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Quantum machine learning

Quantum machine learning (QML) is the study of quantum algorithms for machine learning. It often refers to quantum algorithms for machine learning tasks which analyze classical data, sometimes called quantum-enhanced machine learning. QML algorithms use qubits and quantum operations to try to improve the space and time complexity of classical machine learning algorithms. Hybrid QML methods involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. The term "quantum machine learning" is sometimes used to refer classical machine learning methods applied to data generated from quantum experiments (i.e. machine learning of quantum systems), such as learning the phase transitions of a quantum system or creating new quantum experiments. QML also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa. Furthermore, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory". == Machine learning with quantum computers == Quantum-enhanced machine learning refers to quantum algorithms that solve tasks in machine learning, thereby improving and often expediting classical machine learning techniques. Such algorithms typically require one to encode the given classical data set into a quantum computer to make it accessible for quantum information processing. Subsequently, quantum information processing routines are applied and the result of the quantum computation is read out by measuring the quantum system. For example, the outcome of the measurement of a qubit reveals the result of a binary classification task. While many proposals of QML algorithms are still purely theoretical and require a full-scale universal quantum computer to be tested, others have been implemented on small-scale or special purpose quantum devices. === Quantum associative memories and quantum pattern recognition === Early work on quantum associative memories has been done by Dan Ventura and Tony Martinez and by Carlo A. Trugenberger in the late 1990s and early 2000s. Associative (or content-addressable) memories are able to recognize stored content on the basis of a similarity measure, while random access memories are accessed by the address of stored information and not its content. As such they must be able to retrieve both incomplete and corrupted patterns, the essential machine learning task of pattern recognition. Typical classical associative memories store p patterns in the O ( n 2 ) {\displaystyle O(n^{2})} interactions (synapses) of a real, symmetric energy matrix over a network of n artificial neurons. The encoding is such that the desired patterns are local minima of the energy functional and retrieval is done by minimizing the total energy, starting from an initial configuration. Unfortunately, classical associative memories are severely limited by the phenomenon of cross-talk. When too many patterns are stored, spurious memories appear which quickly proliferate, so that the energy landscape becomes disordered and no retrieval is anymore possible. The number of storable patterns is typically limited by a linear function of the number of neurons, p ≤ O ( n ) {\displaystyle p\leq O(n)} . Quantum associative memories (in their simplest realization) store patterns in a unitary matrix U acting on the Hilbert space of n qubits. Retrieval is realized by the unitary evolution of a fixed initial state to a quantum superposition of the desired patterns with probability distribution peaked on the most similar pattern to an input. By its very quantum nature, the retrieval process is thus probabilistic. Because quantum associative memories are free from cross-talk, however, spurious memories are never generated. Correspondingly, they have a superior capacity than classical ones. The number of parameters in the unitary matrix U is O ( p n ) {\displaystyle O(pn)} . One can thus have efficient, spurious-memory-free quantum associative memories for any polynomial number of patterns. If the matrix U is encoded as a unique operator (as opposed as to a sequence of gates as in the circuit model), e.g. by an optical interferometer, the retrieval becomes efficient even for an exponential number of patterns. === Linear algebra simulation with quantum amplitudes === A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate the amplitudes of a quantum state with the inputs and outputs of computations. Since a state of n {\displaystyle n} qubits is described by 2 n {\displaystyle 2^{n}} complex amplitudes, this information encoding can allow for an exponentially compact representation. Intuitively, this corresponds to associating a discrete probability distribution over binary random variables with a classical vector. The goal of algorithms based on amplitude encoding is to formulate quantum algorithms whose resources grow polynomially in the number of qubits n {\displaystyle n} , which amounts to a logarithmic time complexity in the number of amplitudes and thereby the dimension of the input. Many QML algorithms in this category are based on variations of the quantum algorithm for linear systems of equations (colloquially called HHL, after the paper's authors) which, under specific conditions, performs a matrix inversion using an amount of physical resources growing only logarithmically in the dimensions of the matrix. One of these conditions is that a Hamiltonian which entry-wise corresponds to the matrix can be simulated efficiently, which is known to be possible if the matrix is sparse or low rank. For reference, any known classical algorithm for matrix inversion requires a number of operations that grows more than quadratically in the dimension of the matrix (e.g. O ( n 2.373 ) {\displaystyle O{\mathord {\left(n^{2.373}\right)}}} ), but they are not restricted to sparse matrices. Quantum matrix inversion can be applied to machine learning methods in which the training reduces to solving a linear system of equations, for example in least-squares linear regression, the least-squares version of support vector machines, and Gaussian processes. A crucial bottleneck of methods that simulate linear algebra computations with the amplitudes of quantum states is state preparation, which often requires one to initialise a quantum system in a state whose amplitudes reflect the features of the entire dataset. Although efficient methods for state preparation are known for specific cases, this step easily hides the complexity of the task. === Variational quantum algorithms (VQAs) === In a variational quantum algorithm, a classical computer optimizes the parameters used to prepare a quantum state, while a quantum computer is used to do the actual state preparation and measurement. VQAs are considered promising candidates for noisy intermediate-scale quantum computers. Variational quantum circuits (or parameterized quantum circuits) are a popular class of VQAs where the parameters are those used in a fixed quantum circuit. Researchers have studied VQCs to solve optimization problems and find the ground state energy of complex quantum systems, which were difficult to solve using a classical computer. === Quantum binary classifier === Pattern reorganization is one of the important tasks of machine learning, binary classification is one of the tools or algorithms to find patterns. Binary classification is used in supervised learning and in unsupervised learning. In QML, classical bits are converted to qubits and they are mapped to Hilbert space; complex value data are used in a quantum binary classifier to use the advantage of Hilbert space. By exploiting the quantum mechanic properties such as superposition, entanglement, interference the quantum binary classifier produces the accurate result in short period of time. === Quantum machine learning algorithms based on Grover search === Another approach to improving classical machine learning with quantum information processing uses amplitude amplification methods based on Grover's search algorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. These quantum routines can be employed for learning algorithms that translate into an unstructured search task, as can be done, for instance, in the case of the k-medians and the k-nearest neighbors algorithms. Other applications include quadratic speedups in the training of perceptrons. An e
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Emma Brunskill

Emma Patricia Brunskill is an American computer scientist. Her research combines machine learning with human–computer interaction by studying the effects of AI systems in human-centered applications including educational software and healthcare, and the theory of reinforcement learning in situations where mistakes impose high risks or costs. She is an associate professor of computer science at Stanford University, where she also holds a courtesy appointment in the Stanford Graduate School of Education and is an affiliate of the King Center on Global Development. == Education and career == Brunskill grew up in Seattle and Edmonds, Washington, and entered the University of Washington at age 15. She graduated magna cum laude in 2000, with a bachelor's degree in computer engineering and physics. A Rhodes Scholarship took her to Magdalen College, Oxford in England, where she received a master's degree in neuroscience in 2002. After a summer working in Rwanda, she became a graduate student of computer science at the Massachusetts Institute of Technology, where she completed her Ph.D. in 2009. Her doctoral dissertation, Compact parametric models for efficient sequential decision making in high-dimensional, uncertain domains, was supervised by Nicholas Roy. After working as an NSF Postdoctoral Research Fellow at the University of California, Berkeley, she joined Carnegie Mellon University (CMU) in 2011 as an assistant professor of computer science. She moved from CMU to Stanford University in 2017. == Recognition == Brunskill was a 2014 recipient of the National Science Foundation CAREER Award and a 2015 recipient of the Office of Naval Research Young Investigator Award. She was one of two alumni of the University of Washington's Paul G. Allen School of Computer Science and Engineering to be honored in 2020 by the school's Alumni Impact Awards. She was elected as a Fellow of the Association for the Advancement of Artificial Intelligence in 2025, "for significant contributions to the field of reinforcement learning, and applications for societal benefit, in particular AI for education".
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The Best Free AI Sales Assistant for Beginners

Comparing the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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Wolfgang Ketter

Wolfgang Ketter (born Traben-Trarbach, Germany, 1972) is Chaired Professor of Information Systems for a Sustainable Society at the University of Cologne. and a prominent scientist in the application of artificial intelligence, machine learning and intelligent agents in the design of smart markets, including demand response mechanisms and in particular automated auctions. He is a co-founder of the open energy system platform Power TAC, an automated retail electricity trading platform that simulates the performance of retail markets in an increasingly prosumer- and renewable-energy-influenced electricity landscape. == Career == === Advisory roles === Ketter is an advisor on the energy transition to the German government, in particular, the energy-intensive German state of North Rhine-Westphalia. He is also a fellow of the World Economic Forum and member of the WEF Global Council on Future Mobility and the Global New Mobility Coalition, contributing on the use of AI and machine learning to address issues arising from growth in electrification of energy such as the use of batteries as virtual power plants, the management of electric vehicle charging to prevent grid congestion, or the potential for peer-to-peer electricity trading. Ketter has also been an advisor for over a decade to the Port of Rotterdam on the design of energy cooperatives and energy trading platforms as well as one of the largest auction companies in the world, Royal FloraHolland, where his initial research led to a redesign of auction mechanisms and decision support systems. The cumulative research project team received the Association for Information Systems Impact Award in 2020 === Research === Ketter’s research is multidisciplinary, addressing the overlap of AI and ML in the economics of retail energy and mobility markets. The industry and policy applications of his research interconnect in large-scale projects such as the EU Smart city development project Ruggedised, for which the Erasmus University-based team's publication on the optimization of the City of Rotterdam's electric transit bus network was recognized with the Institute for Operations Research and the Management Sciences Daniel H. Wagner runner-up award. His research focuses on the use of competitive benchmarking and intelligent agents in virtual world simulations of retail energy markets as part of a smart grid. A small-scale version of the Power TAC project led to a publication on demand side management, 'A simulation of household behavior under variable prices' that has several hundred citations in publications representing a variety of scientific disciplines. Two of his publications in the Management Information Systems Quarterly journal and one in Energy Economics form the foundation for the current Power TAC platform. In 2016 and 2019 he was Chair of the Workshop on Information Technologies and Systems. Ketter is Coordinator of the Key Research Initiative Sustainable Smart Energy & Mobility at the University of Cologne, where he is a chaired Professor of Information Systems for a Sustainable Society. At the Rotterdam School of Management, Erasmus University, he is Professor of Next Generation Information Systems as well as Director of the Erasmus Centre for Future Energy Business and Academic Director of Smart Cities and Smart Energy at the Erasmus Centre of Data Analytics. He has been a visiting professor at the Haas School of Business and Berkeley Institute of Data Science, University of California at Berkeley in 2016 to 2017.
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Evolvability (computer science)

The term evolvability is a framework of computational learning introduced by Leslie Valiant in his paper of the same name. The aim of this theory is to model biological evolution and categorize which types of mechanisms are evolvable. Evolution is an extension of PAC learning and learning from statistical queries. == General framework == Let F n {\displaystyle F_{n}\,} and R n {\displaystyle R_{n}\,} be collections of functions on n {\displaystyle n\,} variables. Given an ideal function f ∈ F n {\displaystyle f\in F_{n}} , the goal is to find by local search a representation r ∈ R n {\displaystyle r\in R_{n}} that closely approximates f {\displaystyle f\,} . This closeness is measured by the performance Perf ⁡ ( f , r ) {\displaystyle \operatorname {Perf} (f,r)} of r {\displaystyle r\,} with respect to f {\displaystyle f\,} . As is the case in the biological world, there is a difference between genotype and phenotype. In general, there can be multiple representations (genotypes) that correspond to the same function (phenotype). That is, for some r , r ′ ∈ R n {\displaystyle r,r'\in R_{n}} , with r ≠ r ′ {\displaystyle r\neq r'\,} , still r ( x ) = r ′ ( x ) {\displaystyle r(x)=r'(x)\,} for all x ∈ X n {\displaystyle x\in X_{n}} . However, this need not be the case. The goal then, is to find a representation that closely matches the phenotype of the ideal function, and the spirit of the local search is to allow only small changes in the genotype. Let the neighborhood N ( r ) {\displaystyle N(r)\,} of a representation r {\displaystyle r\,} be the set of possible mutations of r {\displaystyle r\,} . For simplicity, consider Boolean functions on X n = { − 1 , 1 } n {\displaystyle X_{n}=\{-1,1\}^{n}\,} , and let D n {\displaystyle D_{n}\,} be a probability distribution on X n {\displaystyle X_{n}\,} . Define the performance in terms of this. Specifically, Perf ⁡ ( f , r ) = ∑ x ∈ X n f ( x ) r ( x ) D n ( x ) . {\displaystyle \operatorname {Perf} (f,r)=\sum _{x\in X_{n}}f(x)r(x)D_{n}(x).} Note that Perf ⁡ ( f , r ) = Prob ⁡ ( f ( x ) = r ( x ) ) − Prob ⁡ ( f ( x ) ≠ r ( x ) ) . {\displaystyle \operatorname {Perf} (f,r)=\operatorname {Prob} (f(x)=r(x))-\operatorname {Prob} (f(x)\neq r(x)).} In general, for non-Boolean functions, the performance will not correspond directly to the probability that the functions agree, although it will have some relationship. Throughout an organism's life, it will only experience a limited number of environments, so its performance cannot be determined exactly. The empirical performance is defined by Perf s ⁡ ( f , r ) = 1 s ∑ x ∈ S f ( x ) r ( x ) , {\displaystyle \operatorname {Perf} _{s}(f,r)={\frac {1}{s}}\sum _{x\in S}f(x)r(x),} where S {\displaystyle S\,} is a multiset of s {\displaystyle s\,} independent selections from X n {\displaystyle X_{n}\,} according to D n {\displaystyle D_{n}\,} . If s {\displaystyle s\,} is large enough, evidently Perf s ⁡ ( f , r ) {\displaystyle \operatorname {Perf} _{s}(f,r)} will be close to the actual performance Perf ⁡ ( f , r ) {\displaystyle \operatorname {Perf} (f,r)} . Given an ideal function f ∈ F n {\displaystyle f\in F_{n}} , initial representation r ∈ R n {\displaystyle r\in R_{n}} , sample size s {\displaystyle s\,} , and tolerance t {\displaystyle t\,} , the mutator Mut ⁡ ( f , r , s , t ) {\displaystyle \operatorname {Mut} (f,r,s,t)} is a random variable defined as follows. Each r ′ ∈ N ( r ) {\displaystyle r'\in N(r)} is classified as beneficial, neutral, or deleterious, depending on its empirical performance. Specifically, r ′ {\displaystyle r'\,} is a beneficial mutation if Perf s ⁡ ( f , r ′ ) − Perf s ⁡ ( f , r ) ≥ t {\displaystyle \operatorname {Perf} _{s}(f,r')-\operatorname {Perf} _{s}(f,r)\geq t} ; r ′ {\displaystyle r'\,} is a neutral mutation if − t < Perf s ⁡ ( f , r ′ ) − Perf s ⁡ ( f , r ) < t {\displaystyle -t<\operatorname {Perf} _{s}(f,r')-\operatorname {Perf} _{s}(f,r) 0 {\displaystyle \epsilon >0\,} , for all ideal functions f ∈ F n {\displaystyle f\in F_{n}} and representations r 0 ∈ R n {\displaystyle r_{0}\in R_{n}} , with probability at least 1 − ϵ {\displaystyle 1-\epsilon \,} , Perf ⁡ ( f , r g ( n , 1 / ϵ ) ) ≥ 1 − ϵ , {\displaystyle \operatorname {Perf} (f,r_{g(n,1/\epsilon )})\geq 1-\epsilon ,} where the sizes of neighborhoods N ( r ) {\displaystyle N(r)\,} for r ∈ R n {\displaystyle r\in R_{n}\,} are at most p ( n , 1 / ϵ ) {\displaystyle p(n,1/\epsilon )\,} , the sample size is s ( n , 1 / ϵ ) {\displaystyle s(n,1/\epsilon )\,} , the tolerance is t ( 1 / n , ϵ ) {\displaystyle t(1/n,\epsilon )\,} , and the generation size is g ( n , 1 / ϵ ) {\displaystyle g(n,1/\epsilon )\,} . F {\displaystyle F\,} is evolvable over D {\displaystyle D\,} if it is evolvable by some R {\displaystyle R\,} over D {\displaystyle D\,} . F {\displaystyle F\,} is evolvable if it is evolvable over all distributions D {\displaystyle D\,} . == Results == The class of conjunctions and the class of disjunctions are evolvable over the uniform distribution for short conjunctions and disjunctions, respectively. The class of parity functions (which evaluate to the parity of the number of true literals in a given subset of literals) are not evolvable, even for the uniform distribution. Evolvability implies PAC learnability.
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Peter Flach

Pieter "Peter" Adriaan Flach (born 8 April 1961, Sneek) is a Dutch computer scientist and a Professor of Artificial Intelligence in the Department of Computer Science at the University of Bristol. He is author of the acclaimed Simply Logical: Intelligent Reasoning by Example (John Wiley, 1994) and Machine Learning: the Art and Science of Algorithms that Make Sense of Data (Cambridge University Press, 2012). == Education == Flach received an MSc Electrical Engineering from Universiteit Twente in 1987 and a PhD in Computer Science from Tilburg University in 1995. == Research == Flach's research interests are in data mining and machine learning.
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Lillian Lee (computer scientist)

Lillian Lee is a computer scientist whose research involves natural language processing, sentiment analysis, and computational social science. She is a professor of computer science and information science at Cornell University, and co-editor-in-chief of the journal Transactions of the Association for Computational Linguistics. == Education == Lee graduated from Cornell University in 1993 with an undergraduate degree in math and science. She completed her Ph.D. at Harvard University in 1997. Her dissertation, Similarity-Based Approaches to Natural Language Processing, was supervised by Stuart M. Shieber. == Career == Lee has been a member of the Cornell faculty since 1997. == Recognition == Lee has been a fellow of the Association for the Advancement of Artificial Intelligence since 2013, and of the Association for Computational Linguistics since 2017. Lee was elected as an ACM Fellow in 2018 for "contributions to natural language processing, sentiment analysis, and computational social science".
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Marius Lindauer

Marius Lindauer (born December 25, 1985, in Berlin, Germany) is a German computer scientist and professor of machine learning at the institute of artificial intelligence of the Leibniz University Hannover. He is known for his research on Automated Machine Learning and other meta-algorithmic approaches. == Life == Marius Lindauer studied computer science at the University of Potsdam from 2005 to 2010. Under the supervision of Torsten Schaub and Holger Hoos, he received his Dr. rer. nat. at the University of Potsdam in 2015. In 2014, he joined the Machine Learning research lab led by Frank Hutter as the first postdoctoral researcher and helped to build up the group. He then joined the Leibniz University Hannover as a professor in 2019 to lead the Machine learning research lab. He founded the Institute of Artificial Intelligence at the Leibniz University Hannover in 2022. Additionally, he is the co-head of the automl.org research group, automl.space community effort, and co-founder of the COSEAL research network, where he currently serves as an advisory board member. He is also a supporting member of CLAIRE, and a member of ELLIS. His research is published in renowned journals and conferences. == Achievements == During his Ph.D., Marius won several international competitions in the fields of solving hard combinatorial optimization problems, including 1st place in the NP-track of the answer set programming competition 2011 with claspfolio, the Hard Combinatorial SAT+UNSAT of the SAT challenge 2012 with clasp-crafted and two tracks of the configurable SAT solver challenge 2013 with clasp-cssc. During his PostDoc and later on, he was involved in winning tracks of the first and second AutoML challenge with auto-sklearn and the black-box optimization challenge for machine learning at NeurIPS'20. == Research Directions == Marius has delved into many research topics, all of which are unified under the umbrella of automating parts of the Machine Learning pipeline. His research touches many different aspects: Hyperparameter Optimization Multi-Fidelity Optimization Automated Reinforcement Learning Interactive AutoML Green AutoML Explainable AutoML
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Poop Map

Poop Map is a social app where users can track on a map where and when they defecate. In addition to logging location and time of each bowel movement, users can also add a photo, "like" other users' logs, and rate each account. The social elements of the app allow for groups of users to create a competitive league. Certain behaviors unlock achievements in-app. == Development == The app was created by app developer Nino Uzelac. It was launched in July 2013. == Popularity == The app charted at number one on the Apple App Store charts in 2021 after going viral on TikTok. As of September 2024, the app has a 4.8 rating on the App Store and more than 58,000 ratings. It also has more than one million downloads on the Google Play Store. Poop Map is notably popular among hikers, and has been written about in the outdoors magazine Outside.
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AI Customer-support Bots: Free vs Paid (2026)

Curious about the best AI customer-support bot? An AI customer-support bot is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI customer-support bot slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Top 10 AI Essay Writers Compared (2026)

Curious about the best AI essay writer? An AI essay writer is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI essay writer slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Jared Kaplan

Jared Daniel Kaplan is a theoretical physicist and artificial intelligence researcher. He is an associate professor in the Johns Hopkins University Department of Physics & Astronomy, and a co-founder and chief science officer of Anthropic. == Education == Kaplan attended the Illinois Mathematics and Science Academy during high school. He received a bachelor's degree in physics and mathematics from Stanford University and a PhD in physics from Harvard University. His doctoral thesis is titled Aspects of holography, advised by Nima Arkani-Hamed. == Academic career and physics research == Kaplan’s research interests include quantum gravity, holography (AdS/CFT), conformal field theory, and related topics in particle physics and cosmology. He worked as a postdoctoral fellow at SLAC and Stanford University and has been a professor at Johns Hopkins University since 2012. == Machine learning research == Kaplan joined OpenAI in 2019 as a researcher, where he co-authored Scaling Laws for Neural Language Models (2020), which reported that empirically, the performance of language models steadily improves with their size and the amount of data and compute used for training. He is also a co-author of Language Models are Few-Shot Learners (2020), which introduced GPT-3. At the company, he was also involved in the development of Codex. == Anthropic == Kaplan co-founded Anthropic and serves as its chief science officer. In October 2024, Anthropic announced that Kaplan would serve as the company's "Responsible Scaling Officer", overseeing its responsible scaling policy (RSP). In this role, Kaplan determines the safety assessments and precautions to adopt before model release. In December 2025, The Guardian published an interview with Kaplan about AI autonomy and recursive self-improvement timelines. == Honors and recognition == Kaplan was a Hertz Fellow (2005). He has also received a Sloan Research Fellowship and an NSF CAREER award (PHY-1454083). == Selected works == Scaling Laws for Neural Language Models (2020). Language Models are Few-Shot Learners (2020). A Natural Language for AdS/CFT Correlators (2011). == Personal life == As of 2026, Forbes estimated Kaplan's net worth at $3.7 billion. He lives in Pacifica, California, and has a son.
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Knowledge as a service

Knowledge as a service (KaaS) is a computing service that delivers information to users, backed by a knowledge model, which might be drawn from a number of possible models based on decision trees, association rules, or neural networks. A knowledge as a service provider responds to knowledge requests from users through a centralised knowledge server, and provides an interface between users and data owners. KaaS is one of several cloud computing-dependent business models in which computer resources are sold on an on-demand and pay-as-you-use basis. == Overview == At the International Semantic Web Conference 2019, it was described how knowledge can be made live and evolve on the web allowing users to learn directly from elaborated knowledge, now appearing in the form of knowledge graphs. KaaS appear when knowledge graphs are accessed via services This is opposed to DaaS which might "compute large volumes of data; integrate and analyzes that data; and publish it in real-time, using Web service APIs" (from Data as a Service) where the KaaS is able to exploit context - both the context of the user in relation to their information requests of the KaaS (where and when they make the request) and also the context of the information in relation to some objective or purpose of the users either understood by the KaaS automatically or indicated to it by the user. == Differentiating knowledge from data == Conceptual models that make such a differentiation such as the so-called DIKW pyramid have existed for perhaps more than 40 years (see a 1974 journal article about this) however definitions are not stable and universally accepted (see the discussion about the conceptualizations of DIKW within the DIKW Wikipedia article that question value of wisdom). The knowledge component of DIKW is generally agreed to be an elusive concept which is difficult to define, however Rowley 2007, in a well known student textbook differentiated knowledge from data by stating that knowledge is "defined with reference to information" and that it contains more than just facts but also "beliefs and expectations". In relation to knowledge graphs, knowledge may be additional content they provide over and above pure data which is the definition of the categories, properties and relations between the concepts, data and entities that substantiate one, many or all domains of discourse (see the definition of Ontology). The ability to represent "beliefs and expectations", or other forms of not so straightforwardly explicit knowledge is an on-going area of improvement in information sciences (see Tacit knowledge) and, with relation to KaaS, the establishment of recent informatics mechanics to do so it critical to the legitimacy of KaaS as it is differentiated from just value-added DaaS. Knowledge graphs' ability to represent context via the definition of the categories, properties and relations between the concepts, data and entities that substantiate one, many or all domains of discourse that they provide (see the definition of Ontology) has led to the idea that supplying access to KNs might be a required competency of a KaaS. == Delivery of knowledge == Much service-delivered content is dependent on a session to provide much of the context that the user (client) needs to understand answers to questions. For example, using current HTTP internet protocols, a GET request to retrieve information identified by a URI, such as a web page, a client (a human or a machine) may have access information supplied automatically to enable that client to bypass paywalls or other content access controls. Such context, in this case about the client's information access allowances, can alter the information provided. In a logical extension to this internet protocols example, a server would receive from the client, either manually or automatically, a full context which would be information about the situation the client is in and this would allow the server to best interpret the client's request. Current internet protocols allow for formats, languages and related preferences to be expressed by clients but make no mention of what a client already knows and what they may understand. The recent Content Negotiation by Profile proposes additions to both the HTTP internet protocols and related services that allow clients to also request information - a response from the server - that accords with an identified information model. This then allows clients to indicate not just formats and languages that they understand (technically that they prefer) but also domains of discourse that that do, which is a step towards comprehensive client context provision.
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AI Presentation Makers: Free vs Paid (2026)

Curious about the best AI presentation maker? An AI presentation maker is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI presentation maker slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Hapax legomenon

In corpus linguistics, a hapax legomenon ( also or ; pl. hapax legomena; sometimes abbreviated to hapax, plural hapaxes) is a word or an expression that occurs only once within a context: either in the written record of an entire language, in the works of an author, or in a single text. The term is also sometimes used to describe a word that occurs in just one of an author's works but more than once in that particular work. Hapax legomenon is a transliteration of Greek ἅπαξ λεγόμενον, meaning "said once". The related terms dis legomenon, tris legomenon, and tetrakis legomenon respectively (, , ) refer to double, triple, or quadruple occurrences, but are far less commonly used. Hapax legomena are quite common, as predicted by Zipf's law, which states that the frequency of any word in a corpus is inversely proportional to its rank in the frequency table. For large corpora, about 40% to 60% of the words are hapax legomena, and another 10% to 15% are dis legomena. Thus, in the Brown Corpus of American English, about half of the 50,000 distinct words are hapax legomena within that corpus. Hapax legomenon refers to the appearance of a word or an expression in a body of text, not to either its origin or its prevalence in speech. It thus differs from a nonce word, which may never be recorded, may find currency and may be widely recorded, or may appear several times in the work which coins it, and so on. == Significance == Hapax legomena in ancient texts are usually difficult to decipher, since it is easier to infer meaning from multiple contexts than from just one. For example, many of the remaining undeciphered Mayan glyphs are hapax legomena, and Biblical (particularly Hebrew; see § Hebrew) hapax legomena sometimes pose problems in translation. Hapax legomena also pose challenges in natural language processing. Some scholars consider Hapax legomena useful in determining the authorship of written works. P. N. Harrison, in The Problem of the Pastoral Epistles (1921) made hapax legomena popular among Bible scholars, when he argued that there are considerably more of them in the three Pastoral Epistles than in other Pauline Epistles. He argued that the number of hapax legomena in a putative author's corpus indicates his or her vocabulary and is characteristic of the author as an individual. Harrison's theory has faded in significance due to a number of problems raised by other scholars. For example, in 1896, W. P. Workman found the following numbers of hapax legomena in each Pauline Epistle: At first glance, the last three totals (for the Pastoral Epistles) are not out of line with the others. To take account of the varying length of the epistles, Workman also calculated the average number of hapax legomena per page of the Greek text, which ranged from 3.6 to 13, as summarized in the diagram on the right. Although the Pastoral Epistles have more hapax legomena per page, Workman found the differences to be moderate in comparison to the variation among other Epistles. This was reinforced when Workman looked at several plays by Shakespeare, which showed similar variations (from 3.4 to 10.4 per page of Irving's one-volume edition), as summarized in the second diagram on the right. Apart from author identity, there are several other factors that can explain the number of hapax legomena in a work: text length: this directly affects the expected number and percentage of hapax legomena; the brevity of the Pastoral Epistles also makes any statistical analysis problematic. text topic: if the author writes on different subjects, of course many subject-specific words will occur only in limited contexts. text audience: if the author is writing to a peer rather than a student, or their spouse rather than their employer, again quite different vocabulary will appear. time: over the course of years, both the language and an author's knowledge and use of language will change. In the particular case of the Pastoral Epistles, all of these variables are quite different from those in the rest of the Pauline corpus, and hapax legomena are no longer widely accepted as strong indicators of authorship; those who reject Pauline authorship of the Pastorals rely on other arguments. There are also subjective questions over whether two forms amount to "the same word": dog vs. dogs, clue vs. clueless, sign vs. signature; many other gray cases also arise. The Jewish Encyclopedia points out that, although there are 1,500 hapaxes in the Hebrew Bible, only about 400 are not obviously related to other attested word forms. A final difficulty with the use of hapax legomena for authorship determination is that there is considerable variation among works known to be by a single author, and disparate authors often show similar values. In other words, hapax legomena are not a reliable indicator. Authorship studies now usually use a wide range of measures to look for patterns rather than relying upon single measurements. == Computer science == In the fields of computational linguistics and natural language processing (NLP), esp. corpus linguistics and machine-learned NLP, it is common to disregard hapax legomena (and sometimes other infrequent words), as they are likely to have little value for computational techniques. This disregard has the added benefit of significantly reducing the memory use of an application, since, by Zipf's law, many words are hapax legomena. == Examples == The following are some examples of hapax legomena in languages or corpora. === Arabic === In the Qurʾān: The proper nouns Iram (Q 89:7, Iram of the Pillars), Bābil (Q 2:102, Babylon), Bakka(t) (Q 3:96, Bakkah), Jibt (Q 4:51), Ramaḍān (Q 2:185, Ramadan), ar-Rūm (Q 30:2, Byzantine Empire), Tasnīm (Q 83:27), Qurayš (Q 106:1, Quraysh), Majūs (Q 22:17, Magian/Zoroastrian), Mārūt (Q 2:102, Harut and Marut), Makka(t) (Q 48:24, Mecca), Nasr (Q 71:23), (Ḏū) an-Nūn (Q 21:87) and Hārūt (Q 2:102, Harut and Marut) occur only once. zanjabīl (زَنْجَبِيل – ginger) is a Qurʾānic hapax (Q 76:17). zamharīr (زَمْهَرِيرًۭ) is a Qurʾānic hapax (Q 76:13), usually glossed as referring to extreme cold. The epitheton ornans aṣ-ṣamad (الصَّمَد – the One besought) is a Qurʾānic hapax (Q 112:2). ṭūd (طُودْ - mountain) is a Qurʾānic hapax (Q 26:63). === Chinese and Japanese === Classical Chinese and Japanese literature contains many Chinese characters that feature only once in the corpus, and their meaning and pronunciation has often been lost. Known in Japanese as kogo (孤語), literally "lonely characters", these can be considered a type of hapax legomenon. For example, the Classic of Poetry (c. 1000 BC) uses the character 篪 exactly once in the verse 「伯氏吹塤, 仲氏吹篪」, and it was only through the discovery of a description by Guo Pu (276–324 AD) that the character could be associated with a specific type of ancient flute. === English === It is fairly common for authors to "coin" new words to convey a particular meaning or for the sake of entertainment, without any suggestion that they are "proper" words. For example, P.G. Wodehouse and Lewis Carroll frequently coined novel words. Indexy, below, appears to be an example of this. Flother, as a synonym for snowflake, is a hapax legomenon of written English found in a manuscript entitled The XI Pains of Hell (c. 1275). Honorificabilitudinitatibus is a hapax legomenon of Shakespeare's works, coming from Erasmus' Adagia Indexy, in Bram Stoker's Dracula, used as an adjective to describe a situational state with no other further use in the language: "If that man had been an ordinary lunatic I would have taken my chance of trusting him; but he seems so mixed up with the Count in an indexy kind of way that I am afraid of doing anything wrong by helping his fads." Manticratic, meaning "of the rule by the Prophet's family or clan", was apparently invented by T. E. Lawrence and appears once in Seven Pillars of Wisdom. Nortelrye, a word for "education", occurs only once in Chaucer's The Reeve's Tale. Sassigassity, perhaps with the meaning of "audacity", occurs only once in Dickens's short story "A Christmas Tree". Slæpwerigne, "sleep-weary", occurs exactly once in the Old English corpus, in the Exeter Book. There is debate over whether it means "weary with sleep" or "weary for sleep". === German === The name of the 9th-century poem Muspilli is a back-formation from "muspille", Old High German hapax legomenon of unclear meaning only found in this text (see Muspilli § Etymology for discussion). === Ancient Greek === According to classical scholar Clyde Pharr, "the Iliad has 1,097 hapax legomena, while the Odyssey has 868". Others have defined the term differently, however, and count as few as 303 in the Iliad and 191 in the Odyssey. panaōrios (παναώριος), ancient Greek for "very untimely", is one of many words that occur only once in the Iliad. The Greek New Testament contains 686 local hapax legomena, which are sometimes called "New Testament hapaxes". 62 of these occur in 1 Peter and 54 occur in 2 Peter
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