Corpus linguistics is an empirical method for the study of language by text corpus (plural corpora). Corpora are balanced, often stratified collections of authentic, "real world", text of speech or writing that aim to represent a given linguistic variety. Today, corpora are generally machine-readable data collections. Corpus linguistics proposes that a reliable analysis of a language is more feasible with corpora collected in the field—the natural context ("realia") of that language—with minimal experimental interference. Large collections of text, though corpora may also be small in terms of running words, allow linguists to run quantitative analyses on linguistic concepts that may be difficult to test in a qualitative manner. The text-corpus method uses the body of texts in any natural language to derive the set of abstract rules which govern that language. Those results can be used to explore the relationships between that subject language and other languages which have undergone a similar analysis. The first such corpora were manually derived from source texts, but now that work is automated. Corpora have not only been used for linguistics research, they have been increasingly used to compile dictionaries (starting with The American Heritage Dictionary of the English Language in 1969) and reference grammars, with A Comprehensive Grammar of the English Language, published in 1985, as a first. Experts in the field have differing views about the annotation of a corpus. These views range from John McHardy Sinclair, who advocates minimal annotation so texts speak for themselves, to the Survey of English Usage team (University College, London), who advocate annotation as allowing greater linguistic understanding through rigorous recording. == History == Some of the earliest efforts at grammatical description were based at least in part on corpora of particular religious or cultural significance. For example, Prātiśākhya literature described the sound patterns of Sanskrit as found in the Vedas, and Pāṇini's grammar of classical Sanskrit was based at least in part on analysis of that same corpus. Similarly, the early Arabic grammarians paid particular attention to the language of the Quran. In the Western European tradition, scholars prepared concordances to allow detailed study of the language of the Bible and other canonical texts. === English corpora === A landmark in modern corpus linguistics was the publication of Computational Analysis of Present-Day American English in 1967. Written by Henry Kučera and W. Nelson Francis, the work was based on an analysis of the Brown Corpus, which is a structured and balanced corpus of one million words of American English from the year 1961. The corpus comprises 2000 text samples, from a variety of genres. The Brown Corpus was the first computerized corpus designed for linguistic research. Kučera and Francis subjected the Brown Corpus to a variety of computational analyses and then combined elements of linguistics, language teaching, psychology, statistics, and sociology to create a rich and variegated opus. A further key publication was Randolph Quirk's "Towards a description of English Usage" in 1960 in which he introduced the Survey of English Usage. Quirk's corpus was the first modern corpus to be built with the purpose of representing the whole language. Shortly thereafter, Boston publisher Houghton-Mifflin approached Kučera to supply a million-word, three-line citation base for its new American Heritage Dictionary, the first dictionary compiled using corpus linguistics. The AHD took the innovative step of combining prescriptive elements (how language should be used) with descriptive information (how it actually is used). Other publishers followed suit. The British publisher Collins' COBUILD monolingual learner's dictionary, designed for users learning English as a foreign language, was compiled using the Bank of English. The Survey of English Usage Corpus was used in the development of one of the most important Corpus-based Grammars, which was written by Quirk et al. and published in 1985 as A Comprehensive Grammar of the English Language. The Brown Corpus has also spawned a number of similarly structured corpora: the LOB Corpus (1960s British English), Kolhapur (Indian English), Wellington (New Zealand English), Australian Corpus of English (Australian English), the Frown Corpus (early 1990s American English), and the FLOB Corpus (1990s British English). Other corpora represent many languages, varieties and modes, and include the International Corpus of English, and the British National Corpus, a 100 million word collection of a range of spoken and written texts, created in the 1990s by a consortium of publishers, universities (Oxford and Lancaster) and the British Library. For contemporary American English, work has stalled on the American National Corpus, but the 400+ million word Corpus of Contemporary American English (1990–present) is now available through a web interface. The first computerized corpus of transcribed spoken language was constructed in 1971 by the Montreal French Project, containing one million words, which inspired Shana Poplack's much larger corpus of spoken French in the Ottawa-Hull area. === Multilingual corpora === In the 1990s, many of the notable early successes on statistical methods in natural-language programming (NLP) occurred in the field of machine translation, due especially to work at IBM Research. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. There are corpora in non-European languages as well. For example, the National Institute for Japanese Language and Linguistics in Japan has built a number of corpora of spoken and written Japanese. Sign language corpora have also been created using video data. === Ancient languages corpora === Besides these corpora of living languages, computerized corpora have also been made of collections of texts in ancient languages. An example is the Andersen-Forbes database of the Hebrew Bible, developed since the 1970s, in which every clause is parsed using graphs representing up to seven levels of syntax, and every segment tagged with seven fields of information. The Quranic Arabic Corpus is an annotated corpus for the Classical Arabic language of the Quran. This is a recent project with multiple layers of annotation including morphological segmentation, part-of-speech tagging, and syntactic analysis using dependency grammar. The Digital Corpus of Sanskrit (DCS) is a "Sandhi-split corpus of Sanskrit texts with full morphological and lexical analysis... designed for text-historical research in Sanskrit linguistics and philology." === Corpora from specific fields === Besides pure linguistic inquiry, researchers had begun to apply corpus linguistics to other academic and professional fields, such as the emerging sub-discipline of Law and Corpus Linguistics, which seeks to understand legal texts using corpus data and tools. The DBLP Discovery Dataset concentrates on computer science, containing relevant computer science publications with sentient metadata such as author affiliations, citations, or study fields. A more focused dataset was introduced by NLP Scholar, a combination of papers of the ACL Anthology and Google Scholar metadata. Corpora can also aid in translation efforts or in teaching foreign languages. == Methods == Corpus linguistics has generated a number of research methods, which attempt to trace a path from data to theory. Wallis and Nelson (2001) first introduced what they called the 3A perspective: Annotation, Abstraction and Analysis. Annotation consists of the application of a scheme to texts. Annotations may include structural markup, part-of-speech tagging, parsing, and numerous other representations. Abstraction consists of the translation (mapping) of terms in the scheme to terms in a theoretically motivated model or dataset. Abstraction typically includes linguist-directed search but may include e.g., rule-learning for parsers. Analysis consists of statistically probing, manipulating and generalising from the dataset. Analysis might include statistical evaluations, optimisation of rule-bases or knowledge discovery methods. Most lexical corpora today are part-of-speech-tagged (POS-tagged). However even corpus linguists who work with 'unannotated plain text' inevitably apply some method to isolate salient terms. In such situations annotation and abstraction are combined in a lexical search. The advantage of publishing an annotated corpus is that other users can then perform experiments on the corpus (through corpus managers). Linguists with other interests and differing perspectives than the originators' can exploit this work. By sharing data
Dimensions CM
Dimensions CM is a software change and configuration management product developed by OpenText Corporation. It includes revision control, change, build and release management capabilities. Since 2014 (v14.1) Dimensions CM includes PulseUno module providing Code review and Continuous integration capabilities. Starting with the version 14.5.2 (2020) it can also serve as a binary repository manager. == History == Previous product names: PCMS Dimensions (SQL Software) PVCS Dimensions (Merant, Intersolv)
Hubert Dreyfus's views on artificial intelligence
Hubert Dreyfus was a critic of artificial intelligence research. In a series of papers and books, including Alchemy and AI (1965), What Computers Can't Do (1972; 1979; 1992) and Mind over Machine (1986), he presented a skeptical and cautious assessment of AI's progress and a critique of the philosophical foundations of the field. Dreyfus' objections are discussed in most introductions to the philosophy of artificial intelligence, including Russell & Norvig (2021), a standard AI textbook, and in Fearn (2007), a survey of contemporary philosophy. Dreyfus argued that human intelligence and expertise depend primarily on yet-to-be understood informal and unconscious processes rather than symbolic manipulation and that these essentially human skills cannot be fully captured in formal rules. His critique was based on the insights of modern continental philosophers such as Merleau-Ponty and Heidegger, and was directed at the first wave of AI research which tried to reduce intelligence to high level formal symbols. When Dreyfus' ideas were first introduced in the mid-1960s, they were met in the AI community with ridicule and outright hostility. By the 1980s, however, some of his perspectives were rediscovered by researchers working in robotics and the new field of connectionism—approaches that were called "sub-symbolic" at the time because they eschewed early AI research's emphasis on high level symbols. In the 21st century, "sub-symbolic" artificial neural networks and other statistics-based approaches to machine learning were highly successful. Historian and AI researcher Daniel Crevier wrote: "time has proven the accuracy and perceptiveness of some of Dreyfus's comments." Dreyfus said in 2007, "I figure I won and it's over—they've given up." == Dreyfus' critique == === The grandiose promises of artificial intelligence === In Alchemy and AI (1965) and What Computers Can't Do (1972), Dreyfus summarized the history of artificial intelligence and ridiculed the unbridled optimism that permeated the field. For example, Herbert A. Simon, following the success of his program General Problem Solver (1957), predicted that by 1967: A computer would be world champion in chess. A computer would discover and prove an important new mathematical theorem. Most theories in psychology will take the form of computer programs. The press dutifully reported these predictions of the imminent arrival of machine intelligence. Dreyfus felt that this optimism was unwarranted and, in 1965, argued forcefully that predictions like these would not come true. He would eventually be proven right. Pamela McCorduck explains Dreyfus' position: A great misunderstanding accounts for public confusion about thinking machines, a misunderstanding perpetrated by the unrealistic claims researchers in AI have been making, claims that thinking machines are already here, or at any rate, just around the corner. These predictions were based on the success of the cognitive revolution, which promoted an "information processing" model of the mind. It was articulated by Newell and Simon in their physical symbol systems hypothesis, and later expanded into a philosophical position known as computationalism by philosophers such as Jerry Fodor and Hilary Putnam. In AI, the approach is now called symbolic AI or "GOFAI". Dreyfus argued that "symbolic AI" was the latest version of the ancient program of rationalism in philosophy. Rationalism had come under heavy criticism in the 20th century from philosophers like Martin Heidegger and Edmund Husserl. The mind, according to modern continental philosophy, is not "rationalist" and is nothing like a digital computer. Cognitivism led early AI researchers to believe that they had successfully simulated the essential process of human thought, thus it seemed a short step to producing fully intelligent machines. Dreyfus' last paper detailed the ongoing history of the "first step fallacy", where AI researchers tend to wildly extrapolate initial success as promising, perhaps even guaranteeing, wild future successes. === Dreyfus' four assumptions of artificial intelligence research === In Alchemy and AI and What Computers Can't Do, Dreyfus identified four philosophical assumptions, at least one of which he deems necessary for AI to succeed. "In each case," Dreyfus writes, "the assumption is taken by workers in AI as an axiom, guaranteeing results, whereas it is, in fact, one hypothesis among others, to be tested by the success of such work." Dreyfus argues that AI would be impossible without accepting at least one of these four assumptions: The biological assumption The brain processes information in discrete operations by way of some biological equivalent of on/off switches. In the early days of research into neurology, scientists found that neurons fire in all-or-nothing pulses. Several researchers, such as Walter Pitts and Warren McCulloch, speculated with great confidence that neurons functioned similarly to the way Boolean logic gates operate, and so could be imitated by electronic circuitry at the level of the neuron. When digital computers became widely used in the early 50s, this argument was extended to suggest that the brain was a vast physical symbol system, manipulating the binary symbols of zero and one. Dreyfus was able to refute the biological assumption by citing research in neurology that suggested that the action and timing of neuron firing had analog components. But Daniel Crevier observes that "few still held that belief in the early 1970s, and nobody argued against Dreyfus" about the biological assumption. The psychological assumption The mind can be viewed as a device operating on bits of information according to formal rules. He refuted this assumption by showing that much of what we know about the world consists of complex attitudes or tendencies that make us lean towards one interpretation over another. He argued that, even when we use explicit symbols, we are using them against an unconscious and informal background including commonsense knowledge and that without this background our symbols cease to mean anything. This background, in Dreyfus' view, was not implemented in individual brains as explicit individual symbols with explicit individual meanings. The epistemological assumption All knowledge can be formalized. This concerns the philosophical issue of epistemology, or the study of knowledge. Even if we agree that the psychological assumption is false, AI researchers could still argue (as AI founder John McCarthy has) that it is possible for a symbol processing machine to represent all knowledge, regardless of whether human beings represent knowledge the same way. Dreyfus argued that there is no justification for this assumption, since so much of human knowledge is not symbolic or even expressible using formal constructs. The ontological assumption The world consists of independent facts that can be represented by independent symbols AI researchers (and futurists and science fiction writers) often assume that there is no limit to formal, scientific knowledge, because they assume that any phenomenon in the universe can be described by symbols or scientific theories. This assumes that everything that exists can be understood as objects, properties of objects, classes of objects, relations of objects, and so on: precisely those things that can be described by logic, language and mathematics. The study of being or existence is called ontology, and so Dreyfus calls this the ontological assumption. If this is false, then it raises doubts about what we can ultimately know and what intelligent machines will ultimately be able to help us to do. === Knowing-how vs. knowing-that: the primacy of intuition === In Mind Over Machine (1986), written (with his brother) during the heyday of expert systems, Dreyfus analyzed the difference between human expertise and the programs that claimed to capture it. This expanded on ideas from What Computers Can't Do, where he had made a similar argument criticizing the "cognitive simulation" school of AI research practiced by Allen Newell and Herbert A. Simon in the 1960s. Dreyfus argued that human problem solving and expertise depend on our background sense of the context, of what is important and interesting given the situation, rather than on the process of searching through combinations of possibilities to find what we need. Dreyfus would describe it in 1986 as the difference between "knowing-that" and "knowing-how", based on Heidegger's distinction of present-at-hand and ready-to-hand. Knowing-that is our conscious, step-by-step problem solving abilities. We use these skills when we encounter a difficult problem that requires us to stop, step back and search through ideas one at time. At moments like this, the ideas become very precise and simple: they become context free symbols, which we manipulate using logic and language. These are the skills that Newell and Simon had demonstrated with both psy
Linagora
Linagora is a French open source software editor, founded in June 2000 by Alexandre Zapolsky and Michel-Marie Maudet. Located in France, as well as in Belgium, Canada, Vietnam, the United States and Tunisia, the company employs around 200 people. In 2023, Linagora created the OpenLLM France community, alongside other French Artificial Intelligence companies and organizations. In 2025, the company launched Lucie, an opensource Large Language Model. == History == Linagora was founded on June 28, 2000. Its name is a contraction of the words "Linux" and "Agora". The company was founded by Alexandre Zapolsky and Michel-Marie Maudet. Soon after, the two entrepreneurs were joined by Alexandre Zapolsky's wife and brother, who took on the roles of commercial director and administrative and financial director of the SME. In 2007, the company was selected by the French National Assembly to provide the software for Linux computers, replacing Microsoft Windows. Linagora then claimed the position of the leading French open source software company by revenue. In 2015, French Prime Minister Manuel Valls allocated €10.7 million from the "Investments for the Future" fund for a research program aimed at developing a new generation of open source software platforms based on Linagora's offerings. In September 2016, Linagora launched the social network "La Cerise" for the newspaper L'Humanité. This app offered a service and tool for readers and citizens mobilizing for causes. It aimed to share engagement through petitions, discussions, agendas, and contacts. In October 2016, the company won two public contracts for supporting open source software in forty-two French ministries and other administrative entities. In May 2019, Linagora organized a fundraising event in the presence of the French Secretary of State for Digital Affairs, Cédric O, to celebrate its 19th anniversary. The funds were intended for: Supporting parents of hospitalized Polynesian children in France. Equipping primary school students with digital devices (tablets or PCs). Establishing a digital academy "OpenHackademy" in French Polynesia to train unemployed youth in digital skills and help them find jobs. In December 2022, Linagora acquired a property known as "Maison Rocher" and later "Maison Chocolat," located on the Île Saint-Germain in Issy-les-Moulineaux. Renamed "Villa Good Tech" by Linagora, this award-winning architectural work by Éric Daniel-Lacombe became the company's new headquarters, aiming to provide a space for associative actors and companies to develop technologies that contribute to a better world. In July 2023, Linagora launched OpenLLM France, a community initially comprising around twenty actors focused on generative AI. The goal was to develop a sovereign and open source large language model. This initiative, led by co-founder and CEO Michel-Marie Maudet, had more than four hundred French members by early 2024. and announced its expansion to the European sphere during Fosdem 2024. In February 2024, the CNRS and Linagora signed a framework agreement to strengthen their research collaboration. In January 2025, Linagora released Lucie, an open source and sovereign AI that faced ridicule due to tests on an unfinished, uncensored version designed for scientific and experimental use. The platform divided opinions between those who saw it as a technological achievement and those who criticized it as "French bashing" compared to American and Chinese AIs. == Acquisitions == The company acquired: In July 2007, the SME AliaSource, based in Ramonville-Saint-Agne and led by its founder, Pierre Baudracco. In 2008, the open source web hosting company Netaktiv, a member of the GIE Gitoyen, announced during the 2008 Solutions Linux trade show. In 2012, the Toulouse-based company EBM Websourcing, the publisher of the open-source software Petals Link, and took over its development. In 2016, the digital agency Neoma Interactive, specializing in UX design and digital communication strategy. == Locations == In 2017, the company's headquarters was located in Issy-les-Moulineaux, with branches in Lyon, Toulouse, Marseille, and internationally in Brussels, San Francisco, Montreal, Vietnam, and Tunisia. In 2005, the company attempted to establish a presence in Nantes. In 2024, the headquarters was moved to Issy-les-Moulineaux. == Activity == === Software === Twake Workplace One of Linagora's flagship products is Twake Workplace, which stands out as a 100% open-source solution compared with those of the GAFAMs. Twake Workplace is available as a complete platform or module by module. It includes : Twake Mail, a powerful modern messaging solution based on the JMAP protocol and the James email server from the Apache Foundation, for which Linagora provides technical management; Twake Chat, an instant communications solution for businesses developed using the Matrix protocol and compatible with the French government's chat solution, Tchap; Twake Drive, an easy-to-use collaborative platform for group work using OnlyOffice. ==== OpenPaaS ==== In 2018, the search engine Qwant announced that its email service Qwantmail would be based on the OpenPaaS product. In 2022, Qwant announced the abandonment of its Qwantmail project due to Linagora's collection of personal email addresses and serious security breaches. The site Next (formerly PC INpact) published an article in January 2020 criticizing the "failures and delays" of the Qwantmail project led by Linagora, which led to the CNIL's intervention regarding Qwant and Linagora. ==== LinTO ==== In 2017, Linagora launched its open source voice assistant project named LinTO. This enterprise voice assistant, described as "GAFAM Free," was presented at CES 2018 in Las Vegas. The LinTO voice framework was developed as part of the eponymous research project funded by Bpifrance (Grands Défis du Numérique instrument). === Services === ==== OSSA (Open Source Software Assurance) ==== One of the company's main activities is OSSA. Through OSSA, Linagora provided support for open source software for 42 ministries and other administrative entities in 2012. == Legal issues == === Dispute with BlueMind === In 2012, a legal dispute arose between BlueMind and Linagora. Linagora accused BlueMind of copyright infringement, unfair competition, and breach of a non-compete clause, leading to several legal actions. Linagora sued BlueMind for copyright infringement and unfair competition in the Bordeaux court, which ruled in Linagora's favor for unfair competition and parasitism but rejected the copyright claim. BlueMind was ordered to pay nearly €170,000 to Linagora. Linagora sued former associates Pierre Baudracco and Pierre Carlier in the Paris Commercial Court for breach of a non-compete clause and violation of a warranty of eviction. The court dismissed Linagora's claims and ordered it to pay €20,000 each to Baudracco and Carlier. Linagora appealed, and the Paris Court of Appeal partially overturned the decision, awarding Linagora €480,000. BlueMind sued Linagora for defamation and public insult in the Toulouse Criminal Court. The court ruled against Linagora, but the decision was overturned by the Court of Cassation in January 2024, and the case was remanded for retrial. === Conviction for wrongful termination and harassment === On June 14, 2017, France 3 reported on a decision by the Versailles Court of Appeal, which ruled that Linagora had wrongfully terminated an employee and subjected them to moral harassment. The court ordered Linagora to pay the employee €22,000 for wrongful termination, €11,000 for notice pay, €6,600 for legal severance pay, €3,200 for conservative suspension, and €3,000 for moral harassment.
LIFER/LADDER
LIFER/LADDER was one of the first database natural language processing systems. It was designed as a natural language interface to a database of information about US Navy ships. This system, as described in a paper by Hendrix (1978), used a semantic grammar to parse questions and query a distributed database. It was implemented in Interlisp. The LIFER/LADDER system could only support simple one-table queries or multiple table queries with easy join conditions. Some examples of queries it could accept: What are the length, width, and draft of the Kitty Hawk? When will Reeves achieve readiness rating C2? What is the nearest ship to Naples with a doctor on board? What ships are carrying cargo for the United States? Where are they going? Print the American cruisers’ current positions and states of readiness?
Scale-space axioms
In image processing and computer vision, a scale space framework can be used to represent an image as a family of gradually smoothed images. This framework is very general and a variety of scale space representations exist. A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision. == Scale space axioms for the linear scale-space representation == The linear scale space representation L ( x , y , t ) = ( T t f ) ( x , y ) = g ( x , y , t ) ∗ f ( x , y ) {\displaystyle L(x,y,t)=(T_{t}f)(x,y)=g(x,y,t)f(x,y)} of signal f ( x , y ) {\displaystyle f(x,y)} obtained by smoothing with the Gaussian kernel g ( x , y , t ) {\displaystyle g(x,y,t)} satisfies a number of properties 'scale-space axioms' that make it a special form of multi-scale representation: linearity T t ( a f + b h ) = a T t f + b T t h {\displaystyle T_{t}(af+bh)=aT_{t}f+bT_{t}h} where f {\displaystyle f} and h {\displaystyle h} are signals while a {\displaystyle a} and b {\displaystyle b} are constants, shift invariance T t S ( Δ x , Δ y ) f = S ( Δ x , Δ y ) T t f {\displaystyle T_{t}S_{(\Delta x,\Delta _{y})}f=S_{(\Delta x,\Delta _{y})}T_{t}f} where S ( Δ x , Δ y ) {\displaystyle S_{(\Delta x,\Delta _{y})}} denotes the shift (translation) operator ( S ( Δ x , Δ y ) f ) ( x , y ) = f ( x − Δ x , y − Δ y ) {\displaystyle (S_{(\Delta x,\Delta _{y})}f)(x,y)=f(x-\Delta x,y-\Delta y)} semi-group structure g ( x , y , t 1 ) ∗ g ( x , y , t 2 ) = g ( x , y , t 1 + t 2 ) {\displaystyle g(x,y,t_{1})g(x,y,t_{2})=g(x,y,t_{1}+t_{2})} with the associated cascade smoothing property L ( x , y , t 2 ) = g ( x , y , t 2 − t 1 ) ∗ L ( x , y , t 1 ) {\displaystyle L(x,y,t_{2})=g(x,y,t_{2}-t_{1})L(x,y,t_{1})} existence of an infinitesimal generator A {\displaystyle A} ∂ t L ( x , y , t ) = ( A L ) ( x , y , t ) {\displaystyle \partial _{t}L(x,y,t)=(AL)(x,y,t)} non-creation of local extrema (zero-crossings) in one dimension, non-enhancement of local extrema in any number of dimensions ∂ t L ( x , y , t ) ≤ 0 {\displaystyle \partial _{t}L(x,y,t)\leq 0} at spatial maxima and ∂ t L ( x , y , t ) ≥ 0 {\displaystyle \partial _{t}L(x,y,t)\geq 0} at spatial minima, rotational symmetry g ( x , y , t ) = h ( x 2 + y 2 , t ) {\displaystyle g(x,y,t)=h(x^{2}+y^{2},t)} for some function h {\displaystyle h} , scale invariance g ^ ( ω x , ω y , t ) = h ^ ( ω x φ ( t ) , ω x φ ( t ) ) {\displaystyle {\hat {g}}(\omega _{x},\omega _{y},t)={\hat {h}}({\frac {\omega _{x}}{\varphi (t)}},{\frac {\omega _{x}}{\varphi (t)}})} for some functions φ {\displaystyle \varphi } and h ^ {\displaystyle {\hat {h}}} where g ^ {\displaystyle {\hat {g}}} denotes the Fourier transform of g {\displaystyle g} , positivity g ( x , y , t ) ≥ 0 {\displaystyle g(x,y,t)\geq 0} , normalization ∫ x = − ∞ ∞ ∫ y = − ∞ ∞ g ( x , y , t ) d x d y = 1 {\displaystyle \int _{x=-\infty }^{\infty }\int _{y=-\infty }^{\infty }g(x,y,t)\,dx\,dy=1} . In fact, it can be shown that the Gaussian kernel is a unique choice given several different combinations of subsets of these scale-space axioms: most of the axioms (linearity, shift-invariance, semigroup) correspond to scaling being a semigroup of shift-invariant linear operator, which is satisfied by a number of families integral transforms, while "non-creation of local extrema" for one-dimensional signals or "non-enhancement of local extrema" for higher-dimensional signals are the crucial axioms which relate scale-spaces to smoothing (formally, parabolic partial differential equations), and hence select for the Gaussian. The Gaussian kernel is also separable in Cartesian coordinates, i.e. g ( x , y , t ) = g ( x , t ) g ( y , t ) {\displaystyle g(x,y,t)=g(x,t)\,g(y,t)} . Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities, including image deformations caused by viewing variations, approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. In this theory, rotational symmetry is not imposed as a necessary scale-space axiom and is instead replaced by requirements of affine and/or Galilean covariance. The generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. In the computer vision, image processing and signal processing literature there are many other multi-scale approaches, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; please see the article on related multi-scale approaches. There has also been work on discrete scale-space concepts that carry the scale-space properties over to the discrete domain; see the article on scale space implementation for examples and references.
Early-exit network
Early-exit networks are a class of dynamic neural networks designed for efficient inference by allowing models to make confident predictions at intermediate layers, rather than processing the full network. Early-exit mechanisms are methods for deep neural networks that add intermediate classifiers, allowing inference to stop at earlier layers for inputs assessed as low uncertainty. Decisions to exit are typically based on confidence measures such as softmax-derived scores, classification margins, or entropy-based criteria, with the goal of reducing computational cost. These approaches are commonly paired with specialized training procedures and system-level optimizations to improve efficiency while preserving accuracy. The main idea behind the technology is to stop excessive calculations when a good answer can already be given with a high degree of probability, which can save both computation and time. Early-exit networks have also been extended with expert-based exit criteria, where intermediate classifiers are treated as multiple “experts” whose predictions and confidence scores can be aggregated to decide whether to stop computation early. Hardware implementations are also being developed.