AI Art That Looks Real

AI Art That Looks Real — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Jordan Antiquities Database and Information System

    Jordan Antiquities Database and Information System

    The Jordan Antiquities Database and Information System (JADIS) was a computer database of antiquities in Jordan, the first of its kind in the Arab world. It was established by the Department of Antiquities in 1990, in cooperation with the American Center for Oriental Research in Amman and sponsored by the United States Agency for International Development. JADIS was in use until 2002, when it was superseded by a new system, MEGA-J. Over 10,841 antiquities were registered in the database. An introduction and printed summary of the database was published by the Department of Antiquities in 1994, edited by Gaetano Palumbo.

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  • Vector-field consistency

    Vector-field consistency

    Vector-Field Consistency is a consistency model for replicated data (for example, objects), initially described in a paper which was awarded the best-paper prize in the ACM/IFIP/Usenix Middleware Conference 2007. It has since been enhanced for increased scalability and fault-tolerance in a recent paper. == Description == This consistency model was initially designed for replicated data management in ad hoc gaming in order to minimize bandwidth usage without sacrificing playability. Intuitively, it captures the notion that although players require, wish, and take advantage of information regarding the whole of the game world (as opposed to a restricted view to rooms, arenas, etc. of limited size employed in many multiplayer video games), they need to know information with greater freshness, frequency, and accuracy as other game entities are located closer and closer to the player's position. It prescribes a multidimensional divergence bounding scheme, based on a vector field that employs consistency vectors k=(θ,σ,ν), standing for maximum allowed time - or replica staleness, sequence - or missing updates, and value - or user-defined measured replica divergence, applied to all space coordinates in game scenario or world. The consistency vector-fields emanate from field-generators designated as pivots (for example, players) and field intensity attenuates as distance grows from these pivots in concentric or square-like regions. This consistency model unifies locality-awareness techniques employed in message routing and consistency enforcement for multiplayer games, with divergence bounding techniques traditionally employed in replicated database and web scenarios.

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  • Artificial intelligence industry in Italy

    Artificial intelligence industry in Italy

    The artificial intelligence industry in Italy is growing and supports industrial development. In 2024 it reached a new record, reaching 1.2 billion euros with a growth of +58% compared to 2023. While in 2025, the growth of artificial intelligence in the industrial application was even greater than in 2024 both in terms of value and application to industrial sectors. == History == The roots of AI research in Italy extend back to the 1970s, when Italian scholars began exploring automated reasoning, programming language semantics, and pattern recognition. Researchers such as those involved in early projects at the National Research Council and various universities laid the groundwork for subsequent academic and industrial developments in the field. During this period, the focus was predominantly on developing algorithms for automated theorem proving and building systems to reason about complex mathematical problems. This era witnessed the birth of methodologies that would later influence numerous AI subfields, from natural language processing (NLP) to robotics. === Institutional milestones and academic contributions === A turning point in the Italian AI landscape was the formation of the Italian Association for Artificial Intelligence (AIxIA) in 1988. Founded by academics, including Luigia Carlucci Aiello, the association established a platform for collaboration between universities, research centers, and industry. Led by Aiello, AIIA played a role in promoting research, organizing national conferences, and fostering international partnerships that connected Italy's AI community to global networks. At the same time, professors such as Roberto Navigli and numerous practitioners contributed to the advancement of AI in Italy. Navigli has worked in multilingual NLP, including the creation of BabelNet, and led the Minerva project. === Industrial AI === Over recent decades, numerous national and European initiatives supported by funding from programs such as the National Recovery and Resilience Plan (PNRR) have spurred the transition from theoretical research to practical applications. Industrial sectors including manufacturing, banking, and healthcare increasingly embraced AI-driven automation, while research institutions collaborated with industrial partners to deploy cutting-edge solutions. In recent years, Italy has also seen the establishment of specialized research centers and institutes aimed at bridging the gap between academic innovation and industrial application. These initiatives indicate a broader national commitment to integrating AI into the fabric of Italian industry. == Recent developments == === Emergence of generative AI === A landmark in Italy's modern AI evolution is the development of Minerva AI. Developed by the Sapienza NLP research group at Sapienza University of Rome and led by Professor Roberto Navigli, Minerva represents the first family of large language models (LLMs) trained from scratch with a primary focus on the Italian language. ==== Minerva 7B ==== The latest iteration, Minerva 7B, has 7 billion parameters and has been trained on an extensive corpus of over 1.5 trillion words. By using advanced instruction tuning techniques, Minerva 7B is able to produce highly accurate, coherent, and contextually sensitive responses addressing common issues such as hallucinations and inappropriate content generation. This breakthrough sets a benchmark for transparent, open-source AI development in the country. Minerva's development, carried out within the FAIR (Future Artificial Intelligence Research) project in collaboration with CINECA and supported by supercomputing resources like the Leonardo (supercomputer), aligns closely with Italy's cultural and linguistic heritage. === Establishment of AI4I === The recent establishment of the Istituto Italiano per l’Intelligenza Artificiale (AI4I) is part of Italy's strategy to improve its industrial competitiveness in AI. This dedicated institute aims to bridge the gap between research institutions and industrial enterprises; promote training and R&D support to nurture the next generation of Italian AI experts; and enhance national competitiveness. This initiative is expected to serve as a hub for applied AI research, driving innovations that are tailored to the specific needs of Italian industry and public administration. === Benefits of InvestAI === Italy's AI industry stands to benefit from the European InvestAI initiative, a plan unveiled at the recent AI Action Summit in Paris. InvestAI is an effort by the European Commission to mobilize €200 billion for AI investments, with a dedicated €20 billion fund earmarked for building AI gigafactories. These gigafactories are planned as large-scale hubs for training advanced, complex AI models using approximately 100,000 last-generation AI chips. For Italy, this investment presents several major opportunities: Access to State-of-the-Art Infrastructure: Italian companies, research institutions, and start-ups can leverage the gigafactories’ immense computational resources, enabling them to train highly sophisticated language models and other AI systems. Enhanced Competitiveness and Collaboration: With InvestAI's layered funding model where EU funds help de-risk private investments Italian firms can access capital more readily. This will bolster public–private partnerships and create a more dynamic AI ecosystem that spans from academic research to industrial applications. Alignment with National and Regional Initiatives: The Istituto Italiano per l’Intelligenza Artificiale (AI4I), based in Turin, is already recognized as a strategic asset by both Italy and the European Union. As the main recipient of InvestAI funds in Italy, AI4I will play a pivotal role in implementing these investments locally, fostering innovation in sectors like manufacturing, healthcare and aerospace. Commission President Ursula von der Leyen emphasized that InvestAI is designed to democratize AI innovation throughout Europe by ensuring that even smaller companies have access to high-performance computing power. For Italy, this means not only keeping pace with global leaders but also harnessing European-scale investments to transform its AI industry and drive economic growth.

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  • Object storage

    Object storage

    Object storage (also known as object-based storage or blob storage) is a computer data storage approach that manages data as "blobs" or "objects", as opposed to other storage architectures like file systems, which manage data as a file hierarchy, and block storage, which manages data as blocks within sectors and tracks. Each object is typically associated with a variable amount of metadata, and a globally unique identifier. Object storage can be implemented at multiple levels, including the device level (object-storage device), the system level, and the interface level. In each case, object storage seeks to enable capabilities not addressed by other storage architectures, like interfaces that are directly programmable by the application, a namespace that can span multiple instances of physical hardware, and data-management functions like data replication and data distribution at object-level granularity. Object storage systems allow retention of massive amounts of unstructured data in which data is written once and read once (or many times). Object storage is used for purposes such as storing objects like videos and photos on Facebook, songs on Spotify, or files in online collaboration services, such as Dropbox. One of the limitations with object storage is that it is not intended for transactional data, as object storage was not designed to replace NAS file access and sharing; it does not support the locking and sharing mechanisms needed to maintain a single, accurately updated version of a file. == History == === Origins === Jim Starkey coined the term blob working at Digital Equipment Corporation to refer to opaque data entities. The terminology was adopted for Rdb/VMS. Blob is often humorously explained to be an abbreviation for binary large object. According to Starkey, this backronym arose when Terry McKiever, working in marketing at Apollo Computer felt that the term needed to be an abbreviation. McKiever began using the expansion basic large object. This was later eclipsed by the retroactive explanation of blobs as binary large objects. According to Starkey, "Blob don't stand for nothin'." Rejecting the acronym, he explained his motivation behind the coinage, saying, "A blob is the thing that ate Cincinnatti [sic], Cleveland, or whatever", referring to the 1958 science fiction film The Blob. In 1995, research led by Garth Gibson on Network-Attached Secure Disks first promoted the concept of splitting less common operations, like namespace manipulations, from common operations, like reads and writes, to optimize the performance and scale of both. In the same year, a Belgian company – FilePool – was established to build the basis for archiving functions. Object storage was proposed at Gibson's Carnegie Mellon University lab as a research project in 1996. Another key concept was abstracting the writes and reads of data to more flexible data containers (objects). Fine grained access control through object storage architecture was further described by one of the NASD team, Howard Gobioff, who later was one of the inventors of the Google File System. Other related work includes the Coda filesystem project at Carnegie Mellon, which started in 1987, and spawned the Lustre file system. There is also the OceanStore project at UC Berkeley, which started in 1999 and the Logistical Networking project at the University of Tennessee Knoxville, which started in 1998. In 1999, Gibson founded Panasas to commercialize the concepts developed by the NASD team. === Development === Seagate Technology played a central role in the development of object storage. According to the Storage Networking Industry Association (SNIA), "Object storage originated in the late 1990s: Seagate specifications from 1999 Introduced some of the first commands and how operating system effectively removed from consumption of the storage." A preliminary version of the "OBJECT BASED STORAGE DEVICES Command Set Proposal" dated 10/25/1999 was submitted by Seagate as edited by Seagate's Dave Anderson and was the product of work by the National Storage Industry Consortium (NSIC) including contributions by Carnegie Mellon University, Seagate, IBM, Quantum, and StorageTek. This paper was proposed to INCITS T-10 (International Committee for Information Technology Standards) with a goal to form a committee and design a specification based on the SCSI interface protocol. This defined objects as abstracted data, with unique identifiers and metadata, how objects related to file systems, along with many other innovative concepts. Anderson presented many of these ideas at the SNIA conference in October 1999. The presentation revealed an IP Agreement that had been signed in February 1997 between the original collaborators (with Seagate represented by Anderson and Chris Malakapalli) and covered the benefits of object storage, scalable computing, platform independence, and storage management. == Architecture == === Abstraction of storage === One of the design principles of object storage is to abstract some of the lower layers of storage away from the administrators and applications. Thus, data is exposed and managed as objects instead of blocks or (exclusively) files. Objects contain additional descriptive properties which can be used for better indexing or management. Administrators do not have to perform lower-level storage functions like constructing and managing logical volumes to utilize disk capacity or setting RAID levels to deal with disk failure. Object storage also allows the addressing and identification of individual objects by more than just file name and file path. Object storage adds a unique identifier within a bucket, or across the entire system, to support much larger namespaces and eliminate name collisions. === Inclusion of rich custom metadata within the object === Object storage explicitly separates file metadata from data to support additional capabilities. As opposed to fixed metadata in file systems (filename, creation date, type, etc.), object storage provides for full function, custom, object-level metadata in order to: Capture application-specific or user-specific information for better indexing purposes Support data-management policies (e.g. a policy to drive object movement from one storage tier to another) Centralize management of storage across many individual nodes and clusters Optimize metadata storage (e.g. encapsulated, database or key value storage) and caching/indexing (when authoritative metadata is encapsulated with the metadata inside the object) independently from the data storage (e.g. unstructured binary storage) Additionally, in some object-based file-system implementations: The file system clients only contact metadata servers once when the file is opened and then get content directly via object-storage servers (vs. block-based file systems which would require constant metadata access) Data objects can be configured on a per-file basis to allow adaptive stripe width, even across multiple object-storage servers, supporting optimizations in bandwidth and I/O Object-based storage devices (OSD) as well as some software implementations (e.g., DataCore Swarm) manage metadata and data at the storage device level: Instead of providing a block-oriented interface that reads and writes fixed sized blocks of data, data is organized into flexible-sized data containers, called objects Each object has both data (an uninterpreted sequence of bytes) and metadata (an extensible set of attributes describing the object); physically encapsulating both together benefits recoverability. The command interface includes commands to create and delete objects, write bytes and read bytes to and from individual objects, and to set and get attributes on objects Security mechanisms provide per-object and per-command access control === Programmatic data management === Object storage provides programmatic interfaces to allow applications to manipulate data. At the base level, this includes Create, read, update and delete (CRUD) functions for basic read, write and delete operations. Some object storage implementations go further, supporting additional functionality like object/file versioning, object replication, life-cycle management and movement of objects between different tiers and types of storage. Most API implementations are REST-based, allowing the use of many standard HTTP calls. == Implementation == === Cloud storage === The vast majority of cloud storage available in the market leverages an object-storage architecture. Some notable examples are Amazon S3, which debuted in March 2006, Microsoft Azure Blob Storage, IBM Cloud Object Storage, Rackspace Cloud Files (whose code was donated in 2010 to Openstack project and released as OpenStack Swift), and Google Cloud Storage released in May 2010. === Object-based file systems === Some distributed file systems use an object-based architecture, where file metadata is stored in metadata servers and file data is stored i

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  • Topological deep learning

    Topological deep learning

    Topological deep learning (TDL) is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations, including point clouds, meshes, time series, scalar fields graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering a more nuanced representation of data. TDL also encompasses methods from computational and algebraic topology that permit studying properties of neural networks and their training process, such as their predictive performance or generalization properties. The mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on differentiable manifolds, knots, links, tangles, curves, etc. == History and motivation == Traditional techniques from deep learning often operate under the assumption that a dataset is residing in a highly-structured space (like images, where convolutional neural networks exhibit outstanding performance over alternative methods) or a Euclidean space. The prevalence of new types of data, in particular graphs, meshes, and molecules, resulted in the development of new techniques, culminating in the field of geometric deep learning, which originally proposed a signal-processing perspective for treating such data types. While originally confined to graphs, where connectivity is defined based on nodes and edges, follow-up work extended concepts to a larger variety of data types, including simplicial complexes and CW complexes, with recent work proposing a unified perspective of message-passing on general combinatorial complexes. An independent perspective on different types of data originated from topological data analysis, which proposed a new framework for describing structural information of data, i.e., their "shape," that is inherently aware of multiple scales in data, ranging from local information to global information. While at first restricted to smaller datasets, subsequent work developed new descriptors that efficiently summarized topological information of datasets to make them available for traditional machine-learning techniques, such as support vector machines or random forests. Such descriptors ranged from new techniques for feature engineering over new ways of providing suitable coordinates for topological descriptors, or the creation of more efficient dissimilarity measures. Contemporary research in this field is largely concerned with either integrating information about the underlying data topology into existing deep-learning models or obtaining novel ways of training on topological domains. == Learning on topological spaces == One of the core concepts in topological deep learning is considering the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Studying and developing deep learning models that are supported ln topological domains constitute the essence of topological deep learning. Next, we introduce the most common topological domains that are encountered in a deep learning setting. These domains include, but not limited to, graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N {\displaystyle {\mathcal {N}}} on S is an assignment that attach to every point x {\displaystyle x} in S a subset of S or a relation. Such a function can be induced by equipping S with an auxiliary structure. Edges provide one way of defining relations among the entities of S. More specifically, edges in a graph allow one to define the notion of neighborhood using, for instance, the one hop neighborhood notion. Edges however, limited in their modeling capacity as they can only be used to model binary relations among entities of S since every edge is connected typically to two entities. In many applications, it is desirable to permit relations that incorporate more than two entities. The idea of using relations that involve more than two entities is central to topological domains. Such higher-order relations allow for a broader range of neighborhood functions to be defined on S to capture multi-way interactions among entities of S. Next we review the main properties, advantages, and disadvantages of some commonly studied topological domains in the context of deep learning, including (abstract) simplicial complexes, regular cell complexes, hypergraphs, and combinatorial complexes. ==== Comparisons among topological domains ==== Each of the enumerated topological domains has its own characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical structures, making them suitable for various applications. Hodge theory can be naturally defined on simplicial complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes. Provide more flexibility in defining higher-order relations. Each cell in a cell complex is homeomorphic to an open ball, attached together via attaching maps. Boundary cells of each cell in a cell complex are also cells in the complex. Represented combinatorially via incidence matrices. Hypergraphs Allow arbitrary set-type relations among entities. Relations are not imposed by other relations, providing more flexibility. Do not explicitly encode the dimension of cells or relations. Useful when relations in the data do not adhere to constraints imposed by other models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs. Allow for hierarchical structures and set-type relations. Combine features of other complexes while providing more flexibility in modeling relations. Can be represented combinatorially, similar to cell complexes. ==== Hierarchical structure and set-type relations ==== The properties of simplicial complexes, cell complexes, and hypergraphs give rise to two main features of relations on higher-order domains, namely hierarchies of relations and set-type relations. ===== Rank function ===== A rank function on a higher-order domain X is an order-preserving function rk: X → Z, where rk(x) attaches a non-negative integer value to each relation x in X, preserving set inclusion in X. Cell and simplicial complexes are common examples of higher-order domains equipped with rank functions and therefore with hierarchies of relations. ===== Set-type relations ===== Relations in a higher-order domain are called set-type relations if the existence of a relation is not implied by another relation in the domain. Hypergraphs constitute examples of higher-order domains equipped with set-type relations. Given the modeling limitations of simplicial complexes, cell complexes, and hypergraphs, we develop the combinatorial complex, a higher-order domain that features both hierarchies of relations and set-type relations. The learning tasks in TDL can be broadly classified into three categories: Cell classification: Predict targets for each cell in a complex. Examples include triangular mesh segmentation, where the task is to predict the class of each face or edge in a given mesh. Complex classification: Predict targets for an entire complex. For example, predict the class of each input mesh. Cell prediction: Predict properties of cell-cell interactions in a complex, and in some cases, predict whether a cell exists in the complex. An example is the prediction of linkages among entities in hyperedges of a hypergraph. In practice, to perform the aforementioned tasks, deep learning models designed for specific topological spaces must be constructed and implemented. These models, known as topological neural networks, are tailored to operate effectively within these spaces. === Topological neural networks === Central to TDL are topological neural networks (TNNs), specialized architectures designed to operate on data structured in topological domains. Unlike traditional neural networks tailored for grid-like structures, TNNs are adept at handling more intricate data representations, such as graphs

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  • Relational data stream management system

    Relational data stream management system

    A relational data stream management system (RDSMS) is a distributed, in-memory data stream management system (DSMS) that is designed to use standards-compliant SQL queries to process unstructured and structured data streams in real-time. Unlike SQL queries executed in a traditional RDBMS, which return a result and exit, SQL queries executed in a RDSMS do not exit, generating results continuously as new data become available. Continuous SQL queries in a RDSMS use the SQL Window function to analyze, join and aggregate data streams over fixed or sliding windows. Windows can be specified as time-based or row-based. == RDSMS SQL Query Examples == Continuous SQL queries in a RDSMS conform to the ANSI SQL standards. The most common RDSMS SQL query is performed with the declarative SELECT statement. A continuous SQL SELECT operates on data across one or more data streams, with optional keywords and clauses that include FROM with an optional JOIN subclause to specify the rules for joining multiple data streams, the WHERE clause and comparison predicate to restrict the records returned by the query, GROUP BY to project streams with common values into a smaller set, HAVING to filter records resulting from a GROUP BY, and ORDER BY to sort the results. The following is an example of a continuous data stream aggregation using a SELECT query that aggregates a sensor stream from a weather monitoring station. The SELECTquery aggregates the minimum, maximum and average temperature values over a one-second time period, returning a continuous stream of aggregated results at one second intervals. RDSMS SQL queries also operate on data streams over time or row-based windows. The following example shows a second continuous SQL query using the WINDOW clause with a one-second duration. The WINDOW clause changes the behavior of the query, to output a result for each new record as it arrives. Hence the output is a stream of incrementally updated results with zero result latency.

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  • Browsing

    Browsing

    Browsing is a kind of orienting strategy. It is supposed to identify something of relevance for the browsing organism. In context of humans, it is a metaphor taken from the animal kingdom. It is used, for example, about people browsing open shelves in libraries, window shopping, or browsing databases or the Internet. In library and information science, it is an important subject, both purely theoretically and as applied science aiming at designing interfaces which support browsing activities for the user. == Definition == In 2011, Birger Hjørland provided the following definition: "Browsing is a quick examination of the relevance of a number of objects which may or may not lead to a closer examination or acquisition/selection of (some of) these objects. It is a kind of orienting strategy that is formed by our "theories", "expectations" and "subjectivity". == Controversies == As with any kind of human psychology, browsing can be understood in biological, behavioral, or cognitive terms on the one hand or in social, historical, and cultural terms on the other hand. In 2007, Marcia Bates researched browsing from "behavioural" approaches, while Hjørland (2011a+b) defended a social view. Bates found that browsing is rooted in our history as exploratory, motile animals hunting for food and nesting opportunities. According to Hjørland (2011a), on the other hand, Marcia Bates' browsing for information about browsing is governed by her behavioral assumptions, while Hjørland's browsing for information about browsing is governed by his socio-cultural understanding of human psychology. In short: Human browsing is based on our conceptions and interests. === Is browsing a random activity? === Browsing is often understood as a random activity. Dictionary.com, for example, has this definition: "to glance at random through a book, magazine, etc.". Hjørland suggests, however, that browsing is an activity that is governed by our metatheories. We may dynamically change our theories and conceptions but when we browse, the activity is governed by the interests, conceptions, priorities and metatheories that we have at that time. Therefore, browsing is not totally random. == Browsing versus analytical search strategies == In 1997, Gary Marchionini wrote: "A fundamental distinction is made between analytical and browsing strategies [...]. Analytical strategies depend on careful planning, the recall of query terms, and iterative query reformulations and examinations of results. Browsing strategies are heuristic and opportunistic and depend on recognizing relevant information. Analytic strategies are batch oriented and half duplex (turn talking) like human conversation, whereas browsing strategies are more interactive, real-time exchanges and collaborations between the information seeker and the information system. Browsing strategies demand a lower cognitive load in advance and a steadier attentional load throughout the information-seeking process. When it comes to Browsing, giblets are amazing." == Orienting strategies == Some sociologists, such as Berger and Zelditch in 1993, Wagner in 1984, and Wagner & Berger in 1985, have used the term "orienting strategies". They find that orienting strategies should be understood as metatheories: "Consider the very large proportion of sociological theory that is in the form of metatheory. It is discussion about theory: about what concepts it should include, about how those concepts should be linked, and about how theory should be studied. Similar to Kuhn’s paradigms, theories of this sort provide guidelines or strategies for understanding social phenomena and suggest the proper orientation of the theorist to these phenomena; they are orienting strategies. Textbooks in theory frequently focus on orienting strategies such as functionalism, exchange, or ethnomethodology." Sociologists thus use metatheories as orienting strategies. We may generalize and say that all people use metatheories as orienting strategies and that this is what direct our attention and also our browsing – also when we are not conscious about it.

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  • Overcategorization

    Overcategorization

    Overcategorization or category clutter is a phenomenon during classification where too many categories or classes are assigned to a document, record, or item. Overcategorization is related to the library and information science (LIS) concepts of document classification and subject indexing. It is also related to online shopping where excessive product categories can overwhelm users with too many choices or make it more difficult for customers to find the products they need. Although these categories are intended to improve organization and ease of navigation when shipping online, too many categories can lower customer satisfaction, increase difficulty navigating the online store, and reduce future shopping intentions. In LIS, the ideal number of terms that should be assigned to classify an item are measured by the variables precision and recall. Assigning few category labels that are most closely related to the content of the item being classified will result in searches that have high precision, I.e., where a high proportion of the results are closely related to the query. Assigning more category labels to each item will reduce the precision of each search, but increase the recall, retrieving more relevant results. Related LIS concepts include exhaustivity of indexing and information overload. == Basic principles == If too many categories are assigned to a given document, the implications for users depend on how informative the links are. If the user is able to distinguish between useful and not useful links, the damage is limited: The user only wastes time selecting links. In many cases, however, the user cannot judge whether or not a given link will turn out to be fruitful. In that case he or she has to follow the link and to read or skim another document. The worst case scenario is, of course, that even after reading the new document the user is unable to decide whether or not it might be useful if its subject matter is not thoroughly investigated. Overcategorization also has another unpleasant implication: It makes the system (for example in Wikipedia) difficult to maintain in a consistent way. If the system is inconsistent, it means that when the user considers the links in a given category, he or she will not find all documents relevant to that category. Basically, the problem of overcategorization should be understood from the perspective of relevance and the traditional measures of recall and precision. If too few relevant categories are assigned to a document, recall may decrease. If too many non-relevant categories are assigned, precision becomes lower. The hard job is to say which categories are fruitful or relevant for future use of the document.

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  • Hugging Face

    Hugging Face

    Hugging Face, Inc., is an American company based in New York City that develops computation tools for building applications using machine learning. Its transformers library built for natural language processing applications and its platform allow users to share machine learning models and datasets and showcase their work. == History == === Founding === The company was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf in New York City, originally as a company that developed a chatbot app targeted at teenagers. The company was named after the U+1F917 🤗 HUGGING FACE emoji. After open sourcing the model behind the chatbot, the company pivoted to focus on being a platform for machine learning. === AI boom === On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM, a multilingual large language model with 176 billion parameters. In February 2023, the company announced partnership with Amazon Web Services (AWS) which would allow Hugging Face's products to be available to AWS customers to use them as the building blocks for their custom applications. The company also said the next generation of BLOOM will be run on Trainium, a proprietary machine learning chip created by AWS. In June 2024, the company announced, along with Meta and Scaleway, their launch of a new AI accelerator program for European startups. The initiative aimed to help startups integrate open foundation models into their products, accelerating the EU AI ecosystem. The program, based at STATION F in Paris, ran from September 2024 to February 2025. Selected startups received mentoring, and access to AI models and tools and Scaleway's computing power. On September 23, 2024, to further the International Decade of Indigenous Languages, Hugging Face teamed up with Meta and UNESCO to launch a new online language translator. It was built on Meta's No Language Left Behind open-source AI model, enabling free text translation across 200 languages, including many low-resource languages. In April 2025, Hugging Face announced that they acquired a humanoid robotics startup, Pollen Robotics, based in France and founded by Matthieu Lapeyre and Pierre Rouanet in 2016. In an X tweet, Delangue shared his vision to "make Artificial Intelligence robotics Open Source". === Cyberattacks === In early 2026, hackers hijacked the Hugging Face platform to launch Android-targeted attacks involving "powerful malware" which could completely take over a compromised target.

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  • Irish logarithm

    Irish logarithm

    The Irish logarithm was a system of number manipulation invented by Percy Ludgate for machine multiplication. The system used a combination of mechanical cams as lookup tables and mechanical addition to sum pseudo-logarithmic indices to produce partial products, which were then added to produce results. The technique is similar to Zech logarithms (also known as Jacobi logarithms), but uses a system of indices original to Ludgate. == Concept == Ludgate's algorithm compresses the multiplication of two single decimal numbers into two table lookups (to convert the digits into indices), the addition of the two indices to create a new index which is input to a second lookup table that generates the output product. Because both lookup tables are one-dimensional, and the addition of linear movements is simple to implement mechanically, this allows a less complex mechanism than would be needed to implement a two-dimensional 10×10 multiplication lookup table. Ludgate stated that he deliberately chose the values in his tables to be as small as he could make them; given this, Ludgate's tables can be simply constructed from first principles, either via pen-and-paper methods, or a systematic search using only a few tens of lines of program code. They do not correspond to either Zech logarithms, Remak indexes or Korn indexes. == Pseudocode == The following is an implementation of Ludgate's Irish logarithm algorithm in the Python programming language: Table 1 is taken from Ludgate's original paper; given the first table, the contents of Table 2 can be trivially derived from Table 1 and the definition of the algorithm. Note since that the last third of the second table is entirely zeros, this could be exploited to further simplify a mechanical implementation of the algorithm.

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  • Semantic translation

    Semantic translation

    Semantic translation is the process of using semantic information to aid in the translation of data in one representation or data model to another representation or data model. Semantic translation takes advantage of semantics that associate meaning with individual data elements in one dictionary to create an equivalent meaning in a second system. An example of semantic translation is the conversion of XML data from one data model to a second data model using formal ontologies for each system such as the Web Ontology Language (OWL). This is frequently required by intelligent agents that wish to perform searches on remote computer systems that use different data models to store their data elements. The process of allowing a single user to search multiple systems with a single search request is also known as federated search. Semantic translation should be differentiated from data mapping tools that do simple one-to-one translation of data from one system to another without actually associating meaning with each data element. Semantic translation requires that data elements in the source and destination systems have "semantic mappings" to a central registry or registries of data elements. The simplest mapping is of course where there is equivalence. There are three types of Semantic equivalence: Class Equivalence - indicating that class or "concepts" are equivalent. For example: "Person" is the same as "Individual" Property Equivalence - indicating that two properties are equivalent. For example: "PersonGivenName" is the same as "FirstName" Instance Equivalence - indicating that two individual instances of objects are equivalent. For example: "Dan Smith" is the same person as "Daniel Smith" Semantic translation is very difficult if the terms in a particular data model do not have direct one-to-one mappings to data elements in a foreign data model. In that situation, an alternative approach must be used to find mappings from the original data to the foreign data elements. This problem can be alleviated by centralized metadata registries that use the ISO-11179 standards such as the National Information Exchange Model (NIEM).

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  • Terminology extraction

    Terminology extraction

    Terminology extraction (also known as term extraction, glossary extraction, term recognition, or terminology mining) is a subtask of information extraction. The goal of terminology extraction is to automatically extract relevant terms from a given corpus. In the semantic web era, a growing number of communities and networked enterprises started to access and interoperate through the internet. Modeling these communities and their information needs is important for several web applications, like topic-driven web crawlers, web services, recommender systems, etc. The development of terminology extraction is also essential to the language industry. One of the first steps to model a knowledge domain is to collect a vocabulary of domain-relevant terms, constituting the linguistic surface manifestation of domain concepts. Several methods to automatically extract technical terms from domain-specific document warehouses have been described in the literature. Typically, approaches to automatic term extraction make use of linguistic processors (part of speech tagging, phrase chunking) to extract terminological candidates, i.e. syntactically plausible terminological noun phrases. Noun phrases include compounds (e.g. "credit card"), adjective noun phrases (e.g. "local tourist information office"), and prepositional noun phrases (e.g. "board of directors"). In English, the first two (compounds and adjective noun phrases) are the most frequent. Terminological entries are then filtered from the candidate list using statistical and machine learning methods. Once filtered, because of their low ambiguity and high specificity, these terms are particularly useful for conceptualizing a knowledge domain or for supporting the creation of a domain ontology or a terminology base. Furthermore, terminology extraction is a very useful starting point for semantic similarity, knowledge management, human translation and machine translation, etc. == Bilingual terminology extraction == The methods for terminology extraction can be applied to parallel corpora. Combined with e.g. co-occurrence statistics, candidates for term translations can be obtained. Bilingual terminology can be extracted also from comparable corpora (corpora containing texts within the same text type, domain but not translations of documents between each other).

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  • Mark V. Shaney

    Mark V. Shaney

    Mark V. Shaney is a synthetic Usenet user whose postings in the net.singles newsgroups were generated by Markov chain techniques, based on text from other postings. The username is a play on the words "Markov chain". Many readers were fooled into thinking that the quirky, sometimes uncannily topical posts were written by a real person. The system was designed by Rob Pike with coding by Bruce Ellis. Don P. Mitchell wrote the Markov chain code, initially demonstrating it to Pike and Ellis using the Tao Te Ching as a basis. They chose to apply it to the net.singles netnews group. The program is fairly simple. It ingests the sample text (the Tao Te Ching, or the posts of a Usenet group) and creates a massive list of every sequence of three successive words (triplet) which occurs in the text. It then chooses two words at random, and looks for a word which follows those two in one of the triplets in its massive list. If there is more than one, it picks at random (identical triplets count separately, so a sequence which occurs twice is twice as likely to be picked as one which only occurs once). It then adds that word to the generated text. Then, in the same way, it picks a triplet that starts with the second and third words in the generated text, and that gives a fourth word. It adds the fourth word, then repeats with the third and fourth words, and so on. This algorithm is called a third-order Markov chain (because it uses sequences of three words). == Examples == A classic example, from 1984, originally sent as a mail message, later posted to net.singles is reproduced here: >From mvs Fri Nov 16 17:11 EST 1984 remote from alice It looks like Reagan is going to say? Ummm... Oh yes, I was looking for. I'm so glad I remembered it. Yeah, what I have wondered if I had committed a crime. Don't eat with your assessment of Reagon and Mondale. Up your nose with a guy from a firm that specifically researches the teen-age market. As a friend of mine would say, "It really doesn't matter"... It looks like Reagan is holding back the arms of the American eating public have changed dramatically, and it got pretty boring after about 300 games. People, having a much larger number of varieties, and are very different from what one can find in Chinatowns across the country (things like pork buns, steamed dumplings, etc.) They can be cheap, being sold for around 30 to 75 cents apiece (depending on size), are generally not greasy, can be adequately explained by stupidity. Singles have felt insecure since we came down from the Conservative world at large. But Chuqui is the way it happened and the prices are VERY reasonable. Can anyone think of myself as a third sex. Yes, I am expected to have. People often get used to me knowing these things and then a cover is placed over all of them. Along the side of the $$ are spent by (or at least for ) the girls. You can't settle the issue. It seems I've forgotten what it is, but I don't. I know about violence against women, and I really doubt they will ever join together into a large number of jokes. It showed Adam, just after being created. He has a modem and an autodial routine. He calls my number 1440 times a day. So I will conclude by saying that I can well understand that she might soon have the time, it makes sense, again, to get the gist of my argument, I was in that (though it's a Republican administration). _-_-_-_-Mark Other quotations from Mark's Usenet posts are: "I spent an interesting evening recently with a grain of salt." (Alternatively reported as "While at a conference a few weeks back, I spent an interesting evening with a grain of salt.") "I hope that there are sour apples in every bushel." (see also sour grapes) == History == In The Usenet Handbook Mark Harrison writes that after September 1981, students joined Usenet en masse, "creating the USENET we know today: endless dumb questions, endless idiots posing as savants, and (of course) endless victims for practical jokes." In December, Rob Pike created the netnews group net.suicide as prank, "a forum for bad jokes". Some users thought it was a legitimate forum, some discussed "riding motorcycles without helmets". At first, most posters were "real people", but soon "characters" began posting. Pike created a "vicious" character named Bimmler. At its peak, net.suicide had ten frequent posters; nine were "known to be characters." But ultimately, Pike deleted the newsgroup because it was too much work to maintain; Bimmler messages were created "by hand". The "obvious alternative" was software, running on a Bell Labs computer created by Bruce Ellis, based on the Markov code by Don Mitchell, which became the online character Mark V. Shaney. Kernighan and Pike listed Mark V. Shaney in the acknowledgements in The Practice of Programming, noting its roots in Mitchell's markov, which, adapted as shaney, was used for "humorous deconstructionist activities" in the 1980s. Dewdney pointed out "perhaps Mark V. Shaney's magnum opus: a 20-page commentary on the deconstructionist philosophy of Jean Baudrillard" directed by Pike, with assistance from Henry S. Baird and Catherine Richards, to be distributed by email. The piece was based on Jean Baudrillard's "The Precession of Simulacra", published in Simulacra and Simulation (1981). == Reception == The program was discussed by A. K. Dewdney in the Scientific American "Computer Recreations" column in 1989, by Penn Jillette in his PC Computing column in 1991, and in several books, including the Usenet Handbook, Bots: the Origin of New Species, Hippo Eats Dwarf: A Field Guide to Hoaxes and Other B.S., and non-computer-related journals such as Texas Studies in Literature and Language. Dewdney wrote about the program's output, "The overall impression is not unlike what remains in the brain of an inattentive student after a late-night study session. Indeed, after reading the output of Mark V. Shaney, I find ordinary writing almost equally strange and incomprehensible!" He noted the reactions of newsgroup users, who have "shuddered at Mark V. Shaney's reflections, some with rage and others with laughter:" The opinions of the new net.singles correspondent drew mixed reviews. Serious users of the bulletin board's services sensed satire. Outraged, they urged that someone "pull the plug" on Mark V. Shaney's monstrous rantings. Others inquired almost admiringly whether the program was a secret artificial intelligence project that was being tested in a human conversational environment. A few may even have thought that Mark V. Shaney was a real person, a tortured schizophrenic desperately seeking a like-minded companion. Concluding, Dewdney wrote, "If the purpose of computer prose is to fool people into thinking that it was written by a sane person, Mark V. Shaney probably falls short." A 2012 article in Observer compared Mark V. Shaney's "strangely beautiful" postings to the Horse_ebooks account on Twitter and music reviews at Pitchfork, saying that "this mash-up of gibberish and human sentiment" is what "made Mark V. Shaney so endlessly fascinating".

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  • DIKW pyramid

    DIKW pyramid

    The DIKW pyramid (also known as the knowledge pyramid or information hierarchy) is a model describing relationships between data, information, knowledge and wisdom sometimes also stylized as a chain, refer to models of possible structural and functional relationships between a set of components—often four, data, information, knowledge, and wisdom. The concept has roots predating the 1980s. In the latter years of that decade, interest in the models grew after explicit presentations and discussions, including from Milan Zeleny, Russell Ackoff, and Robert W. Lucky. Subsequent important discussions extended along theoretical and practical lines into the coming decades. While debate continues as to actual meaning of the component terms of DIKW-type models, and the actual nature of their relationships—including occasional doubt being cast over any simple, linear, unidirectional model—even so they have become very popular visual representations in use by business, the military, and others. Among the academic and popular, not all versions of the DIKW-type models include all four components (earlier ones excluding data, later ones excluding or downplaying wisdom, and several including additional components (for instance Ackoff inserting "understanding" before and Zeleny adding "enlightenment" after the wisdom component). In addition, DIKW-type models are no longer always presented as pyramids, instead also as a chart or framework (e.g., by Zeleny), as flow diagrams (e.g., by Liew, and by Chisholm et al.), and sometimes as a continuum (e.g., by Choo et al.). == Short description == As Rowley noted in 2007, the DIKW model "is often quoted, or used implicitly, in definitions of data, information and knowledge in the information management, information systems and knowledge management literatures, but [as of that date] there ha[d] been limited direct discussion of the hierarchy". Reviews of textbooks and a survey of scholars in relevant fields indicate that there was not a consensus as to definitions used in the model as of that date, and as reviewed by Liew in that year, even less "in the description of the processes that transform components lower in the hierarchy into those above them". Zins work, published in 2007—from studies in 2003-2005 that documented "130 definitions of data, information, and knowledge formulated by 45 scholars", published in 2007—to suggest that the data–information–knowledge components of DIKW refer to a class of no less than five models, as a function of whether data, information, and knowledge are each conceived of as subjective, objective (what Zins terms, "universal" or "collective") or both. In Zins' usage, subjective and objective "are not related to arbitrariness and truthfulness, which are usually attached to the concepts of subjective knowledge and objective knowledge". Information science, Zins argues, studies data and information, but not knowledge, as knowledge is an internal (subjective) rather than an external (universal–collective) phenomenon. == Representations == === Graphical representation === DIKW is a hierarchical model often depicted as a pyramid, sometimes as a chain, with data at its base and wisdom at its apex (or chain-beginning and -end). Both Zeleny and Ackoff have been credited with originating the pyramid representation, although neither used a pyramid to present their ideas. According to Wallace, Debons and colleagues may have been the first to "present the hierarchy graphically". Many variations of the DIKW-type pyramid have been produced. One, in use by knowledge managers in the United States Department of Defense, attempts to show the DIKW progression to enable effective decisions and consequent activities supporting shared understanding throughout defense organizations, as well as supporting management of risks associated with decisions. DIKW-type hierarchical information paradigms have also been represented as two-dimensional charts, and as flow diagrams, where relationships between the components may be presented less hierarchically, with defining aspects of the relationships, feedback loops, etc. === Computational representation === Intelligent decision support systems are trying to improve decision making by introducing new technologies and methods from the domain of modeling and simulation in general, and in particular from the domain of intelligent software agents in the contexts of agent-based modeling. The following example describes a military decision support system, but the architecture and underlying conceptual idea are transferable to other application domains: The value chain starts with data quality describing the information within the underlying command and control systems. Information quality tracks the completeness, correctness, currency, consistency and precision of the data items and information statements available. Knowledge quality deals with procedural knowledge and information embedded in the command and control system such as templates for adversary forces, assumptions about entities such as ranges and weapons, and doctrinal assumptions, often coded as rules. Awareness quality measures the degree of using the information and knowledge embedded within the command and control system. Awareness is explicitly placed in the cognitive domain. By the introduction of a common operational picture, data are put into context, which leads to information instead of data. The next step, which is enabled by service-oriented web-based infrastructures (but not yet operationally used), is the use of models and simulations for decision support. Simulation systems are the prototype for procedural knowledge, which is the basis for knowledge quality. Finally, using intelligent software agents to continually observe the battle sphere, apply models and simulations to analyze what is going on, to monitor the execution of a plan, and to do all the tasks necessary to make the decision maker aware of what is going on, command and control systems could even support situational awareness, the level in the value chain traditionally limited to pure cognitive methods. == History == Danny P. Wallace, a professor of library and information science, explained that the origin of the DIKW pyramid is uncertain: The presentation of the relationships among data, information, knowledge, and sometimes wisdom in a hierarchical arrangement has been part of the language of information science for many years. Although it is uncertain when and by whom those relationships were first presented, the ubiquity of the notion of a hierarchy is embedded in the use of the acronym DIKW as a shorthand representation for the data-to-information-to-knowledge-to-wisdom transformation.Many authors think that the idea of the DIKW relationship originated from two lines in the poem "Choruses", by T. S. Eliot, that appeared in the pageant play The Rock, in 1934: === Knowledge, intelligence, and wisdom === In 1927, Clarence W. Barron addressed his employees at Dow Jones & Company on the hierarchy: "Knowledge, Intelligence and Wisdom". === Data, information, knowledge === In 1955, English-American economist and educator Kenneth Boulding presented a variation on the hierarchy consisting of "signals, messages, information, and knowledge". However, "[t]he first author to distinguish among data, information, and knowledge and to also employ the term 'knowledge management' may have been American educator Nicholas L. Henry", in a 1974 journal article. === Data, information, knowledge, wisdom === Other early versions (prior to 1982) of the hierarchy that refer to a data tier include those of Chinese-American geographer Yi-Fu Tuan and sociologist-historian Daniel Bell.. In 1980, Irish-born engineer Mike Cooley invoked the same hierarchy in his critique of automation and computerization, in his book Architect or Bee?: The Human / Technology Relationship. Thereafter, in 1987, Czechoslovakia-born educator Milan Zeleny mapped the components of the hierarchy to knowledge forms: know-nothing, know-what, know-how, and know-why. Zeleny "has frequently been credited with proposing the [representation of DIKW as a pyramid ]... although he actually made no reference to any such graphical model." The hierarchy appears again in a 1988 address to the International Society for General Systems Research, by American organizational theorist Russell Ackoff, published in 1989. Subsequent authors and textbooks cite Ackoff's as the "original articulation" of the hierarchy or otherwise credit Ackoff with its proposal. Ackoff's version of the model includes an understanding tier (as Adler had, before him), interposed between knowledge and wisdom. Although Ackoff did not present the hierarchy graphically, he has also been credited with its representation as a pyramid. In 1989, Bell Labs veteran Robert W. Lucky wrote about the four-tier "information hierarchy" in the form of a pyramid in his book Silicon Dreams. In the same year as Ackoff presented his a

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  • Kullback–Leibler Upper Confidence Bound

    Kullback–Leibler Upper Confidence Bound

    In multi-armed bandit problems, KL-UCB (for Kullback–Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent Lai-Robbins lower bound. == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {D}},\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} δ t {\displaystyle \delta _{t}} is a well-chosen sequence of positive numbers, often equal to ln ⁡ t + c ln ⁡ ln ⁡ t {\displaystyle \ln t+c\ln \ln t} with c > 0 {\displaystyle c>0} . Then we choose the arm a t {\displaystyle a_{t}} with the highest index: a t := arg ⁡ max a U a ( t ) {\displaystyle a_{t}:=\arg \max _{a}U_{a}(t)} We note that the algorithm does not require knowledge of T {\displaystyle T} . === Example === In the special case of Gaussian distribution with fixed variance σ 2 {\displaystyle \sigma ^{2}} , we have: U a ( t ) = μ ^ a ( t ) + 2 σ 2 δ t N a ( t ) {\displaystyle U_{a}(t)={\hat {\mu }}_{a}(t)+{\sqrt {\frac {2\sigma ^{2}\delta _{t}}{N_{a}(t)}}}} with μ ^ a ( t ) {\displaystyle {\hat {\mu }}_{a}(t)} being the empirical mean of arm a {\displaystyle a} at turn t {\displaystyle t} . === Pseudocode === The player gets the set D for each arm i do: n[i] ← 1; nu[i] ← None; d ← ln(K) for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution for t from K+1 to T do: for each arm i do: index[i] ← compute_index(n[i], nu[i], D, d) select arm a with highest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution d ← ln(t+1) == Theoretical results == In the multi-armed bandit problem we have the Lai–Robbins asymptotic lower bound on regret. The algorithm KL-UCB matches this lower bound for one-dimensional exponential families with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} with δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} . === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. It states that for every consistent algorithm on the set D {\displaystyle {\mathcal {D}}} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ D K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {D}}^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + o T → + ∞ ( ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+o_{T\to +\infty }(\ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it. === Regret bound for KL-UCB === The algorithm matches the Lai–Robbins lower bound for one-dimensional exponential-family distributions and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} . ==== One-dimensional exponential family ==== For D {\displaystyle {\mathcal {D}}} being the set of one-dimensional exponential families, with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}({\sqrt {\ln T}}).} ==== Bounded distributions in [0,1] ==== For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} (the set of distributions supported on [ 0 , 1 ] {\displaystyle [0,1]} ), and for δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} , we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ( ln ⁡ T ) 4 / 5 ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}{\big (}(\ln T)^{4/5}\ln \ln T{\big )}.} === Runtime === For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} , the runtime needed per step and for an arm k {\displaystyle k} with n {\displaystyle n} observations is O ( n ( ln ⁡ n ) 2 ) {\displaystyle {\mathcal {O}}{\big (}n(\ln n)^{2}{\big )}} . This is higher than that of other optimal algorithms, such as NPTS with O ( n ) {\displaystyle {\mathcal {O}}(n)} . MED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . and IMED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . The high runtime of KL-UCB is due to a two-level optimisation: for each arm and candidate mean μ {\displaystyle \mu } , the algorithm evaluates K inf ( ν ^ a ( t ) , μ , D ) {\displaystyle {\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})} and then maximises μ {\displaystyle \mu } subject to N a ( t ) K inf ( ν ^ a ( t ) , μ , D ) ≤ δ t {\displaystyle N_{a}(t)\,{\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})\leq \delta _{t}} . For distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} the inner problem has no closed form and must be solved numerically, which increases the per-step cost.

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