AI Assistant Gemini

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  Cybernetic Serendipity

  Cybernetic Serendipity was an exhibition of cybernetic art curated by Jasia Reichardt, shown at the Institute of Contemporary Arts, London, England, from 2 August to 20 October 1968, and then toured across the United States. Two stops in the United States were the Corcoran Annex (Corcoran Gallery of Art), Washington, D.C., from 16 July to 31 August 1969, and the newly opened Exploratorium in San Francisco, from 1 November to 18 December 1969. == Content == One part of the exhibition was concerned with algorithms and devices for generating music. Some exhibits were pamphlets describing the algorithms, whilst others showed musical notation produced by computers. Devices made musical effects and played tapes of sounds made by computers. Peter Zinovieff lent part of his studio equipment - visitors could sing or whistle a tune into a microphone and his equipment would improvise a piece of music based on the tune. Another part described computer projects such as Gustav Metzger's self-destructive Five Screens With Computer, a design for a new hospital, a computer programmed structure, and dance choreography. The machines and installations were a very noticeable part of the exhibition. Gordon Pask produced a collection of large mobiles (Colloquy of Mobiles (1968)) with interacting parts that let the viewers join in the conversation. Many machines formed kinetic environments or displayed moving images. Bruce Lacey contributed his radio-controlled robots and a light-sensitive owl. Nam June Paik was represented by Robot K-456 and televisions with distorted images. Jean Tinguely provided two of his painting machines. Edward Ihnatowicz's biomorphic hydraulic ear (Sound Activated Mobile (SAM, 1968)) turned toward sounds and John Billingsley's Albert 1967 turned to face light. Wen-Ying Tsai presented his interactive cybernetic sculptures of vibrating stainless-steel rods, stroboscopic light, and audio feedback control. Several artists exhibited machines that drew patterns that the visitor could take away, or involved visitors in games. Cartoonist Rowland Emett designed the mechanical computer Forget-me-not, which was commissioned by Honeywell. Another section explored the computer's ability to produce text - both essays and poetry. Different programs produced Haiku, children's stories, and essays. One of the first computer-generated poems, by Alison Knowles and James Tenney, was included in the exhibition and catalogue. Computer-generated movies were represented by John Whitney's Permutations and a Bell Labs movie on their technology for producing movies. Some samples included images of tesseracts rotating in four dimensions, a satellite orbiting the Earth, and an animated data structure. Computer graphics were also represented, including pictures produced on cathode ray oscilloscopes and digital plotters. There was a variety of posters and graphics demonstrating the power of computers to do complex (and apparently random) calculations. Other graphics showed a simulated Mondrian and the iconic decreasing squares spiral that appeared on the exhibition's poster and book. The Boeing Company exhibited their use of wireframe graphics. The innovative computer-generated sculpture, Quad 1, was displayed at the Cybernetic Serendipity exhibit. Created by the American abstract expressionist sculptor, Robert Mallary, in 1968, Quad 1 is widely believed to be the world's first Computer Aided Design sculpture. Keith Albarn & Partners contributed to the design of the exhibition. Reflecting the prominence of music in the show, a ten-track album Cybernetic Serendipity Music was released by the ICA to accompany the show. Artists featured included Iannis Xenakis, John Cage, and Peter Zinovieff, a detail of whose graphic score for 'Four Sacred April Rounds’ (1968) was used as the cover artwork. == Attendance == Time magazine noted that there had been 40,000 visitors to the London exhibition. Other reports suggested visitor numbers were as high as 44,000 to 60,000. However, the ICA did not accurately count visitors. == After-effects == The exhibition provided the energy for the formation of British Computer Arts Society which continued to explore the interaction between science, technology and art, and put on exhibitions (for example Event One at the Royal College of Art). Several pieces were purchased by the Exploratorium in 1971, some of which are on display to this day. In 2014 the ICA held a retrospective exhibition Cybernetic Serendipity: A Documentation which included documents, installation photographs, press reviews and publications and a series of discussions in one of which Peter Zinovieff took part. To coincide with the exhibition, Cybernetic Serendipity Music was re-released as a limited-edition vinyl LP by The Vinyl Factory. The Victoria and Albert Museum marked the 50th anniversary with an exhibition in 2018 entitled "Chance and Control: Art in the Age of Computers". The V&A exhibition included many works by artists who featured in the original ICA show, plus related ephemera. "Chance and Control" subsequently toured to Chester Visual Arts and Firstsite, Colchester. In 2020, The Centre Pompidou exhibited the replica of Gordon Pask's 1968 Colloquy of Mobiles, reproduced by Paul Pangaro and TJ McLeish in 2018. In 2022 the Australian National University's School of Cybernetics launched the school by presenting an exhibition Australian Cybernetic: a point through time. The exhibition included works from Cybernetic Serendipity (1968), Australia ‘75: Festival of Creative Arts and Science (1975), and contemporary pieces curated by the School of Cybernetics. In describing Reichardt's Cybernetic Serendipity exhibition the school stated that it "represented points of expanding the cybernetic imagination" and was a "ground-breaking" "glimpse of a future in which computers were entangled with people and cultures, and through this she fashioned a blueprint for the future of computing that has since inspired generations".

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  Model inversion attack

  Model inversion attack is a type of adversarial machine learning attack where an attacker tries to reconstruct or infer sensitive information about a model's training data by analyzing the outputs of a trained machine learning model. Instead of directly querying the underlying dataset, attackers query the model (usually via APIs or prediction interfaces), and leverage patterns in the model responses to infer properties of the original inputs. These attacks leverage the fact that machine learning models encode statistical information about their training data in their parameters and outputs, which can unintentionally leak private or proprietary information. Depending on the access level to the target model, model inversion attacks can be performed in both black-box and white-box settings. In a generic attack, an adversary makes several queries to a model and leverages the responses (e.g. confidence scores, predictions) to train a surrogate or inversion model that learns to approximate the inverse mapping from outputs to inputs. This process may enable the reconstruction of sensitive attributes, e.g., facial features, medical data, or user behavior patterns, from models trained on such data. The technique has been demonstrated against various models like deep neural networks, classification systems etc. The technique has significant privacy risks in areas like healthcare, finance, biometric identification etc. Mitigation strategies include restricting model access, reducing output granularity, using differential privacy and monitoring anomalous query patterns.

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  Flex (lexical analyzer generator)

  Flex (fast lexical analyzer generator) is a free and open-source software alternative to lex. It is a computer program that generates lexical analyzers (also known as "scanners" or "lexers"). It is frequently used as the lex implementation together with Berkeley Yacc parser generator on BSD-derived operating systems (as both lex and yacc are part of POSIX), or together with GNU bison (a version of yacc) in BSD ports and in Linux distributions. Unlike Bison, flex is not part of the GNU Project and is not released under the GNU General Public License, although a manual for Flex was produced and published by the Free Software Foundation. == History == Flex was written in C around 1987 by Vern Paxson, with the help of many ideas and much inspiration from Van Jacobson. Original version by Jef Poskanzer. The fast table representation is a partial implementation of a design done by Van Jacobson. The implementation was done by Kevin Gong and Vern Paxson. == Example lexical analyzer == This is an example of a Flex scanner for the instructional programming language PL/0. The tokens recognized are: '+', '-', '', '/', '=', '(', ')', ',', ';', '.', ':=', '<', '<=', '<>', '>', '>='; numbers: 0-9 {0-9}; identifiers: a-zA-Z {a-zA-Z0-9} and keywords: begin, call, const, do, end, if, odd, procedure, then, var, while. == Internals == These programs perform character parsing and tokenizing via the use of a deterministic finite automaton (DFA). A DFA is a theoretical machine accepting regular languages, and is equivalent to read-only right moving Turing machines. The syntax is based on the use of regular expressions. See also nondeterministic finite automaton. == Issues == === Time complexity === A Flex lexical analyzer usually has time complexity O ( n ) {\displaystyle O(n)} in the length of the input. That is, it performs a constant number of operations for each input symbol. This constant is quite low: GCC generates 12 instructions for the DFA match loop. Note that the constant is independent of the length of the token, the length of the regular expression and the size of the DFA. However, using the REJECT macro in a scanner with the potential to match extremely long tokens can cause Flex to generate a scanner with non-linear performance. This feature is optional. In this case, the programmer has explicitly told Flex to "go back and try again" after it has already matched some input. This will cause the DFA to backtrack to find other accept states. The REJECT feature is not enabled by default, and because of its performance implications its use is discouraged in the Flex manual. === Reentrancy === By default the scanner generated by Flex is not reentrant. This can cause serious problems for programs that use the generated scanner from different threads. To overcome this issue there are options that Flex provides in order to achieve reentrancy. A detailed description of these options can be found in the Flex manual. === Usage under non-Unix environments === Normally the generated scanner contains references to the unistd.h header file, which is Unix specific. To avoid generating code that includes unistd.h, %option nounistd should be used. Another issue is the call to isatty (a Unix library function), which can be found in the generated code. The %option never-interactive forces flex to generate code that does not use isatty. === Using flex from other languages === Flex can only generate code for C and C++. To use the scanner code generated by flex from other languages a language binding tool such as SWIG can be used. === Unicode support === Flex is limited to matching 1-byte (8-bit) binary values and therefore does not support Unicode. RE/flex and other alternatives do support Unicode matching. == Flex++ == flex++ is a similar lexical scanner for C++ which is included as part of the flex package. The generated code does not depend on any runtime or external library except for a memory allocator (malloc or a user-supplied alternative) unless the input also depends on it. This can be useful in embedded and similar situations where traditional operating system or C runtime facilities may not be available. The flex++ generated C++ scanner includes the header file FlexLexer.h, which defines the interfaces of the two C++ generated classes.

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  Ofer Dekel (researcher)

  Ofer Dekel (Hebrew: עופר דקל) is a computer science researcher in the Machine Learning Department of Microsoft Research. He obtained his PhD in computer science from the Hebrew University of Jerusalem and is an affiliate faculty at the Computer Science & Engineering department at the University of Washington. == Areas of research == Dekel's research topics include machine learning, online prediction, statistical learning theory, and stochastic optimization. He is currently engaged in the application of machine learning techniques in the development of the Bing search engine.

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  Likewise, Inc.

  Likewise, Inc., is an American technology startup company which provides a social networking service for finding and saving content recommendations for movies, TV shows, books, and podcasts. A team of ex-Microsoft employees founded Likewise in October 2017 with financial investment from Microsoft co-founder Bill Gates. The company is led by CEO Ian Morris and as of 2020 had a team of about 35 employees. Its headquarters operates in Bellevue, Washington. As of July 2020, 1 million users had joined the platform. == History == === Ideation (October 2017) === In 2017, former Microsoft Communications Chief Larry Cohen came up with the idea for Likewise in Bill Gates’ private office, Gates Ventures. Cohen currently serves as Gates Ventures’ CEO and managing partner. Cohen collaborated with colleagues Michael Dix and Ian Morris to co-found what would become Likewise, with Morris as its CEO. Gates funded the company's early development. The company developed its platform in stealth mode before launching publicly in October 2018. === Release (October 2018) === Likewise officially released its platform in the US and Canada on October 3, 2018. === Growth (2020 COVID-19 pandemic) === Likewise experienced accelerated growth alongside the COVID-19 pandemic. From March 2020 to July 2020, the platform's monthly active users tripled in numbers. The company reached one million users in July 2020. == Applications == === Mobile === Likewise is available as a mobile app for the Android and iOS mobile operating systems. Users receive recommendations from the Likewise algorithm, people they follow, and the Likewise editorial team. === Likewise TV === In October 2019, the company launched its Apple TV app called Likewise TV. The television app organizes shows across streaming services under one watchlist. On July 20, 2020, Likewise TV expanded to Android TV and Amazon Fire TV users.

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  Intelligent character recognition

  Intelligent character recognition (ICR) is a method of extracting handwritten text from images. It is a more sophisticated type of OCR technology that recognizes different handwriting styles and fonts to intelligently interpret data from physical documents. ICR is used to organize paper-based unstructured data by scanning documents, extracting information, and adapting extracted data for database storage. ICR algorithms collaborate with OCR to automate data entry from forms by removing the need for keystrokes. It has a high degree of accuracy and is a dependable method for processing various handwritten media quickly. == Capabilities == Most ICR software has a self-learning neural network-based algorithms, which automatically update the recognition database for new handwriting patterns. It extends the usefulness of scanning devices for the purpose of document processing, from printed character recognition (a function of OCR) to hand-written matter recognition. Because this process is involved in recognizing hand writing, accuracy levels may, in some circumstances, not be very good but can achieve 97%+ accuracy rates in reading handwriting in structured forms. Often to achieve these high recognition rates several read engines are used within the software and each is given elective voting rights to determine the true reading of characters. In numeric fields, engines which are designed to read numbers take preference, while in alpha fields, engines designed to read hand written letters have higher elective rights. When used in conjunction with a bespoke interface hub, hand-written data can be automatically populated into a back office system avoiding laborious manual keying and can be more accurate than traditional human data entry. === Automated forms processing === An important development of ICR was the invention of automated forms processing in 1993 by Joseph Corcoran who was awarded a patent on the invention. This involved a three-stage process of capturing the image of the form to be processed by ICR and preparing it to enable the ICR engine to give best results, then capturing the information using the ICR engine and finally processing the results to automatically validate the output from the ICR engine. This application of ICR increased the usefulness of the technology and made it applicable for use with real world forms in normal business applications. Modern software applications use ICR as a technology of recognizing text in forms filled in by hand (hand-printed). == Differences between ICR and OCR == === OCR === Optical character recognition (OCR) is commonly considered to apply to any recognition technique that reads machine printed text. An example of a traditional OCR use case would be to translate the characters from an image of a printed document, such as a book page, newspaper clipping, or legal contract, into a separate file that could be searched and updated with a word processor or document viewer. It's also quite helpful for automating the processing of forms. Information can be swiftly extracted from form fields and entered into another application, like a spreadsheet or database, by zonally applying the OCR engine to those fields. Yet, data is typically manually input rather than typed into form fields. Character identification becomes even more challenging while reading handwritten material. The diversity of more than 700,000 printed font variants is tiny compared to the near unlimited variations in hand-printed characters. The recognition program must take into account not just stylistic differences but also the kind of writing implement used, the standard of the paper, errors, hand stability, and smudges or running ink. === ICR === Intelligent character recognition (ICR) makes use of continuously improving algorithms to collect more information about the variances in hand-printed characters and more precisely identify them. ICR, which was created in the early 1990s to aid in the automation of forms processing, enables the conversion of manually entered data into text that is simple to read, search for, and change. When used to read characters that are obviously divided into distinct areas or zones, such as fixed fields seen on many structured forms, it works best. Both OCR and ICR can be configured to read a variety of languages; however, limiting the expected character set to a smaller number of languages will produce better recognition outcomes. ICR cannot read cursive handwriting since it must still be able to assess each character individually. While writing in cursive, it might be difficult to tell where one character ends and another one begins, and there are more differences across samples than when hand-printing text. A more recent method called intelligent word recognition (IWR) focuses on reading a word in context rather than recognizing individual characters. == Intelligent word recognition == Intelligent word recognition (IWR) can recognize and extract not only printed-handwritten information, cursive handwriting as well. ICR recognizes on the character-level, whereas IWR works with full words or phrases. Capable of capturing unstructured information from every day pages, IWR is said to be more evolved than hand print ICR. Not meant to replace conventional ICR and OCR systems, IWR is optimized for processing real-world documents that contain mostly free-form, hard-to-recognize data fields that are inherently unsuitable for ICR. This means that the highest and best use of IWR is to eliminate a high percentage of the manual entry of handwritten data and run-on hand print fields on documents that otherwise could be keyed only by humans.

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  Mark Keane (cognitive scientist)

  Mark Thomas Gerard Keane (Irish: Marcus Ó Cathain, born 3 July 1961, Dublin, Ireland) is a cognitive scientist and author of several books on human cognition and artificial intelligence, including Cognitive Psychology: A Student's Handbook (8 editions, with Michael Eysenck), Advances in the Psychology of Thinking (1992, with Ken Gilhooly), Novice Programming Environments (1992/2018, with Marc Eisenstadt and Tim Rajan), Advances in Case-Based Reasoning (1995, with J-P Haton and Michel Manago)., Case-Based Reasoning: Research & Development (2022, with N Wiratunga). == Education == Keane received a B.A. in Psychology from University College Dublin in 1982. He then received a Ph.D. from Trinity College Dublin in 1987. He then moved to postdoctoral positions in Queen Mary University of London and the Open University. == Academic career == He was a Lecturer in Psychology at Cardiff University. He became a lecturer in Computer Science at Trinity College Dublin in 1990, and became a fellow in 1994. Keane moved to become Chair of Computer Science at University College Dublin in 1998. In 2006, he was seconded to Science Foundation Ireland as Director of ICT, overseeing on a $700m research investment. He advised the Irish Government on its 3.7B euro Strategy for Science, Technology & Innovation (SSTI). From 2006 to 2007, he was Director General of Science Foundation Ireland before returning to University College Dublin where he was appointed VP of Innovation & Partnerships (2007-2009). Keane's research has been split between cognitive science and computer science. His cognitive science research has been in analogy, metaphor, conceptual combination and similarity. His computer science research has been in natural language processing, machine learning, case-based reasoning, text analytics and explainable artificial intelligence. He has been a PI in the Science Foundation Ireland funded Insight Centre for Data Analytics working on digital journalism and digital humanities. More recently, he was deputy director of the VistaMilk SFI Research Centre that is exploring precision agriculture in the dairy sector.

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  Glottochronology

  Glottochronology (from Attic Greek γλῶττα 'tongue, language' and χρόνος 'time') is the part of lexicostatistics which involves comparative linguistics and deals with the chronological relationship between languages. The idea was developed by Morris Swadesh in the 1950s in his article on Salish internal relationships. He developed the idea under two assumptions: there indeed exists a relatively stable basic vocabulary (referred to as Swadesh lists) in all languages of the world; and, any replacements happen in a way analogous to radioactive decay in a constant percentage per time elapsed. Using mathematics and statistics, Swadesh developed an equation to determine when languages separated and give an approximate time of when the separation occurred. His methods aimed to aid linguistic anthropologists by giving them a definitive way to determine a separation date between two languages. The formula provides an approximate number of centuries since two languages were supposed to have separated from a singular common ancestor. His methods also purported to provide information on when ancient languages may have existed. Despite multiple studies and literature containing the information of glottochronology, it is not widely used today and is surrounded with controversy. Glottochronology tracks language separation from thousands of years ago but many linguists are skeptical of the concept because it is more of a 'probability' rather than a 'certainty.' On the other hand, some linguists may say that glottochronology is gaining traction because of its relatedness to archaeological dates. Glottochronology is not as accurate as archaeological data, but some linguists still believe that it can provide a solid estimate. Over time many different extensions of the Swadesh method evolved; however, Swadesh's original method is so well known that 'glottochronology' is usually associated with him. == Methodology == The original method of glottochronology presumed that the core vocabulary of a language is replaced at a constant (or constant average) rate across all languages and cultures and so can be used to measure the passage of time. The process makes use of a list of lexical terms and morphemes which are similar to multiple languages. Lists were compiled by Morris Swadesh and assumed to be resistant against borrowing (originally designed in 1952 as a list of 200 items, but the refined 100-word list in Swadesh (1955) is much more common among modern day linguists). The core vocabulary was designed to encompass concepts common to every human language such as personal pronouns, body parts, heavenly bodies and living beings, verbs of basic actions, numerals, basic adjectives, kin terms, and natural occurrences and events. Through a basic word list, one eliminates concepts that are specific to a particular culture or time period. It has been found through differentiating word lists that the ideal is really impossible and that the meaning set may need to be tailored to the languages being compared. Word lists are not homogenous throughout studies and they are often changed and designed to suit both languages being studied. Linguists find that it is difficult to find a word list where all words used are culturally unbiased. Many alternative word lists have been compiled by other linguists and often use fewer meaning slots. The percentage of cognates (words with a common origin) in the word lists is then measured. The larger the percentage of cognates, the more recently the two languages being compared are presumed to have separated. === Glottochronologic constant === Determining word lists rely on morpheme decay or change in vocabulary. Morpheme decay must stay at a constant rate for glottochronology to be applied to a language. This leads to a critique of the glottochronologic formula because some linguists argue that the morpheme decay rate is not guaranteed to stay the same throughout history. American Linguist Robert Lees obtained a value for the "glottochronological constant" (r) of words by considering the known changes in 13 pairs of languages using the 200 word list. He obtained a value of 0.8048 ± 0.0176 with 90% confidence. For his 100-word list Swadesh obtained a value of 0.86, the higher value reflecting the elimination of semantically unstable words. === Divergence time === The basic formula of glottochronology proposed by Morris Swadesh is: t = − ln ⁡ ( c ) 2 ln ⁡ ( r ) {\displaystyle t=-{\frac {\ln(c)}{2\ln(r)}}} t = a given period of time from one stage of the language to another (measured in millennia), c = proportion of wordlist items retained at the end of that period and r = rate of replacement for that word list. By testing historically verifiable cases in which t is known by nonlinguistic data (such as the approximate distance from Classical Latin to modern Romance languages), Swadesh arrived at the empirical value of approximately 0.14 for L, (c?) which means that the rate of replacement constitutes around 14 words from the 100-wordlist per millennium. This is represented in the table below. === Results === Glottochronology was applied to a range of language families, including Salishan, Indo-European, Japonic, Afro-Asiatic, Chinese and Mayan and other American languages. For Amerind, correlations have been obtained with radiocarbon dating and blood groups as well as archaeology. === Example Wordlist === Below is an example of a basic word list composed of basic Turkish words and their English translations. == Discussion == The concept of language change is old, and its history is reviewed in Hymes (1973) and Wells (1973). In some sense, glottochronology is a reconstruction of history and can often be closely related to archaeology. Many linguistic studies find the success of glottochronology to be found alongside archaeological data. Glottochronology itself dates back to the mid-20th century. An introduction to the subject is given in Embleton (1986) and in McMahon and McMahon (2005). Glottochronology has been controversial ever since, partly because of issues of accuracy but also because of the question of whether its basis is sound (for example, Bergsland 1958; Bergsland and Vogt 1962; Fodor 1961; Chrétien 1962; Guy 1980). The concerns have been addressed by Dobson et al. (1972), Dyen (1973) and Kruskal, Dyen and Black (1973). The assumption of a single-word replacement rate can distort the divergence-time estimate when borrowed words are included (Thomason and Kaufman 1988). The presentations vary from "Why linguists don't do dates" to the one by Starostin discussed below. Since its original inception, glottochronology has been rejected by many linguists, mostly Indo-Europeanists of the school of the traditional comparative method. Criticisms have been answered in particular around three points of discussion: Criticism levelled against the higher stability of lexemes in Swadesh lists alone (Haarmann 1990) misses the point because a certain amount of losses only enables the computations (Sankoff 1970). The non-homogeneity of word lists often leads to lack of understanding between linguists. Linguists also have difficulties finding a completely unbiased list of basic cultural words. it can take a long time for linguists to find a viable word list which can take several test lists to find a usable list. Traditional glottochronology presumes that language changes at a stable rate. Thus, in Bergsland & Vogt (1962), the authors make an impressive demonstration, on the basis of actual language data verifiable by extralinguistic sources, that the "rate of change" for Icelandic constituted around 4% per millennium, but for closely connected Riksmal (Literary Norwegian), it would amount to as much as 20% (Swadesh's proposed "constant rate" was supposed to be around 14% per millennium). That and several other similar examples effectively proved that Swadesh's formula would not work on all available material, which is a serious accusation since evidence that can be used to "calibrate" the meaning of L (language history recorded during prolonged periods of time) is not overwhelmingly large in the first place. It is highly likely that the chance of replacement is different for every word or feature ("each word has its own history", among hundreds of other sources:). That global assumption has been modified and downgraded to single words, even in single languages, in many newer attempts (see below). There is a lack of understanding of Swadesh's mathematical/statistical methods. Some linguists reject the methods in full because the statistics lead to 'probabilities' when linguists trust 'certainties' more. A serious argument is that language change arises from socio-historical events that are, of course, unforeseeable and, therefore, uncomputable. == Modifications == Somewhere in between the original concept of Swadesh and the rejection of glottochronology in its entirety lies the idea that glottochronology as a formal method of linguistic

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  Kolmogorov–Arnold Networks

  Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.

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  Thompson's construction

  In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson. Regular expressions and nondeterministic finite automata are two representations of formal languages. For instance, text processing utilities use regular expressions to describe advanced search patterns, but NFAs are better suited for execution on a computer. Hence, this algorithm is of practical interest, since it can compile regular expressions into NFAs. From a theoretical point of view, this algorithm is a part of the proof that they both accept exactly the same languages, that is, the regular languages. An NFA can be made deterministic by the powerset construction and then be minimized to get an optimal automaton corresponding to the given regular expression. However, an NFA may also be interpreted directly. To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree. == The algorithm == The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. More precisely, from a regular expression E, the obtained automaton A with the transition function Δ respects the following properties: A has exactly one initial state q0, which is not accessible from any other state. That is, for any state q and any letter a, Δ ( q , a ) {\displaystyle \Delta (q,a)} does not contain q0. A has exactly one final state qf, which is not co-accessible from any other state. That is, for any letter a, Δ ( q f , a ) = ∅ {\displaystyle \Delta (q_{f},a)=\emptyset } . Let c be the number of concatenation of the regular expression E and let s be the number of symbols apart from parentheses — that is, |, , a and ε. Then, the number of states of A is 2s − c (linear in the size of E). The number of transitions leaving any state is at most two. Since an NFA of m states and at most e transitions from each state can match a string of length n in time O(emn), a Thompson NFA can do pattern matching in linear time, assuming a fixed-size alphabet. === Rules === The following rules are depicted according to Aho et al. (2007), p. 122. In what follows, N(s) and N(t) are the NFA of the subexpressions s and t, respectively. The empty-expression ε is converted to A symbol a of the input alphabet is converted to The union expression s|t is converted to State q goes via ε either to the initial state of N(s) or N(t). Their final states become intermediate states of the whole NFA and merge via two ε-transitions into the final state of the NFA. The concatenation expression st is converted to The initial state of N(s) is the initial state of the whole NFA. The final state of N(s) becomes the initial state of N(t). The final state of N(t) is the final state of the whole NFA. The Kleene star expression s is converted to An ε-transition connects initial and final state of the NFA with the sub-NFA N(s) in between. Another ε-transition from the inner final to the inner initial state of N(s) allows for repetition of expression s according to the star operator. The parenthesized expression (s) is converted to N(s) itself. With these rules, using the empty expression and symbol rules as base cases, it is possible to prove with structural induction that any regular expression may be converted into an equivalent NFA. == Example == Two examples are now given, a small informal one with the result, and a bigger with a step by step application of the algorithm. === Small Example === The picture below shows the result of Thompson's construction on (ε|ab). The purple oval corresponds to a, the teal oval corresponds to a, the green oval corresponds to b, the orange oval corresponds to ab, and the blue oval corresponds to ε. === Application of the algorithm === As an example, the picture shows the result of Thompson's construction algorithm on the regular expression (0|(1(01(00)0)1)) that denotes the set of binary numbers that are multiples of 3: { ε, "0", "00", "11", "000", "011", "110", "0000", "0011", "0110", "1001", "1100", "1111", "00000", ... }. The upper right part shows the logical structure (syntax tree) of the expression, with "." denoting concatenation (assumed to have variable arity); subexpressions are named a-q for reference purposes. The left part shows the nondeterministic finite automaton resulting from Thompson's algorithm, with the entry and exit state of each subexpression colored in magenta and cyan, respectively. An ε as transition label is omitted for clarity — unlabelled transitions are in fact ε transitions. The entry and exit state corresponding to the root expression q is the start and accept state of the automaton, respectively. The algorithm's steps are as follows: An equivalent minimal deterministic automaton is shown below. == Relation to other algorithms == Thompson's is one of several algorithms for constructing NFAs from regular expressions; an earlier algorithm was given by McNaughton and Yamada. Converse to Thompson's construction, Kleene's algorithm transforms a finite automaton into a regular expression. Glushkov's construction algorithm is similar to Thompson's construction, once the ε-transitions are removed. == Use in string pattern matching == Regular expressions are often used to specify patterns that software is then asked to match. Generating an NFA by Thompson's construction, and using an appropriate algorithm to simulate it, it is possible to create pattern-matching software with performance that is ⁠ O ( m n ) {\displaystyle O(mn)} ⁠, where m is the length of the regular expression and n is the length of the string being matched. This is much better than is achieved by many popular programming-language implementations; however, it is restricted to purely regular expressions and does not support patterns for non-regular languages like backreferences.

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  Halbert White

  Halbert Lynn White Jr. (November 19, 1950 – March 31, 2012) was the Chancellor's Associates Distinguished Professor of Economics at the University of California, San Diego, and a Fellow of the Econometric Society and the American Academy of Arts and Sciences. == Education and career == White, a native of Kansas City, Missouri, graduated salutatorian from Southwest High School in 1968. He went on to study at Princeton University, receiving his B.A. in economics in 1972. He earned his Ph.D. in economics at the Massachusetts Institute of Technology in 1976, under the supervision of Jerry A. Hausman and Robert Solow. White spent his first years as an assistant professor in the University of Rochester before moving to University of California, San Diego (UCSD) in 1979. He remained at UCSD until his untimely death from cancer. == Research == White was well known in the field of econometrics for his 1980 paper on robust standard errors (which is among the most-cited paper in economics since 1970), and for the heteroscedasticity-consistent estimator and the test for heteroskedasticity that are named after him. A 1982 paper by White contributed strongly to the development of quasi-maximum likelihood estimation. He also contributed to numerous other areas such as neural networks and medicine. In 1999, White co-founded an economic consulting firm, Bates White, which is based in Washington, D.C.

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  Probabilistic context-free grammar

  In theoretical linguistics and computational linguistics, probabilistic context free grammars (PCFGs) extend context-free grammars, similar to how hidden Markov models extend regular grammars. Each production is assigned a probability. The probability of a derivation (parse) is the product of the probabilities of the productions used in that derivation. These probabilities can be viewed as parameters of the model, and for large problems it is convenient to learn these parameters via machine learning. A probabilistic grammar's validity is constrained by context of its training dataset. PCFGs originated from grammar theory, and have application in areas as diverse as natural language processing to the study the structure of RNA molecules and design of programming languages. Designing efficient PCFGs has to weigh factors of scalability and generality. Issues such as grammar ambiguity must be resolved. The grammar design affects results accuracy. Grammar parsing algorithms have various time and memory requirements. == Definitions == Derivation: The process of recursive generation of strings from a grammar. Parsing: Finding a valid derivation using an automaton. Parse Tree: The alignment of the grammar to a sequence. An example of a parser for PCFG grammars is the pushdown automaton. The algorithm parses grammar nonterminals from left to right in a stack-like manner. This brute-force approach is not very efficient. In RNA secondary structure prediction variants of the Cocke–Younger–Kasami (CYK) algorithm provide more efficient alternatives to grammar parsing than pushdown automata. Another example of a PCFG parser is the Stanford Statistical Parser which has been trained using Treebank. == Formal definition == Similar to a CFG, a probabilistic context-free grammar G can be defined by a quintuple: G = ( M , T , R , S , P ) {\displaystyle G=(M,T,R,S,P)} where M is the set of non-terminal symbols T is the set of terminal symbols R is the set of production rules S is the start symbol P is the set of probabilities on production rules == Relation with hidden Markov models == PCFGs models extend context-free grammars the same way as hidden Markov models extend regular grammars. The Inside-Outside algorithm is an analogue of the Forward-Backward algorithm. It computes the total probability of all derivations that are consistent with a given sequence, based on some PCFG. This is equivalent to the probability of the PCFG generating the sequence, and is intuitively a measure of how consistent the sequence is with the given grammar. The Inside-Outside algorithm is used in model parametrization to estimate prior frequencies observed from training sequences in the case of RNAs. Dynamic programming variants of the CYK algorithm find the Viterbi parse of a RNA sequence for a PCFG model. This parse is the most likely derivation of the sequence by the given PCFG. == Grammar construction == Context-free grammars are represented as a set of rules inspired from attempts to model natural languages. The rules are absolute and have a typical syntax representation known as Backus–Naur form. The production rules consist of terminal { a , b } {\displaystyle \left\{a,b\right\}} and non-terminal S symbols and a blank ϵ {\displaystyle \epsilon } may also be used as an end point. In the production rules of CFG and PCFG the left side has only one nonterminal whereas the right side can be any string of terminal or nonterminals. In PCFG nulls are excluded. An example of a grammar: S → a S , S → b S , S → ϵ {\displaystyle S\to aS,S\to bS,S\to \epsilon } This grammar can be shortened using the '|' ('or') character into: S → a S | b S | ϵ {\displaystyle S\to aS|bS|\epsilon } Terminals in a grammar are words and through the grammar rules a non-terminal symbol is transformed into a string of either terminals and/or non-terminals. The above grammar is read as "beginning from a non-terminal S the emission can generate either a or b or ϵ {\displaystyle \epsilon } ". Its derivation is: S ⇒ a S ⇒ a b S ⇒ a b b S ⇒ a b b {\displaystyle S\Rightarrow aS\Rightarrow abS\Rightarrow abbS\Rightarrow abb} Ambiguous grammar may result in ambiguous parsing if applied on homographs since the same word sequence can have more than one interpretation. Pun sentences such as the newspaper headline "Iraqi Head Seeks Arms" are an example of ambiguous parses. One strategy of dealing with ambiguous parses (originating with grammarians as early as Pāṇini) is to add yet more rules, or prioritize them so that one rule takes precedence over others. This, however, has the drawback of proliferating the rules, often to the point where they become difficult to manage. Another difficulty is overgeneration, where unlicensed structures are also generated. Probabilistic grammars circumvent these problems by ranking various productions on frequency weights, resulting in a "most likely" (winner-take-all) interpretation. As usage patterns are altered in diachronic shifts, these probabilistic rules can be re-learned, thus updating the grammar. Assigning probability to production rules makes a PCFG. These probabilities are informed by observing distributions on a training set of similar composition to the language to be modeled. On most samples of broad language, probabilistic grammars where probabilities are estimated from data typically outperform hand-crafted grammars. CFGs when contrasted with PCFGs are not applicable to RNA structure prediction because while they incorporate sequence-structure relationship they lack the scoring metrics that reveal a sequence structural potential == Weighted context-free grammar == A weighted context-free grammar (WCFG) is a more general category of context-free grammar, where each production has a numeric weight associated with it. The weight of a specific parse tree in a WCFG is the product (or sum ) of all rule weights in the tree. Each rule weight is included as often as the rule is used in the tree. A special case of WCFGs are PCFGs, where the weights are (logarithms of ) probabilities. An extended version of the CYK algorithm can be used to find the "lightest" (least-weight) derivation of a string given some WCFG. When the tree weight is the product of the rule weights, WCFGs and PCFGs can express the same set of probability distributions. == Applications == === RNA structure prediction === Since the 1990s, PCFG has been applied to model RNA structures. Energy minimization and PCFG provide ways of predicting RNA secondary structure with comparable performance. However structure prediction by PCFGs is scored probabilistically rather than by minimum free energy calculation. PCFG model parameters are directly derived from frequencies of different features observed in databases of RNA structures rather than by experimental determination as is the case with energy minimization methods. The types of various structure that can be modeled by a PCFG include long range interactions, pairwise structure and other nested structures. However, pseudoknots can not be modeled. PCFGs extend CFG by assigning probabilities to each production rule. A maximum probability parse tree from the grammar implies a maximum probability structure. Since RNAs preserve their structures over their primary sequence, RNA structure prediction can be guided by combining evolutionary information from comparative sequence analysis with biophysical knowledge about a structure plausibility based on such probabilities. Also search results for structural homologs using PCFG rules are scored according to PCFG derivations probabilities. Therefore, building grammar to model the behavior of base-pairs and single-stranded regions starts with exploring features of structural multiple sequence alignment of related RNAs. S → a S a | b S b | a a | b b {\displaystyle S\to aSa|bSb|aa|bb} The above grammar generates a string in an outside-in fashion, that is the basepair on the furthest extremes of the terminal is derived first. So a string such as a a b a a b a a {\displaystyle aabaabaa} is derived by first generating the distal a's on both sides before moving inwards: S ⇒ a S a ⇒ a a S a a ⇒ a a b S b a a ⇒ a a b a a b a a {\displaystyle S\Rightarrow aSa\Rightarrow aaSaa\Rightarrow aabSbaa\Rightarrow aabaabaa} A PCFG model extendibility allows constraining structure prediction by incorporating expectations about different features of an RNA . Such expectation may reflect for example the propensity for assuming a certain structure by an RNA. However incorporation of too much information may increase PCFG space and memory complexity and it is desirable that a PCFG-based model be as simple as possible. Every possible string x a grammar generates is assigned a probability weight P ( x | θ ) {\displaystyle P(x|\theta )} given the PCFG model θ {\displaystyle \theta } . It follows that the sum of all probabilities to all possible grammar productions is ∑ x P ( x | θ ) = 1 {\displaystyle \sum _{\text{x}}P(x|\theta )=1} . The scores

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  Prompt engineering

  Prompt engineering is the process of structuring natural language inputs (known as prompts) to produce specified outputs from a generative artificial intelligence (GenAI) model. Context engineering is the related area of software engineering that focuses on the management of non-prompt contexts supplied to the GenAI model, such as metadata, API tools, and tokens. It can also be defined as the practice of designing and refining input instructions given to a generative AI model to produce more accurate, relevant, or useful outputs. Effective prompt engineering involves understanding how a model interprets language, and may include techniques such as few-shot prompting, chain-of-thought prompting, and role assignment. It is increasingly considered a skill for working with large language models (LLMs) in both research and professional contexts. During the 2020s AI boom, prompt engineering became regarded as a business capability across corporations and industries. Employees with the title prompt engineer were hired to create prompts that would increase productivity and efficacy, although the individual title has since lost traction amid AI models that produce better prompts than humans and corporate training in prompting for general employees. Common prompting techniques include multi-shot, chain-of-thought, and tree-of-thought prompting, as well as the use of assigning roles to the model. Automated prompt generation methods, such as retrieval-augmented generation (RAG), provide for greater accuracy and a wider scope of functions for prompt engineers. Prompt injection is a type of cybersecurity attack that targets machine learning models through malicious prompts. == Terminology == The Oxford English Dictionary defines prompt engineering as "The action or process of formulating and refining prompts for an artificial intelligence program, algorithm, etc., in order to optimize its output or to achieve a desired outcome; the discipline or profession concerned with this." In 2023, prompt ("an instruction given to an artificial intelligence program, algorithm, etc., which determines or influences the content it generates") was the runner-up to Oxford's word of the year. === Prompt === A prompt is some natural language text that describes and prescribes the task that an artificial intelligence (AI) should perform. A prompt for a text-to-text language model can be a query, a command, or a longer statement referencing context, instructions, and conversation history. The process of prompt engineering may involve designing clear queries, refining wording, providing relevant context, specifying the style of output, and assigning a character for the AI to mimic in order to guide the model toward more accurate, useful, and consistent responses. When communicating with a text-to-image or a text-to-audio model, a typical prompt contains a description of a desired output such as "a high-quality photo of an astronaut riding a horse" or "Lo-fi slow BPM electro chill with organic samples". Prompt engineering may be applied to text-to-image models to achieve a desired subject, style, layout, lighting, and aesthetic. === Techniques === Common terms used to describe various specific prompt engineering techniques include chain-of-thought, tree-of-thought, and retrieval-augmented generation (RAG). A 2024 survey of the field identified over 50 distinct text-based prompting techniques, 40 multimodal variants, and a vocabulary of 33 terms used across prompting research, highlighting a present lack of standardised terminology for prompt engineering. Vibe coding is an AI-assisted software development method where a user prompts an LLM with a description of what they want and lets it generate or edit the code. In 2025, "vibe coding" was the Collins Dictionary word of the year. === Context engineering === Context engineering is a related process that focuses on the context elements that accompany user prompts, which include system instructions, retrieved knowledge, tool definitions, conversation summaries, and task metadata. Context engineering is performed to improve reliability, provenance and token efficiency in production LLM systems. The concept emphasises operational practices such as token budgeting, provenance tags, versioning of context artifacts, observability (logging which context was supplied), and context regression tests to ensure that changes to supplied context do not silently alter system behaviour. == Rationale == Research has found that the performance of large language models (LLMs) is highly sensitive to choices such as the ordering of examples, the quality of demonstration labels, and even small variations in phrasing. In some cases, reordering examples in a prompt produced accuracy shifts of more than 40 percent. === In-context learning === A model's ability to temporarily learn from prompts is known as in-context learning. In-context learning is an emergent ability of large language models. It is an emergent property of model scale, meaning that breaks in scaling laws occur, leading to its efficacy increasing at a different rate in larger models than in smaller models. Unlike training and fine-tuning, which produce lasting changes, in-context learning is temporary. Training models to perform in-context learning can be viewed as a form of meta-learning, or "learning to learn". === Prompting to estimate model sensitivity === Research consistently demonstrates that LLMs are highly sensitive to subtle variations in prompt formatting, structure, and linguistic properties. Some studies have shown up to 76 accuracy points across formatting changes in few-shot settings. Linguistic features significantly influence prompt effectiveness—such as morphology, syntax, and lexico-semantic changes—which meaningfully enhance task performance across a variety of tasks. Clausal syntax, for example, improves consistency and reduces uncertainty in knowledge retrieval. This sensitivity persists even with larger model sizes, additional few-shot examples, or instruction tuning. To address sensitivity of models and make them more robust, several evaluative methods have been proposed. FormatSpread facilitates systematic analysis by evaluating a range of plausible prompt formats, offering a more comprehensive performance interval. Similarly, PromptEval estimates performance distributions across diverse prompts, enabling robust metrics such as performance quantiles and accurate evaluations under constrained budgets. == Prompting techniques == === Multi-shot === A prompt may include a few examples for a model to learn from in context, an approach called few-shot learning. For example, the prompt may ask the model to complete "maison → house, chat → cat, chien →", with the expected response being dog. === Chain-of-thought === Chain-of-thought (CoT) prompting is a technique that allows large language models (LLMs) to solve a problem as a series of intermediate steps before giving a final answer. In 2022, Google Brain reported that chain-of-thought prompting improves reasoning ability by inducing the model to answer a multi-step problem with steps of reasoning that mimic a train of thought. Chain-of-thought techniques were developed to help LLMs handle multi-step reasoning tasks, such as arithmetic or commonsense reasoning questions. When applied to PaLM, a 540 billion parameter language model, according to Google, CoT prompting significantly aided the model, allowing it to perform comparably with task-specific fine-tuned models on several tasks, achieving state-of-the-art results at the time on the GSM8K mathematical reasoning benchmark. It is possible to fine-tune models on CoT reasoning datasets to enhance this capability further and stimulate better interpretability. As originally proposed by Google, each CoT prompt is accompanied by a set of input/output examples—called exemplars—to demonstrate the desired model output, making it a few-shot prompting technique. However, according to a later paper from researchers at Google and the University of Tokyo, simply appending the words "Let's think step-by-step" was also effective, which allowed for CoT to be employed as a zero-shot technique. ==== Self-consistency ==== Self-consistency performs several chain-of-thought rollouts, then selects the most commonly reached conclusion out of all the rollouts. === Tree-of-thought === Tree-of-thought prompting generalizes chain-of-thought by generating multiple lines of reasoning in parallel, with the ability to backtrack or explore other paths. It can use tree search algorithms like breadth-first, depth-first, or beam. === Text-to-image prompting === In 2022, text-to-image models like DALL-E 2, Stable Diffusion, and Midjourney were released to the public. These models take text prompts as input and use them to generate images. Early text-to-image models typically do not understand negation, grammar and sentence structure in the same way as large language models, and may thus requi

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  Stefan Schaal

  Stefan Schaal (born 1961) is a German-American computer scientist specializing in robotics, machine learning, autonomous systems, and computational neuroscience. == Education and career == Schaal was born in Frankfurt am Main in Germany, Schaal grew up in the North Bavarian town of Nürnberg. After graduating from school, he served in the German army in the Ski Patrol Division of Bad Reichenhall, where he honorably discharged with the rank of a Lieutenant. Schaal studied mechanical engineering at the Technical University of Munich, graduating in 1987 with a Diploma degree (summa cum laude). Subsequently, Schaal did his Ph.D. in computer aided design and artificial intelligence at the Technical University of Munich and the Massachusetts Institute of Technology, receiving his Ph.D. in 1991 (Summa Cum Laude) under Klaus Ehrlenspiel. In 1991, Schaal was a Postdoctoral Fellow at the Department and Brain and Cognitive Science and the Artificial Intelligence Lab at the Massachusetts Institute of Technology, funded by the Alexander von Humboldt Foundation and the German Academic Scholarship Foundation. Starting from 1992, he became an invited researcher at the ATR Computational Neuroscience Labs in Japan, where he created a robotics lab focusing on biological principles of motor control and learning. In 1994, Schaal moved to the Georgia Institute of Technology as an adjunct assistant professor, and also held the same rank at the Pennsylvania State University. In 1996, Schaal assumed a group leader position in the ERATO Kawato Dynamic Brain Project in Japan. Schaal joined the University of Southern California (USC) in 1997, where he advanced from the ranks of assistant professor, to associate professor, to full professor. In 2009, Schaal became a founder in defining and creating the Max Planck Institute for Intelligent Systems in Tübingen and Stuttgart, Germany, an institute focusing on principles of perception-action-learning systems in synthetic intelligence. In 2012, Schaal founded the Autonomous Motion Department (AMD) at this institute, while maintaining a partial appointment at USC. Stefan Schaal joined Google X as lead of a robotics research team in late 2018. == Research == Stefan Schaal's interests focus on autonomous perception-action-learning systems, in particular anthropomorphic robotic systems. He works on topics of machine learning for control, control theory, computational neuroscience for neuromotor control, experimental robotics, reinforcement learning, artificial intelligence, and nonlinear dynamical systems. Stefan has co-authored more than 400 publications in top conferences and journals, and served as organizer on various top conferences in machine learning and robotics. He has received numerous best paper awards and honors in his scientific community. Stefan Schaal has been noted as one of the five leaders in robotics in 2011, and among the top robotics experts in the world. == Controversy == In 2018, the German newsjournal Der Spiegel published an article reporting on his double affiliation with USC and the Max-Planck Society, both with full salaries, which was apparently unknown to either party. Schaal rejected the allegations, but was forced to leave his position at the Max Planck Institute.

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  How to Choose an AI Text-to-video Tool

  Comparing the best AI text-to-video tool? An AI text-to-video tool 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 text-to-video tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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