AI Project Management Tools

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  Foreign key

  A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S; furthermore that those attributes must also be a candidate key in S. In other words, a foreign key is a set of attributes that references a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON. == Summary == The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a candidate key is a set of zero or more attributes, the values of which are guaranteed to be unique for each tuple (row) in a relation. The value or combination of values of candidate key attributes for any tuple cannot be duplicated for any other tuple in that relation. Since the purpose of the foreign key is to identify a particular row of referenced table, it is generally required that the foreign key is equal to the candidate key in some row of the primary table, or else have no value (the NULL value.). This rule is called a referential integrity constraint between the two tables. Because violations of these constraints can be the source of many database problems, most database management systems provide mechanisms to ensure that every non-null foreign key corresponds to a row of the referenced table. For example, consider a database with two tables: a CUSTOMER table that includes all customer data and an ORDER table that includes all customer orders. Suppose the business requires that each order must refer to a single customer. To reflect this in the database, a foreign key column is added to the ORDER table (e.g., CUSTOMERID), which references the primary key of CUSTOMER (e.g. ID). Because the primary key of a table must be unique, and because CUSTOMERID only contains values from that primary key field, we may assume that, when it has a value, CUSTOMERID will identify the particular customer which placed the order. However, this can no longer be assumed if the ORDER table is not kept up to date when rows of the CUSTOMER table are deleted or the ID column altered, and working with these tables may become more difficult. Many real world databases work around this problem by 'inactivating' rather than physically deleting master table foreign keys, or by complex update programs that modify all references to a foreign key when a change is needed. Foreign keys play an essential role in database design. One important part of database design is making sure that relationships between real-world entities are reflected in the database by references, using foreign keys to refer from one table to another. Another important part of database design is database normalization, in which tables are broken apart and foreign keys make it possible for them to be reconstructed. Multiple rows in the referencing (or child) table may refer to the same row in the referenced (or parent) table. In this case, the relationship between the two tables is called a one to many relationship between the referencing table and the referenced table. In addition, the child and parent table may, in fact, be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in SQL:2003 as a self-referencing or recursive foreign key. In database management systems, this is often accomplished by linking a first and second reference to the same table. A table may have multiple foreign keys, and each foreign key can have a different parent table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys. A foreign key is defined as an attribute or set of attributes in a relation whose values match a primary key in another relation. The syntax to add such a constraint to an existing table is defined in SQL:2003 as shown below. Omitting the column list in the REFERENCES clause implies that the foreign key shall reference the primary key of the referenced table. Likewise, foreign keys can be defined as part of the CREATE TABLE SQL statement. If the foreign key is a single column only, the column can be marked as such using the following syntax: Foreign keys can be defined with a stored procedure statement. child_table: the name of the table or view that contains the foreign key to be defined. parent_table: the name of the table or view that has the primary key to which the foreign key applies. The primary key must already be defined. col3 and col4: the name of the columns that make up the foreign key. The foreign key must have at least one column and at most eight columns. == Referential actions == Because the database management system enforces referential constraints, it must ensure data integrity if rows in a referenced table are to be deleted (or updated). If dependent rows in referencing tables still exist, those references have to be considered. SQL:2003 specifies 5 different referential actions that shall take place in such occurrences: CASCADE RESTRICT NO ACTION SET NULL SET DEFAULT === CASCADE === Whenever rows in the parent (referenced) table are deleted (or updated), the respective rows of the child (referencing) table with a matching foreign key column will be deleted (or updated) as well. This is called a cascade delete (or update). === RESTRICT === A value cannot be updated or deleted when a row exists in a referencing or child table that references the value in the referenced table. Similarly, a row cannot be deleted as long as there is a reference to it from a referencing or child table. To understand RESTRICT (and CASCADE) better, it may be helpful to notice the following difference, which might not be immediately clear. The referential action CASCADE modifies the "behavior" of the (child) table itself where the word CASCADE is used. For example, ON DELETE CASCADE effectively says "When the referenced row is deleted from the other table (master table), then delete also from me". However, the referential action RESTRICT modifies the "behavior" of the master table, not the child table, although the word RESTRICT appears in the child table and not in the master table! So, ON DELETE RESTRICT effectively says: "When someone tries to delete the row from the other table (master table), prevent deletion from that other table (and of course, also don't delete from me, but that's not the main point here)." RESTRICT is not supported by Microsoft SQL 2012 and earlier. === NO ACTION === NO ACTION and RESTRICT are very much alike. The main difference between NO ACTION and RESTRICT is that with NO ACTION the referential integrity check is done after trying to alter the table. RESTRICT does the check before trying to execute the UPDATE or DELETE statement. Both referential actions act the same if the referential integrity check fails: the UPDATE or DELETE statement will result in an error. In other words, when an UPDATE or DELETE statement is executed on the referenced table using the referential action NO ACTION, the DBMS verifies at the end of the statement execution that none of the referential relationships are violated. This is different from RESTRICT, which assumes at the outset that the operation will violate the constraint. Using NO ACTION, the triggers or the semantics of the statement itself may yield an end state in which no foreign key relationships are violated by the time the constraint is finally checked, thus allowing the statement to complete successfully. === SET NULL, SET DEFAULT === In general, the action taken by the DBMS for SET NULL or SET DEFAULT is the same for both ON DELETE or ON UPDATE: the value of the affected referencing attributes is changed to NULL for SET NULL, and to the specified default value for SET DEFAULT. === Triggers === Referential actions are generally implemented as implied triggers (i.e. triggers with system-generated names, often hidden.) As such, they are subject to the same limitations as user-defined triggers, and their order of execution relative to other triggers may need to be considered; in some cases it may become necessary to replace the referential action with its equivalent user-defined trigger to ensure proper execution order, or to work around mutating-table limitations. Another important limitation appears with transaction isolation: your changes to a row may not be able to fully cascade because the row is ref

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  Bayesian programming

  Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot". Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs. == Formalism == A Bayesian program is a means of specifying a family of probability distributions. The constituent elements of a Bayesian program are presented below: Program { Description { Specification ( π ) { Variables Decomposition Forms Identification (based on δ ) Question {\displaystyle {\text{Program}}{\begin{cases}{\text{Description}}{\begin{cases}{\text{Specification}}(\pi ){\begin{cases}{\text{Variables}}\\{\text{Decomposition}}\\{\text{Forms}}\\\end{cases}}\\{\text{Identification (based on }}\delta )\end{cases}}\\{\text{Question}}\end{cases}}} A program is constructed from a description and a question. A description is constructed using some specification ( π {\displaystyle \pi } ) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set ( δ {\displaystyle \delta } ). A specification is constructed from a set of pertinent variables, a decomposition and a set of forms. Forms are either parametric forms or questions to other Bayesian programs. A question specifies which probability distribution has to be computed. === Description === The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} given a set of experimental data δ {\displaystyle \delta } and some specification π {\displaystyle \pi } . This joint distribution is denoted as: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} . To specify preliminary knowledge π {\displaystyle \pi } , the programmer must undertake the following: Define the set of relevant variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} on which the joint distribution is defined. Decompose the joint distribution (break it into relevant independent or conditional probabilities). Define the forms of each of the distributions (e.g., for each variable, one of the list of probability distributions). ==== Decomposition ==== Given a partition of { X 1 , X 2 , … , X N } {\displaystyle \left\{X_{1},X_{2},\ldots ,X_{N}\right\}} containing K {\displaystyle K} subsets, K {\displaystyle K} variables are defined L 1 , ⋯ , L K {\displaystyle L_{1},\cdots ,L_{K}} , each corresponding to one of these subsets. Each variable L k {\displaystyle L_{k}} is obtained as the conjunction of the variables { X k 1 , X k 2 , ⋯ } {\displaystyle \left\{X_{k_{1}},X_{k_{2}},\cdots \right\}} belonging to the k t h {\displaystyle k^{th}} subset. Recursive application of Bayes' theorem leads to: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∧ ⋯ ∧ L K ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ L 1 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ L K − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\wedge \cdots \wedge L_{K}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid L_{1}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid L_{K-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable L k {\displaystyle L_{k}} is defined by choosing some variable X n {\displaystyle X_{n}} among the variables appearing in the conjunction L k − 1 ∧ ⋯ ∧ L 2 ∧ L 1 {\displaystyle L_{k-1}\wedge \cdots \wedge L_{2}\wedge L_{1}} , labelling R k {\displaystyle R_{k}} as the conjunction of these chosen variables and setting: P ( L k ∣ L k − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) = P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid L_{k-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)=P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} We then obtain: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ R 2 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ R K ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid R_{2}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid R_{K}\wedge \delta \wedge \pi \right)\end{aligned}}} Such a simplification of the joint distribution as a product of simpler distributions is called a decomposition, derived using the chain rule. This ensures that each variable appears at the most once on the left of a conditioning bar, which is the necessary and sufficient condition to write mathematically valid decompositions. ==== Forms ==== Each distribution P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} appearing in the product is then associated with either a parametric form (i.e., a function f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} ) or a question to another Bayesian program P ( L k ∣ R k ∧ δ ∧ π ) = P ( L ∣ R ∧ δ ^ ∧ π ^ ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)=P\left(L\mid R\wedge {\widehat {\delta }}\wedge {\widehat {\pi }}\right)} . When it is a form f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} , in general, μ {\displaystyle \mu } is a vector of parameters that may depend on R k {\displaystyle R_{k}} or δ {\displaystyle \delta } or both. Learning takes place when some of these parameters are computed using the data set δ {\displaystyle \delta } . An important feature of Bayesian programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} is obtained by some inferences done by another Bayesian program defined by the specifications π ^ {\displaystyle {\widehat {\pi }}} and the data δ ^ {\displaystyle {\widehat {\delta }}} . This is similar to calling a subroutine in classical programming and provides an easy way to build hierarchical models. === Question === Given a description (i.e., P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} ), a question is obtained by partitioning { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} into three sets: the searched variables, the known variables and the free variables. The 3 variables S e a r c h e d {\displaystyle Searched} , K n o w n {\displaystyle Known} and F r e e {\displaystyle Free} are defined as the conjunction of the variables belonging to these sets. A question is defined as the set of distributions: P ( S e a r c h e d ∣ Known ∧ δ ∧ π ) {\displaystyle P\left(Searched\mid {\text{Known}}\wedge \delta \wedge \pi \right)} made of many "instantiated questions" as the cardinal of K n o w n {\displaystyle Known} , each instantiated question being the distribution: P ( Searched ∣ Known ∧ δ ∧ π ) {\displaystyle P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)} === Inference === Given the joint distribution P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} , it is always possible to compute any possible question using the following general inference: P ( Searched ∣ Known ∧ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∣ Known ∧ δ ∧ π ) ] = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] P ( Known ∣ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] ∑ Free ∧ Searched [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] = 1 Z × ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] {\displaystyle {\begin{aligned}&P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)\\={}&\sum _{\text{Free}}\left[P\left({\text{Searched}}\wedge {\text{Free}}\mid {\text{Known}}\wedge \delta \wedge \

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  Belief–desire–intention model

  For popular psychology, the belief–desire–intention (BDI) model of human practical reasoning was developed by Michael Bratman as a way of explaining future-directed intention. BDI is fundamentally reliant on folk psychology (the 'theory theory'), which is the notion that our mental models of the world are theories. It was used as a basis for developing the belief–desire–intention software model. == Applications == BDI was part of the inspiration behind the BDI software architecture, which Bratman was also involved in developing. Here, the notion of intention was seen as a way of limiting time spent on deliberating about what to do, by eliminating choices inconsistent with current intentions. BDI has also aroused some interest in psychology. BDI formed the basis for a computational model of childlike reasoning CRIBB.

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  AI data center

  An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w

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  Inverse consistency

  In image registration, inverse consistency measures the consistency of mappings between images produced by a registration algorithm. The inverse consistency error, introduced by Christiansen and Johnson in 2001, quantifies the distance between the composition of the mappings from each image to the other, produced by the registration procedure, and the identity function, and is used as a regularisation constraint in the loss function of many registration algorithms to enforce consistent mappings. Inverse consistency is necessary for good image registration but it is not sufficient, since a mapping can be perfectly consistent but not register the images at all. == Definition == Image registration is the process of establishing a common coordinate system between two images, and given two images I 1 : Ω 1 → R I 2 : Ω 2 → R {\displaystyle {\begin{aligned}I_{1}:\Omega _{1}\to \mathbb {R} \\I_{2}:\Omega _{2}\to \mathbb {R} \end{aligned}}} registering a source image I 1 {\displaystyle I_{1}} to a target image I 2 {\displaystyle I_{2}} consists of determining a transformation f 1 : Ω 2 → Ω 1 {\displaystyle f_{1}:\Omega _{2}\to \Omega _{1}} that maps points from the target space to the source space. An ideal registration algorithm should not be sensitive to which image in the pair is used as source or target, and the registration operator should be antisymmetric such that the mappings f 1 : Ω 2 → Ω 1 f 2 : Ω 1 → Ω 2 {\displaystyle {\begin{aligned}f_{1}:\Omega _{2}\to \Omega _{1}\\f_{2}:\Omega _{1}\to \Omega _{2}\end{aligned}}} produced when registering I 1 {\displaystyle I_{1}} to I 2 {\displaystyle I_{2}} and I 2 {\displaystyle I_{2}} to I 1 {\displaystyle I_{1}} respectively should be the inverse of each other, i.e. f 2 = f 1 − 1 {\displaystyle f_{2}=f_{1}^{-1}} and f 1 = f 2 − 1 {\displaystyle f_{1}=f_{2}^{-1}} or, equivalently, f 2 ∘ f 1 = id Ω 2 {\displaystyle f_{2}\circ f_{1}=\operatorname {id} _{\Omega _{2}}} and f 1 ∘ f 2 = id Ω 1 {\displaystyle f_{1}\circ f_{2}=\operatorname {id} _{\Omega _{1}}} , where ∘ {\displaystyle \circ } denotes the function composition operator. Real algorithms are not perfect, and when swapping the role of source and target image in a registration problem the so obtained transformations are not the inverse of each other. Inverse consistency can be enforced by adding to the loss function of the registration a symmetric regularisation term that penalises inconsistent transformations ∫ Ω 2 ‖ f 2 ( f 1 ( x ) ) − x ‖ 2 d x + ∫ Ω 1 ‖ f 1 ( f 2 ( x ) ) − x ‖ 2 d x . {\displaystyle \int _{\Omega _{2}}\left\Vert f_{2}(f_{1}(x))-x\right\Vert ^{2}\mathrm {d} x+\int _{\Omega _{1}}\left\Vert f_{1}(f_{2}(x))-x\right\Vert ^{2}\mathrm {d} x.} Inverse consistency can be used as a quality metric to evaluate image registration results. The inverse consistency error ( I C E {\displaystyle ICE} ) measures the distance between the composition of the two transforms and the identity function, and it can be formulated in terms of both average ( I C E a {\displaystyle ICE_{a}} ) or maximum ( I C E m {\displaystyle ICE_{m}} ) over a region of interest Ω {\displaystyle \Omega } of the image: I C E a = 1 ∫ Ω d x ∫ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ d x I C E m = max x ∈ Ω ‖ f 2 ( f 1 ( x ) ) − x ‖ . {\displaystyle {\begin{aligned}ICE_{a}&={\frac {1}{\int _{\Omega }\mathrm {d} x}}\int _{\Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert \mathrm {d} x\\ICE_{m}&=\max _{x\in \Omega }\left\Vert f_{2}(f_{1}(x))-x\right\Vert .\end{aligned}}} While inverse consistency is a necessary property of good registration algorithms, inverse consistency error alone is not a sufficient metric to evaluate the quality of image registration results, since a perfectly consistent mapping, with no other constraint, may be not even close to correctly register a pair of images.

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  Leakage (machine learning)

  In statistics and machine learning, leakage (also known as data leakage or target leakage) refers to the use of information during model training that would not be available at prediction time. This results in overly optimistic performance estimates, as the model appears to perform better during evaluation than it actually would in a production environment. Leakage is often subtle and indirect, making it difficult to detect and eliminate. It can lead a statistician or modeler to select a suboptimal model, which may be outperformed by a leakage-free alternative. == Leakage modes == Leakage can occur at multiple stages of the machine learning workflow. Broadly, its sources can be divided into two categories: those arising from features and those arising from training examples. === Feature leakage === Feature or column-wise leakage is caused by the inclusion of columns which are one of the following: a duplicate label, a proxy for the label, or the label itself. These features, known as anachronisms, will not be available when the model is used for predictions, and result in leakage if included when the model is trained. For example, including a "MonthlySalary" column when predicting "YearlySalary"; or "MinutesLate" when predicting "IsLate". === Training example leakage === Row-wise leakage is caused by improper sharing of information between rows of data. Types of row-wise leakage include: Premature featurization; leaking from premature featurization before Cross-validation/Train/Test split (must fit MinMax/ngrams/etc on only the train split, then transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different rotations/augmentations of a single image; bootstrap sampling before splitting; or duplicating rows to up sample the minority class) Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test set using a train/test split or rolling-origin cross-validation) Group leakage—not including a grouping split column (for example, Andrew Ng's group had 100k x-rays of 30k patients, meaning ~3 images per patient. The paper used random splitting instead of ensuring that all images of a patient were in the same split. Hence the model partially memorized the patients instead of learning to recognize pneumonia in chest x-rays.) A 2023 review found data leakage to be "a widespread failure mode in machine-learning (ML)-based science", having affected at least 294 academic publications across 17 disciplines, and causing a potential reproducibility crisis. == Detection == Data leakage in machine learning can be detected through various methods, focusing on performance analysis, feature examination, data auditing, and model behavior analysis. Performance-wise, unusually high accuracy or significant discrepancies between training and test results often indicate leakage. Inconsistent cross-validation outcomes may also signal issues. Feature examination involves scrutinizing feature importance rankings and ensuring temporal integrity in time series data. A thorough audit of the data pipeline is crucial, reviewing pre-processing steps, feature engineering, and data splitting processes. Detecting duplicate entries across dataset splits is also important. For language models, the Min-K% method can detect the presence of data in a pretraining dataset. It presents a sentence suspected to be present in the pretraining dataset, and computes the log-likelihood of each token, then compute the average of the lowest K of these. If this exceeds a threshold, then the sentence is likely present. This method is improved by comparing against a baseline of the mean and variance. Analyzing model behavior can reveal leakage. Models relying heavily on counter-intuitive features or showing unexpected prediction patterns warrant investigation. Performance degradation over time when tested on new data may suggest earlier inflated metrics due to leakage. Advanced techniques include backward feature elimination, where suspicious features are temporarily removed to observe performance changes. Using a separate hold-out dataset for final validation before deployment is advisable.

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  Human-centered AI

  Human-centered AI is the initiative at the intersection of the fields of artificial intelligence (AI) and human-computer interaction (HCI) to develop AI systems in a way that prioritizes human values, needs, and general flourishing. Emphasis is placed on the recognition that artificial intelligence systems are rapidly changing, and will continue to influence, many aspects of the human experience, in areas ranging from scientific inquiry, governance and policy, labor and the economy, and creative expression, with an aim set to adapt current developments and guide future developments on a trajectory which is most beneficial to the human population at large, with the goal of augmenting human intelligence and capacities across these areas, as opposed to replacing them. Particular attention is paid to mitigating negative effects of AI automation on the livelihoods of the labor force, the use of AI in healthcare fields, and imbuing AI systems with societal values. Human-centered AI is linked to related endeavors in AI alignment and AI safety, but while these fields primarily focus on mitigating risks posed by AI that is unaligned to human values and/or uncontrollable AI self-development, human-centered AI places significant focus in exploring how AI systems can augment human capacities and serve as collaborators. == Conceptual history == The importance of the alignment of artificial intelligence development towards human values in some sense predates artificial intelligence itself, as before the modern conception of artificial intelligence as coined at the 1956 Dartmouth Workshop, the conception of robots as constructed, autonomous agents entered the cultural consciousness as early as the 1920s, with Karel Capek's Rossum's Universal Robots. The imagined issues relating to robots' aims and values requiring intentional alignment and direction with those of humans followed soon after, most widely known from science fiction author Isaac Asimov’s Three Laws of Robotics, dating to his 1942 short story “Runaround”. Two of the three eponymous laws are directly concerned with robots’ interaction with and positioned deference towards humans, and have in recent times been reexamined in the face of modern AI. In 1985, after artificial intelligence research had taken off and its effects were more acutely conceptualized, Asimov added a Rule Zero, treating robots' relationship with humanity as a whole, distinct from individual humans. While modern artificial intelligence is largely distinct from robotics, the conceptualization of both robots and AI systems as autonomous agents positions this as a foundation for conceptions of human-centered AI. Aside from robots, artificially intelligent autonomous agents in interaction with humans have been conceived of for at least 75 years. In 1950, Alan Turing published his famous "Imitation Game", often also called the Turing Test, a thought experiment that uses human-machine interaction as an assessor for the intelligence of a system. In recent times, artificial intelligence researchers such as Stanford's Erik Brynjolfsson have conceived of rapid AI development leading to a so-called "Turing Trap". == Augmentation and automation == A major stated aim of human-centered AI is to promote the development of AI in ways that augment human capabilities, rather than replacing them. To this end, organizations and initiatives that take a human-centered approach to AI development focus on frameworks that encourage collaboration between humans and artificial intelligence systems to build towards even greater progress, rather than attempting to automate tasks currently handled by humans. Such avenues include everything from data visualization for big data, allowing human engineers to better understand extremely large datasets, allowing for the design of better machine learning models to handle them, to AI-powered sensors to monitor vitals, allowing for better responsiveness from healthcare providers. Many human-centered AI initiatives often position it as a better alternative to the apparent mainstream in AI development, which is primarily concerned with automation. Driven by the pressures of the market economy, AI development that does replace tasks currently performed by humans with automated processes is incentivized, as it allows for greater profit margins; this often comes at the detriment of the human whose performance is replaced, thus leading to an environment wherein human workers are outcompeted by AI systems across various service-sector and technology-based industries. At the same time, automation and augmentation are not always incompatible; a major aim of human-centered AI is towards the automation of rote tasks that would otherwise hinder a human’s productivity or creativity, freeing them to direct their energy and intelligence towards higher-level tasks, thus achieving augmentation through automation. Empirical research in pharmaceutical sales has shown that a human-centered implementation - where work procedures, training, and incentives are designed around individuals' cognitive needs - improves augmentation performance, while implementation without such adaptation can worsen outcomes relative to a legacy system. == Research == Much of the work done on human-centered AI comes from research institutes, within universities, companies, and as freestanding organizations. The Stanford Institute for Human-Centered AI (abbreviated to HAI) is one such group, engaging academics, industry professionals, and policymakers centered in Stanford University to conduct research and inform policy in various areas in human-centered AI, including on aspects of the intelligence itself, augmentation, and on measuring the impacts of AI systems on sociopolitcal and cultural institutions. Similar groups exist at other universities, including the Chicago Human + AI (CHAI) Lab at the University of Chicago, the HCAI@GU group at the University of Gothenburg, and the Human-Centered AI (HAI) Lab at the University of Oxford. Outside of the academy, companies such as IBM have research initiatives dedicated to advancements in human-centered AI. At Kenyon College, the Integrated Program for Humane Studies (IPHS) launched a human-centered AI program in 2016 integrating artificial intelligence research with humanities and social science inquiry. This approach treats computation and humanistic scholarship as a single unified field of research rather than as separate disciplines requiring collaboration. The program's researchers have published in both AI venues (such as the International Conference on Machine Learning and Frontiers of Computer Science) and humanities journals (such as PMLA and Poetics Today), and the lab was selected in December 2025 by Schmidt Sciences for its Humanities and AI Virtual Institute to apply AI methods to cultural heritage preservation.

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  Robotic process automation

  Robotic process automation (RPA) is a form of business process automation that is based on software robots (bots) or artificial intelligence (AI) agents. RPA should not be confused with artificial intelligence as it is based on automation technology following a predefined workflow. It is sometimes referred to as software robotics (not to be confused with robot software). In traditional workflow automation tools, a software developer produces a list of actions to automate a task and interface to the back end system using internal application programming interfaces (APIs) or dedicated scripting language. In contrast, RPA systems develop the action list by watching the user perform that task in the application's graphical user interface (GUI) and then perform the automation by repeating those tasks directly in the GUI. This can lower the barrier to the use of automation in products that might not otherwise feature APIs for this purpose. RPA tools have strong technical similarities to graphical user interface testing tools. These tools also automate interactions with the GUI, and often do so by repeating a set of demonstration actions performed by a user. RPA tools differ from such systems in that they allow data to be handled in and between multiple applications, for instance, receiving email containing an invoice, extracting the data, and then typing that into a bookkeeping system. == Historic evolution == As a form of automation, the concept has been around for a long time in the form of screen scraping, so long that to early PC users the reminder of it often blurs with the idea of malware infection. Yet compared to screen scraping, RPA is much more extensible, consisting of API integration into other enterprise applications, connectors into ITSM systems, terminal services and even some types of AI (e.g. machine learning) services such as image recognition. It is considered to be a significant technological evolution in the sense that new software platforms are emerging which are sufficiently mature, resilient, scalable and reliable to make this approach viable for use in large enterprises (who would otherwise be reluctant due to perceived risks to quality and reputation). == Use == The hosting of RPA services also aligns with the metaphor of a software robot, with each robotic instance having its own virtual workstation, much like a human worker. The robot uses keyboard and mouse controls to take actions and execute automations. Normally, all of these actions take place in a virtual environment and not on screen; the robot does not need a physical screen to operate, rather it interprets the screen display electronically. The scalability of modern solutions based on architectures such as these owes much to the advent of virtualization technology, without which the scalability of large deployments would be limited by the available capacity to manage physical hardware and by the associated costs. The implementation of RPA in business enterprises has shown dramatic cost savings when compared to traditional non-RPA solutions. === RPA actual use === Banking and finance process automation Mortgage and lending processes Customer care automation eCommerce merchandising operations Social media marketing Optical character recognition applications Data extraction process Fixed automation process Manual and repetitive tasks automation Voice recognition and digital dictation software linked to join up business processes for straight through processing without manual intervention Specialised remote infrastructure management software featuring automated investigation and resolution of problems, using robots for the first line IT support Chatbots used by internet retailers and service providers to service customer requests for information. Also used by companies to service employee requests for information from internal databases Presentation layer automation software, increasingly used by business process outsourcers to displace human labour Interactive voice response (IVR) systems incorporating intelligent interaction with callers == Impact on employment == According to Harvard Business Review, most operations groups adopting RPA have promised their employees that automation would not result in layoffs. Instead, workers have been redeployed to do more interesting work. One academic study highlighted that knowledge workers did not feel threatened by automation: they embraced it and viewed the robots as team-mates. The same study highlighted that, rather than resulting in a lower "headcount", the technology was deployed in such a way as to achieve more work and greater productivity with the same number of people. Conversely, however, some analysts proffer that RPA represents a threat to the business process outsourcing (BPO) industry. The thesis behind this notion is that RPA will enable enterprises to "repatriate" processes from offshore locations into local data centers, with the benefit of this new technology. The effect, if true, will be to create high-value jobs for skilled process designers in onshore locations (and within the associated supply chain of IT hardware, data center management, etc.) but to decrease the available opportunity to low-skilled workers offshore. On the other hand, this discussion appears to be healthy ground for debate as another academic study was at pains to counter the so-called "myth" that RPA will bring back many jobs from offshore. === Impact on society === Academic studies project that RPA, among other technological trends, is expected to drive a new wave of productivity and efficiency gains in the global labour market. Although not directly attributable to RPA alone, Oxford University conjectures that up to 35% of all jobs might be automated by 2035. There are geographic implications to the trend in robotic automation. In the example above where an offshored process is "repatriated" under the control of the client organization (or even displaced by a business process outsourcer) from an offshore location to a data centre, the impact will be a deficit in economic activity to the offshore location and an economic benefit to the originating economy. On this basis, developed economies – with skills and technological infrastructure to develop and support a robotic automation capability – can be expected to achieve a net benefit from the trend. In a TEDx talk hosted by University College London (UCL), entrepreneur David Moss explains that digital labour in the form of RPA is likely to revolutionize the cost model of the services industry by driving the price of products and services down, while simultaneously improving the quality of outcomes and creating increased opportunity for the personalization of services. In a separate TEDx in 2019 talk, Japanese business executive, and former CIO of Barclays bank, Koichi Hasegawa noted that digital robots can be a positive effect on society if we start using a robot with empathy to help every person. He provides a case study of the Japanese insurance companies – Sompo Japan and Aioi – both of whom introduced bots to speed up the process of insurance pay-outs in past massive disaster incidents. Meanwhile, Professor Willcocks, author of the LSE paper cited above, speaks of increased job satisfaction and intellectual stimulation, characterising the technology as having the ability to "take the robot out of the human", a reference to the notion that robots will take over the mundane and repetitive portions of people's daily workload, leaving them to be used in more interpersonal roles or to concentrate on the remaining, more meaningful, portions of their day. It was also found in a 2021 study observing the effects of robotization in Europe that, the gender pay gap increased at a rate of .18% for every 1% increase in robotization of a given industry. == Unassisted RPA == Unassisted RPA, or RPAAI, is the next generation of RPA related technologies. Technological advancements around artificial intelligence allow a process to be run on a computer without needing input from a user. == Hyperautomation == Hyperautomation is the application of advanced technologies like RPA, artificial intelligence, machine learning (ML) and process mining to augment workers and automate processes in ways that are significantly more impactful than traditional automation capabilities. Hyperautomation is the combination of technologies that allow faster application authorship (like low-code and no-code) with automation technologies that coordinate different worker types (i.e. human and artificial) for intelligent and strategic workflow optimization. Gartner's report notes that this trend was kicked off with robotic process automation (RPA). The report notes that, "RPA alone is not hyperautomation. Hyperautomation requires a combination of tools to help support replicating pieces of where the human is involved in a task." == Outsourcing == Back office clerical processes outsourced by large organisations

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  Absher (application)

  Absher (Arabic: أبشر ‘Absher, roughly meaning "good tidings" or "yes, done") is a smartphone application and web portal which allows citizens and residents of Saudi Arabia to use a variety of governmental services. Amongst several other services with the Absher app, it can be used to apply for jobs and Hajj permits, passport info can be updated, and electronic crimes can be reported. The application provides around 280 services for residents of Saudi Arabia including but not limited to making appointments, renewing passports, residents' cards, IDs, driver's licenses and others, and, controversially, enables Saudi men to track the whereabouts of women they control as part of the country's male guardianship system. The app can be downloaded from the Google Play Store and Apple App Store and is supplied by the Saudi Interior Ministry. According to the Ministry of the Interior, Absher has more than 20 million users. As of February 2019, Absher has been downloaded 4.2 million times from the App Store. Some services provided through Absher can also be accessed through the website absher.sa. In March 2021, Saudi Arabia launched the digital version of the Absher for individuals app through which the users can download a copy of their digital ID. Then, new services were added to the platform such as online birth and death registration services, requesting amendments to academic credentials, correcting names in English and marital status and requesting civil records of children. == Impact on women's rights == The app has been criticized by various human rights activists, human rights organisations and international communities. The US and European countries have also condemned the app and urged the kingdom to end its male guardianship system. Absher gained media attention in 2019 for its functions supporting the Saudi policy of male guardianship following an investigation by Business Insider. The app allows for designated guardians to receive notifications if a woman under their guardianship passes through an airport and subsequently gives them the option to withdraw her right to travel. In a few cases, this system has been circumvented by women who have been able to gain control over its settings and use it to allow themselves to travel. US Senator Ron Wyden of Oregon wrote a letter to the CEO's of Apple and Google, criticizing the app and demanding for its removal immediately. Wyden said "American companies should not enable or facilitate the Saudi government's patriarchy," and called the Saudi system of control over women "abhorrent". According to the EU lawmakers, current rules imposed over the women by the Saudi government make women “second-class citizens”. The lawmakers also asked the EU states to continue to build pressure on Riyadh so as to improve the conditions of women and human rights. Amnesty International and Human Rights Watch accused Apple and Google of helping "enforce gender apartheid" by hosting the app. US congresswomen Rep. Katherine Clark and Rep. Carolyn B. Maloney condemned the kingdom's male guardianship system that reflected from the app, calling Absher a "patriarchal weapon" and asking for its removal. In response to the criticism received by Absher, Apple chief executive officer Tim Cook stated in February 2019 that he intended to investigate the situation. Similarly, Google announced that it would also review the application. After a prompt review, Google declined to remove the app from Google Play, citing that it did not violate the agreed upon terms and conditions of the store. Saudi doctor Khawla Al-Kuraya supported this app an editorial in Bloomberg News. Kuraya wrote that Absher helped Saudi women avoid governmental bureaucracy as it allows their male guardians to process their travel permits anywhere and anytime through Absher. Although she believes that the guardianship system needs to be reconsidered, she thinks that Absher is an important step towards facilitating women-guardians related issues in Saudi Arabia. Absher manager Atiyah Al-Anazy announced in 2019 that two million women were using the application in Saudi Arabia to facilitate their transactions. Some female users stated that the application has made their movement and travel-related issues easier. New measures were introduced that year to allow Saudi women above the age of 18 to travel without their male guardians, which ultimately released male authoritative rights on women. A law was subsequently passed allowing women over the age of 21 to receive a passport and travel without prior male permission.

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  The 2028 Global Intelligence Crisis

  The 2028 Global Intelligence Crisis is a report authored by James van Geelen and Alap Shah and published by Citrini Research in February 2026, on the impact of artificial intelligence on humanity's future. Written in the form of a scenario analysis, it was viewed millions of times online and reportedly caused a fall in the stock market prices of major tech and financial firms. It also received criticism among others, for its allegedly flawed economic logic. The 'thought exercise', as the authors called it, painted a gloomy picture for the near future, where outputs keep growing while consumer's ability to spend collapses. "...driven by ai agents that don’t sleep, take sick days or require health insurance”, "outputs that are shown in national accounts increases, "but never circulates through the real economy"(which the report calls 'Ghost GDP'), the authors argued. In other words, the authors predict a scenario where the owners of the AI firms will accumulate a vast fortune but there will be scant demand from consumers as AI would cause massive unemployment. The authors caution the reader that what they make is a scenario and not a prediction. In the scenario they visualise, any service whose value proposition is “I will navigate complexity that you find tedious” is getting disrupted. The reports argues that the unique ability of human beings to analyse, decide, create, persuade, and coordinate was “the thing that could not be replicated at scale,” and call the historical scarcity of this precious entity 'friction'. When this friction becomes zero, a gamut of changes occur which then triggers a cascading of changes across the economy. ”Travel booking platforms are an early casualty; Financial advice. tax prep., and routine legal work follow suit. National unemployment rate go as high 10.2% and the S&P 500 goes for a massive 38% peak-to-trough crash. In contrast to the previous technological revolutions the high-earning professionals suffers more and get forced to take up roles in the gig economy. Labour supply becomes abundant and this cuts wages all across the economy. The dent in income for the employees then affects other sectors of the economy such as the residential mortgage market. The losses for the software companies triggers loan defaults and heralds peril for the private credit sector.

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  Gibberlink

  GibberLink is an acoustic data transmission project, with an open-source client available on GitHub, in which two conversational AI agents switch from speaking to one another in a Human-listenable language (such as English) to their own unique language that consists of a sound-level protocol after confirming they are both AI agents. The project was created by Anton Pidkuiko and Boris Starkov. == Reception == The project won the global top prize at the ElevenLabs Worldwide Hackathon. It has also been cited as raising questions around AI ethics and oversight. On February 23, 2025, a YouTube video of two independent conversational ElevenLabs AI agents being prompted to chat about booking a hotel (one as a caller, one as a receptionist) received coverage for going viral. In this video, both agents are prompted to switch to ggwave data-over-sound protocol when they identify the other side as AI, and keep speaking in English otherwise.

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  Virtual intelligence

  Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.

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  Learning automaton

  A learning automaton is one type of machine learning algorithm studied since 1970s. Learning automata select their current action based on past experiences from the environment. It will fall into the range of reinforcement learning if the environment is stochastic and a Markov decision process (MDP) is used. == History == Research in learning automata can be traced back to the work of Michael Lvovitch Tsetlin in the early 1960s in the Soviet Union. Together with some colleagues, he published a collection of papers on how to use matrices to describe automata functions. Additionally, Tsetlin worked on reasonable and collective automata behaviour, and on automata games. Learning automata were also investigated by researches in the United States in the 1960s. However, the term learning automaton was not used until Narendra and Thathachar introduced it in a survey paper in 1974. == Definition == A learning automaton is an adaptive decision-making unit situated in a random environment that learns the optimal action through repeated interactions with its environment. The actions are chosen according to a specific probability distribution which is updated based on the environment response the automaton obtains by performing a particular action. With respect to the field of reinforcement learning, learning automata are characterized as policy iterators. In contrast to other reinforcement learners, policy iterators directly manipulate the policy π. Another example for policy iterators are evolutionary algorithms. Formally, Narendra and Thathachar define a stochastic automaton to consist of: a set X of possible inputs, a set Φ = { Φ1, ..., Φs } of possible internal states, a set α = { α1, ..., αr } of possible outputs, or actions, with r ≤ s, an initial state probability vector p(0) = ≪ p1(0), ..., ps(0) ≫, a computable function A which after each time step t generates p(t+1) from p(t), the current input, and the current state, and a function G: Φ → α which generates the output at each time step. In their paper, they investigate only stochastic automata with r = s and G being bijective, allowing them to confuse actions and states. The states of such an automaton correspond to the states of a "discrete-state discrete-parameter Markov process". At each time step t=0,1,2,3,..., the automaton reads an input from its environment, updates p(t) to p(t+1) by A, randomly chooses a successor state according to the probabilities p(t+1) and outputs the corresponding action. The automaton's environment, in turn, reads the action and sends the next input to the automaton. Frequently, the input set X = { 0,1 } is used, with 0 and 1 corresponding to a nonpenalty and a penalty response of the environment, respectively; in this case, the automaton should learn to minimize the number of penalty responses, and the feedback loop of automaton and environment is called a "P-model". More generally, a "Q-model" allows an arbitrary finite input set X, and an "S-model" uses the interval [0,1] of real numbers as X. A visualised demo/ Art Work of a single Learning Automaton had been developed by μSystems (microSystems) Research Group at Newcastle University. == Finite action-set learning automata == Finite action-set learning automata (FALA) are a class of learning automata for which the number of possible actions is finite or, in more mathematical terms, for which the size of the action-set is finite.

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  AI agent

  In the context of generative artificial intelligence, AI agents (also referred to as compound AI systems or agentic AI) are a class of intelligent agents that can pursue goals, use tools, and take actions with varying degrees of autonomy. In practice, they usually operate within human-defined objectives, constraints, and available tools. == Overview == AI agents possess several key attributes, including goal-directed behavior, natural language interfaces, the capacity to use external tools, and the ability to perform multi-step tasks. Their control flow is frequently driven by large language models (LLMs). Agent systems may also include memory components, planning logic, tool interfaces, and orchestration software for coordinating agent components. AI agents do not have a standard definition. NIST describes agentic AI as an emerging area requiring standards for secure operation, interoperability, and reliable interaction with external systems. A common application of AI agents is task automation: for example, booking travel plans based on a user's prompted request. Companies such as Google, Microsoft and Amazon Web Services have offered platforms for deploying pre-built AI agents. Several protocols have been proposed for standardizing inter-agent communication, with examples including the Model Context Protocol, Gibberlink, and many others. Some of these protocols are also used for connecting agents to external applications. In December 2025, Linux Foundation announced the formation of the Agentic AI Foundation (AAIF), with the goal of ensuring agentic AI evolves transparently and collaboratively. == History == AI agents have been traced back to research from the 1990s, with Harvard professor Milind Tambe noting that the definition of an AI agent was not clear at the time. Researcher Andrew Ng has been credited with spreading the term "agentic" to a wider audience in 2024. == Training and testing == Researchers have attempted to build world models and reinforcement learning environments to train or evaluate AI agents. For example, video games such as Minecraft and No Man's Sky as well as replicas of company websites, have also been used for training such agents. == Autonomous capabilities == The Financial Times compared the autonomy of AI agents to the SAE classification of self-driving cars, likening most applications to level 2 or level 3, with some achieving level 4 in highly specialized circumstances, and level 5 being theoretical. == Cognitive architecture == The following are some internal design options for reasoning within an agent: Retrieval-augmented generation ReAct (Reason + Act) pattern is an iterative process in which an AI agent alternates between reasoning and taking actions, receives observations from the environment or external tools, and integrates these observations into subsequent reasoning steps. Reflexion, which uses an LLM to create feedback on the agent's plan of action and stores that feedback in a memory cache. A tool/agent registry, for organizing software functions or other agents that the agent can use. One-shot model querying, which queries the model once to create the plan of action. === Reference architecture === Ken Huang proposed an AI agent reference architecture, which consists of seven interconnected layers, with each layer building on the functionality of the layers beneath it: Layer 1: Foundation models - provide the core AI engines to power agent capabilities. Layer 2: Data operations - manage the complex data infrastructure required for AI agent operations, including Vector database, data loaders, RAG. Layer 3: Agent frameworks - sophisticated software and tools that simplify the development and management of the AI agents. Layer 4: Deployment and infrastructure - provide the robust technical foundation for running AI agents. Layer 5: Evaluation and observability - focus on assessing the safety and performance of AI agents. Layer 6: Security and compliance - a crucial protective framework ensuring AI agents operate safely, securely, and conform to regulatory boundaries. At this layer security and compliance features embedded into all the AI agent stack layers are integrated together. Layer 7: Agent ecosystem - represents the AI agents' interface with real-world applications and users. == Orchestration patterns == To execute complex tasks, autonomous agents are often integrated with other agents or specialized tools. These configurations, known as orchestration patterns or workflows, include the following: Prompt chaining: A sequence where the output of one step serves as the input for the next. Routing: The classification of an input to direct it to a specialized downstream task or tool. Parallelization: The simultaneous execution of multiple tasks. Sequential processing: A fixed, linear progression of tasks through a predefined pipeline. Planner-critic: An iterative pattern where one agent generates a proposal and another evaluates it to provide feedback for refinement. == Multimodal AI agents == In addition to large language models (LLMs), vision-language models (VLMs) and multimodal foundation models can be used as the basis for agents. In September 2024, Allen Institute for AI released an open-source vision-language model. Nvidia released a framework for developers to use VLMs, LLMs and retrieval-augmented generation for building AI agents that can analyze images and videos, including video search and video summarization. Microsoft released a multimodal agent model – trained on images, video, software user interface interactions, and robotics data – that the company claimed can manipulate software and robots. == Applications == As of April 2025, per the Associated Press, there are few real-world applications of AI agents. As of June 2025, per Fortune, many companies are primarily experimenting with AI agents. The Information divided AI agents into seven archetypes: business-task agents, for acting within enterprise software; conversational agents, which act as chatbots for customer support; research agents, for querying and analyzing information (such as OpenAI Deep Research); analytics agents, for analyzing data to create reports; software developer or coding agents (such as Cursor); domain-specific agents, which include specific subject matter knowledge; and web browser agents (such as OpenAI Operator). By mid-2025, AI agents have been used in video game development, gambling (including sports betting), cryptocurrency wallets (including cryptocurrency trading and meme coins) and social media. In August 2025, New York Magazine described software development as the most definitive use case of AI agents. Likewise, by October 2025, noting a decline in expectations, The Information noted AI coding agents and customer support as the primary use cases by businesses. In November 2025, The Wall Street Journal reported that few companies that deployed AI agents have received a return on investment. === Applications in government === Several government bodies in the United States and United Kingdom have deployed or announced the deployment of agents, at the local and national level. The city of Kyle, Texas deployed an AI agent from Salesforce in March 2025 for 311 customer service. In November 2025, the Internal Revenue Service stated that it would use Agentforce, AI agents from Salesforce, for the Office of Chief Counsel, Taxpayer Advocate Services and the Office of Appeals. That same month, Staffordshire Police announced that they would trial Agentforce agents for handling non-emergency 101 calls in the United Kingdom starting in 2026. In December 2025, the Department of Neighborhoods in Detroit, Michigan, in partnership with a local business, deployed a pilot project in two Detroit districts for an AI agent to be used for customer service calls. In February 2025, Thomas Shedd, the director of the Technology Transformation Services, proposed using AI coding agents across the United States federal government. A recruiter for the Department of Government Efficiency proposed in April 2025 to use AI agents to automate the work of about 70,000 United States federal government employees, as part of a startup with funding from OpenAI and a partnership agreement with Palantir. This proposal was criticized by experts for its impracticality, if not impossibility, and the lack of corresponding widespread adoption by businesses. In December 2025, the Food and Drug Administration announced that it would offer "agentic AI capabilities" to its staff for "meeting management, pre-market reviews, review validation, post-market surveillance, inspections and compliance and administrative functions." That same month, the United States Department of Defense launched GenAI.mil, an internal platform for American military personnel to use generative AI-based applications based on Google Gemini, including "intelligent agentic workflows". Defense Secretary Pete Hegseth listed applications such as "[conducting] deep r

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  Data preprocessing

  Data preprocessing can refer to manipulation, filtration or augmentation of data before it is analyzed, and is often an important step in the data mining process. Data collection methods are often loosely controlled, resulting in out-of-range values, impossible data combinations, and missing values, amongst other issues. Preprocessing is the process by which unstructured data is transformed into intelligible representations suitable for machine-learning models. This phase of model deals with noise in order to arrive at better and improved results from the original data set which was noisy. This dataset also has some level of missing value present in it. The preprocessing pipeline used can often have large effects on the conclusions drawn from the downstream analysis. Thus, representation and quality of data is necessary before running any analysis. If there is a high proportion of irrelevant and redundant information present or noisy and unreliable data, then knowledge discovery during the training phase may be more difficult. Data preparation and filtering steps can take a considerable amount of processing time. Examples of methods used in data preprocessing include cleaning, instance selection, normalization, one-hot encoding, data transformation, feature extraction and feature selection. == Applications == === Data mining === Data preprocessing allows for the removal of unwanted data with the use of data cleaning, this allows the user to have a dataset to contain more valuable information after the preprocessing stage for data manipulation later in the data mining process. Editing such dataset to either correct data corruption or human error is a crucial step to get accurate quantifiers like true positives, true negatives, false positives and false negatives found in a confusion matrix that are commonly used for a medical diagnosis. Users are able to join data files together and use preprocessing to filter any unnecessary noise from the data which can allow for higher accuracy. Users use Python programming scripts accompanied by the pandas library which gives them the ability to import data from a comma-separated values as a data-frame. The data-frame is then used to manipulate data that can be challenging otherwise to do in Excel. Pandas (software) which is a powerful tool that allows for data analysis and manipulation; which makes data visualizations, statistical operations and much more, a lot easier. Many also use the R programming language to do such tasks as well. The reason why a user transforms existing files into a new one is because of many reasons. Aspects of data preprocessing may include imputing missing values, aggregating numerical quantities and transforming continuous data into categories (data binning). More advanced techniques like principal component analysis and feature selection are working with statistical formulas and are applied to complex datasets which are recorded by GPS trackers and motion capture devices. === Semantic data preprocessing === Semantic data mining is a subset of data mining that specifically seeks to incorporate domain knowledge, such as formal semantics, into the data mining process. Domain knowledge is the knowledge of the environment the data was processed in. Domain knowledge can have a positive influence on many aspects of data mining, such as filtering out redundant or inconsistent data during the preprocessing phase. Domain knowledge also works as constraint. It does this by using working as set of prior knowledge to reduce the space required for searching and acting as a guide to the data. Simply put, semantic preprocessing seeks to filter data using the original environment of said data more correctly and efficiently. There are increasingly complex problems which are asking to be solved by more elaborate techniques to better analyze existing information. Instead of creating a simple script for aggregating different numerical values into a single value, it make sense to focus on semantic based data preprocessing. The idea is to build a dedicated ontology, which explains on a higher level what the problem is about. In regards to semantic data mining and semantic pre-processing, ontologies are a way to conceptualize and formally define semantic knowledge and data. The Protégé (software) is the standard tool for constructing an ontology. In general, the use of ontologies bridges the gaps between data, applications, algorithms, and results that occur from semantic mismatches. As a result, semantic data mining combined with ontology has many applications where semantic ambiguity can impact the usefulness and efficiency of data systems. Applications include the medical field, language processing, banking, and even tutoring, among many more. There are various strengths to using a semantic data mining and ontological based approach. As previously mentioned, these tools can help during the per-processing phase by filtering out non-desirable data from the data set. Additionally, well-structured formal semantics integrated into well designed ontologies can return powerful data that can be easily read and processed by machines. A specifically useful example of this exists in the medical use of semantic data processing. As an example, a patient is having a medical emergency and is being rushed to hospital. The emergency responders are trying to figure out the best medicine to administer to help the patient. Under normal data processing, scouring all the patient’s medical data to ensure they are getting the best treatment could take too long and risk the patients’ health or even life. However, using semantically processed ontologies, the first responders could save the patient’s life. Tools like a semantic reasoner can use ontology to infer the what best medicine to administer to the patient is based on their medical history, such as if they have a certain cancer or other conditions, simply by examining the natural language used in the patient's medical records. This would allow the first responders to quickly and efficiently search for medicine without having worry about the patient’s medical history themselves, as the semantic reasoner would already have analyzed this data and found solutions. In general, this illustrates the incredible strength of using semantic data mining and ontologies. They allow for quicker and more efficient data extraction on the user side, as the user has fewer variables to account for, since the semantically pre-processed data and ontology built for the data have already accounted for many of these variables. However, there are some drawbacks to this approach. Namely, it requires a high amount of computational power and complexity, even with relatively small data sets. This could result in higher costs and increased difficulties in building and maintaining semantic data processing systems. This can be mitigated somewhat if the data set is already well organized and formatted, but even then, the complexity is still higher when compared to standard data processing. Below is a simple a diagram combining some of the processes, in particular semantic data mining and their use in ontology. The diagram depicts a data set being broken up into two parts: the characteristics of its domain, or domain knowledge, and then the actual acquired data. The domain characteristics are then processed to become user understood domain knowledge that can be applied to the data. Meanwhile, the data set is processed and stored so that the domain knowledge can applied to it, so that the process may continue. This application forms the ontology. From there, the ontology can be used to analyze data and process results. Fuzzy preprocessing is another, more advanced technique for solving complex problems. Fuzzy preprocessing and fuzzy data mining make use of fuzzy sets. These data sets are composed of two elements: a set and a membership function for the set which comprises 0 and 1. Fuzzy preprocessing uses this fuzzy data set to ground numerical values with linguistic information. Raw data is then transformed into natural language. Ultimately, fuzzy data mining's goal is to help deal with inexact information, such as an incomplete database. Currently fuzzy preprocessing, as well as other fuzzy based data mining techniques see frequent use with neural networks and artificial intelligence.

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