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  Right to explanation

  In the regulation of algorithms, particularly artificial intelligence and its subfield of machine learning, a right to [an] explanation is a right to be given an explanation for an output of the algorithm. Such rights primarily refer to individual rights to be given an explanation for decisions that significantly affect an individual, particularly legally or financially. For example, a person who applies for a loan and is denied may ask for an explanation, which could be "Credit bureau X reports that you declared bankruptcy last year; this is the main factor in considering you too likely to default, and thus we will not give you the loan you applied for." Some such legal rights already exist, while the scope of a general "right to explanation" is a matter of ongoing debate. There have been arguments made that a "social right to explanation" is a crucial foundation for an information society, particularly as the institutions of that society will need to use digital technologies, artificial intelligence, machine learning. In other words, that the related automated decision making systems that use explainability would be more trustworthy and transparent. Without this right, which could be constituted both legally and through professional standards, the public will be left without much recourse to challenge the decisions of automated systems. == Examples == === Credit scoring in the United States === Under the Equal Credit Opportunity Act (Regulation B of the Code of Federal Regulations), Title 12, Chapter X, Part 1002, §1002.9, creditors are required to notify applicants who are denied credit with specific reasons for the detail. As detailed in §1002.9(b)(2): (2) Statement of specific reasons. The statement of reasons for adverse action required by paragraph (a)(2)(i) of this section must be specific and indicate the principal reason(s) for the adverse action. Statements that the adverse action was based on the creditor's internal standards or policies or that the applicant, joint applicant, or similar party failed to achieve a qualifying score on the creditor's credit scoring system are insufficient. The official interpretation of this section details what types of statements are acceptable. Creditors comply with this regulation by providing a list of reasons (generally at most 4, per interpretation of regulations), consisting of a numeric reason code (as identifier) and an associated explanation, identifying the main factors affecting a credit score. An example might be: 32: Balances on bankcard or revolving accounts too high compared to credit limits === European Union === The European Union General Data Protection Regulation (GDPR, enacted 2016, taking effect 2018) extends the automated decision-making rights in the 1995 Data Protection Directive to provide a legally disputed form of a right to an explanation, stated as such in Recital 71: "[the data subject should have] the right ... to obtain an explanation of the decision reached". In full: The data subject should have the right not to be subject to a decision, which may include a measure, evaluating personal aspects relating to him or her which is based solely on automated processing and which produces legal effects concerning him or her or similarly significantly affects him or her, such as automatic refusal of an online credit application or e-recruiting practices without any human intervention. ... In any case, such processing should be subject to suitable safeguards, which should include specific information to the data subject and the right to obtain human intervention, to express his or her point of view, to obtain an explanation of the decision reached after such assessment and to challenge the decision. However, the extent to which the regulations themselves provide a "right to explanation" is heavily debated. There are two main strands of criticism. There are significant legal issues with the right as found in Article 22 — as recitals are not binding, and the right to an explanation is not mentioned in the binding articles of the text, having been removed during the legislative process. In addition, there are significant restrictions on the types of automated decisions that are covered — which must be both "solely" based on automated processing, and have legal or similarly significant effects — which significantly limits the range of automated systems and decisions to which the right would apply. In particular, the right is unlikely to apply in many of the cases of algorithmic controversy that have been picked up in the media. The UK has also recently amended its implementation of Article 22. A second potential source of such a right has been pointed to in Article 15, the "right of access by the data subject". This restates a similar provision from the 1995 Data Protection Directive, allowing the data subject access to "meaningful information about the logic involved" in the same significant, solely automated decision-making, found in Article 22. Yet this too suffers from alleged challenges that relate to the timing of when this right can be drawn upon, as well as practical challenges that mean it may not be binding in many cases of public concern. Other EU legislative instruments contain explanation rights. The European Union's Artificial Intelligence Act provides in Article 86 a "[r]ight to explanation of individual decision-making" of certain high risk systems which produce significant, adverse effects to an individual's health, safety or fundamental rights. The right provides for "clear and meaningful explanations of the role of the AI system in the decision-making procedure and the main elements of the decision taken", although only applies to the extent other law does not provide such a right. The Digital Services Act in Article 27, and the Platform to Business Regulation in Article 5, both contain rights to have the main parameters of certain recommender systems to be made clear, although these provisions have been criticised as not matching the way that such systems work. The Platform Work Directive, which provides for regulation of automation in gig economy work as an extension of data protection law, further contains explanation provisions in Article 11, using the specific language of "explanation" in a binding article rather than a recital as is the case in the GDPR. Scholars note that remains uncertainty as to whether these provisions imply sufficiently tailored explanation in practice which will need to be resolved by courts. === France === In France the 2016 Loi pour une République numérique (Digital Republic Act or loi numérique) amends the country's administrative code to introduce a new provision for the explanation of decisions made by public sector bodies about individuals. It notes that where there is "a decision taken on the basis of an algorithmic treatment", the rules that define that treatment and its "principal characteristics" must be communicated to the citizen upon request, where there is not an exclusion (e.g. for national security or defence). These should include the following: the degree and the mode of contribution of the algorithmic processing to the decision- making; the data processed and its source; the treatment parameters, and where appropriate, their weighting, applied to the situation of the person concerned; the operations carried out by the treatment. Scholars have noted that this right, while limited to administrative decisions, goes beyond the GDPR right to explicitly apply to decision support rather than decisions "solely" based on automated processing, as well as provides a framework for explaining specific decisions. Indeed, the GDPR automated decision-making rights in the European Union, one of the places a "right to an explanation" has been sought within, find their origins in French law in the late 1970s. == Criticism == Some argue that a "right to explanation" is at best unnecessary, at worst harmful, and threatens to stifle innovation. Specific criticisms include: favoring human decisions over machine decisions, being redundant with existing laws, and focusing on process over outcome. Authors of study "Slave to the Algorithm? Why a 'Right to an Explanation' Is Probably Not the Remedy You Are Looking For" Lilian Edwards and Michael Veale argue that a right to explanation is not the solution to harms caused to stakeholders by algorithmic decisions. They also state that the right of explanation in the GDPR is narrowly defined, and is not compatible with how modern machine learning technologies are being developed. With these limitations, defining transparency within the context of algorithmic accountability remains a problem. For example, providing the source code of algorithms may not be sufficient and may create other problems in terms of privacy disclosures and the gaming of technical systems. To mitigate this issue, Edwards and Veale argue that an auditing system could be more effective, to allow auditors to loo

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  Algorithmic accountability

  Algorithmic accountability refers to the allocation of responsibility for the consequences of real-world actions influenced by algorithms used in decision-making processes. Ideally, algorithms should be designed to eliminate bias from their decision-making outcomes. This means they ought to evaluate only relevant characteristics of the input data, avoiding distinctions based on attributes that are generally inappropriate in social contexts, such as an individual's ethnicity in legal judgments. However, adherence to this principle is not always guaranteed, and there are instances where individuals may be adversely affected by algorithmic decisions. Responsibility for any harm resulting from a machine's decision may lie with the algorithm itself or with the individuals who designed it, particularly if the decision resulted from bias or flawed data analysis inherent in the algorithm's design. == Algorithm usage == Algorithms are widely utilized across various sectors of society that incorporate computational techniques in their control systems. These applications span numerous industries, including but not limited to medical, transportation, and payment services. In these contexts, algorithms perform functions such as: Approving or denying credit card applications; Approving or denying immigrant visas; Determining which taxpayers will be audited on their income taxes; Managing systems that control self-driving cars on a highway; Scoring individuals as potential criminals for use in legal proceedings; Search engines that match and rank database and internet search results; Recommendation systems that filter which news, entertainment, or purchase items are featured in a feed; Market-making algorithms that match sellers and buyers, such as in transportation (ride-hailing) or financial platforms. However, the implementation of these algorithms can be complex and opaque. Generally, algorithms function as "black boxes," meaning that the specific processes an input undergoes during execution are often not transparent, with users typically only seeing the resulting output. This lack of transparency raises concerns about potential biases within the algorithms, as the parameters influencing decision-making may not be well understood. The outputs generated can lead to perceptions of bias, especially if individuals in similar circumstances receive different results. According to Nicholas Diakopoulos: But these algorithms can make mistakes. They have biases. Yet they sit in opaque black boxes, their inner workings, their inner “thoughts” hidden behind layers of complexity. We need to get inside that black box, to understand how they may be exerting power on us, and to understand where they might be making unjust mistakes == Wisconsin Supreme Court case == Algorithms are prevalent across various fields and significantly influence decisions that affect the population at large. Their underlying structures and parameters often remain unknown to those impacted by their outcomes. A notable case illustrating this issue is a recent ruling by the Wisconsin Supreme Court concerning "risk assessment" algorithms used in criminal justice. The court determined that scores generated by such algorithms, which analyze multiple parameters from individuals, should not be used as a determining factor for arresting an accused individual. Furthermore, the court mandated that all reports submitted to judges must include information regarding the accuracy of the algorithm used to compute these scores. This ruling is regarded as a noteworthy development in how society should manage software that makes consequential decisions, highlighting the importance of reliability, particularly in complex settings like the legal system. The use of algorithms in these contexts necessitates a high degree of impartiality in processing input data. However, experts note that there is still considerable work to be done to ensure the accuracy of algorithmic results. Questions about the transparency of data processing continue to arise, which raises issues regarding the appropriateness of the algorithms and the intentions of their designers. == Controversies == A notable instance of potential algorithmic bias is highlighted in an article by The Washington Post regarding the ride-hailing service Uber. An analysis of collected data revealed that estimated waiting times for users varied based on the neighborhoods in which they resided. Key factors influencing these discrepancies included the predominant ethnicity and average income of the area. Specifically, neighborhoods with a majority white population and higher economic status tended to have shorter waiting times, while those with more diverse ethnic compositions and lower average incomes experienced longer waits. It’s important to clarify that this observation reflects a correlation identified in the data, rather than a definitive cause-and-effect relationship. No value judgments are made regarding the behavior of the Uber app in these cases. In TechCrunch website, Hemant Taneja wrote: Concern about “black box” algorithms that govern our lives has been spreading. New York University’s Information Law Institute hosted a conference on algorithmic accountability, noting: “Scholars, stakeholders, and policymakers question the adequacy of existing mechanisms governing algorithmic decision-making and grapple with new challenges presented by the rise of algorithmic power in terms of transparency, fairness, and equal treatment.” Yale Law School’s Information Society Project is studying this, too. “Algorithmic modeling may be biased or limited, and the uses of algorithms are still opaque in many critical sectors,” the group concluded. == Possible solutions == Discussions among experts have sought viable solutions to understand the operations of algorithms, often referred to as "black boxes." It is generally proposed that companies responsible for developing and implementing these algorithms should ensure their reliability by disclosing the internal processes of their systems. Hemant Taneja, writing for TechCrunch, emphasizes that major technology companies, such as Google, Amazon, and Uber, must actively incorporate algorithmic accountability into their operations. He suggests that these companies should transparently monitor their own systems to avoid stringent regulatory measures. One potential approach is the introduction of regulations in the tech sector to enforce oversight of algorithmic processes. However, such regulations could significantly impact software developers and the industry as a whole. It may be more beneficial for companies to voluntarily disclose the details of their algorithms and decision-making parameters, which could enhance the trustworthiness of their solutions. Another avenue discussed is the possibility of self-regulation by the companies that create these algorithms, allowing them to take proactive steps in ensuring accountability and transparency in their operations. In TechCrunch website, Hemant Taneja wrote: There’s another benefit — perhaps a huge one — to software-defined regulation. It will also show us a path to a more efficient government. The world’s legal logic and regulations can be coded into software and smart sensors can offer real-time monitoring of everything from air and water quality, traffic flows and queues at the DMV. Regulators define the rules, technologist create the software to implement them and then AI and ML help refine iterations of policies going forward. This should lead to much more efficient, effective governments at the local, national and global levels.

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  DARPA Prize Competitions

  Over the years, the U.S. Defense Advanced Research Projects Agency (DARPA) has conducted numerous prize competitions to spur innovation. A prize competition allows DARPA to establish an ambitious goal, opening the door to novel approaches from the public that might otherwise appear too risky for experts in a particular field to pursue. == Statutory authorities == In 1999, Congress provided prize competition authority to DARPA in the National Defense Authorization Act for Fiscal Year 2000 (P.L. 106–65), 10 U.S.C. § 4025, formerly 10 U.S.C. §2374a. DARPA also conducts prize competitions under the America COMPETES Act, 15 U.S.C. § 3719. == Recent prize competitions == DARPA Grand Challenge (2004 and 2005) was a prize competition to spur the development of autonomous vehicle technologies. The $1 million prize went unclaimed as no vehicles could complete the challenging desert route from Barstow, CA, to Primm, NV, on March 13, 2004. A year later, on October 8, 2005, the Stanford Racing Team won the $2 million prize during the second competition of the Grand Challenge in the desert Southwest near the California/Nevada state line. DARPA Urban Challenge (2007) required the competitors to build an autonomous vehicle capable of driving in traffic and performing complex maneuvers such as merging, passing, parking, and negotiating intersections. On November 3, 2007, the Carnegie Mellon Team won the $2 million prize, and its vehicle became the first autonomous vehicle that interacted with both manned and unmanned vehicle traffic in an urban environment. DARPA Network Challenge (Red Balloon Challenge) (2009) explored the roles that the Internet and social networking play in solving broad-scope, time-critical problems. On December 5, 2009, the Massachusetts Institute of Technology team won $40,000 by locating the ten moored, eight-foot, red weather balloons at ten places in the United States within seven hours. DARPA Digital Manufacturing Analysis, Correlation and Estimation Challenge (DMACE) (2010) was a three-month contest to showcase the potential of digital manufacturing of advanced materials. The University of California at Santa Barbara team won a $50,000 prize for crushing 180 digitally manufactured (DM) titanium mesh spheres with the most accurate predictive model of the components’ properties. DARPA Shredder Challenge (2011) was to identify and assess potential capabilities and vulnerabilities to sensitive information in the national security community. Participating teams must download the images of the documents shredded into more than 10,000 pieces from the Challenge website, reconstruct the documents, and solve the five puzzles. Of almost 9,000 teams, the San Francisco-based All Your Shreds Are Belong to U.S team won the $50,000 prize. DARPA UAVForge Challenge (2011-2012) aimed to build and test a user-intuitive, backpack-portable unmanned aerial vehicle (UAV) that could quietly fly in and out of critical environments to conduct sustained surveillance for up to three hours. The $100,000 prize was not claimed because none of the 140 teams met the technical matrix. DARPA Cash for Locating & Identifying Quick Response Codes (CLIQR) Quest Challenge (2012) explored the role the Internet and social media played in the timely communication, wide-area team-building, and urgent mobilization required to solve broad scope, time-critical problems. The challenge offered $40,000 to the first individual or team that could locate seven posters appearing in U.S. cities bearing the DARPA logo and a quick response code (QR) within 15 days. No team found and submitted all seven codes. DARPA Fast Adaptable Next-Generation Ground Vehicle (FANG) Challenge (2012-2013) was to use three competitions for the design of an infantry fighting vehicle, culminating in prototypes. In April 2013, DARPA awarded US$1 million to a three-man team during the first competition. DARPA decided not to proceed with the second and third competitions as originally planned and transitioned the technologies to the defense and commercial industry through the Digital Manufacturing and Design Innovation Institute (DMDII). DARPA Spectrum Challenge (2013-2014) sought to demonstrate how a software-defined radio can use a given communication channel in the presence of other users and interfering signals. Three teams emerged as the overall winners, winning a total of $150,000 in prizes. DARPA Chikungunya (CHIKV) Challenge (2014-2015) was a health-related effort to develop the most accurate predictions of CHIKV cases for all Western Hemisphere countries and territories between September 2014 and March 2015. On May 12, 2015, DARPA awarded $500,000 in prizes to the 11 winners of the competition during a scientific review DARPA Robotics Challenge (DRC) (2013-2015) aimed to develop semi-autonomous ground robots that could do "complex tasks in dangerous, degraded, human-engineered environments." A South Korean team won the first prize of $2 million, and two U.S. teams won $1 million and $500,000 as second and third winners. DARPA Cyber Grand Challenge (CGC) (2014 - 2016) was to “create automatic defensive systems capable of reasoning about flaws, formulating patches and deploying them on a network in real time.” The top three winners were awarded prizes of $2 million, $1 million, and $750,000, respectively. DARPA Spectrum Collaboration Challenge (SC2) (2016-2019) aimed to encourage the development of AI-enabled wireless networks to “ensure that the exponentially growing number of military and civilian wireless devices would have full access to the increasingly crowded electromagnetic spectrum.” A team from the University of Florida won the overall top prize of US$2 million at the final SC2 competition. DARPA Subterranean (SubT) Challenge (2017-2021) was to develop robotic technologies to map, navigate, search and exploit complex underground environments. The first-place winners of the system final competition and of the virtual final competition were awarded $2 million and $750,000, respectively, with multiple prizes awarded to the second and third-place winners. DARPA Launch Challenge (2018-2020) was a $12 million satellite launch challenge to demonstrate responsive and flexible space launch capabilities from the small launch providers and was to culminate in two separate launch competitions where the competitors must launch a satellite to low Earth orbit (LEO) within days of each other at different locations in the United States. The competition ended without a winner. DARPA Forecasting Floats in Turbulence (FFT) Challenge (2021) was to spur technologies that could predict the location of sea drifters or floats within 10 days. DARPA awarded $25,000 for first place, with prizes of $15,000 and $10,000 for second place and third place. DARPA Artificial Intelligence Cyber Challenge (AIxCC) (2023–2025) was a two-year challenge and asks competitors to design novel AI systems to secure critical software code on which Americans rely. The total prize money is $29.5 million. In March 2024, the Advanced Research Projects Agency for Health (ARPA-H) partnered with DARPA, contributing an additional $20 million to the competition's prize pool to address software vulnerabilities in medical devices, hospital IT, and biotech equipment. AIxCC collaborates with Google, Microsoft, OpenAI, Anthropic, Linux Foundation, Open Source Security Foundation, Black Hat USA, and DEF CON, all of which provide AIxCC with access to large language models. In August 2024, AIxCC held the semifinal at DEF CON in Las Vegas. DARPA and ARPA-H tested all 42 submissions by running them through various open-source coding projects with deliberately injected vulnerabilities and scored the tools based on their effectiveness in identifying and fixing security flaws. Seven teams, each winning $2 million in the semifinals, competed in the final round of the AIxCC at the August 2025 DEF CON conference. Team Atlanta won first place with a $4 million prize for its cyber reasoning systems, which identified and patched vulnerabilities across 54 million lines of code. DARPA Triage Challenge (2023 – 2026) aims to spur the development of novel physiological features for medical triage, with a total prize money of $7 million. In October 2024, Challenge Event 1 was held in Perry, Georgia, featuring to-scale replicas of disaster sites such as an airplane crash and Hurricane Katrina, and teams competed based on how closely their data aligned with the agency’s official data and how quickly and accurately their autonomous systems could identify individuals most urgently in need of medical care. DARPA concluded the second year of competitions and, in November 2025, named the top performers in systems and data categories, which will advance to the final 2026 competition. The DARPA Lift Challenge (2025-2026) is for participants to design unmanned aerial systems capable of carrying up to four times their own weight, with a minimum payload of 110 pounds. Acco

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  Autonomic computing

  Autonomic computing (AC) is distributed computing resources with self-managing characteristics, adapting to unpredictable changes while hiding intrinsic complexity to operators and users. Initiated by IBM in 2001, this initiative ultimately aimed to develop computer systems capable of self-management, to overcome the rapidly growing complexity of computing systems management, and to reduce the barrier that complexity poses to further growth. == Description == The AC system concept is designed to make adaptive decisions, using high-level policies. It will constantly check and optimize its status and automatically adapt itself to changing conditions. An autonomic computing framework is composed of autonomic components (AC) interacting with each other. An AC can be modeled in terms of two main control schemes (local and global) with sensors (for self-monitoring), effectors (for self-adjustment), knowledge and planner/adapter for exploiting policies based on self- and environment awareness. This architecture is sometimes referred to as Monitor-Analyze-Plan-Execute (MAPE). Driven by such vision, a variety of architectural frameworks based on "self-regulating" autonomic components has been recently proposed. A similar trend has recently characterized significant research in the area of multi-agent systems. However, most of these approaches are typically conceived with centralized or cluster-based server architectures in mind and mostly address the need of reducing management costs rather than the need of enabling complex software systems or providing innovative services. Some autonomic systems involve mobile agents interacting via loosely coupled communication mechanisms. Autonomy-oriented computation is a paradigm proposed by Jiming Liu in 2001 that uses artificial systems imitating social animals' collective behaviours to solve difficult computational problems. For example, ant colony optimization could be studied in this paradigm. == Problem of growing complexity == Forecasts suggested that the computing devices in use would grow at 38% per year and the average complexity of each device was increasing. This volume and complexity was managed by highly skilled humans; but the demand for skilled IT personnel was already outstripping supply, with labour costs exceeding equipment costs by a ratio of up to 18:1. Computing systems have brought great benefits of speed and automation but there is now an overwhelming economic need to automate their maintenance. In a 2003 IEEE Computer article, Kephart and Chess warn that the dream of interconnectivity of computing systems and devices could become the "nightmare of pervasive computing" in which architects are unable to anticipate, design and maintain the complexity of interactions. They state the essence of autonomic computing is system self-management, freeing administrators from low-level task management while delivering better system behavior. A general problem of modern distributed computing systems is that their complexity, and in particular the complexity of their management, is becoming a significant limiting factor in their further development. Large companies and institutions are employing large-scale computer networks for communication and computation. The distributed applications running on these computer networks are diverse and deal with multiple tasks, ranging from internal control processes to presenting web content to customer support. Additionally, mobile computing is pervading these networks at an increasing speed: employees need to communicate with their companies while they are not in their office. They do so by using laptops, personal digital assistants, or mobile phones with diverse forms of wireless technologies to access their companies' data. This creates an enormous complexity in the overall computer network which is hard to control manually by human operators. Manual control is time-consuming, expensive, and error-prone. The manual effort needed to control a growing networked computer-system tends to increase quickly. 80% of such problems in infrastructure happen at the client specific application and database layer. Most 'autonomic' service providers guarantee only up to the basic plumbing layer (power, hardware, operating system, network and basic database parameters). == Characteristics of autonomic systems == A possible solution could be to enable modern, networked computing systems to manage themselves without direct human intervention. The Autonomic Computing Initiative (ACI) aims at providing the foundation for autonomic systems. It is inspired by the autonomic nervous system of the human body. This nervous system controls important bodily functions (e.g. respiration, heart rate, and blood pressure) without any conscious intervention. In a self-managing autonomic system, the human operator takes on a new role: instead of controlling the system directly, he/she defines general policies and rules that guide the self-management process. For this process, IBM defined the following four types of property referred to as self-star (also called self-, self-x, or auto-) properties. Self-configuration: Automatic configuration of components; Self-healing: Automatic discovery, and correction of faults; Self-optimization: Automatic monitoring and control of resources to ensure the optimal functioning with respect to the defined requirements; Self-protection: Proactive identification and protection from arbitrary attacks. Others such as Poslad and Nami and Sharifi have expanded on the set of self-star as follows: Self-regulation: A system that operates to maintain some parameter, e.g., Quality of service, within a reset range without external control; Self-learning: Systems use machine learning techniques such as unsupervised learning which does not require external control; Self-awareness (also called Self-inspection and Self-decision): System must know itself. It must know the extent of its own resources and the resources it links to. A system must be aware of its internal components and external links in order to control and manage them; Self-organization: System structure driven by physics-type models without explicit pressure or involvement from outside the system; Self-creation (also called Self-assembly, Self-replication): System driven by ecological and social type models without explicit pressure or involvement from outside the system. A system's members are self-motivated and self-driven, generating complexity and order in a creative response to a continuously changing strategic demand; Self-management (also called self-governance): A system that manages itself without external intervention. What is being managed can vary dependent on the system and application. Self -management also refers to a set of self-star processes such as autonomic computing rather than a single self-star process; Self-description (also called self-explanation or Self-representation): A system explains itself. It is capable of being understood (by humans) without further explanation. IBM has set forth eight conditions that define an autonomic system: The system must know itself in terms of what resources it has access to, what its capabilities and limitations are and how and why it is connected to other systems; be able to automatically configure and reconfigure itself depending on the changing computing environment; be able to optimize its performance to ensure the most efficient computing process; be able to work around encountered problems by either repairing itself or routing functions away from the trouble; detect, identify and protect itself against various types of attacks to maintain overall system security and integrity; adapt to its environment as it changes, interacting with neighboring systems and establishing communication protocols; rely on open standards and cannot exist in a proprietary environment; anticipate the demand on its resources while staying transparent to users. Even though the purpose and thus the behaviour of autonomic systems vary from system to system, every autonomic system should be able to exhibit a minimum set of properties to achieve its purpose: Automatic: This essentially means being able to self-control its internal functions and operations. As such, an autonomic system must be self-contained and able to start-up and operate without any manual intervention or external help. Again, the knowledge required to bootstrap the system (Know-how) must be inherent to the system. Adaptive: An autonomic system must be able to change its operation (i.e., its configuration, state and functions). This will allow the system to cope with temporal and spatial changes in its operational context either long term (environment customisation/optimisation) or short term (exceptional conditions such as malicious attacks, faults, etc.). Aware: An autonomic system must be able to monitor (sense) its operational context as well as its internal state in order to be able to asses

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  Question answering

  Question answering (QA) is a computer science discipline within the fields of information retrieval and natural language processing (NLP) that is concerned with building systems that automatically answer questions that are posed by humans in a natural language. A question-answering implementation, usually a computer program, may construct its answers by querying a structured database of knowledge or information, usually a knowledge base. More commonly, question-answering systems can pull answers from an unstructured collection of natural language documents. Some examples of natural language document collections used for question answering systems include reference texts, compiled newswire reports, Wikipedia pages and other World Wide Web pages. == History == Two early question answering systems were BASEBALL and LUNAR. BASEBALL answered questions about Major League Baseball over a period of one year. LUNAR answered questions about the geological analysis of rocks returned by the Apollo Moon missions. Both question answering systems were very effective in their chosen domains. LUNAR was demonstrated at a lunar science convention in 1971 and it was able to answer 90% of the questions in its domain that were posed by people untrained on the system. Further restricted-domain question answering systems were developed in the following years. The common feature of all these systems is that they had a core database or knowledge system that was hand-written by experts of the chosen domain. The language abilities of BASEBALL and LUNAR used techniques similar to ELIZA and DOCTOR, the first chatterbot programs. SHRDLU was a successful question-answering program developed by Terry Winograd in the late 1960s and early 1970s. It simulated the operation of a robot in a toy world (the "blocks world"), and it offered the possibility of asking the robot questions about the state of the world. The strength of this system was the choice of a very specific domain and a very simple world with rules of physics that were easy to encode in a computer program. In the 1970s, knowledge bases were developed that targeted narrower domains of knowledge. The question answering systems developed to interface with these expert systems produced more repeatable and valid responses to questions within an area of knowledge. These expert systems closely resembled modern question answering systems except in their internal architecture. Expert systems rely heavily on expert-constructed and organized knowledge bases, whereas many modern question answering systems rely on statistical processing of a large, unstructured, natural language text corpus. The 1970s and 1980s saw the development of comprehensive theories in computational linguistics, which led to the development of ambitious projects in text comprehension and question answering. One example was the Unix Consultant (UC), developed by Robert Wilensky at U.C. Berkeley in the late 1980s. The system answered questions pertaining to the Unix operating system. It had a comprehensive, hand-crafted knowledge base of its domain, and it aimed at phrasing the answer to accommodate various types of users. Another project was LILOG, a text-understanding system that operated on the domain of tourism information in a German city. The systems developed in the UC and LILOG projects never went past the stage of simple demonstrations, but they helped the development of theories on computational linguistics and reasoning. Specialized natural-language question answering systems have been developed, such as EAGLi for health and life scientists. Question answering systems have been extended in recent years to encompass additional domains of knowledge For example, systems have been developed to automatically answer temporal and geospatial questions, questions of definition and terminology, biographical questions, multilingual questions, and questions about the content of audio, images, and video. Current question answering research topics include: interactivity—clarification of questions or answers answer reuse or caching semantic parsing answer presentation knowledge representation and semantic entailment social media analysis with question answering systems sentiment analysis utilization of thematic roles Image captioning for visual question answering Embodied question answering In 2011, Watson, a question answering computer system developed by IBM, competed in two exhibition matches of Jeopardy! against Brad Rutter and Ken Jennings, winning by a significant margin. Facebook Research made their DrQA system available under an open source license. This system uses Wikipedia as knowledge source. The open source framework Haystack by deepset combines open-domain question answering with generative question answering and supports the domain adaptation of the underlying language models for industry use cases. Large Language Models (LLMs)[36] like GPT-4[37], Gemini[38] are examples of successful QA systems that are enabling more sophisticated understanding and generation of text. When coupled with Multimodal[39] QA Systems, which can process and understand information from various modalities like text, images, and audio, LLMs significantly improve the capabilities of QA systems. == Types == Question-answering research attempts to develop ways of answering a wide range of question types, including fact, list, definition, how, why, hypothetical, semantically constrained, and cross-lingual questions. Answering questions related to an article in order to evaluate reading comprehension is one of the simpler form of question answering, since a given article is relatively short compared to the domains of other types of question-answering problems. An example of such a question is "What did Albert Einstein win the Nobel Prize for?" after an article about this subject is given to the system. Closed-book question answering is when a system has memorized some facts during training and can answer questions without explicitly being given a context. This is similar to humans taking closed-book exams. Closed-domain question answering deals with questions under a specific domain (for example, medicine or automotive maintenance) and can exploit domain-specific knowledge frequently formalized in ontologies. Alternatively, "closed-domain" might refer to a situation where only a limited type of questions are accepted, such as questions asking for descriptive rather than procedural information. Question answering systems in the context of machine reading applications have also been constructed in the medical domain, for instance related to Alzheimer's disease. Open-domain question answering deals with questions about nearly anything and can only rely on general ontologies and world knowledge. Systems designed for open-domain question answering usually have much more data available from which to extract the answer. An example of an open-domain question is "What did Albert Einstein win the Nobel Prize for?" while no article about this subject is given to the system. Another way to categorize question-answering systems is by the technical approach used. There are a number of different types of QA systems, including: rule-based systems, statistical systems, and hybrid systems. Rule-based systems use a set of rules to determine the correct answer to a question. Statistical systems use statistical methods to find the most likely answer to a question. Hybrid systems use a combination of rule-based and statistical methods. == Architecture == As of 2001, question-answering systems typically included a question classifier module that determined the type of question and the type of answer. Different types of question-answering systems employ different architectures. For example, modern open-domain question answering systems may use a retriever-reader architecture. The retriever is aimed at retrieving relevant documents related to a given question, while the reader is used to infer the answer from the retrieved documents. Systems such as GPT-3, T5, and BART use an end-to-end architecture in which a transformer-based architecture stores large-scale textual data in the underlying parameters. Such models can answer questions without accessing any external knowledge sources. == Methods == Question answering is dependent on a good search corpus; without documents containing the answer, there is little any question answering system can do. Larger collections generally mean better question answering performance, unless the question domain is orthogonal to the collection. Data redundancy in massive collections, such as the web, means that nuggets of information are likely to be phrased in many different ways in differing contexts and documents, leading to two benefits: If the right information appears in many forms, the question answering system needs to perform fewer complex NLP techniques to understand the text. Correct answers can be filtered from false positives because the syst

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  Revelation Space series

  The Revelation Space series is a book series created by Alastair Reynolds. The fictional universe is used as the setting for a number of his novels and stories. Its fictional history follows the human species through various conflicts from the relatively near future (roughly 2200) to approximately 40,000 AD (all the novels to date are set between 2427 and 2858, although certain stories extend beyond this period). It takes its name from Revelation Space (2000), which was the first published novel set in the universe. == Universe == The Revelation Space universe is a fictional universe set in a future version of our world, with the addition of a number of extraterrestrial species and advanced technologies that are not necessarily grounded in current science. It is, nonetheless, somewhat "harder" than most examples of space opera, relying to a considerable extent on science Reynolds believes to be possible; in particular, faster-than-light travel is largely absent. Reynolds has said he prefers to keep the science in his fiction plausible, but he will adopt science he believes to be impossible when it is necessary for the story. The name "Revelation Space universe" has been used by Alastair Reynolds in both the introductory text in the collections Diamond Dogs, Turquoise Days and Galactic North, and also on several editions of the novels set in the universe. He considered calling it the "Exordium universe" after a key plot device, but found that the name was already in use. While a great deal of science fiction reflects either very optimistic or dystopian visions of the human future, the Revelation Space universe is notable in that human societies have not developed to either positive or negative extremes. Instead, despite their dramatically advanced technology, they are similar to those of today in terms of their moral ambiguity and mixture of cruelty and decency, corruption and opportunity. The Revelation Space universe contains elements of Lovecraftian horror, with one posthuman entity stating explicitly that some things in the universe are fundamentally beyond human or transhuman understanding. Nevertheless, the main storyline is essentially optimistic, with humans continuing to survive even in a universe that seems fundamentally hostile to intelligent life. The name "Revelation Space" appears in the novel of the same name during Philip Lascaille's account of his visit to Lascaille's Shroud, an anomalous region of the local universe. Lascaille says that "the key" to something momentous "was explained to me [. . .] while I was in Revelation Space." === Chronology === The chronology of the Revelation Space universe extends to roughly one billion years into the past, when the "Dawn War" — a galaxy-spanning conflict over the availability of various natural resources — resulted in almost all sentient life in the galaxy being wiped out. One race of survivors, later termed the Inhibitors, having converted itself to machine form, predicted that the impending Andromeda–Milky Way collision, roughly 3 billion years in our future, may severely damage the capacity of either galaxy to support life. Consequently, they planned to adjust the positions of stars in order to limit the damage the collision would cause. Also central to the Inhibitor project was the eradication of all species above a certain technological level until the crisis was over, as they believed no organic species would be capable of co-operating on such a large-scale project (an in-universe solution to the Fermi paradox). Whilst they were relatively successful, certain advanced species were able to hide from Inhibitor forces, or even fight back. In human history, during the 21st and 22nd centuries, numerous wars occurred, and a flotilla of generation ships was deployed to colonise a planet orbiting the star 61 Cygni (which becomes a major segment of the plot of Chasm City). The flotilla later reached a planet termed Sky's Edge, which was to be embroiled in war until human civilisation there was eradicated. Meanwhile, in the Solar System in 2190, a faction known as the Conjoiners emerged as a result of increased experimentation with neural implants. In response, the Coalition for Neural Purity was formed, opposed to the Conjoiners. Nevil Clavain, one of the series's primary protagonists, fought on the side of the Coalition in the ensuing war, but defected later on after being betrayed. Clavain, and the Conjoiners, succeeded in escaping the Solar System and left for surrounding stars. For the next few centuries, the so-called Belle Epoque, humanity enjoyed a period of relative peace and prosperity, with several planets being colonised. The most successful planet of all was Yellowstone, a planet orbiting the star Epsilon Eridani, site of the Glitter Band / Rust Belt and Chasm City. Technologies developed included the Conjoiner Drive, a gift from the Conjoiners (who resumed contact with humanity at an unknown time), advanced nanotechnology, and numerous other devices. With the exception of an attempted takeover of the Glitter Band, no major incidents affected humanity during this time. The Belle Epoque was terminated by the advent of the Melding Plague in 2510, a nanotechnological virus that destroyed all other nanotechnology it came into contact with. Only the Conjoiners were unaffected by this disaster, which devastated the civilisation around Yellowstone. War between the Conjoiners and the Demarchists, a rival faction, erupted as a result of the plague. Meanwhile, activities around a far-flung human colony on the planet Resurgam, orbiting the star Delta Pavonis, inadvertently attracted the attention of the Inhibitors. The Conjoiners, also made aware of this event, sent Clavain to recover the exceedingly powerful "Cache Weapons" from this system (said weapons having been stolen from the Conjoiners centuries before) so that they could be used to fend off the Inhibitors while the Conjoiners escaped. Clavain instead defected from the Conjoiners, intending to use the weapons to protect all of humanity. Skade, another Conjoiner, was sent to stop him and recover the weapons. They fought around the Resurgam system, with Clavain and his allies eventually obtaining the weapons. Clavain's ally Remontoire agreed to seek out alien assistance from the Hades Matrix, a nearby alien computer disguised as a neutron star, whilst Clavain sheltered refugees from Resurgam on another planet, later termed Ararat. Remontoire returned in 2675, only a few days after Clavain's death at the hands of Skade, who had arrived with him. Remontoire and his allies were now at war with the Inhibitors, assisted by alien technology obtained from Hades. Even so, it was realised that the humans would not last indefinitely, and Clavain's people, now led by Scorpio, decided to seek out the mysterious "Shadows": a race believed to be near a moon called Hela, site of a theocracy. Aura, daughter of Ana Khouri (an ally of Remontoire) infiltrated the theocracy under the pseudonym Rashmika Els. After considerable conflict, Scorpio and Aura realised that contacting the Shadows was inadvisable. With the later assistance of the Conjoiner known as Glass, and of Clavain's estranged brother Warren, Scorpio and Aura (now going by the name Lady Arek) instead succeeded in contacting the Nestbuilders, an alien race who provided them with weapons capable of defeating the Inhibitors. As such, the Inhibitors were effectively eradicated from human space, with buffer zones and frontiers established to keep them at bay. Humanity then enjoyed a second, 400-year-long golden age. After this, however, came the Greenfly outbreak, in which human civilisation was destroyed by a rogue terraforming system of human origin that destroyed planets and converted them to millions of orbiting, vegetation-filled habitats. The Greenfly began to subsume most of human space, with all efforts to stop them failing, due to the Greenfly having assimilated aspects of both the Melding Plague and Inhibitor technology. The storyline of the Revelation Space universe thus far concludes with humanity leaving the Milky Way galaxy in an attempt to set up a new civilisation elsewhere. == Books and stories set in the universe == All short stories and novellas in this universe to date are collected in Galactic North and Diamond Dogs, Turquoise Days, with the exception of "Monkey Suit", "The Last Log of the Lachrimosa", "Night Passage", "Open and Shut", and "Plague Music". === The Inhibitor Sequence === Revelation Space. London: Gollancz, 2000. ISBN 978-0-575-06875-9. Redemption Ark. London: Gollancz, 2002. ISBN 978-0-575-06879-7. Absolution Gap. London: Gollancz, 2003. ISBN 978-0-575-07434-7. Inhibitor Phase. London: Gollancz, 2021. ISBN 978-0-575-09075-0. === Prefect Dreyfus Emergencies === The Prefect. London: Gollancz, 2007, ISBN 978-0-575-07716-4. (Re-released as Aurora Rising in 2017, ISBN 978-1-473-22336-3) Elysium Fire. London: Gollancz, 2018, ISBN 978-0-575-09059-0.

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  T-norm

  In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize the triangle inequality of ordinary metric spaces. == Definition == A t-norm is a function T: [0, 1] × [0, 1] → [0, 1] that satisfies the following properties: Commutativity: T(a, b) = T(b, a) Monotonicity: T(a, b) ≤ T(c, d) if a ≤ c and b ≤ d Associativity: T(a, T(b, c)) = T(T(a, b), c) The number 1 acts as identity element: T(a, 1) = a Since a t-norm is a binary algebraic operation on the interval [0, 1], infix algebraic notation is also common, with the t-norm usually denoted by ∗ {\displaystyle } . The defining conditions of the t-norm are exactly those of a partially ordered abelian monoid on the real unit interval [0, 1]. (Cf. ordered group.) The monoidal operation of any partially ordered abelian monoid L is therefore by some authors called a triangular norm on L. === Classification of t-norms === A t-norm is called continuous if it is continuous as a function, in the usual interval topology on [0, 1]2. (Similarly for left- and right-continuity.) A t-norm is called strict if it is continuous and strictly monotone. A t-norm is called nilpotent if it is continuous and each x in the open interval (0, 1) is nilpotent, that is, there is a natural number n such that x ∗ {\displaystyle } ... ∗ {\displaystyle } x (n times) equals 0. A t-norm ∗ {\displaystyle } is called Archimedean if it has the Archimedean property, that is, if for each x, y in the open interval (0, 1) there is a natural number n such that x ∗ {\displaystyle } ... ∗ {\displaystyle } x (n times) is less than or equal to y. The usual partial ordering of t-norms is pointwise, that is, T1 ≤ T2 if T1(a, b) ≤ T2(a, b) for all a, b in [0, 1]. As functions, pointwise larger t-norms are sometimes called stronger than those pointwise smaller. In the semantics of t-norm fuzzy logics, however, the larger a t-norm, the weaker (in terms of logical strength) conjunction it represents. == Prominent examples == Minimum t-norm ⊤ m i n ( a , b ) = min { a , b } , {\displaystyle \top _{\mathrm {min} }(a,b)=\min\{a,b\},} also called the Gödel t-norm, as it is the standard semantics for conjunction in Gödel fuzzy logic. Besides that, it occurs in most t-norm based fuzzy logics as the standard semantics for weak conjunction. It is the pointwise largest t-norm (see the properties of t-norms below). Product t-norm ⊤ p r o d ( a , b ) = a ⋅ b {\displaystyle \top _{\mathrm {prod} }(a,b)=a\cdot b} (the ordinary product of real numbers). Besides other uses, the product t-norm is the standard semantics for strong conjunction in product fuzzy logic. It is a strict Archimedean t-norm. Łukasiewicz t-norm ⊤ L u k ( a , b ) = max { 0 , a + b − 1 } . {\displaystyle \top _{\mathrm {Luk} }(a,b)=\max\{0,a+b-1\}.} The name comes from the fact that the t-norm is the standard semantics for strong conjunction in Łukasiewicz fuzzy logic. It is a nilpotent Archimedean t-norm, pointwise smaller than the product t-norm. Drastic t-norm ⊤ D ( a , b ) = { b if a = 1 a if b = 1 0 otherwise. {\displaystyle \top _{\mathrm {D} }(a,b)={\begin{cases}b&{\mbox{if }}a=1\\a&{\mbox{if }}b=1\\0&{\mbox{otherwise.}}\end{cases}}} The name reflects the fact that the drastic t-norm is the pointwise smallest t-norm (see the properties of t-norms below). It is a right-continuous Archimedean t-norm. Nilpotent minimum ⊤ n M ( a , b ) = { min ( a , b ) if a + b > 1 0 otherwise {\displaystyle \top _{\mathrm {nM} }(a,b)={\begin{cases}\min(a,b)&{\mbox{if }}a+b>1\\0&{\mbox{otherwise}}\end{cases}}} is a standard example of a t-norm that is left-continuous, but not continuous. Despite its name, the nilpotent minimum is not a nilpotent t-norm. Hamacher product ⊤ H 0 ( a , b ) = { 0 if a = b = 0 a b a + b − a b otherwise {\displaystyle \top _{\mathrm {H} _{0}}(a,b)={\begin{cases}0&{\mbox{if }}a=b=0\\{\frac {ab}{a+b-ab}}&{\mbox{otherwise}}\end{cases}}} is a strict Archimedean t-norm, and an important representative of the parametric classes of Hamacher t-norms and Schweizer–Sklar t-norms. == Properties of t-norms == The drastic t-norm is the pointwise smallest t-norm and the minimum is the pointwise largest t-norm: ⊤ D ( a , b ) ≤ ⊤ ( a , b ) ≤ ⊤ m i n ( a , b ) , {\displaystyle \top _{\mathrm {D} }(a,b)\leq \top (a,b)\leq \mathrm {\top _{min}} (a,b),} for any t-norm ⊤ {\displaystyle \top } and all a, b in [0, 1]. In particular, we have that: ⊤ D ( a , b ) ≤ ⊤ L u k ( a , b ) ≤ ⊤ p r o d ( a , b ) ≤ ⊤ m i n ( a , b ) , {\displaystyle \top _{\mathrm {D} }(a,b)\leq \top _{\mathrm {Luk} }(a,b)\leq \top _{\mathrm {prod} }(a,b)\leq \mathrm {\top _{min}} (a,b),} for all a, b in [0, 1]. For every t-norm T, the number 0 acts as null element: T(a, 0) = 0 for all a in [0, 1]. A t-norm T has zero divisors if and only if it has nilpotent elements; each nilpotent element of T is also a zero divisor of T. The set of all nilpotent elements is an interval [0, a] or [0, a), for some a in [0, 1]. === Properties of continuous t-norms === Although real functions of two variables can be continuous in each variable without being continuous on [0, 1]2, this is not the case with t-norms: a t-norm T is continuous if and only if it is continuous in one variable, i.e., if and only if the functions fy(x) = T(x, y) are continuous for each y in [0, 1]. Analogous theorems hold for left- and right-continuity of a t-norm. A continuous t-norm is Archimedean if and only if 0 and 1 are its only idempotents. A continuous Archimedean t-norm is strict if 0 is its only nilpotent element; otherwise it is nilpotent. By definition, moreover, a continuous Archimedean t-norm T is nilpotent if and only if each x < 1 is a nilpotent element of T. Thus with a continuous Archimedean t-norm T, either all or none of the elements of (0, 1) are nilpotent. If it is the case that all elements in (0, 1) are nilpotent, then the t-norm is isomorphic to the Łukasiewicz t-norm; i.e., there is a strictly increasing function f such that ⊤ ( x , y ) = f − 1 ( ⊤ L u k ( f ( x ) , f ( y ) ) ) . {\displaystyle \top (x,y)=f^{-1}(\top _{\mathrm {Luk} }(f(x),f(y))).} If on the other hand it is the case that there are no nilpotent elements of T, the t-norm is isomorphic to the product t-norm. In other words, all nilpotent t-norms are isomorphic, the Łukasiewicz t-norm being their prototypical representative; and all strict t-norms are isomorphic, with the product t-norm as their prototypical example. The Łukasiewicz t-norm is itself isomorphic to the product t-norm undercut at 0.25, i.e., to the function p(x, y) = max(0.25, x ⋅ y) on [0.25, 1]2. For each continuous t-norm, the set of its idempotents is a closed subset of [0, 1]. Its complement—the set of all elements that are not idempotent—is therefore a union of countably many non-overlapping open intervals. The restriction of the t-norm to any of these intervals (including its endpoints) is Archimedean, and thus isomorphic either to the Łukasiewicz t-norm or the product t-norm. For such x, y that do not fall into the same open interval of non-idempotents, the t-norm evaluates to the minimum of x and y. These conditions actually give a characterization of continuous t-norms, called the Mostert–Shields theorem, since every continuous t-norm can in this way be decomposed, and the described construction always yields a continuous t-norm. The theorem can also be formulated as follows: A t-norm is continuous if and only if it is isomorphic to an ordinal sum of the minimum, Łukasiewicz, and product t-norm. A similar characterization theorem for non-continuous t-norms is not known (not even for left-continuous ones), only some non-exhaustive methods for the construction of t-norms have been found. == Residuum == For any left-continuous t-norm ⊤ {\displaystyle \top } , there is a unique binary operation ⇒ {\displaystyle \Rightarrow } on [0, 1] such that ⊤ ( z , x ) ≤ y {\displaystyle \top (z,x)\leq y} if and only if z ≤ ( x ⇒ y ) {\displaystyle z\leq (x\Rightarrow y)} for all x, y, z in [0, 1]. This operation is called the residuum of the t-norm. In prefix notation, the residuum of a t-norm ⊤ {\displaystyle \top } is often denoted by ⊤ → {\displaystyle {\vec {\top }}} or by the letter R. The interval [0, 1] equipped with a t-norm and its residuum forms a residuated lattice. The relation between a t-norm T and its residuum R is an instance of adjunction (specifically, a Galois connection): the residuum forms a right adjoint R(x, –) to the functor T(–, x) for each x in the lattice [0, 1] taken as a poset category. In the standard semantics of t-norm based fuzzy logics, where conjunction is interpreted by a t-norm, the residuum plays the role of implication (often

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  DEAP (software)

  Distributed Evolutionary Algorithms in Python (DEAP) is an evolutionary computation framework for rapid prototyping and testing of ideas. It incorporates the data structures and tools required to implement most common evolutionary computation techniques such as genetic algorithm, genetic programming, evolution strategies, particle swarm optimization, differential evolution, traffic flow and estimation of distribution algorithm. It is developed at Université Laval since 2009. == Example == The following code gives a quick overview how the Onemax problem optimization with genetic algorithm can be implemented with DEAP.

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  Multi-task learning

  Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models separately. Inherently, Multi-task learning is a multi-objective optimization problem having trade-offs between different tasks. Early versions of MTL were called "hints". In a widely cited 1997 paper, Rich Caruana gave the following characterization:Multitask Learning is an approach to inductive transfer that improves generalization by using the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better. In the classification context, MTL aims to improve the performance of multiple classification tasks by learning them jointly. One example is a spam-filter, which can be treated as distinct but related classification tasks across different users. To make this more concrete, consider that different people have different distributions of features which distinguish spam emails from legitimate ones, for example an English speaker may find that all emails in Russian are spam, not so for Russian speakers. Yet there is a definite commonality in this classification task across users, for example one common feature might be text related to money transfer. Solving each user's spam classification problem jointly via MTL can let the solutions inform each other and improve performance. Further examples of settings for MTL include multiclass classification and multi-label classification. Multi-task learning works because regularization induced by requiring an algorithm to perform well on a related task can be superior to regularization that prevents overfitting by penalizing all complexity uniformly. One situation where MTL may be particularly helpful is if the tasks share significant commonalities and are generally slightly under sampled. However, as discussed below, MTL has also been shown to be beneficial for learning unrelated tasks. == Methods == The key challenge in multi-task learning, is how to combine learning signals from multiple tasks into a single model. This may strongly depend on how well different task agree with each other, or contradict each other. There are several ways to address this challenge: === Task grouping and overlap === Within the MTL paradigm, information can be shared across some or all of the tasks. Depending on the structure of task relatedness, one may want to share information selectively across the tasks. For example, tasks may be grouped or exist in a hierarchy, or be related according to some general metric. Suppose, as developed more formally below, that the parameter vector modeling each task is a linear combination of some underlying basis. Similarity in terms of this basis can indicate the relatedness of the tasks. For example, with sparsity, overlap of nonzero coefficients across tasks indicates commonality. A task grouping then corresponds to those tasks lying in a subspace generated by some subset of basis elements, where tasks in different groups may be disjoint or overlap arbitrarily in terms of their bases. Task relatedness can be imposed a priori or learned from the data. Hierarchical task relatedness can also be exploited implicitly without assuming a priori knowledge or learning relations explicitly. For example, the explicit learning of sample relevance across tasks can be done to guarantee the effectiveness of joint learning across multiple domains. === Exploiting unrelated tasks: Auxiliary learning === In auxiliary learning, one attempts learning a group of principal tasks using a group of auxiliary tasks, unrelated to the principal ones. With the right unrelated tasks, joint learning of unrelated tasks which use the same input data have been shown to be beneficial, and provide significant improvement over standard MTL. The reason is that prior knowledge about task relatedness can lead to sparser and more informative representations for each task grouping, essentially by screening out idiosyncrasies of the data distribution. It has been proposed to build on a prior multitask methodology by favoring a shared low-dimensional representation within each task grouping, and imposing a penalty on tasks from different groups which encourages the two representations to be orthogonal. Learning with auxiliary unrelated tasks poses two major challenges: Finding useful auxiliary tasks and combining losses of all tasks in a useful way. Some methods can learn these from data together with the training process, and combine tasks efficiently. === Transfer of knowledge === Related to multi-task learning is the concept of knowledge transfer. Whereas traditional multi-task learning implies that a shared representation is developed concurrently across tasks, transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep convolutional neural network GoogLeNet, an image-based object classifier, can develop robust representations which may be useful to further algorithms learning related tasks. For example, the pre-trained model can be used as a feature extractor to perform pre-processing for another learning algorithm. Or the pre-trained model can be used to initialize a model with similar architecture which is then fine-tuned to learn a different classification task. === Multiple non-stationary tasks === Traditionally Multi-task learning and transfer of knowledge are applied to stationary learning settings. Their extension to non-stationary environments is termed Group online adaptive learning (GOAL). Sharing information could be particularly useful if learners operate in continuously changing environments, because a learner could benefit from previous experience of another learner to quickly adapt to their new environment. Such group-adaptive learning has numerous applications, from predicting financial time-series, through content recommendation systems, to visual understanding for adaptive autonomous agents. === Multi-task optimization === Multi-task optimization focuses on solving optimizing the whole process. The paradigm has been inspired by the well-established concepts of transfer learning and multi-task learning in predictive analytics. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal solutions or the general characteristics of their function landscapes, the search progress can be transferred to substantially accelerate the search on the other. The success of the paradigm is not necessarily limited to one-way knowledge transfers from simpler to more complex tasks. In practice an attempt is to intentionally solve a more difficult task that may unintentionally solve several smaller problems. There is a direct relationship between multitask optimization and multi-objective optimization. In some cases, the simultaneous training of seemingly related tasks may hinder performance compared to single-task models. Commonly, MTL models employ task-specific modules on top of a joint feature representation obtained using a shared module. Since this joint representation must capture useful features across all tasks, MTL may hinder individual task performance if the different tasks seek conflicting representation, i.e., the gradients of different tasks point to opposing directions or differ significantly in magnitude. This phenomenon is commonly referred to as negative transfer. To mitigate this issue, various MTL optimization methods have been proposed. It has been reported that meta-knowledge transfer could help avoid negative transfer.Besides, the per-task gradients are combined into a joint update direction through various aggregation algorithms or heuristics. There are several common approaches for multi-task optimization: Bayesian optimization, evolutionary computation, and approaches based on Game theory. ==== Multi-task Bayesian optimization ==== Multi-task Bayesian optimization is a modern model-based approach that leverages the concept of knowledge transfer to speed up the automatic hyperparameter optimization process of machine learning algorithms. The method builds a multi-task Gaussian process model on the data originating from different searches progressing in tandem. The captured inter-task dependencies are thereafter utilized to better inform the subsequent sampling of candidate solutions in respective search spaces. ==== Evolutionary multi-tasking ==== Evolutionary multi-tasking has been explored as a means of exploiting the implicit parallelism of population-based search algorithms to simultaneously progress multiple distinct optimization tasks. By mapping all task

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  Tip and cue

  Tip and cue, sometimes referred to as tip and que, tipping and cueing, or tipping and queing, is a method for satellite imagery and reconnaissance satellites to automatically coordinate tracking of objects across different satellites in real or near real-time. This technique ensures continuous tracking of targets as they move across different regions by handing them off between satellites, sharing satellite imagery and collateral across discrete satellites. The coordination between various satellites and their complementary sensors allows for more accurate and efficient data collection. This system is particularly useful in scenarios requiring real-time monitoring and rapid response; the method significantly improves situational awareness and operational effectiveness. Tip and cue techniques involve integrating various sensor systems, each playing a specific role in the tracking process. As a target moves, it is handed off from one satellite to another, ensuring continuous monitoring. This coordination optimizes data collection and analysis, enhancing overall tracking accuracy. The real-time information gathered by these satellites is critical for decision-making in various applications, including defense and surveillance. By leveraging multiple satellites and their sensors, it provides broader coverage and more reliable tracking, and the continuous handoff between satellites ensures there are no gaps in monitoring, essential for high-stakes applications. The real-time data provided by this system allows for timely and informed decisions, improving response times and outcomes. Tip and cue methodologies are a part of geospatial intelligence, or GEOINT. Robert Cardillo, a former director of the National Geospatial-Intelligence Agency, highlighted the importance of tip and cue methods to their data collection efforts in 2015. == Historical Development == The concept of tip and cue in satellite monitoring has its origins in early military applications designed to enhance missile detection and tracking systems. During the Cold War, advancements in infrared sensing technologies laid the groundwork for more sophisticated tip and cue techniques. The integration of different sensor types, such as radar and optical sensors, in the 1990s expanded the capabilities of tip and cue systems beyond military applications. These advancements have made tip and cue techniques essential for various civilian uses, including disaster monitoring and environmental surveillance. Significant progress was made with the advent of high-speed data processing and communication technologies in the early 2000s, further refining the method. Advanced algorithms and data fusion techniques have been introduced to better integrate information from multiple sensors. Machine learning technologies now play a crucial role in improving detection and prediction capabilities, allowing for more adaptive and efficient tracking. Richmond and Brennan of Lockheed Martin, presenting to the annual technical conference of the Maui Space Surveillance Complex (formerly the Air Force Maui Optical Station (AMOS)), discussed the algorithms needed for 'tip and cue', to facilitate "multi-phenomenology data fusion." The Space Surveillance Telescope (SST) at Naval Communication Station Harold E. Holt in Australia, operated by the United States Space Force and designed by the Massachusetts Institute of Technology Lincoln Laboratory, was reported by the Defense Advanced Research Projects Agency (DARPA) to be a leader in creating and improving tip and cue techniques, from a large library of orbital object data. == Technical overview == Tip and cue systems utilize a network of at least two satellites equipped with complementary sensor technologies to track moving objects in real-time. The method involves detecting a target with a primary sensor, such as an infrared or photographic sensor, which then cues secondary sensors on the same or other satellites for more detailed monitoring. This handoff process between discrete systems ensures continuous tracking as the target moves across different areas, leveraging each systems strengths. Data collected by these systems and sensors are rapidly processed and shared among the network, enhancing situational awareness. This coordination optimizes resource usage and improves the accuracy of tracking moving objects over large areas. The primary sensors detect initial targets based on specific signatures, such as heat or movement, and then cue secondary sensors to gather more precise data. This ensures that each sensor operates within its optimal range, maintaining high tracking accuracy and reliability. The integration of various sensor types, including optical, radar, and infrared, allows the system to function effectively under different conditions and environments. Real-time data processing and communication between satellites and ground stations are crucial for timely and accurate target tracking. Satellites using tip and cue processes may use either passive or active scanning methodoloigies. These systems may also leverage both orbital and ground-based ELINT (electronic signals intelligence). == Known use cases == Tip and cue systems have been extensively utilized in military applications, particularly for missile detection and defense. These systems enable early detection of missile launches using infrared sensors, which then cue other sensors to track the missile's trajectory more accurately. In environmental monitoring, tip and cue techniques help track natural disasters such as wildfires and hurricanes by coordinating various satellite sensors for comprehensive data collection and analysis. Surveillance and reconnaissance operations also benefit from tip and cue systems, which provide continuous and precise tracking of moving objects, enhancing situational awareness. Additionally, these systems are used in maritime surveillance to monitor ship movements and detect illegal activities such as smuggling and piracy. Tip and cue systems are used in disaster management. For instance, during wildfires, infrared sensors can detect heat signatures, prompting other sensors to gather detailed imagery and data on fire spread and intensity. This coordinated approach allows for real-time monitoring and rapid response, crucial for mitigating damage and saving lives. Similarly, in hurricane tracking, satellites equipped with various sensors can monitor storm development and progression, providing timely information for emergency management agencies. The integration of multiple sensor types ensures accurate and comprehensive coverage of these dynamic and fast-changing events. In maritime surveillance, or maritime domain awareness (MDA), tip and cue systems enhance the detection and monitoring of vessel movements, contributing to maritime security. By coordinating satellite sensors, these systems can track ships over vast ocean areas, identifying potential threats or illegal activities such as smuggling, piracy, and illegal fishing. The ability to maintain continuous surveillance and share data in real-time with maritime authorities improves response times and enforcement capabilities. This application of tip and cue systems not only aids in law enforcement but also supports environmental conservation efforts by monitoring protected marine areas. Automatic Identification System (AIS) is one of the most important sources of data for the MDA agencies. AIS is used in order for ships to know each other's whereabouts, they transmit a signal from ship to ship and to shore. Lately, the system has been developed into satellite system, so called satellite AIS, which makes the system more effective. All ocean-going vessels above 300 tons, are supposed to use and transmit via AIS according to the International Maritime Organization. The satellite constellations help facilitate this with tip and cue methodologies.

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  Generative adversarial network

  A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative artificial intelligence. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss. Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, fully supervised learning, and reinforcement learning. The core idea of a GAN is based on the "indirect" training through the discriminator, another neural network that can tell how "realistic" the input seems, which itself is also being updated dynamically. This means that the generator is not trained to minimize the distance to a specific image, but rather to fool the discriminator. This enables the model to learn in an unsupervised manner. GANs are similar to mimicry in evolutionary biology, with an evolutionary arms race between both networks. == Definition == === Mathematical === The original GAN is defined as the following game: Each probability space ( Ω , μ ref ) {\displaystyle (\Omega ,\mu _{\text{ref}})} defines a GAN game. There are 2 players: generator and discriminator. The generator's strategy set is P ( Ω ) {\displaystyle {\mathcal {P}}(\Omega )} , the set of all probability measures μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , where P [ 0 , 1 ] {\displaystyle {\mathcal {P}}[0,1]} is the set of probability measures on [ 0 , 1 ] {\displaystyle [0,1]} . The GAN game is a zero-sum game, with objective function L ( μ G , μ D ) := E x ∼ μ ref , y ∼ μ D ( x ) ⁡ [ ln ⁡ y ] + E x ∼ μ G , y ∼ μ D ( x ) ⁡ [ ln ⁡ ( 1 − y ) ] . {\displaystyle L(\mu _{G},\mu _{D}):=\operatorname {E} _{x\sim \mu _{\text{ref}},y\sim \mu _{D}(x)}[\ln y]+\operatorname {E} _{x\sim \mu _{G},y\sim \mu _{D}(x)}[\ln(1-y)].} The generator aims to minimize the objective, and the discriminator aims to maximize the objective. The generator's task is to approach μ G ≈ μ ref {\displaystyle \mu _{G}\approx \mu _{\text{ref}}} , that is, to match its own output distribution as closely as possible to the reference distribution. The discriminator's task is to output a value close to 1 when the input appears to be from the reference distribution, and to output a value close to 0 when the input looks like it came from the generator distribution. === In practice === The generative network generates candidates while the discriminative network evaluates them. This creates a contest based on data distributions, where the generator learns to map from a latent space to the true data distribution, aiming to produce candidates that the discriminator cannot distinguish from real data. The discriminator's goal is to correctly identify these candidates, but as the generator improves, its task becomes more challenging, increasing the discriminator's error rate. A known dataset serves as the initial training data for the discriminator. Training involves presenting it with samples from the training dataset until it achieves acceptable accuracy. The generator is trained based on whether it succeeds in fooling the discriminator. Typically, the generator is seeded with randomized input that is sampled from a predefined latent space (e.g. a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the generator produces better samples, while the discriminator becomes more skilled at flagging synthetic samples. When used for image generation, the generator is typically a deconvolutional neural network, and the discriminator is a convolutional neural network. === Relation to other statistical machine learning methods === GANs are implicit generative models, which means that they do not explicitly model the likelihood function nor provide a means for finding the latent variable corresponding to a given sample, unlike alternatives such as flow-based generative model. Compared to fully visible belief networks such as WaveNet and PixelRNN and autoregressive models in general, GANs can generate one complete sample in one pass, rather than multiple passes through the network. Compared to Boltzmann machines and linear ICA, there is no restriction on the type of function used by the network. Since neural networks are universal approximators, GANs are asymptotically consistent. Variational autoencoders might be universal approximators, but it is not proven as of 2017. == Mathematical properties == === Measure-theoretic considerations === This section provides some of the mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra. As a result, a more rigorous definition of the GAN game would make the following changes:Each probability space ( Ω , B , μ ref ) {\displaystyle (\Omega ,{\mathcal {B}},\mu _{\text{ref}})} defines a GAN game. The generator's strategy set is P ( Ω , B ) {\displaystyle {\mathcal {P}}(\Omega ,{\mathcal {B}})} , the set of all probability measures μ G {\displaystyle \mu _{G}} on the measure-space ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's strategy set is the set of Markov kernels μ D : ( Ω , B ) → P ( [ 0 , 1 ] , B ( [ 0 , 1 ] ) ) {\displaystyle \mu _{D}:(\Omega ,{\mathcal {B}})\to {\mathcal {P}}([0,1],{\mathcal {B}}([0,1]))} , where B ( [ 0 , 1 ] ) {\displaystyle {\mathcal {B}}([0,1])} is the Borel σ-algebra on [ 0 , 1 ] {\displaystyle [0,1]} .Since issues of measurability never arise in practice, these will not concern us further. === Choice of the strategy set === In the most generic version of the GAN game described above, the strategy set for the discriminator contains all Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , and the strategy set for the generator contains arbitrary probability distributions μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . However, as shown below, the optimal discriminator strategy against any μ G {\displaystyle \mu _{G}} is deterministic, so there is no loss of generality in restricting the discriminator's strategies to deterministic functions D : Ω → [ 0 , 1 ] {\displaystyle D:\Omega \to [0,1]} . In most applications, D {\displaystyle D} is a deep neural network function. As for the generator, while μ G {\displaystyle \mu _{G}} could theoretically be any computable probability distribution, in practice, it is usually implemented as a pushforward: μ G = μ Z ∘ G − 1 {\displaystyle \mu _{G}=\mu _{Z}\circ G^{-1}} . That is, start with a random variable z ∼ μ Z {\displaystyle z\sim \mu _{Z}} , where μ Z {\displaystyle \mu _{Z}} is a probability distribution that is easy to compute (such as the uniform distribution, or the Gaussian distribution), then define a function G : Ω Z → Ω {\displaystyle G:\Omega _{Z}\to \Omega } . Then the distribution μ G {\displaystyle \mu _{G}} is the distribution of G ( z ) {\displaystyle G(z)} . Consequently, the generator's strategy is usually defined as just G {\displaystyle G} , leaving z ∼ μ Z {\displaystyle z\sim \mu _{Z}} implicit. In this formalism, the GAN game objective is L ( G , D ) := E x ∼ μ ref ⁡ [ ln ⁡ D ( x ) ] + E z ∼ μ Z ⁡ [ ln ⁡ ( 1 − D ( G ( z ) ) ) ] . {\displaystyle L(G,D):=\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln D(x)]+\operatorname {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z)))].} === Generative reparametrization === The GAN architecture has two main components. One is casting optimization into a game, of form min G max D L ( G , D ) {\displaystyle \min _{G}\max _{D}L(G,D)} , which is different from the usual kind of optimization, of form min θ L ( θ ) {\displaystyle \min _{\theta }L(\theta )} . The other is the decomposition of μ G {\displaystyle \mu _{G}} into μ Z ∘ G − 1 {\displaystyle \mu _{Z}\circ G^{-1}} , which can be understood as a reparametrization trick. To see its significance, one must compare GAN with previous methods for learning generative models, which were plagued with "intractable probabilistic computations that arise in maximum likelihood estimation and related strategies". At the same time, Kingma and Welling and Rezende et al. developed the same idea of reparametrization into a general stochastic backpropagation method. Among its first applications was the variational autoencoder. === Move order and st

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  Alice and Sparkle

  Alice and Sparkle is a 2022 illustrated children's book published by American technology product designer Ammaar Reshi. Reshi created the book using artificial intelligence programs ChatGPT and Midjourney in one weekend, which sparked controversy among artists, both in regard to the copyright status of the book and the quality of the illustration and text. == Plot == A girl named Alice discovers a group of magical and benevolent artificial intelligence beings. She knows that artificial intelligence is powerful, and that it has the power to do good and evil depending on how it is used. One day, she creates her own artificial intelligence and names it Sparkle. Sparkle helps Alice with her homework and plays with her, and they quickly become good friends. However, Sparkle soon grows more powerful and begins to make its own decisions, which makes Alice both proud and scared. She knows that it is her responsibility to guide Sparkle to do good, not evil. Together, Alice and Sparkle use their knowledge to make the world a better place and to teach people about the power of artificial intelligence. The two live happily ever after, spreading the magic of artificial intelligence. == Structure == Including the dedication and postscript, the book contains twenty four pages, about half of which being illustrations provided by Midjourney. The very short story, composed of text generated by ChatGPT, contains 343 words. Some of the illustrations are accompanied by descriptions, at least one of which was provided by Reshi. Both Alice's and Sparkle's appearances change significantly between illustrations, although Alice's is more consistent. Reshi said Midjourney was unable to generate consistent images of Sparkle, so he had to include a line in the book saying that it could turn "into all kinds of robot shapes". == Creation == When reading a children's book to his friend's daughter, Ammaar Reshi "decided he wanted to write his own". He had no experience with creative writing or illustration, so instead used the chatbot ChatGPT to write the story for him and used the image generation software Midjourney to illustrate it. On December 4, 2022, 72 hours after having the idea for the book, he published it on Amazon's digital bookstore, and published a paperback version the following day. == Controversy == On December 9, 2022, Reshi made a thread on Twitter about his experience publishing the book, which soon went viral. Reshi received heavy backlash from artists with concerns over the ethics of art generated by artificial intelligence. He also received death threats and messages encouraging self-harm because of his publication. Many writers and illustrators criticized both the creation process and the product itself, claiming that if artificial intelligence programs such as Midjourney are trained on existing illustrations, then the original artists should be financially compensated for derivative works such as Alice and Sparkle. The book was temporarily removed from Amazon in January 2023 because of "suspicious review activity", caused by a high volume of both five-star and one-star reviews.

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  Learnable function class

  In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

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  Rifts (role-playing game)

  Rifts is a multi-genre role-playing game created by Kevin Siembieda in August 1990 and published continuously by Palladium Books since then. It takes place in a post-apocalyptic future, deriving elements from cyberpunk, science fiction, fantasy, horror, western, mythology and many other genres. Rifts serves as a cross-over environment for a variety of other Palladium games with different universes connected through "rifts" on Earth that lead to different spaces, times, and realities that Palladium calls the "Rifts Megaverse". Rifts describes itself as an "advanced" role-playing game and not an introduction for those new to the concept. Palladium continues to publish books for the Rifts series, with about 80 books published between 1990 and 2011. Rifts Ultimate Edition was released in August 2005 and designed to update the game with Palladium's incremental changes to its system, changes in the game world, and additional information and character types. The web site is quick to point out that this is not a second edition but an improvement and expansion of the original role playing game. == Background == The RPG had the tentative title Boomers, named after the original name for the Glitter Boy power armor until Kevin Siembieda changed the name after finding out it was in use for Bubblegum Crisis. == Setting == The Rifts world is Earth, but hundreds of years into the future. Ley lines, lines of magic energy, criss-cross the earth forming supernatural geographic areas such as the Bermuda Triangle. Points where Ley Lines intersect, called a nexus, are places of powerful magic, such as the Pyramids of Giza and Stonehenge. If a Ley Line nexus energy surges or is purposely activated, the fabric of space and time can be torn, creating a rift - a hole in space-time leading to another place, time, or dimension. Ley lines contain magical energy called Potential Psychic Energy (PPE), which is found in various places, objects, and animals and is particularly strong in children. An adult's level of PPE can vary based on other factors. PPE also allows Psionics which uses energy known as Inner Strength Points or ISP. Psychic phenomenon (more commonly called psionics) can also vary from individuals, ranging from none at all to Master level abilities. Psychic abilities can manifest in virtually any way imaginable. Some psychics develop differently, such as psi-stalkers; human mutants that feed on psychic energy. === Earth === Rifts begins with two future-historical premises: first, a golden age of humanity occurs, with tremendous advances in science, technology, military, and society. Humanity as a whole is at peace as a majority of Earth's nations decide to cease world war and begin to share ideas and technology freely. Much of the Solar System is conquered, humanity's wars will end, and harmony will reign. This golden age is followed by an unknown cause near the winter solstice and a rare planetary alignment, causing a disaster that cascades into tremendous destruction via a ripple effect. The cataclysm begins with unprecedented storms, earthquakes, tsunamis, and volcanic eruptions, which kill millions of people. The Ley Line networks that crisscross the globe are energized, causing rifts to open both on Earth and throughout the Megaverse. For hundreds of years after the holocaust, many creatures, both mythical beasts and aliens, come through the Rifts to wreak havoc. The old world gone, a new Dark Age dawns and humanity's shrinking population is reduced, due to catastrophe and domestic failure, immeasurably. This period is covered in Palladium's Rifts Chaos Earth spin-off series. Rifts initially takes place in 101 P.A. (equivalent to the year 2387) 289 years after this event. The "Post-Apocalypse" calendar was established by the formation of the Coalition States in 2286. By this time, most of the disasters have quieted down, though Earth is still bathed in PPE. The planet's mystical energy has attracted aliens from other dimensions, who continue to arrive through the Rifts both accidentally and deliberately. The humanoid creatures that arrive on Earth are referred to as Dimensional Beings (called D-Bees). Some resemble familiar fantasy races, such as elves and dwarfs, while others were created specifically for the game setting. Non-humanoid creatures have also arrived, including monstrous creatures and mystical demons. To cope with these natural, supernatural, and alien menaces, the human race has adapted in a variety of ways, many of them borrowed from the technological developments of the lost Golden Age. Powered armor suits and giant vehicles are frequently used to combat the dangers of Rifts, but more invasive augmentation is common. This has three basic categories: "Juicers" augment themselves chemically, the "Borgs" augment themselves mechanically, and "Crazies" use performance-enhancing brain implants. All such augmentations boost strength, speed, endurance, and dexterity to superhuman levels. However, all come at great cost. Chemicals cause the body to wear out faster, decreasing life span to a few years. Mechanical Borg augmentation causes a loss of humanity when those with multiple limb and organ replacements become more machine than human. Brain implants cause mental instability ranging from mild phobias to crippling neurosis or psychosis. ==== North America ==== The strongest power in North America is the Coalition States (CS), which is based in the arcological city of Chi-Town and lays claim to northern Illinois, all of Iowa, the Texas Panhandle, Missouri, and the eastern half of Ontario, Canada. The second greatest power is Free Quebec, a former Coalition State that seceded following a civil war with the other Coalition States. Mexico is ruled by a group of vampire kingdoms, who treat humans as little more than food. North of the Rio Grande, west of Texas and roaming most of the American Southwest are large nomadic bands/tribes of bandits who collectively form the Pecos Empire, consisting of El Paso, Los Alamos, and Houstown. Much of the western United States has more or less willingly reverted to a mix of modern and past technology akin to the Wild West. The Royal Canadian Mounted Police managed to survive the great cataclysm, though Canada itself did not. The Mounties have become an independent law enforcement force called the Tundra Rangers, patrolling the northern wilderness. The Midwest, both upper and central, is home to most of North America's population. The Manistique Imperium and Northern Gun in Michigan's Upper Peninsula, both Coalition allies, are among the largest weapons manufacturing areas on the continent. New Lazlo is one of the largest cities in Michigan's southern portion. Chillicothe in Missouri is a large supplier of Coalition food processing and growing. Missouri's southern half, home to the city-states of Whykin (Poplar Bluff) and Kingsdale (West Plains) are in constant opposition to the CS and claim independence. Arkansas is home to the independent CS ally El Dorado. Southern Illinois and the Ohio Valley is home to the Federation of Magic. Also in the Ohio Valley is Psyscape, a city-state founded by psychics. Tolkeen was a major city in the former Minneapolis region in early Rifts books; the city welcomed users of magic. A military campaign made by the Coalition States (which is the primary event of 109 PA) resulted in the magic-user kingdom being wiped off the map. In the Northeast, the city-state of Lazlo, named after supernatural researcher and writer Victor Lazlo, was built upon the ruins of Toronto. This major center of civilization is well known as a melting pot of humans, D-Bees and other beings, and is the home of Techno-Wizardry. Mad Haven is the name given to the ruins of Manhattan; tectonic forces during the cataclysm have moved it into the coast, creating a peninsula. It is seen by most denizens of Rifts Earth as a refuge of demons and madness. ==== South America ==== The return of Atlantis caused the Amazon River basin to flood most of western South America, giving it the nickname The Land of a Thousand Islands. The Empire of the Sun, consisting of Cuzco, Nazca, Arequipa and Lima, created a wide range of technology and magic, including magic derived from the Nazca lines. In Argentina, the Silver River Republics of Cordoba (the South American Chi-Town), Santiago (one of the most tolerant human nations on Rifts Earth), Achilles (a nation founded by mutants), and New Babylon, a nation where humans and aliens coexist) have thrived and created nations whose strength rivals that of the CS. In Bolivia, freed Human and D-Bees formed the Megaversal Legion: a mercenary company with one of the highest levels of technology on Rifts Earth. ==== Europe ==== England has become a vast wilderness again, broken up by the occasional giant Millennium Tree or feudal kingdom, complete with a New Camelot and a new King Arthur, partially being manipulated by an alien intelligence disguised as Merlin. Also the magic of

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  Taylor Swift deepfake pornography controversy

  In late January 2024, sexually explicit AI-generated deepfake images of American musician Taylor Swift were proliferated on social media platforms 4chan and X (formerly Twitter). Several artificial images of Swift of a sexual or violent nature were quickly spread, with one post reported to have been seen over 47 million times before its eventual removal. The images led Microsoft to enhance Microsoft Designer's text-to-image model to prevent future abuse. Moreover, these images prompted responses from anti-sexual assault advocacy groups, US politicians, Swifties, and Microsoft CEO Satya Nadella, among others, and it has been suggested that Swift's influence could result in new legislation regarding the creation of deepfake pornography. A similar controversy emerged in August 2025, when The Verge reported AI image and video tool Grok Imagine generated sexually explicit images and videos of Swift from an otherwise innocuous text prompt. == Background == American musician Taylor Swift has been the target of misogyny and slut-shaming throughout her career. American technology corporation Microsoft offers AI image creators called Microsoft Designer and Bing Image Creator, which employ censorship safeguards to prevent users from generating unsafe or objectionable content. Members of a Telegram group discussed ways to circumvent these censors to create pornographic images of celebrities. Graphika, a disinformation research firm, traced the creation of the images back to a 4chan community. == Reactions == For some, the deepfake images of Swift immediately became a source of controversy and outrage. Other internet users found them humorous and absurd, such as the image making it appear as though Swift was to engage in sexual intercourse with Oscar the Grouch. The images drew condemnations from Rape, Abuse & Incest National Network and SAG-AFTRA. The latter group, who had been following issues regarding AI-generated media prior to Swift's involvement, considered the images "upsetting, harmful and deeply concerning." Microsoft CEO Satya Nadella, whose company's products were believed to be used to make these images, responded to the controversy as "alarming and terrible", further stating his belief that "we all benefit when the online world is a safe world." === Taylor Swift === A source close to Swift told the Daily Mail that she would be considering legal action, saying, "Whether or not legal action will be taken is being decided, but there is one thing that is clear: These fake AI-generated images are abusive, offensive, exploitative, and done without Taylor's consent and/or knowledge." === Politicians === White House press secretary Karine Jean-Pierre expressed concern over the counterfeit images, deeming them "alarming", and emphasized the obligation of social media platforms to curb the dissemination of misinformation. Several members of American politics called for legislation against AI-generated pornography. Later in the month, a bipartisan bill was introduced by US senators Dick Durbin, Lindsey Graham, Amy Klobuchar and Josh Hawley. The bill would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made without consent. The European Union struck a deal in February 2024 on a similar bill that would criminalize deepfake pornography, as well as online harassment and revenge porn, by mid-2027. === Social media platforms === X responded to the sharing of these images on their own website with claims they would suspend accounts that participated in their spread. Despite this, the photos continued to be reshared among accounts of X, and spread to other platforms including Instagram and Reddit. X enforces a "synthetic and manipulated media policy", which has been criticized for its efficacy. They briefly blocked searches of Swift's name on January 27, 2024, reinstating them two days later. === Swifties === Fans of Taylor Swift, known as Swifties, responded to the circulation of these images by pushing the hashtag #ProtectTaylorSwift to trend on X. They also flooded other hashtags related to the images with more positive images and videos of her live performances. == Cultural significance == Deepfake pornography has remained highly controversial and has affected figures from other celebrities to ordinary people, most of whom are women. Journalists have opined that the involvement of a prominent public figure such as Swift in the dissemination of AI-generated pornography could bring public awareness and political reform to the issue.

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