone handicaps. In 2013, Crazy Stone beat Yoshio Ishida (9p) at a four-stone handicap. According to DeepMind's David Silver, the AlphaGo research project was formed around 2014 to test how well a neural network using deep learning can compete at Go. AlphaGo represents a significant improvement over previous Go programs. In 500 games against other available Go programs, including Crazy Stone and Zen, AlphaGo running on a single computer won all but one. In a similar matchup, AlphaGo running on multiple computers won all 500 games played against other Go programs, and 77% of games played against AlphaGo running on a single computer. The distributed version in October 2015 was using 1,202 CPUs and 176 GPUs. === Match against Fan Hui === In October 2015, the distributed version of AlphaGo defeated the European Go champion Fan Hui, a 2-dan (out of 9 dan possible) professional, five to zero. This was the first time a computer Go program had beaten a professional human player on a full-sized board without handicap. The announcement of the news was delayed until 27 January 2016 to coincide with the publication of a paper in the journal Nature describing the algorithms used. === Match against Lee Sedol === AlphaGo played South Korean professional Go player Lee Sedol, ranked 9-dan, one of the best players at Go, with five games taking place at the Four Seasons Hotel in Seoul, South Korea on 9, 10, 12, 13, and 15 March 2016, which were video-streamed live. Out of five games, AlphaGo won four games and Lee won the fourth game which made him recorded as the only human player who beat AlphaGo in all of its 74 official games. AlphaGo ran on Google's cloud computing with its servers located in the United States. The match used Chinese rules with a 7.5-point komi, and each side had two hours of thinking time plus three 60-second byoyomi periods. The version of AlphaGo playing against Lee used a similar amount of computing power as was used in the Fan Hui match. The Economist reported that it used 1,920 CPUs and 280 GPUs. At the time of play, Lee Sedol had the second-highest number of Go international championship victories in the world after South Korean player Lee Chang-ho who kept the world championship title for 16 years. Since there is no single official method of ranking in international Go, the rankings may vary among the sources. While he was ranked top sometimes, some sources ranked Lee Sedol as the fourth-best player in the world at the time. AlphaGo was not specifically trained to face Lee nor was designed to compete with any specific human players. The first three games were won by AlphaGo following resignations by Lee. However, Lee beat AlphaGo in the fourth game, winning by resignation at move 180. AlphaGo then continued to achieve a fourth win, winning the fifth game by resignation. The prize was US$1 million. Since AlphaGo won four out of five and thus the series, the prize will be donated to charities, including UNICEF. Lee Sedol received $150,000 for participating in all five games and an additional $20,000 for his win in Game 4. In June 2016, at a presentation held at a university in the Netherlands, Aja Huang, one of the Deep Mind team, revealed that they had patched the logical weakness that occurred during the 4th game of the match between AlphaGo and Lee, and that after move 78 (which was dubbed the "divine move" by many professionals), it would play as intended and maintain Black's advantage. Before move 78, AlphaGo was leading throughout the game, but Lee's move caused the program's computing powers to be diverted and confused. Huang explained that AlphaGo's policy network of finding the most accurate move order and continuation did not precisely guide AlphaGo to make the correct continuation after move 78, since its value network did not determine Lee's 78th move as being the most likely, and therefore when the move was made AlphaGo could not make the right adjustment to the logical continuation. === Sixty online games === On 29 December 2016, a new account on the Tygem server named "Magister" (shown as 'Magist' at the server's Chinese version) from South Korea began to play games with professional players. It changed its account name to "Master" on 30 December, then moved to the FoxGo server on 1 January 2017. On 4 January, DeepMind confirmed that the "Magister" and the "Master" were both played by an updated version of AlphaGo, called AlphaGo Master. As of 5 January 2017, AlphaGo Master's online record was 60 wins and 0 losses, including three victories over Go's top-ranked player, Ke Jie, who had been quietly briefed in advance that Master was a version of AlphaGo. After losing to Master, Gu Li offered a bounty of 100,000 yuan (US$14,400) to the first human player who could defeat Master. Master played at the pace of 10 games per day. Many quickly suspected it to be an AI player due to little or no resting between games. Its adversaries included many world champions such as Ke Jie, Park Jeong-hwan, Yuta Iyama, Tuo Jiaxi, Mi Yuting, Shi Yue, Chen Yaoye, Li Qincheng, Gu Li, Chang Hao, Tang Weixing, Fan Tingyu, Zhou Ruiyang, Jiang Weijie, Chou Chun-hsun, Kim Ji-seok, Kang Dong-yun, Park Yeong-hun, and Won Seong-jin; national champions or world championship runners-up such as Lian Xiao, Tan Xiao, Meng Tailing, Dang Yifei, Huang Yunsong, Yang Dingxin, Gu Zihao, Shin Jinseo, Cho Han-seung, and An Sungjoon. All 60 games except one were fast-paced games with three 20 or 30 seconds byo-yomi. Master offered to extend the byo-yomi to one minute when playing with Nie Weiping in consideration of his age. After winning its 59th game Master revealed itse

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  • Kinematic chain

    Kinematic chain

    In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pairs and the surface contact joints critical to cams and gearing, called higher pairs. These joints are generally modeled as holonomic constraints. A kinematic diagram is a schematic of the mechanical system that shows the kinematic chain. The modern use of kinematic chains includes analysis of Linkages (mechanical), compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems. == Mobility formula == The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c = 6 − f. In the case of a hinge or slider, which are one-degree-of-freedom joints, have f = 1 and therefore c = 6 − 1 = 5. The result in general where d {\displaystyle d} is the degrees of freedom for the mobility of a kinematic chain formed from n moving links and j joints each with freedom fi, i = 1, 2, …, j, is given by M = d n − ∑ i = 1 j ( d − f i ) = d ( N − 1 − j ) + ∑ i = 1 j f i {\displaystyle M=dn-\sum _{i=1}^{j}(d-f_{i})=d(N-1-j)+\sum _{i=1}^{j}f_{i}} Where N is the total number of links and includes the fixed link. Spacial linkages used d = 6 {\displaystyle d=6} and planar linkages use d = 3 {\displaystyle d=3} . This result is known as the Chebychev–Grübler–Kutzbach criterion. == Analysis of kinematic chains == The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom. The constraint equations for a kinematic chain are obtained using rigid transformations [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations, [ T ] = [ Z 1 ] [ X 1 ] [ Z 2 ] [ X 2 ] ⋯ [ X n − 1 ] [ Z n ] , {\displaystyle [T]=[Z_{1}][X_{1}][Z_{2}][X_{2}]\cdots [X_{n-1}][Z_{n}],\!} where [T] is the transformation locating the end-link—notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain. Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph. Its geometrical form: how are neighbouring joints spatially connected to each other? Explanation Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system. == Synthesis of kinematic chains == The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory. Ferdinand Freudenstein is often called the father of modern kinematics for his contributions to the kinematic synthesis of linkages beginning in the 1950s. His use of the newly developed computer to solve Freudenstein's equation became the prototype of computer-aided design systems. This work has been generalized to the synthesis of spherical and spatial mechanisms.

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  • AlphaGeometry

    AlphaGeometry

    AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM) and a rule-based symbolic engine (Deductive Database Arithmetic Reasoning). It was developed by DeepMind, a subsidiary of Google. The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist. For comparison, the previous AI program, called Wu's method, managed to solve only 10 problems. DeepMind published a paper about AlphaGeometry in the peer-reviewed journal Nature on 17 January 2024. AlphaGeometry was featured in MIT Technology Review on the same day. Traditional geometry programs are symbolic engines that rely exclusively on human-coded rules to generate rigorous proofs, which makes them lack flexibility in unusual situations. AlphaGeometry combines such a symbolic engine with a specialized large language model trained on synthetic data of geometrical proofs. When the symbolic engine doesn't manage to find a formal and rigorous proof on its own, it solicits the large language model, which suggests a geometrical construct to move forward. However, it is unclear how applicable this method is to other domains of mathematics or reasoning, because symbolic engines rely on domain-specific rules and because of the need for synthetic data. == AlphaGeometry 2 == AlphaGeometry 2 is an improved version of AlphaGeometry, published on February 5, 2025. They added more features to the representation language to describe more geometry problems that involve movements of objects, and problems containing linear equations of angles, ratios, and distances. They targeted IMO geometry questions from 2000 to 2024. The expanded representation language allowed them to cover 88% of the questions. It uses Gemini finetuned on a synthetically generated dataset of problems and solutions in the representation language. The model is used for making auxiliary constructions like lines and points, to help the tree search. It is also used for autoformalization, i.e. converting a problem in English to a problem in the representation language.

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  • R2ML

    R2ML

    The REWERSE Rule Markup Language (R2ML) is developed by the REWERSE Working Group I1 for the purpose of rules interchange between different systems and tools. == Scope == An XML based rule language; Support for: integrity rules, derivation rules, production rules and reaction rules; Integrate functional languages (such as OCL) with Datalog languages (such as SWRL); Serialization and interchange of rules by specific software tools; Integrating rule reasoning with actual server side technologies; Deploying, publishing and communicating rules in a network. == Design principles == Modeled using MDA; Rule concepts defined with the help of MOF/UML; Required to accommodate: Web naming concepts, such as URIs and XML namespaces; The ontological distinction between objects and data values; The datatype concepts of RDF and user-defined datatypes; Actions (following OMG PRR submission); Events; EBNF abstract syntax; XML based concrete syntax validated by an XML Schema; Allowing different semantics for rules.

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  • Minimum intelligent signal test

    Minimum intelligent signal test

    The minimum intelligent signal test, or MIST, is a variation of the Turing test proposed by Chris McKinstry in which only boolean (yes/no or true/false) answers may be given to questions. The purpose of such a test is to provide a quantitative statistical measure of humanness, which may subsequently be used to optimize the performance of artificial intelligence systems intended to imitate human responses. McKinstry gathered approximately 80,000 propositions that could be answered yes or no, e.g.: Is Earth a planet? Was Abraham Lincoln once President of the United States? Is the sun bigger than my foot? Do people sometimes lie? He called these propositions Mindpixels. These questions test both specific knowledge of aspects of culture, and basic facts about the meaning of various words and concepts. It could therefore be compared with the SAT, intelligence testing and other controversial measures of mental ability. McKinstry's aim was not to distinguish between shades of intelligence but to identify whether a computer program could be considered intelligent at all. According to McKinstry, a program able to do much better than chance on a large number of MIST questions would be judged to have some level of intelligence and understanding. For example, on a 20-question test, if a program were guessing the answers at random, it could be expected to score 10 correct on average. But the probability of a program scoring 20 out of 20 correct by guesswork is only one in 220, i.e. one in 1,048,576; so if a program were able to sustain this level of performance over several independent trials, with no prior access to the propositions, it should be considered intelligent. == Discussion == McKinstry criticized existing approaches to artificial intelligence such as chatterbots, saying that his questions could "kill" AI programs by quickly exposing their weaknesses. He contrasted his approach, a series of direct questions assessing an AI's capabilities, to the Turing test and Loebner Prize method of engaging an AI in undirected typed conversation. Critics of the MIST have noted that it would be easy to "kill" a McKinstry-style AI too, due to the impossibility of supplying it with correct answers to all possible yes/no questions by ways of a finite set of human-generated Mindpixels: the fact that an AI can answer the question "Is the sun bigger than my foot?" correctly does not mean that it can answer variations like "Is the sun bigger than (my hand | my liver | an egg yolk | Alpha Centauri A | ...)" correctly, too. However, the late McKinstry might have replied that a truly intelligent, knowledgeable entity (on a par with humans) would be able to work out answers such as (yes | yes | yes | don't know | ...) by applying its knowledge of the relative sizes of the objects named. In other words, the MIST was intended as a test of AI, not as a suggestion for implementing AI. It can also be argued that the MIST is a more objective test of intelligence than the Turing test, a subjective assessment that some might consider to be more a measure of the interrogator's gullibility than of the machine's intelligence. According to this argument, a human's judgment of a Turing test is vulnerable to the ELIZA effect, a tendency to mistake superficial signs of intelligence for the real thing, anthropomorphizing the program. The response, suggested by Alan Turing's essay Computing Machinery and Intelligence, is that if a program is a convincing imitation of an intelligent being, it is in fact intelligent. The dispute is thus over what it means for a program to have "real" intelligence, and by what signs it can be detected. A similar debate exists in the controversy over great ape language, in which nonhuman primates are said to have learned some aspects of sign languages but the significance of this learning is disputed.

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  • Exercism

    Exercism

    Exercism is an online, open-source, free coding platform that offers code practice and mentorship on 77 different programming languages. == History == Software developer Katrina Owen created Exercism while she was teaching programming at Jumpstart Labs. The platform was developed as an internal tool to solve the problem of her own students not receiving feedback on the coding problems they were practicing. Katrina put the site publicly online and found that people were sharing it with their friends, practicing together and giving each other feedback. Within 12 months, the site had organically grown to see over 6,000 users had submitted code or feedback, and hundreds of volunteers contribute to the languages or tooling on the platform. In 2016, Jeremy Walker joined as co-founder and CEO. In July 2018, the site was relaunched with a new design and centered around a formal mentoring mode, at which point Katrina stepped back from day-to-day involvement. == Product == In the past, the website differed from other coding platforms by requiring students to download exercises through a command line client, solve the code on their own computers then submit the solution for feedback, at which point they can also view other's solutions to the same problem. Since its second relaunch in 2021, solutions can be edited and submitted through a web editor, though the command line client remains available. Exercism has tracks for 74 programming languages. Among the notable languages taught: ABAP, C, C#, C++, CoffeeScript, Delphi, Elm, Erlang, F#, Gleam, Go, Java, JavaScript, Julia, Kotlin, Objective-C, PHP, Python, Raku, Red, Ruby, Rust, Scala, Swift, and V (Vlang). In 2023, the site launched a "12 in 23" challenge for users to learn the basics of 12 different languages - one per month in 2023. == Open source == The Exercism codebase is open source. In April 2016, it consisted of 50 repositories including website code, API code, command-line code and, most of all, over 40 stand-alone repositories for different language tracks. As of February 2024 Exercism has 14,344 contributors, maintains 366 repositories, and 19,603 mentors.

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  • GermaNet

    GermaNet

    GermaNet is a semantic network for the German language. It relates nouns, verbs, and adjectives semantically by grouping lexical units that express the same concept into synsets and by defining semantic relations between these synsets. GermaNet is free for academic use, after signing a license. GermaNet shares much in common with the English WordNet and can be viewed as an online thesaurus or a light-weight ontology. GermaNet has been developed and maintained at the University of Tübingen since 1997 within the research group for General and Computational Linguistics. It has been integrated into the EuroWordNet, a multilingual lexical-semantic database. == Database == === Contents === GermaNet partitions the lexical space into a set of concepts that are interlinked by semantic relations. A semantic concept is modeled by a synset. A synset is a set of words (called lexical units) where all the words are taken to have the same or almost the same meaning. Thus, a synset is a set of synonyms grouped under one definition, or "gloss". In addition to the gloss, synsets are labeled with their syntactic function and accompanied by example sentences for each distinct meaning in the synset. Just as in WordNet, for each word category the semantic space is divided into a number of semantic fields closely related to major nodes in the semantic network: Ort, or "location", Körper, or "body", etc. As of version 20.0 (release November 2025), GermaNet contains: Synsets: 179438 Lexical units: 231500 Literals: 216517 1.29 lexical units per synset Number of conceptual relations: 194367 Number of lexical relations: 13602 (synonymy excluded) Number of split compounds: 130901 Number of Interlingual Index (ILI) records: 28561 Number of Wiktionary sense descriptions: 29539 === Format === All GermaNet data is stored in a PostgreSQL relational database. The database schema follows the internal structure of GermaNet: there are tables to store synsets, lexical units, conceptual and lexical relations, etc. GermaNet data is distributed both in this database format and as XML files. In the XML data, two types of files, one for synsets and the other for relations, represent all data available in the GermaNet database. == Interfaces == There are software libraries and APIs available for Java and Python. These programs are distributed under free-software licenses and provide easy access to all information in various versions of GermaNet. GermaNet Rover is an on-line application that can be used to search for synsets in GermaNet, explore the data associated with them, and calculate the semantic similarity of pairs of synsets. It features visualizations of the hypernym relation and advanced filtering options for synset searching. == Licenses == GermaNet 20.0 (released November 2025) can be distributed under one of the following types of license agreements: Academic Research License Agreement: for the purpose of research at academic institutions. There is no license fee for academic use. Licenses are not given to individual students, and those seeking a license are required to talk to an academic advisor. Research and Development License Agreement: applies to non-academic institutions and research consortia. To be used strictly for technology development and internal research. Commercial License Agreement: applies to non-academic institutions and commercial enterprises. It permits technology development and internal research, as well as giving the non-exclusive right to distribute and market any derived product or service. == Alternatives == Open-de-WordNet is a freely available alternative to GermaNet which is compatible with WordNet. == Linguistic applications == GermaNet has been used for a variety of applications, including: semantic analysis shallow recognition of implicit document structure compound analysis analyzing sectional preferences word sense disambiguation

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  • Personal knowledge base

    Personal knowledge base

    A personal knowledge base (PKB) is an electronic tool used by an individual to express, capture, and later retrieve personal knowledge. It differs from a traditional database in that it contains subjective material particular to the owner, that others may not agree with nor care about. Importantly, a PKB consists primarily of knowledge, rather than information; in other words, it is not a collection of documents or other sources an individual has encountered, but rather an expression of the distilled knowledge the owner has extracted from those sources or from elsewhere. The term personal knowledge base was mentioned as early as the 1980s, but the term came to prominence in the 2000s when it was described at length in publications by computer scientist Stephen Davies and colleagues, who compared PKBs on a number of different dimensions, the most important of which is the data model that each PKB uses to organize knowledge. == Data models == Davies and colleagues examined three aspects of the data models of PKBs: their structural framework, which prescribes rules about how knowledge elements can be structured and interrelated (as a tree, graph, tree plus graph, spatially, categorically, as n-ary links, chronologically, or ZigZag); their knowledge elements, or basic building blocks of information that a user creates and works with, and the level of granularity of those knowledge elements (such as word/concept, phrase/proposition, free text notes, links to information sources, or composite); and their schema, which involves the level of formal semantics introduced into the data model (such as a type system and related schemas, keywords, attribute–value pairs, etc.). Davies and colleagues also emphasized the principle of transclusion, "the ability to view the same knowledge element (not a copy) in multiple contexts", which they considered to be "pivotal" to an ideal PKB. They concluded, after reviewing many design goals, that the ideal PKB was still to come in the future. === Personal knowledge graph === In their publications on PKBs, Davies and colleagues discussed knowledge graphs as they were implemented in some software of the time. Later, other writers used the term personal knowledge graph (PKG) to refer to a PKB featuring a graph structure and graph visualization. However, the term personal knowledge graph is also used by software engineers to refer to the different subject of a knowledge graph about a person, in contrast to a knowledge graph created by a person in a PKB. == Software architecture == Davies and colleagues also differentiated PKBs according to their software architecture: file-based, database-based, or client–server systems (including Internet-based systems accessed through desktop computers and/or handheld mobile devices). == History == Non-electronic personal knowledge bases have probably existed in some form for centuries: Leonardo da Vinci's journals and notes are a famous example of the use of notebooks. Commonplace books, florilegia, annotated private libraries, and card files (in German, Zettelkästen) of index cards and edge-notched cards are examples of formats that have served this function in the pre-electronic age. Undoubtedly the most famous early formulation of an electronic PKB was Vannevar Bush's description of the "memex" in 1945. In a 1962 technical report, human–computer interaction pioneer Douglas Engelbart (who would later become famous for his 1968 "Mother of All Demos" that demonstrated almost all the fundamental elements of modern personal computing) described his use of edge-notched cards to partially model Bush's memex. == Examples == The following software applications have been used to build PKBs using various data models and architectures. The list includes software mentioned by Davies and colleagues in their 2005 paper, and additional software. Open source Compendium Haystack (MIT project) Joplin Logseq NoteCards Org-mode QOwnNotes TiddlyWiki Closed source Evernote Microsoft OneNote MindManager MyLifeBits Notion Obsidian Personal Knowbase PersonalBrain Roam Tinderbox

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  • Norm (artificial intelligence)

    Norm (artificial intelligence)

    Norms can be considered from different perspectives in artificial intelligence to create computers and computer software that are capable of intelligent behaviour. In artificial intelligence and law, legal norms are considered in computational tools to automatically reason upon them. In multi-agent systems (MAS), a branch of artificial intelligence (AI), a norm is a guide for the common conduct of agents, thereby easing their decision-making, coordination and organization. Since most problems concerning regulation of the interaction of autonomous agents are linked to issues traditionally addressed by legal studies, and since law is the most pervasive and developed normative system, efforts to account for norms in artificial intelligence and law and in normative multi-agent systems often overlap. == Artificial intelligence and law == With the arrival of computer applications into the legal domain, and especially artificial intelligence applied to it, logic has been used as the major tool to formalize legal reasoning and has been developed in many directions, ranging from deontic logics to formal systems of argumentation. The knowledge base of legal reasoning systems usually includes legal norms (such as governmental regulations and contracts), and as a consequence, legal rules are the focus of knowledge representation and reasoning approaches to automatize and solve complex legal tasks. Legal norms are typically represented into a logic-based formalism, such as deontic logic. Artificial intelligence and law applications using an explicit representation of norms range from checking the compliance of business processes and the automatic execution of smart contracts to legal expert systems advising people on legal matters. == Multi-agent systems == Norms in multi-agent systems may appear with different degrees of explicitness ranging from fully unambiguous written prescriptions to implicit unwritten norms or tacit emerging patterns. Computer scientists’ studies mirror this polarity. Explicit norms are typically investigated in formal logics (e.g. deontic logics and argumentation) to represent and reason upon them, leading eventually to architecture for cognitive agents, while implicit norms are accounted as patterns emerging from repeated interactions amongst agents (typically reinforced learning agents). Explicit and implicit norms can be used together to coordinate agents. Explicit norms are typically represented as a deontic statement that aims at regulating the life of software agents and the interactions among them. It can be an obligation, a permission or a prohibition, and is often represented with some dialect or extension of Deontic logic. At the opposite, implicit norms are social norms that are not written, and they usually emerge from the repetitive interactions of agents.

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  • TipTop Technologies

    TipTop Technologies

    TipTop Technologies is a real-time web and social search engine with a platform for semantic analysis of natural language. Tip-Top Search provides results capturing individual and group sentiment, opinions, and experiences there from the content of various sorts such as real-time messages from Twitter or consumer product reviews on Amazon.com. TipTop Technologies and ITC Infotech collaborated to create a search interface suitable for both enterprise and consumer applications. Tip-Top's products are part of the "emerging Web 3.0 applications which use semantic technologies to augment the underlying Web system's functionalities." Their main product is 360, an AI tool that incorporates multiple AI applications under one wing. Jonathan AlBright professor at Elon University, found videos generated by TipTop Technologies software on YouTube in his research into artificial intelligence, described it as AI-generated "fake news". Through semantic analysis of large data sets, TipTop gleaned behavioral insights from Tweets around events like Halloween, Thanksgiving, Holiday Gifting, the Super Bowl, and the Oscar Nominees for the Academy Awards coverage. Sentiment analysis, concept trend tracking, and real-time market research are other applications included in the TipTop Search product. TipTop's insight engine solves the problem of real-time data noise, and its ability to "sort the 'good tweets' from the 'bad tweets' when it comes to a product, service, or a region..." In addition, products like TipTop Shopping with customizable search widgets bring together consumer reviews, social search, and sentiment analysis enabling product comparisons across attributes like the overall value and aiding purchasing decisions through user-driven product tips and pits. TipTop Finance adds another complexity to real-time search results by incorporating corporate sentiment, company stock tickers, and social media into TipTop's existing social search platform. Additional success applying semantic technologies has been with polling, "if you compare these Gallup results with TipTop, a sentiment engine based on Twitter, the results are not way off. It does surprise you but it tells me that sentiment analysis in case of public opinion about a burning social issue or a famous personality is relatively easier." With the increasing amount of unstructured, opinion-oriented, and user-generated content available on the Web, TipTop's technology aims to make sense of all this data, and deliver it in a useful way for consumer and enterprise users alike. TipTop Technologies is a privately held company with its headquarters in the San Francisco Bay Area, and team members are located globally.

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  • Alec Radford

    Alec Radford

    Alec Radford is an American artificial intelligence researcher. == Biography == Radford grew up in Texas. He graduated from Cistercian Preparatory School in 2011, where he became an Eagle Scout, and dropped out of Olin College in August 2014, where he and fellow students Slater Victoroff, Diana Yuan, and Madison May had formed the startup Indico in their dorm room. In 2015, the quartet were joined by Luke Metz and the firm and the Facebook AI research lab in New York used generative adversarial networks to create realistic low pixel images. A demonstration of Indico's technology was used without proper attribution in an April 2016 demonstration by Nvidia chief executive Jensen Huang. Radford joined OpenAI around 2016, where he worked on natural-language processing. The following year, Radford trained a neural network on Amazon reviews. The model was fairly basic, with layers which allowed for human understanding. Upon exploring it, he saw that it had a special neuron linked to the sentiment of the reviews, which it had created on its own. This was a drastic improvement from previous neural networks that had analysed sentiment, because they had to be told to do so and specially trained on data that was explicitly labeled according to sentiment. This development made OpenAI chief scientist Ilya Sutskever consider that a future model, using more diverse language data, could map far more structures of meaning, eventually becoming a "learned core module" for superintelligence. In 2018, Radford was the lead author on OpenAI's seminal research paper on generative pre-trained transformers, which form the foundation of ChatGPT. At OpenAI, he worked on early GPT models, Whisper, a speech recognition model, and the image generator DALL-E. He left OpenAI in December 2024 to pursue independent research. Around March 2025, Radford joined Thinking Machines Lab as an advisor. He joined along with Bob McGrew who was previously the chief research officer of OpenAI. In April 2026, Radford, Nick Levine, and David Duvenaud released Talkie, an AI model trained on books, newspapers, scientific journals, patents, and case law published before December 31, 1930. When asked about the state of the world in 2026, it stated that one billion people would live in Europe, that London and New York would be connected by steamships that transit between the two in ten days, and "winter will be passed in Paris, and the summer in London."

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  • Quantum Artificial Intelligence Lab

    Quantum Artificial Intelligence Lab

    The Quantum Artificial Intelligence Lab (also called the Quantum AI Lab or QuAIL) is a joint initiative of NASA, Universities Space Research Association, and Google (specifically, Google Research) whose goal is to pioneer research on how quantum computing might help with machine learning and other difficult computer science problems. The lab is hosted at NASA's Ames Research Center. == History == The Quantum AI Lab was announced by Google Research in a blog post on May 16, 2013. At the time of launch, the Lab was using the most advanced commercially available quantum computer, D-Wave Two from D-Wave Systems. On October 10, 2013, Google released a short film describing the current state of the Quantum AI Lab. On October 18, 2013, Google announced that it had incorporated quantum physics into Minecraft. In January 2014, Google reported results comparing the performance of the D-Wave Two in the lab with that of classical computers. The results were ambiguous and provoked heated discussion on the Internet. On 2 September 2014, it was announced that the Google Quantum AI Lab, in partnership with UC Santa Barbara, would be launching an initiative to create quantum information processors based on superconducting electronics. On the 23rd of October 2019, the Quantum AI Lab announced in a paper that it had achieved quantum supremacy with their Sycamore processor. The claim of quantum supremacy achievement has since been debated, with a far more accurate simulation on a classical computer being possible in 2.5 days as a conservative estimate. == Present == On December 9, 2024, Google introduced the Willow processor, describing it as a "state-of-the-art quantum chip". Google claims that this new chip takes just five minutes to solve a problem that takes traditional supercomputers ten septillion years. However, experts say Willow is, for now, a largely experimental device.

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