AI And Analytics Course

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Attempto Controlled English

Attempto Controlled English (ACE) is a controlled natural language, i.e. a subset of standard English with a restricted syntax and restricted semantics described by a small set of construction and interpretation rules. It has been under development at the University of Zurich since 1995. In 2013, ACE version 6.7 was announced. ACE can serve as knowledge representation, specification, and query language, and is intended for professionals who want to use formal notations and formal methods, but may not be familiar with them. Though ACE appears perfectly natural—it can be read and understood by any speaker of English—it is in fact a formal language. ACE and its related tools have been used in the fields of software specifications, theorem proving, proof assistants, text summaries, ontologies, rules, querying, medical documentation and planning. Here are some simple examples: Every woman is a human. A woman is a human. A man tries-on a new tie. If the tie pleases his wife then the man buys it. ACE construction rules require that each noun be introduced by a determiner (a, every, no, some, at least 5, ...). Regarding the list of examples above, ACE interpretation rules decide that (1) is interpreted as universally quantified, while (2) is interpreted as existentially quantified. Sentences like "Women are human" do not follow ACE syntax and are consequently not valid. Interpretation rules resolve the anaphoric references in (3): the tie and it of the second sentence refer to a new tie of the first sentence, while his and the man of the second sentence refer to a man of the first sentence. Thus an ACE text is a coherent entity of anaphorically linked sentences. The Attempto Parsing Engine (APE) translates ACE texts unambiguously into discourse representation structures (DRS) that use a variant of the language of first-order logic. A DRS can be further translated into other formal languages, for instance AceRules with various semantics, OWL, and SWRL. Translating an ACE text into (a fragment of) first-order logic allows users to reason about the text, for instance to verify, to validate, and to query it. == Overview == As an overview of the current version 6.6 of ACE this section: Briefly describes the vocabulary Gives an account of the syntax Summarises the handling of ambiguity Explains the processing of anaphoric references. === Vocabulary === The vocabulary of ACE comprises: Predefined function words (e.g. determiners, conjunctions) Predefined phrases (e.g. "it is false that ...", "it is possible that ...") Content words (e.g. nouns, verbs, adjectives, adverbs). === Grammar === The grammar of ACE defines and constrains the form and the meaning of ACE sentences and texts. ACE's grammar is expressed as a set of construction rules. The meaning of sentences is described as a small set of interpretation rules. A Troubleshooting Guide describes how to use ACE and how to avoid pitfalls. ==== ACE texts ==== An ACE text is a sequence of declarative sentences that can be anaphorically interrelated. Furthermore, ACE supports questions and commands. ==== Simple sentences ==== A simple sentence asserts that something is the case—a fact, an event, a state. The temperature is −2 °C. A customer inserts 2 cards. A card and a code are valid. Simple ACE sentences have the following general structure: subject + verb + complements + adjuncts Every sentence has a subject and a verb. Complements (direct and indirect objects) are necessary for transitive verbs (insert something) and ditransitive verbs (give something to somebody), whereas adjuncts (adverbs, prepositional phrases) are optional. All elements of a simple sentence can be elaborated upon to describe the situation in more detail. To further specify the nouns customer and card, we could add adjectives: A trusted customer inserts two valid cards. possessive nouns and of-prepositional phrases: John's customer inserts a card of Mary. or variables as appositions: John inserts a card A. Other modifications of nouns are possible through relative sentences: A customer who is trusted inserts a card that he owns. which are described below since they make a sentence composite. We can also detail the insertion event, e.g. by adding an adverb: A customer inserts some cards manually. or, equivalently: A customer manually inserts some cards. or, by adding prepositional phrases: A customer inserts some cards into a slot. We can combine all of these elaborations to arrive at: John's customer who is trusted inserts a valid card of Mary manually into a slot A. ==== Composite sentences ==== Composite sentences are recursively built from simpler sentences through coordination, subordination, quantification, and negation. Note that ACE composite sentences overlap with what linguists call compound sentences and complex sentences. ===== Coordination ===== Coordination by and is possible between sentences and between phrases of the same syntactic type. A customer inserts a card and the machine checks the code. There is a customer who inserts a card and who enters a code. A customer inserts a card and enters a code. An old and trusted customer enters a card and a code. Note that the coordination of the noun phrases a card and a code represents a plural object. Coordination by or is possible between sentences, verb phrases, and relative clauses. A customer inserts a card or the machine checks the code. A customer inserts a card or enters a code. A customer owns a card that is invalid or that is damaged. Coordination by and and or is governed by the standard binding order of logic, i.e. and binds stronger than or. Commas can be used to override the standard binding order. Thus the sentence: A customer inserts a VisaCard or inserts a MasterCard, and inserts a code. means that the customer inserts a VisaCard and a code, or alternatively a MasterCard and a code. ===== Subordination ===== There are four constructs of subordination: relative sentences, if-then sentences, modality, and sentence subordination. Relative sentences starting with who, which, and that allow to add detail to nouns: A customer who is trusted inserts a card that he owns. With the help of if-then sentences we can specify conditional or hypothetical situations: If a card is valid then a customer inserts it. Note the anaphoric reference via the pronoun it in the then-part to the noun phrase a card in the if-part. Modality allows us to express possibility and necessity: A trusted customer can/must insert a card. It is possible/necessary that a trusted customer inserts a card. Sentence subordination comes in various forms: It is true/false that a customer inserts a card. It is not provable that a customer inserts a card. A clerk believes that a customer inserts a card. ===== Quantification ===== Quantification allows us to speak about all objects of a certain class (universal quantification), or to denote explicitly the existence of at least one object of this class (existential quantification). The textual occurrence of a universal or existential quantifier opens its scope that extends to the end of the sentence, or in coordinations to the end of the respective coordinated sentence. To express that all involved customers insert cards we can write Every customer inserts a card. This sentence means that each customer inserts a card that may, or may not, be the same as the one inserted by another customer. To specify that all customers insert the same card—however unrealistic that situation seems—we can write: A card is inserted by every customer. or, equivalently: There is a card that every customer inserts. To state that every card is inserted by a customer we write: Every card is inserted by a customer. or, somewhat indirectly: For every card there is a customer who inserts it. ===== Negation ===== Negation allows us to express that something is not the case: A customer does not insert a card. A card is not valid. To negate something for all objects of a certain class one uses no: No customer inserts more than 2 cards. or, there is no: There is no customer who inserts a card. To negate a complete statement one uses sentence negation: It is false that a customer inserts a card. These forms of negation are logical negations, i.e. they state that something is provably not the case. Negation as failure states that a state of affairs cannot be proved, i.e. there is no information whether the state of affairs is the case or not. It is not provable that a customer inserts a card. ==== Queries ==== ACE supports two forms of queries: yes/no-queries and wh-queries. Yes/no-queries ask for the existence or non-existence of a specified situation. If we specified: A customer inserts a card. then we can ask: Does a customer insert a card? to get a positive answer. Note that interrogative sentences always end with a question mark. With the help of wh-queries, i.e. queries with query words, we can interrogate a text for details of the specified situation. If we specified: A
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ARMA International

ARMA International (formerly the Association of Records Managers and Administrators) is an American not-for-profit professional association for information professionals – primarily information management (including records management) and information governance, and related industry practitioners and vendors. The association provides educational opportunities and publications covering aspects of information management broadly. == History == The Association was founded in 1955. In 1975, the Association of Records Executives and Administrators (AREA) and the American Records Management Association merged to form ARMA International. The headquarters for ARMA International is located in Overland Park, Kansas. == Operations == ARMA International services professionals in the United States, Canada, Japan, and the United Kingdom. Its members include records managers, attorneys, information technology professionals, consultants, and archivists involved in various aspects of managing records and information assets. ARMA hosts an annual conference with the goal of bringing together record and information management professionals from around the world – In 2023, ARMA hosted conferences in both the United States and Canada. Topics addressed in the 120+ educational sessions include advanced technology, creating information structure, ediscovery and information law, information management fundamentals, information project management, and reducing organizational information risk. The expo features exhibitors displaying records and information technologies, products, and services.
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Ordered key–value store

An ordered key–value store (OKVS) is a type of data storage paradigm that can support multi-model databases. An OKVS is an ordered mapping of bytes to bytes. An OKVS will keep the key–value pairs sorted by the key lexicographic order. OKVS systems provides different set of features and performance trade-offs. Most of them are shipped as a library without network interfaces, in order to be embedded in another process. Most OKVS support ACID guarantees. Some OKVS are distributed databases. Ordered key–value stores found their way into many modern database systems including NewSQL database systems. == History == The origin of ordered key–value store stems from the work of Ken Thompson on dbm in 1979. Later in 1991, Berkeley DB was released that featured a B-Tree backend that allowed the keys to stay sorted. Berkeley DB was said to be very fast and made its way into various commercial product. It was included in Python standard library until 2.7. In 2009, Tokyo Cabinet was released that was superseded by Kyoto Cabinet that support both transaction and ordered keys. In 2011, LMDB was created to replace Berkeley DB in OpenLDAP. There is also Google's LevelDB that was forked by Facebook in 2012 as RocksDB. In 2014, WiredTiger, successor of Berkeley DB was acquired by MongoDB and is since 2019 the primary backend of MongoDB database. Other notable implementation of the OKVS paradigm are Sophia and SQLite3 LSM extension. Another notable use of OKVS paradigm is the multi-model database system called ArangoDB based on RocksDB. Some NewSQL databases are supported by ordered key–value stores. JanusGraph, a property graph database, has both a Berkeley DB backend and FoundationDB backend. == Key concepts == === Lexicographic encoding === There are algorithms that encode basic data types (boolean, string, number) and composition of those data types inside sorted containers (tuple, list, vector) that preserve their natural ordering. It is possible to work with an ordered key–value store without having to work directly with bytes. In FoundationDB, it is called the tuple layer. === Range query === Inside an OKVS, keys are ordered, and because of that it is possible to do range queries. A range query retrieves all keys between two specified keys, ensuring that the fetched keys are returned in a sorted order. === Subspaces === === Key composition === One can construct key spaces to build higher level abstractions. The idea is to construct keys, that takes advantage of the ordered nature of the top level key space. When taking advantage of the ordered nature of the key space, one can query ranges of keys that have particular pattern. === Denormalization === Denormalization, as in, repeating the same piece of data in multiple subspace is common practice. It allows to create secondary representation, also called indices, that will allow to speed up queries. == Higher level abstractions == The following abstraction or databases were built on top ordered key–value stores: Timeseries database, Record Database, also known as Row store databases, they behave similarly to what is dubbed RDBMS, Tuple Stores, also known as Triple Store or Quad Store but also Generic Tuple Store, Document database, that mimics MongoDB API, Full-text search Geographic Information Systems Property Graph Versioned Data Vector space database for Approximate Nearest Neighbor All those abstraction can co-exist with the same OKVS database and when ACID is supported, the operations happens with the guarantees offered by the transaction system. == Feature matrix == == Use-cases == OKVS are useful to implement two strategies: optimize a small feature e.g. to make a 10% improvement in read or write latency; the second strategy is to take advantage of the distributed nature of FoundationDB, and TiKV, for which there is no equivalent at very large scale in resilience. Both users need to re-implement the needed high level abstractions, because there are no portable ready-to-use libraries of high-level abstraction. There is still a complex balance, of complexity, maintainability, fine-tuning, and readily available features that makes it still a choice of experts. Sometime more specialized data-structures can be faster than a high-level abstraction on top of an OKVS. Another interest of OKVS paradigm stems from it simple, and versatile interface, that makes it an interesting target for experimental storage algorithms, and data structures.
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Secure Electronic Delivery

Secure Electronic Delivery (SED) is a service created in 2003 and provided by the British Library Document Supply Service (BLDSS). Its purpose is to enable faster delivery of digital materials as encrypted, copyright-compliant PDF Documents, to a personal e-mail address. These documents are supplied from the British Library via its On Demand service. When the British Library supplies articles electronically, it sends them securely in order to ensure its usage is permitted (research purposes) and copyright law is observed. == Methods == As the publishing industry, authors and creators become highly protective of their assets and intellectual property, they impose strict rules on delivery methods to prevent copyright infringement. Nowadays, DRM-enabled secure delivery appears to be the most widely used solution to address issues faced by libraries in supplying ebooks and digital materials to their users. SED, one of these solutions, is using Adobe LiveCycle Digital Rights Management (LCDRM) as an encryption method to deliver documents. == Advantages == SED offers convenience, quality and speed as documents are delivered upon request at any location and on any device. Requested articles are scanned for high quality reproduction, opened anywhere on any machine, including mobile devices. == Restrictions == The following are restrictions hold in a SED service implementation: The digital material is accessible only for 14 days via a link sent to a personal message. Due to copyright reasons, the material can be opened only once, saved for 14 days and does not allow a copy-paste action. Upon display, the material must be printed from the same device and reprinted only once. The On Demand encryption technology works best on the default Safari browser although other browsers may accommodate it.
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Round-trip engineering

Round-trip engineering (RTE) in the context of model-driven architecture is a functionality of software development tools that synchronizes two or more related software artifacts, such as, source code, models, configuration files, documentation, etc. between each other. The need for round-trip engineering arises when the same information is present in multiple artifacts and when an inconsistency may arise in case some artifacts are updated. For example, some piece of information was added to/changed in only one artifact (source code) and, as a result, it became missing in/inconsistent with the other artifacts (in models). == Overview == Round-trip engineering is closely related to traditional software engineering disciplines: forward engineering (creating software from specifications), reverse engineering (creating specifications from existing software), and reengineering (understanding existing software and modifying it). Round-trip engineering is often wrongly defined as simply supporting both forward and reverse engineering. In fact, the key characteristic of round-trip engineering that distinguishes it from forward and reverse engineering is the ability to synchronize existing artifacts that evolved concurrently by incrementally updating each artifact to reflect changes made to the other artifacts. Furthermore, forward engineering can be seen as a special instance of RTE in which only the specification is present and reverse engineering can be seen as a special instance of RTE in which only the software is present. Many reengineering activities can also be understood as RTE when the software is updated to reflect changes made to the previously reverse engineered specification. === Types === Various books describe two types of RTE: partial or uni-directional RTE: changes made to a higher level representation of a code and model are reflected in lower level, but not otherwise; the latter might be allowed, but with limitations that may not affect higher-level abstractions full or bi-directional RTE: regardless of changes, both higher and lower-level code and model representations are synchronized if any of them altered === Auto synchronization === Another characteristic of round-trip engineering is automatic update of the artifacts in response to automatically detected inconsistencies. In that sense, it is different from forward- and reverse engineering which can be both manual (traditionally) and automatic (via automatic generation or analysis of the artifacts). The automatic update can be either instantaneous or on-demand. In instantaneous RTE, all related artifacts are immediately updated after each change made to one of them. In on-demand RTE, authors of the artifacts may concurrently update the artifacts (even in a distributed setting) and at some point choose to execute matching to identify inconsistencies and choose to propagate some of them and reconcile potential conflicts. === Iterative approach === Round trip engineering may involve an iterative development process. After you have synchronized your model with revised code, you are still free to choose the best way to work – make further modifications to the code or make changes to your model. You can synchronize in either direction at any time and you can repeat the cycle as many times as necessary. == Software == Many commercial tools and research prototypes support this form of RTE; a 2007 book lists Rational Rose, Together, ESS-Model, BlueJ, and Fujaba among those capable, with Fujaba said to be capable to also identify design patterns. == Limitations == A 2005 book on Visual Studio notes for instance that a common problem in RTE tools is that the model reversed is not the same as the original one, unless the tools are aided by leaving laborious annotations in the source code. The behavioral parts of UML impose even more challenges for RTE. Usually, UML class diagrams are supported to some degree; however, certain UML concepts, such as associations and containment do not have straightforward representations in many programming languages which limits the usability of the created code and accuracy of code analysis/reverse engineering (e.g., containment is hard to recognize in the code). A more tractable form of round-trip engineering is implemented in the context of framework application programming interfaces (APIs), whereby a model describing the usage of a framework API by an application is synchronized with that application's code. In this setting, the API prescribes all correct ways the framework can be used in applications, which allows precise and complete detection of API usages in the code as well as creation of useful code implementing correct API usages. Two prominent RTE implementations in this category are framework-specific modeling languages and Spring Roo (Java). Round-trip engineering is critical for maintaining consistency among multiple models and between the models and the code in Object Management Group's (OMG) Model-driven architecture. OMG proposed the QVT (query/view/transformation) standard to handle model transformations required for MDA. To date, a few implementations of the standard have been created. (Need to present practical experiences with MDA in relation to RTE). == Controversies == === Code generation controversy === Code generation (forward-engineering) from models means that the user abstractly models solutions, which are connoted by some model data, and then an automated tool derives from the models parts or all of the source code for the software system. In some tools, the user can provide a skeleton of the program source code, in the form of a source code template where predefined tokens are then replaced with program source code parts during the code generation process. UML (if used for MDA) diagrams specification was criticized for lack the detail which is needed to contain the same information as is covered with the program source. Some developers even claim that "the Code is the design". == Disadvantages == There is a serious risk that the generated code will rapidly differ from the model or that the reverse-engineered model will lose its reflection on the code or a mix of these two problems as result of cycled reengineering efforts. Regarding behavioral/dynamic part of UML for features like statechart diagram there is no equivalents in programming languages. Their translation during code-generation will result in common programming statement (.e.g if,switch,enum) being either missing or misinterpreted. If edited and imported back may result in different or incomplete model. The same goes for code snippets used for code generation stage for the pattern-implementation and user-specific logic: intermixed they may not be easily reverse-engineered back. There is also general lack of advanced tooling for modelling that are comparable to that of modern IDEs (for testing, debugging, navigation, etc.) for general-purpose programming languages and domain-specific languages. == Examples in software engineering == Perhaps the most common form of round-trip engineering is synchronization between UML (Unified Modeling Language) models and the corresponding source code and entity–relationship diagrams in data modelling and database modelling. Round-trip engineering based on Unified Modeling Language (UML) needs three basic tools for software development: Source Code Editor; UML Editor for the Attributes and Methods; Visualisation of UML structure
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DPVweb

DPVweb is a database for virologists working on plant viruses combining taxonomic, bioinformatic and symptom data. == Description == DPVweb is a central web-based source of information about viruses, viroids and satellites of plants, fungi and protozoa. It provides comprehensive taxonomic information, including brief descriptions of each family and genus, and classified lists of virus sequences. It makes use of a large database that also holds detailed, curated, information for all sequences of viruses, viroids and satellites of plants, fungi and protozoa that are complete or that contain at least one complete gene. There are currently about 10,000 such sequences. For comparative purposes, DPVweb also contains a representative sequence of all other fully sequenced virus species with an RNA or single-stranded DNA genome. For each curated sequence the database contains the start and end positions of each feature (gene, non-translated region, etc.), and these have been checked for accuracy. As far as possible, the nomenclature for genes and proteins are standardized within genera and families. Sequences of features (either as DNA or amino acid sequences) can be directly downloaded from the website in FASTA format. The sequence information can also be accessed via client software for personal computers. == History == The Descriptions of Plant Viruses (DPVs) were first published by the Association of Applied Biologists in 1970 as a series of leaflets, each one written by an expert describing a particular plant virus. In 1998 all of the 354 DPVs published in paper were scanned, and converted into an electronic format in a database and distributed on CDROM. In 2001 the descriptions were made available on the new DPVweb site, providing open access to the now 400+ DPVs (currently 415) as well as taxonomic and sequence data on all plant viruses. == Uses == DPVweb is an aid to researchers in the field of plant virology as well as an educational resource for students of virology and molecular biology. The site provides a single point of access for all known plant virus genome sequences making it easy to collect these sequences together for further analysis and comparison. Sequence data from the DPVweb database have proved valuable for a number of projects: survey of codon usage bias amongst all plant viruses, two-way comparisons between comprehensive sets of sequences from the families Flexiviridae and Potyviridae that have helped inform taxonomy and clarify genus and species discrimination criteria, a survey and verification of the polyprotein cleavage sites within the family Potyviridae.
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Causal AI

Causal AI is a technique in artificial intelligence that builds a causal model and can thereby make inferences using causality rather than just correlation. One practical use for causal AI is for organisations to explain decision-making and the causes for a decision. Systems based on causal AI, by identifying the underlying web of causality for a behaviour or event, provide insights that solely predictive AI models might fail to extract from historical data. An analysis of causality may be used to supplement human decisions in situations where understanding the causes behind an outcome is necessary, such as quantifying the impact of different interventions, policy decisions or performing scenario planning. A 2024 paper from Google DeepMind demonstrated mathematically that "Any agent capable of adapting to a sufficiently large set of distributional shifts must have learned a causal model". The paper offers the interpretation that learning to generalise beyond the original training set requires learning a causal model, concluding that causal AI is necessary for artificial general intelligence. == History == The concept of causal AI and the limits of machine learning were raised by Judea Pearl, the Turing Award-winning computer scientist and philosopher, in 2018's The Book of Why: The New Science of Cause and Effect. Pearl asserted: “Machines' lack of understanding of causal relations is perhaps the biggest roadblock to giving them human-level intelligence.” In 2020, Columbia University established a Causal AI Lab under Director Elias Bareinboim. Professor Bareinboim's research focuses on causal and counterfactual inference and their applications to data-driven fields in the health and social sciences as well as artificial intelligence and machine learning. Technological research and consulting firm Gartner for the first time included causal AI in its 2022 Hype Cycle report, citing it as one of five critical technologies in accelerated AI automation. Causal AI is closely related to but distinct from fields such as causal inference, explainable AI and causal reasoning. While causal inference focuses on estimating cause-effect relationships (often from observational data), causal AI emphasises the integration of those causal models into AI systems for prediction, planning and adaptation.
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Small Data

Small Data: the Tiny Clues that Uncover Huge Trends is Martin Lindstrom's seventh book. It chronicles his work as a branding expert, working with consumers across the world to better understand their behavior. The theory behind the book is that businesses can better create products and services based on observing consumer behavior in their homes, as opposed to relying solely on big data. == Content == The book is based on a several year period of consumer studies for major corporations across the globe. It features case studies of the author's work interviewing consumers in their homes and using his observations to create hypotheses as to why they use products the way that they do. == Public reception == The book was a New York Times Bestseller upon release and was positively reviewed on several websites, Including Entrepreneur and Forbes. In 2016, it was named a Best Business Book by strategy+business and one of Inc. Magazine's Best Sales and Marketing books.
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Scale space

Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter t {\displaystyle t} in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about t {\displaystyle {\sqrt {t}}} have largely been smoothed away in the scale-space level at scale t {\displaystyle t} . The main type of scale space is the linear (Gaussian) scale space, which has wide applicability as well as the attractive property of being possible to derive from a small set of scale-space axioms. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made scale invariant, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances. == Definition == The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. Consider a given image f {\displaystyle f} where f ( x , y ) {\displaystyle f(x,y)} is the greyscale value of the pixel at position ( x , y ) {\displaystyle (x,y)} . The linear (Gaussian) scale-space representation of f {\displaystyle f} is a family of derived signals L ( x , y ; t ) {\displaystyle L(x,y;t)} defined by the convolution of f ( x , y ) {\displaystyle f(x,y)} with the two-dimensional Gaussian kernel g ( x , y ; t ) = 1 2 π t e − ( x 2 + y 2 ) / 2 t {\displaystyle g(x,y;t)={\frac {1}{2\pi t}}e^{-(x^{2}+y^{2})/2t}\,} such that L ( ⋅ , ⋅ ; t ) = g ( ⋅ , ⋅ ; t ) ∗ f ( ⋅ , ⋅ ) , {\displaystyle L(\cdot ,\cdot ;t)\ =g(\cdot ,\cdot ;t)f(\cdot ,\cdot ),} where the semicolon in the argument of L {\displaystyle L} implies that the convolution is performed only over the variables x , y {\displaystyle x,y} , while the scale parameter t {\displaystyle t} after the semicolon just indicates which scale level is being defined. This definition of L {\displaystyle L} works for a continuum of scales t ≥ 0 {\displaystyle t\geq 0} , but typically only a finite discrete set of levels in the scale-space representation would be actually considered. The scale parameter t = σ 2 {\displaystyle t=\sigma ^{2}} is the variance of the Gaussian filter and as a limit for t = 0 {\displaystyle t=0} the filter g {\displaystyle g} becomes an impulse function such that L ( x , y ; 0 ) = f ( x , y ) , {\displaystyle L(x,y;0)=f(x,y),} that is, the scale-space representation at scale level t = 0 {\displaystyle t=0} is the image f {\displaystyle f} itself. As t {\displaystyle t} increases, L {\displaystyle L} is the result of smoothing f {\displaystyle f} with a larger and larger filter, thereby removing more and more of the details that the image contains. Since the standard deviation of the filter is σ = t {\displaystyle \sigma ={\sqrt {t}}} , details that are significantly smaller than this value are to a large extent removed from the image at scale parameter t {\displaystyle t} , see the following figures and for graphical illustrations. === Why a Gaussian filter? === When faced with the task of generating a multi-scale representation one may ask: could any filter g of low-pass type and with a parameter t which determines its width be used to generate a scale space? The answer is no, as it is of crucial importance that the smoothing filter does not introduce new spurious structures at coarse scales that do not correspond to simplifications of corresponding structures at finer scales. In the scale-space literature, a number of different ways have been expressed to formulate this criterion in precise mathematical terms. The conclusion from several different axiomatic derivations that have been presented is that the Gaussian scale space constitutes the canonical way to generate a linear scale space, based on the essential requirement that new structures must not be created when going from a fine scale to any coarser scale. Conditions, referred to as scale-space axioms, that have been used for deriving the uniqueness of the Gaussian kernel include linearity, shift invariance, semi-group structure, non-enhancement of local extrema, scale invariance and rotational invariance. In the works, the uniqueness claimed in the arguments based on scale invariance has been criticized, and alternative self-similar scale-space kernels have been proposed. The Gaussian kernel is, however, a unique choice according to the scale-space axiomatics based on causality or non-enhancement of local extrema. === Alternative definition === Equivalently, the scale-space family can be defined as the solution of the diffusion equation (for example in terms of the heat equation), ∂ t L = 1 2 ∇ 2 L , {\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This formulation of the scale-space representation L means that it is possible to interpret the intensity values of the image f as a "temperature distribution" in the image plane and that the process that generates the scale-space representation as a function of t corresponds to heat diffusion in the image plane over time t (assuming the thermal conductivity of the material equal to the arbitrarily chosen constant ⁠1/2⁠). Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2+1-D volume generated by the scale space, thus within the framework of partial differential equations. Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion. Hence, one may say that the primary way to generate a scale space is by the diffusion equation, and that the Gaussian kernel arises as the Green's function of this specific partial differential equation. == Motivations == The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. This implies that real-world objects, in contrast to idealized mathematical entities such as points or lines, may appear in different ways depending on the scale of observation. For example, the concept of a "tree" is appropriate at the scale of meters, while concepts such as leaves and molecules are more appropriate at finer scales. For a computer vision system analysing an unknown scene, there is no way to know a priori what scales are appropriate for describing the interesting structures in the image data. Hence, the only reasonable approach is to consider descriptions at multiple scales in order to be able to capture the unknown scale variations that may occur. Taken to the limit, a scale-space representation considers representations at all scales. Another motivation to the scale-space concept originates from the process of performing a physical measurement on real-world data. In order to extract any information from a measurement process, one has to apply operators of non-infinitesimal size to the data. In many branches of computer science and applied mathematics, the size of the measurement operator is disregarded in the theoretical modelling of a problem. The scale-space theory on the other hand explicitly incorporates the need for a non-infinitesimal size of the image operators as an integral part of any measurement as well as any other operation that depends on a real-world measurement. There is a close link between scale-space theory and biological vision. Many scale-space operations show a high degree of similarity with receptive field profiles recorded from the mammalian retina and the first stages in the visual cortex. In these respects, the scale-space framework can be seen as a theoretically well-founded paradigm for early vision, which in addition has been thoroughly tested by algorithms and experiments. == Gaussian derivatives == At any scale in scale space, we c
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AlphaTensor

AlphaTensor is an artificial intelligence system developed by DeepMind for discovering efficient matrix multiplication algorithms using reinforcement learning. Introduced in 2022, the system was based on AlphaZero and formulated the search for matrix multiplication algorithms as a single-player game called TensorGame. AlphaTensor was designed to search for new ways to multiply matrices with fewer scalar multiplication operations. Matrix multiplication is a fundamental operation in linear algebra, numerical analysis, scientific computing, computer graphics, and machine learning. The system discovered thousands of matrix multiplication algorithms, including algorithms that rediscovered known human-designed methods and others that improved on previously known results for particular matrix sizes and mathematical settings. == Background == Matrix multiplication is one of the basic operations in numerical computing. The standard algorithm for multiplying two square matrices has cubic time complexity, while faster algorithms such as the Strassen algorithm reduce the number of multiplication operations by using more complex algebraic decompositions. Finding optimal matrix multiplication algorithms can be difficult because it involves searching through a large space of possible tensor decompositions. AlphaTensor approached this problem by representing algorithm discovery as TensorGame, in which each move corresponds to an operation that reduces a tensor representing matrix multiplication. The goal of the game is to find a low-rank decomposition of the matrix multiplication tensor, corresponding to an efficient multiplication algorithm. == Development == AlphaTensor was developed by DeepMind and described in a paper published in Nature in October 2022. The system built on the reinforcement-learning approach used in AlphaZero, which had previously been applied to games such as Go, chess, and shogi. Unlike those games, TensorGame involved a very large search space, requiring changes to the AlphaZero-style search method and neural network architecture. DeepMind released source code and discovered algorithms associated with the publication through a public GitHub repository. == Results == AlphaTensor discovered matrix multiplication algorithms over both standard arithmetic and finite fields. One widely reported result was a method for multiplying 4 × 4 matrices over the field with two elements using 47 multiplication operations, improving on the 49 operations required by applying Strassen's algorithm recursively in that setting. The system also found algorithms optimized for particular computer hardware, including algorithms designed for graphics processing units and Tensor Processing Units. DeepMind stated that some of the hardware-specific algorithms improved practical execution time compared with commonly used algorithms on the tested hardware. == Significance == AlphaTensor was described as an example of using machine learning not only to apply existing algorithms, but to assist in discovering new ones. The work was connected to broader research in algorithm discovery, automated machine learning, program synthesis, and computational complexity theory, especially the open problem of determining the optimal complexity of matrix multiplication. AlphaTensor later became part of a broader group of Google DeepMind systems for algorithm and mathematical discovery, alongside systems such as AlphaDev and AlphaEvolve.
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Information quality

Information quality (IQ) is a contextual property of or a perspective to the content within information systems. There exist two complementary yet partially conflicting definitions of high-quality: firstly, information is considered high quality if it is fit for its intended purpose ; secondly, it is deemed high quality if it conforms to specified requirements . The primary distinction between these definitions is that Juran's perspective focuses on the suitability of information for its intended purpose, which can be measured by the success of its application even without direct access to or exact knowledge of the data. For example, a black-box AI with access to English Wikipedia can work well for users' purposes but using Estonian Wikipedia fails for the same purposes. Given that the AI remains the same, it can be concluded that English version data would be of higher quality in comparison to Estonian version, even without exact comparison of data contents and their properties in each version. In contrast, Crosby emphasizes adherence to predefined specifications, assuming specific criteria rather than measuring the success of its use; for instance, information in Wikipedia could be proven to be good based on criteria such as existing peer validation and academic references, even if the AI results are poor. This approach falls into problems when data is not completely accessible or all quality properties cannot be known and measured leading to false impression of quality due to lacking and misleading metrics. Numerous IQ frameworks and methodologies provide tangible approach to assess and measure DQ/IQ in a robust and rigorous manner. == Conceptual problems == Although the foundational definitions are usable for most everyday purposes, specialists often use more complex models for information quality. It has been suggested, however, that higher the quality the greater will be the confidence in meeting more general, less specific contexts. == Dimensions and metrics of information quality == "Information quality" is a measure of its fitness for use or conformance to requirements. In this way, "quality" is considered contextual and it can then vary across users and uses of the information. The exact degree of quality is often described with dimensions such as accuracy, timeliness, completeness, and similar scales. Although a huge amount of academic research has been directed to these dimensions, there does not exist consensus on their definitions or practical usefulness . Historically, Richard Wang and Diane Strong proposed a list of dimensions or elements used in assessing Information Quality is: Intrinsic IQ: accuracy, objectivity, believability, reputation Contextual IQ: relevance, value-added, timeliness, completeness, amount of information Representational IQ: interpretability, format, coherence, compatibility Accessibility IQ: accessibility, access security Other authors propose similar but different lists of dimensions for analysis, and emphasize measurement and reporting as information quality metrics. Larry English prefers the term "characteristics" to dimensions. However, a considerable amount of information quality research involves investigating and describing various categories of desirable attributes (or dimensions) of data. Research has recently shown the huge diversity of terms and classification structures used. === Quality metrics === Source: Authority/verifiability Authority refers to the expertise or recognized official status of a source. Consider the reputation of the author and publisher. When working with legal or government information, consider whether the source is the official provider of the information. Verifiability refers to the ability of a reader to verify the validity of the information irrespective of how authoritative the source is. To verify the facts is part of the duty of care of the journalistic deontology, as well as, where possible, to provide the sources of information so that they can be verified Scope of coverage Scope of coverage refers to the extent to which a source explores a topic. Consider time periods, geography or jurisdiction and coverage of related or narrower topics. Composition and organization Composition and organization has to do with the ability of the information source to present its particular message in a coherent, logically sequential manner. Objectivity Objectivity is the bias or opinion expressed when a writer interprets or analyze facts. Consider the use of persuasive language, the source's presentation of other viewpoints, its reason for providing the information and advertising. Integrity Adherence to moral and ethical principles; soundness of moral character The state of being whole, entire, or undiminished Comprehensiveness Of large scope; covering or involving much; inclusive: a comprehensive study. Comprehending mentally; having an extensive mental grasp. Insurance. covering or providing broad protection against loss. Validity Validity of some information has to do with the degree of obvious truthfulness which the information carries Uniqueness As much as 'uniqueness' of a given piece of information is intuitive in meaning, it also significantly implies not only the originating point of the information but also the manner in which it is presented and thus the perception which it conjures. The essence of any piece of information we process consists to a large extent of those two elements. Timeliness Timeliness refers to information that is current at the time of publication. Consider publication, creation and revision dates. Beware of Web site scripting that automatically reflects the current day's date on a page. Reproducibility (utilized primarily when referring to instructive information) Means that documented methods are capable of being used on the same data set to achieve a consistent result. == Professional associations == IQ International—the International Association for Information and Data Quality IQ International is a not-for-profit, vendor neutral, professional association formed in 2004, dedicated to building the information and data quality profession. CDOIQ Society Chief Data Officers and Information Quality Society is a global professional society supporting data leaders with networking, meetings, best practices, experience, certification, and training. == Information quality conferences == A number of major conferences relevant to information quality are held annually: Annual MIT Chief Data Officer & Information Quality (CDOIQ) Symposium Annual conferences held at the Massachusetts Institute of Technology, Cambridge, MA, USA Data Governance and Information Quality Conference Commercial conferences held each year in the USA Data Quality Asia Pacific Commercial conference held annually in Sydney or Melbourne, Australia Enterprise Data and Business Intelligence Conference Europe Commercial conferences held annually in London, England. Information and Data Quality Conference Not for profit conference run annually by IQ International (the International Association for Information and Data Quality) in the USA International Conference on Information Quality Academic Conference launched through MITIQ held annually at a University Master Data Management & Data Governance Conferences Six major conferences are run annually by the MDM Institute in venues such as London, San Francisco, Sydney, Toronto, Madrid, Frankfurt, Shanghai and New York City.
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Open Compute Project

The Open Compute Project (OCP) is an organization that facilitates the sharing of data center product designs and industry best practices among companies. Founded in 2011, OCP has significantly influenced the design and operation of large-scale computing facilities worldwide. As of February 2025, over 400 companies across the world are members of OCP, including Arm, Meta, IBM, Wiwynn, Intel, Nokia, Google, Microsoft, Seagate Technology, Dell, Rackspace, Hewlett Packard Enterprise, NVIDIA, Cisco, Goldman Sachs, Fidelity, Lenovo, Accton Technology Corporation and Alibaba Group. == Structure == The Open Compute Project Foundation is a 501(c)(6) non-profit incorporated in the state of Delaware, United States. OCP has multiple committees, including the board of directors, advisory board and steering committee to govern its operations. As of July 2020, there are seven members who serve on the board of directors which is made up of one individual member and six organizational members. Mark Roenigk (Facebook) is the Foundation's president and chairman. Andy Bechtolsheim is the individual member. In addition to Mark Roenigk who represents Facebook, other organizations on the Open Compute board of directors include Intel (Rebecca Weekly), Microsoft (Kushagra Vaid), Google (Partha Ranganathan), and Rackspace (Jim Hawkins). A list of members can be found on the OCP website. == History == The Open Compute Project began at Facebook (now Meta) in 2009 as an internal project called "Project Freedom". The hardware designs and engineering teams were led by Amir Michael (Manager, Hardware Design) and sponsored by Jonathan Heiliger (VP, Technical Operations) and Frank Frankovsky (Director, Hardware Design and Infrastructure). The three would later open source the designs of Project Freedom and co-found the Open Compute Project. The project was announced at a press event at Facebook's headquarters in Palo Alto on April 7, 2011. == OCP projects == The Open Compute Project Foundation maintains a number of OCP projects, such as: === Server designs === In 2013, two years after the Open Compute Project had started, it was noted that the goal of a more modular server design was "still a long way from live data centers". However, by then some aspects published had been used in Facebook's Prineville data center to improve energy efficiency, as measured by the power usage effectiveness index defined by The Green Grid. Efforts to advance server compute node designs included one for Intel processors and one for AMD processors. Also in 2013, Calxeda contributed a design with ARM architecture processors. Since then, several generations of OCP server designs have been deployed: Wildcat (Intel), Spitfire (AMD), Windmill (Intel E5-2600), Watermark (AMD), Winterfell (Intel E5-2600 v2) and Leopard (Intel E5-2600 v3). === OCP Accelerator Module === OCP Accelerator Module (OAM) is a design specification for hardware architectures that implement artificial intelligence systems that require high module-to-module bandwidth. OAM is used in some of AMD's Instinct accelerator modules. === Rack and power designs === Designs for a mechanical mounting system to replace standard 19-inch racks have been published, with a cabinet the same outside width (600 mm) and depth as existing racks, but with an interior space allowing for wider equipment chassis with a 537 mm width (21 inches). This allows more equipment to fit in the same volume and improves air flow. Compute chassis sizes are defined in multiples of an OpenU or OU, which is 48 mm, slightly taller than the 44 mm rack unit defined for 19-inch racks. As of March 2026, the most current base mechanical definition is the Open Rack V3.1 Specification. At the time the base specification was released, Meta also defined in greater depth the specifications for the rectifiers and power shelf. Specifications for the power monitoring interface (PMI), a communications interface enabling upstream communications between the rectifiers and battery backup unit(BBU) were published by Meta that same year, with Delta Electronics as the main technical contributor to the BBU spec. However, since 2022 the AI boom in the data center has created higher power requirements in order to satisfy the demands of AI accelerators that have been released. As of September 2024, Meta is in the process of updating its Open Rack v3 rectifier, power shelf, battery backup and power management interface specifications to accommodate this increased energy demand. In May 2024, at an Open Compute regional summit, Meta and Rittal outlined their plans for development of their High Power Rack (HPR) ecosystem in conjunction with rack, power and cable partners, increasing power capacity in the rack to 92 kilowatts or more. At the same meeting, Delta Electronics and Advanced Energy reported on their progress in developing new Open Compute standard specifications for power shelf and rectifier designs for HPR applications. Rittal also outlined their collaboration with Meta in designing airflow containment, busbar designs and grounding schemes for the new HPR requirements. === Data storage === Open Vault storage building blocks (also called "Knox") offer high disk densities, with 30 drives in a 2 OU Open Rack chassis designed for easy disk drive replacement. The 3.5 inch disks are stored in two drawers, five across and three deep in each drawer, with connections via serial attached SCSI. There is a "cold storage" variant where idle disks power down to reduce energy consumption. Another design concept was contributed by Hyve Solutions, a division of Synnex, in 2012. At the OCP Summit 2016 Facebook, together with Taiwanese ODM Wistron's spin-off Wiwynn, introduced "Lightning", a flexible NVMe JBOF (just a bunch of flash), based on the existing Open Vault (Knox) design. === Energy efficient data centers === The OCP has published data center designs for energy efficiency. These include power distribution at three-phase 277/480 VAC, which eliminates one transformer stage in typical North American data centers, a single voltage (12.5 VDC) power supply designed to work with 277/480 VAC input, and 48 VDC battery backup. For European (and other 230V countries) datacenters, there is a specification for 230/400 VAC power distribution and its conversion to 12.5 VDC. === Open networking switches === On May 8, 2013, an effort to define an open network switch was announced. The plan was to allow Facebook to load its own operating system software onto its top-of-rack switches. Press reports predicted that more expensive and higher-performance switches would continue to be popular, while less expensive products treated more like a commodity. The first attempt at an open networking switch by Facebook was designed together with Taiwanese ODM Accton using Broadcom Trident II chip and is called "Wedge"; the Linux OS that it runs is called "FBOSS". Later switch contributions include "6-pack" and Wedge-100, based on Broadcom Tomahawk chips. Similar switch hardware designs have been contributed by: Accton Technology Corporation (and its Edgecore Networks subsidiary), Mellanox Technologies, Interface Masters Technologies, Agema Systems. Capable of running Open Network Install Environment (ONIE)-compatible network operating systems such as Cumulus Linux, Switch Light OS by Big Switch Networks, or PICOS by Pica8. A similar project for a custom switch for the Google platform had been rumored, and evolved to use the OpenFlow protocol. === Servers === A sub-project for Mezzanine (NIC) OCP NIC 3.0 specification 1v00 was released in late 2019 establishing three form factors: SFF, TSFF, and LFF. == Litigation == In March, 2015, BladeRoom Group Limited and Bripco (UK) Limited sued Facebook, Emerson Electric Co. and others alleging that Facebook has disclosed BladeRoom and Bripco's trade secrets for prefabricated data centers in the Open Compute Project. Facebook petitioned for the lawsuit to be dismissed, but this was rejected in 2017. A confidential mid-trial settlement was agreed in April 2018.
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Adobe Encore

Adobe Encore (previously Adobe Encore DVD) was a DVD authoring software tool produced by Adobe Systems and targeted at professional video producers. Video and audio resources could be used in their current format for development, allowing the user to transcode them to MPEG-2 video and Dolby Digital audio upon project completion. DVD menus could be created and edited in Adobe Photoshop using special layering techniques. Adobe Encore did not support writing to a Blu-ray Disc using AVCHD 2.0. Encore is bundled with Adobe Premiere Pro CS6. Adobe Encore CS6 was the last release. While Premiere Pro CC has moved to the Creative Cloud, Encore has now been discontinued. == Licensing == All forms of Adobe Encore used a proprietary licensing system from its developer, Adobe Systems. Versions 1.0 and 1.5 required a separate license fee (rather than making 1.5 available as a free update). Version 3, also known as CS3, was sold only in bundle with Premiere CS3. Encore CS4, CS5, CS5.5 and CS6 were only sold in the Premiere Pro CS4, CS5, CS5.5 and CS6 bundles, respectively. Adobe CC subscribers no longer have access to Adobe Encore CS6. Adobe Encore is not included with Premiere Pro CC. == Functionality == Adobe Encore allowed for creating interactive DVD menus from Photoshop documents, which could be tweaked from within Encore. Video and audio streams could be embedded in the DVD and be made to play when certain elements of the menu are interacted with. It had similar functionality to Adobe Flash and Premiere Pro, due to its ability to both edit video on a timeline and embed interactive content.
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BioCreative

BioCreAtIvE (A critical assessment of text mining methods in molecular biology) consists in a community-wide effort for evaluating information extraction and text mining developments in the biological domain. It was preceded by the Knowledge Discovery and Data Mining (KDD) Challenge Cup for detection of gene mentions. == Community Challenges == === First edition (2004-2005) === Three main tasks were posed at the first BioCreAtIvE challenge: the entity extraction task, the gene name normalization task, and the functional annotation of gene products task. The data sets produced by this contest serve as a Gold Standard training and test set to evaluate and train Bio-NER tools and annotation extraction tools. === Second edition (2006-2007) === The second BioCreAtIvE challenge (2006-2007) had also 3 tasks: detection of gene mentions, extraction of unique idenfiers for genes and extraction information related to physical protein-protein interactions. It counted with participation of 44 teams from 13 countries. === Third edition (2011-2012) === The third edition of BioCreative included for the first time the InterActive Task (IAT), designed to evaluate the practical usability of text mining tools in real-world biocuration tasks. === Fifth edition (2016) === BioCreative V had 5 different tracks, including an interactive task (IAT) for usability of text mining systems and a track using the BioC format for curating information for BioGRID.
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TurboQuant

TurboQuant is an online vector quantization algorithm for compressing high-dimensional Euclidean vectors while preserving their geometric structure. It was proposed in 2025 by Amir Zandieh, Majid Daliri, Majid Hadian, and Vahab Mirrokni in the paper TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. The paper lists Zandieh and Mirrokni as affiliated with Google Research, Daliri with New York University, and Hadian with Google DeepMind. The method was developed for applications including large language model (LLM) inference, key–value (KV) cache compression, vector databases, and nearest neighbor search. TurboQuant consists of two related algorithms: TurboQuantmse, which is optimized for mean squared error (MSE), and TurboQuantprod, which is optimized for unbiased inner product estimation. The algorithm uses a random rotation of input vectors, applies scalar quantizers to the rotated coordinates, and, for inner-product estimation, applies a one-bit Quantized Johnson–Lindenstrauss (QJL) transform to the residual error. == Background == Vector quantization is a compression method that maps high-dimensional vectors to a finite set of codewords. The problem has roots in Shannon's source coding theory and rate–distortion theory. In machine learning and information retrieval, vector quantization is used to reduce the memory required to store embeddings, activation vectors, and other numerical representations. In Transformer-based large language models, the KV cache stores key and value vectors from previous tokens during autoregressive decoding. The size of this cache grows with context length, the number of attention heads, and the number of concurrent requests, making it a major memory bottleneck in LLM serving. Similar compression problems appear in vector search, where large collections of embedding vectors must be stored and searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction. The TurboQuant paper argues that many existing methods either require offline preprocessing and calibration or suffer from suboptimal distortion guarantees in online settings. == Algorithm == === TurboQuantmse === TurboQuantmse is the version of the algorithm optimized for mean-squared error. For a unit vector x ∈ S d − 1 {\displaystyle x\in S^{d-1}} , the algorithm first applies a random rotation matrix Π ∈ R d × d {\displaystyle \Pi \in \mathbb {R} ^{d\times d}} and sets z = Π x {\displaystyle z=\Pi x} . Each coordinate of the rotated vector follows a shifted and scaled beta distribution, which converges to a normal distribution in high dimensions. In high dimensions, distinct coordinates also become nearly independent, allowing the algorithm to apply scalar quantizers independently to each coordinate. The scalar quantizer is constructed by solving a one-dimensional continuous k-means or Lloyd–Max quantization problem. If the centroids are c 1 , c 2 , … , c 2 b {\displaystyle c_{1},c_{2},\ldots ,c_{2^{b}}} , the quantization step stores, for each coordinate, i d x j = ⁡ a r g m i n k ∈ [ 2 b ] | z j − c k | . {\displaystyle \mathrm {idx} _{j}=\operatorname {} {arg\,min}_{k\in [2^{b}]}|z_{j}-c_{k}|.} During dequantization, the stored index for each coordinate is replaced by the corresponding centroid, giving a reconstructed rotated vector z ~ {\displaystyle {\tilde {z}}} . The algorithm then rotates back: x ~ = Π ⊤ z ~ . {\displaystyle {\tilde {x}}=\Pi ^{\top }{\tilde {z}}.} The paper gives the following bound for TurboQuantmse: D m s e ≤ 3 π 2 ⋅ 1 4 b . {\displaystyle D_{\mathrm {mse} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {1}{4^{b}}}.} It also reports finer-grained MSE values of approximately 0.36, 0.117, 0.03, and 0.009 for bit-widths b = 1 , 2 , 3 , 4 {\displaystyle b=1,2,3,4} , respectively. === TurboQuantprod === TurboQuantprod is optimized for unbiased inner-product estimation. The authors note that an MSE-optimized quantizer may introduce bias when used to estimate inner products. To address this, TurboQuantprod first applies TurboQuantmse with bit-width b − 1 {\displaystyle b-1} , then applies a one-bit Quantized Johnson–Lindenstrauss transform to the remaining residual vector. Let r = x − Q m s e − 1 ( Q m s e ( x ) ) {\displaystyle r=x-Q_{\mathrm {mse} }^{-1}(Q_{\mathrm {mse} }(x))} be the residual after MSE quantization, and let γ = ‖ r ‖ 2 {\displaystyle \gamma =\|r\|_{2}} . The QJL step stores a sign vector for the residual. For γ ≠ 0 {\displaystyle \gamma \neq 0} , this can be written using the normalized residual u = r / γ {\displaystyle u=r/\gamma } : q j l = sign ⁡ ( S u ) , {\displaystyle qjl=\operatorname {sign} (Su),} where S ∈ R d × d {\displaystyle S\in \mathbb {R} ^{d\times d}} is a random projection matrix. Since the sign function is invariant under positive rescaling, this is equivalent to sign ⁡ ( S r ) {\displaystyle \operatorname {sign} (Sr)} when r ≠ 0 {\displaystyle r\neq 0} . If γ = 0 {\displaystyle \gamma =0} , the residual correction is zero. TurboQuantprod stores the MSE quantization, the QJL sign vector, and the residual norm: Q p r o d ( x ) = [ Q m s e ( x ) , q j l , γ ] . {\displaystyle Q_{\mathrm {prod} }(x)=\left[Q_{\mathrm {mse} }(x),qjl,\gamma \right].} The dequantized vector is reconstructed as x ~ = x ~ m s e + π / 2 d γ S ⊤ q j l . {\displaystyle {\tilde {x}}={\tilde {x}}_{\mathrm {mse} }+{\frac {\sqrt {\pi /2}}{d}}\,\gamma S^{\top }qjl.} The paper proves that TurboQuantprod is unbiased for inner-product estimation: E x ~ [ ⟨ y , x ~ ⟩ ] = ⟨ y , x ⟩ . {\displaystyle \mathbb {E} _{\tilde {x}}\left[\langle y,{\tilde {x}}\rangle \right]=\langle y,x\rangle .} It also gives the distortion bound D p r o d ≤ 3 π 2 ⋅ ‖ y ‖ 2 2 d ⋅ 1 4 b . {\displaystyle D_{\mathrm {prod} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {\|y\|_{2}^{2}}{d}}\cdot {\frac {1}{4^{b}}}.} == Performance and applications == The TurboQuant paper reports that the algorithm achieves near-optimal distortion rates within a small constant factor of information-theoretic lower bounds. The authors report that, for KV cache quantization, TurboQuant achieved quality neutrality at 3.5 bits per channel and marginal degradation at 2.5 bits per channel. In long-context LLM experiments using Llama 3.1 8B Instruct, the paper evaluated the method on a "needle-in-a-haystack" retrieval task with document lengths from 4,000 to 104,000 tokens. It reported that TurboQuant matched the uncompressed full-precision baseline while using more than 4× compression, and compared the method against PolarQuant, SnapKV, PyramidKV, and KIVI. Google Research stated that TurboQuant was evaluated on long-context benchmarks including LongBench, Needle in a Haystack, ZeroSCROLLS, RULER, and L-Eval using open-source models including Gemma and Mistral. According to a report in Tom's Hardware, Google described the method as reducing KV-cache memory by at least six times and achieving up to an eightfold improvement in attention-logit computation on Nvidia H100 GPUs compared with unquantized 32-bit keys. TurboQuant has also been applied to nearest-neighbor vector search. The original paper reports experiments on DBpedia entity embeddings and GloVe embeddings, comparing TurboQuant with product quantization and other vector-search quantization baselines. == Relationship to other methods == TurboQuant is related to several methods for efficient large language model inference and high-dimensional search: Product quantization – a vector quantization technique widely used for approximate nearest-neighbor search Quantization (machine learning) – reducing the numerical precision of weights, activations, or cached tensors in machine learning models PagedAttention – a memory-management algorithm for LLM serving that reduces fragmentation in the KV cache Johnson–Lindenstrauss lemma – a result in high-dimensional geometry used in random projection methods Lloyd's algorithm – an algorithm for scalar and vector quantization, including k-means-style codebook construction Unlike PagedAttention, which focuses on memory allocation and cache layout, TurboQuant reduces the numerical storage cost of the vectors themselves. Unlike many product-quantization methods, TurboQuant is designed to be data-oblivious and online, avoiding dataset-specific codebook training. == Limitations == The strongest performance claims for TurboQuant come from the original paper and Google Research's own publication. Coverage in technology media has noted that the broader impact of the method will depend on real-world implementation details, workloads, and hardware architectures.
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