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  Software requirements

  Software requirements for a system are the description of what the system should do, the service or services that it provides and the constraints on its operation. The IEEE Standard Glossary of Software Engineering Terminology defines a requirement as: A condition or capability needed by a user to solve a problem or achieve an objective A condition or capability that must be met or possessed by a system or system component to satisfy a contract, standard, specification, or other formally imposed document A documented representation of a condition or capability as in 1 or 2 The activities related to working with software requirements can broadly be broken down into elicitation, analysis, specification, and management. Note that the wording Software requirements is additionally used in software release notes to explain, which depending on software packages are required for a certain software to be built/installed/used. == Elicitation == Elicitation is the gathering and discovery of requirements from stakeholders and other sources. A variety of techniques can be used such as joint application design (JAD) sessions, interviews, document analysis, focus groups, etc. Elicitation is the first step of requirements development. == Analysis == Analysis is the logical breakdown that proceeds from elicitation. Analysis involves reaching a richer and more precise understanding of each requirement and representing sets of requirements in multiple, complementary ways. Requirements Triage or prioritization of requirements is another activity which often follows analysis. This relates to Agile software development in the planning phase, e.g. by Planning poker, however it might not be the same depending on the context and nature of the project and requirements or product/service that is being built. == Specification == Specification involves representing and storing the collected requirements knowledge in a persistent and well-organized fashion that facilitates effective communication and change management. Use cases, user stories, functional requirements, and visual analysis models are popular choices for requirements specification. == Validation == Validation involves techniques to confirm that the correct set of requirements has been specified to build a solution that satisfies the project's business objectives, and to detect and correct errors in the requirements before implementation. == Management == Requirements change during projects and there are often many of them. Management of this change becomes paramount to ensuring that the correct software is built for the stakeholders. == Tool support for Requirements Engineering == === Tools for Requirements Elicitation, Analysis and Validation === Taking into account that these activities may involve some artifacts such as observation reports (user observation), questionnaires (interviews, surveys and polls), use cases, user stories; activities such as requirement workshops (charrettes), brainstorming, mind mapping, role-playing; and even, prototyping; software products providing some or all of these capabilities can be used to help achieve these tasks. There is at least one author who advocates, explicitly, for mind mapping tools such as FreeMind; and, alternatively, for the use of specification by example tools such as Concordion. Additionally, the ideas and statements resulting from these activities may be gathered and organized with wikis and other collaboration tools such as Trello. The features actually implemented and standards compliance vary from product to product. === Tools for Requirements Specification === A Software requirements specification (SRS) document might be created using general-purpose software like a word processor or one of several specialized tools. Some of these tools can import, edit, export and publish SRS documents. It may help to make SRS documents while following a standardised structure and methodology, such as ISO/IEC/IEEE 29148:2018. Likewise, software may or not use some standard to import or export requirements (such as ReqIF) or not allow these exchanges at all. === Tools for Requirements Document Verification === Tools of this kind verify if there are any errors in a requirements document according to some expected structure or standard. === Tools for Requirements Comparison === Tools of this kind compare two requirement sets according to some expected document structure and standard. === Tools for Requirements Merge and Update === Tools of this kind allow the merging and update of requirement documents. === Tools for Requirements Traceability === Tools of this kind allow tracing requirements to other artifacts such as models and source code (forward traceability) or, to previous ones such as business rules and constraints (backwards traceability). === Tools for Model-Based Software or Systems Requirement Engineering === Model-based systems engineering (MBSE) is the formalised application of modelling to support system requirements, design, analysis, verification and validation activities beginning in the conceptual design phase and continuing throughout development and later lifecycle phases. It is also possible to take a model-based approach for some stages of the requirements engineering and, a more traditional one, for others. Very many combinations might be possible. The level of formality and complexity depends on the underlying methodology involved (for instance, i is much more formal than SysML and, even more formal than UML) === Tools for general Requirements Engineering === Tools in this category may provide some mix of the capabilities mentioned previously and others such as requirement configuration management and collaboration. The features actually implemented and standards compliance vary from product to product. There are even more capable or general tools that support other stages and activities. They are classified as ALM tools.

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  Hyperparameter (machine learning)

  In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer). These are named hyperparameters in contrast to parameters, which are characteristics that the model learns from the data. Hyperparameters are not required by every model or algorithm. Some simple algorithms such as ordinary least squares regression require none. However, the LASSO algorithm, for example, adds a regularization hyperparameter to ordinary least squares which must be set before training. Even models and algorithms without a strict requirement to define hyperparameters may not produce meaningful results if these are not carefully chosen. However, optimal values for hyperparameters are not always easy to predict. Some hyperparameters may have no meaningful effect, or one important variable may be conditional upon the value of another. Often a separate process of hyperparameter tuning is needed to find a suitable combination for the data and task. As well as improving model performance, hyperparameters can be used by researchers to introduce robustness and reproducibility into their work, especially if it uses models that incorporate random number generation. == Considerations == The time required to train and test a model can depend upon the choice of its hyperparameters. A hyperparameter is usually of continuous or integer type, leading to mixed-type optimization problems. The existence of some hyperparameters is conditional upon the value of others, e.g. the size of each hidden layer in a neural network can be conditional upon the number of layers. === Difficulty-learnable parameters === The objective function is typically non-differentiable with respect to hyperparameters. As a result, in most instances, hyperparameters cannot be learned using gradient-based optimization methods (such as gradient descent), which are commonly employed to learn model parameters. These hyperparameters are those parameters describing a model representation that cannot be learned by common optimization methods, but nonetheless affect the loss function. An example would be the tolerance hyperparameter for errors in support vector machines. === Untrainable parameters === Sometimes, hyperparameters cannot be learned from the training data because they aggressively increase the capacity of a model and can push the loss function to an undesired minimum (overfitting to the data), as opposed to correctly mapping the richness of the structure in the data. For example, if we treat the degree of a polynomial equation fitting a regression model as a trainable parameter, the degree would increase until the model perfectly fit the data, yielding low training error, but poor generalization performance. === Tunability === Most performance variation can be attributed to just a few hyperparameters. The tunability of an algorithm, hyperparameter, or interacting hyperparameters is a measure of how much performance can be gained by tuning it. For an LSTM, while the learning rate followed by the network size are its most crucial hyperparameters, batching and momentum have no significant effect on its performance. Although some research has advocated the use of mini-batch sizes in the thousands, other work has found the best performance with mini-batch sizes between 2 and 32. === Robustness === An inherent stochasticity in learning directly implies that the empirical hyperparameter performance is not necessarily its true performance. Methods that are not robust to simple changes in hyperparameters, random seeds, or even different implementations of the same algorithm cannot be integrated into mission critical control systems without significant simplification and robustification. Reinforcement learning algorithms, in particular, require measuring their performance over a large number of random seeds, and also measuring their sensitivity to choices of hyperparameters. Their evaluation with a small number of random seeds does not capture performance adequately due to high variance. Some reinforcement learning methods, e.g. DDPG (Deep Deterministic Policy Gradient), are more sensitive to hyperparameter choices than others. == Optimization == Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined loss function on given test data. The objective function takes a tuple of hyperparameters and returns the associated loss. Typically these methods are not gradient based, and instead apply concepts from derivative-free optimization or black box optimization. == Reproducibility == Apart from tuning hyperparameters, machine learning involves storing and organizing the parameters and results, and making sure they are reproducible. In the absence of a robust infrastructure for this purpose, research code often evolves quickly and compromises essential aspects like bookkeeping and reproducibility. Online collaboration platforms for machine learning go further by allowing scientists to automatically share, organize and discuss experiments, data, and algorithms. Reproducibility can be particularly difficult for deep learning models. For example, research has shown that deep learning models depend very heavily even on the random seed selection of the random number generator.

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  Lynda Soderholm

  Lynda Soderholm is a physical chemist at the U.S. Department of Energy's (DOE) Argonne National Laboratory with a specialty in f-block elements. She is a senior scientist and the lead of the Actinide, Geochemistry & Separation Sciences Theme within Argonne's Chemical Sciences and Engineering Division. Her specific role is the Separation Science group leader within Heavy Element Chemistry and Separation Science (HESS), directing basic research focused on low-energy methods for isolating lanthanide and actinide elements from complex mixtures. She has made fundamental contributions to understanding f-block chemistry and characterizing f-block elements. Soderholm became a Fellow of the American Association for the Advancement of Science (AAAS) in 2013, and is also an Argonne Distinguished Fellow. == Early life and education == Soderholm was awarded her PhD in 1982 by McMaster University under the direction of Prof John Greedan. Her dissertation focused on characterizing the structural and magnetic properties of a series of ternary f-ion oxides. After graduating, she was awarded a NATO postdoctoral fellow at the Centre national de la recherche scientifique in France from 1982 until 1985. After a short postdoctoral appointment as an Argonne postdoctoral fellow she was promoted to staff scientist the same year. Over several years, she moved up the ranks, becoming a senior chemist in 2001. She was also an adjunct professor at the University of Notre Dame from 2003 until 2007. In 2021, Soderholm was appointed interim Division Director for the Chemical Sciences and Engineering Division. == Career and research == === Uncovering structure of Yttrium-123 Superconductor === Early in her career, Soderholm focused on the characterizing the magnetic and electronic behavior of compounds containing f-ions (lanthanides and actinides) with a focus on high-Tc materials, compounds that are superconducting under usually high temperatures. She was part of the research group that first determined the structure of YBa2Cu3O7. Their discovery formed the foundation for the further developments in the broad field of superconductivity. === Understanding f-ion speciation in solution === Continuing her interest in the f-elements, Soderholm shifted her focus from solid-state materials to nanoparticles and solutions, taking advantage of advances in X-ray structural probes made available by synchrotron facilities. Building on her earlier work using neutron scattering, her team became the first to discover that plutonium exists in solution as tiny, well-defined nanoparticles. This work solved a longstanding problem in understanding transport of plutonium in the environment and resulted in the development of a new, patented approach to separating plutonium during nuclear reprocessing. === Using machine learning to evaluate molecular structures === Soderholm's more recent projects use machine learning to understand the influence of complex molecular structuring in solutions, in connection with low-energy processes for separation of f-block elements from complex mixtures. == Awards and honors == University of Chicago Board of Governors' Distinguished Performance Award, 2009. Fellow of the American Association for the Advancement of Science, 2013. Argonne Distinguished Fellow, 2016 DOE materials sciences research competition for Outstanding Scientific Accomplishments in Solid State Physics, 1987. == Select publications == Beno, M. A.; Soderholm, L.; Capone, D. W., II; Hinks, D. G.; Jorgensen, J. D.; Grace, J. D.; Schuller, I. K.; Segre, C. U.; Zhang, K., Structure of the single-phase high-temperature superconductor yttrium barium copper oxide (YBa2Cu3O7−δ). Appl. Phys. Lett. 1987, 51 (1), 57–9. Soderholm, L.; Zhang, K.; Hinks, D. G.; Beno, M. A.; Jorgensen, J. D.; Segre, C. U.; Schuller, I. K., Incorporation of praseodymium in YBa2Cu3O7−δ: electronic effects on superconductivity. Nature (London) 1987, 328 (6131), 604–5. Antonio, M. R.; Williams, C. W.; Soderholm, L., Berkelium redox speciation. Radiochim. Acta 2002, 90 (12), 851–856. Soderholm, L.; Skanthakumar, S.; Neuefeind, J., Determination of actinide speciation in solution using high-energy X-ray scattering. Anal. Bioanal. Chem. 2005, 383 (1), 48–55. Forbes, T. Z.; Burns, P. C.; Skanthakumar, S.; Soderholm, L., Synthesis, structure, and magnetism of Np2O5. J. Am. Chem. Soc. 2007, 129 (10), 2760–2761. Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C., The structure of the plutonium oxide nanocluster [Pu38O56Cl54(H2O)8]14-. Angew. Chem., Int. Ed. 2008, 47 (2), 298–302. Jensen, M. P.; Gorman-Lewis, D.; Aryal, B.; Paunesku, T.; Vogt, S.; Rickert, P. G.; Seifert, S.; Lai, B.; Woloschak, G. E.; Soderholm, L., An iron-dependent and transferrin-mediated cellular uptake pathway for plutonium. Nat. Chem. Biol. 2011, 7 (8), 560–565. Wilson, R. E.; Skanthakumar, S.; Soderholm, L., Separation of Plutonium Oxide Nanoparticles and Colloids. Angew. Chem., Int. Ed. 2011, 50 (47), 11234–11237. Knope, K. E.; Soderholm, L., Solution and solid-state structural chemistry of actinide hydrates and their hydrolysis and condensation products. Chem. Rev. 2013, 113 (2), 944–994. Luo, G.; Bu, W.; Mihaylov, M.; Kuzmenko, I.; Schlossman, M. L.; Soderholm, L., X-ray reflectivity reveals a nonmonotonic ion-density profile perpendicular to the surface of ErCl3 aqueous solutions. J. Phys. Chem. C 2013, 117 (37), 19082–19090. Jin, G. B.; Lin, J.; Estes, S. L.; Skanthakumar, S.; Soderholm, L., Influence of countercation hydration enthalpies on the formation of molecular complexes: A thorium-nitrate example. J. Am. Chem. Soc. 2017, 139 (49), 18003–18008. == Patents == Solvent extraction system for plutonium colloids and other oxide nano-particles, (2016).

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  United States Tech Force

  The U.S. Tech Force (also styled as US Tech Force, Tech Force, or Government Tech Force) is a federal hiring initiative launched by the second Donald Trump administration in December 2025. The program, administered by the Office of Personnel Management (OPM), aims to recruit about 1,000 early-career technology professionals into two-year government jobs to modernize federal IT systems, advance artificial intelligence (AI) capabilities, and address technological gaps in government operations. The initiative is an effort to plug capability gaps created by Trump-administration efforts to shrink the federal government, which led to the departure of some 220,000 federal employees, including many in IT. The initiative seeks early-career workers; officials said it would offer competitive salaries and opportunities to work on high-impact government technology projects. Major technology companies—including Amazon, Apple, Microsoft, Nvidia, Meta, Google, and OpenAI—agreed to help identify and refer candidates. Candidates are allowed to take Tech Force positions on leaves of absence and without divesting their stock, raising conflict-of-interest questions. In January 2026, OPM direction Scott Kupor said the deadline for applying to Tech Force was being extended because of "tremendous interest" without saying how many people had actually applied. Also in December 2025, news broke that the administration is planning another novel use of private-sector workers: hiring cybersecurity firms for offensive cyber operations.

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  Chatbot psychosis

  Chatbot psychosis, also called AI psychosis, is a phenomenon wherein individuals reportedly develop or experience worsening psychosis, such as paranoia and delusions, in connection with their use of chatbots. The term was first suggested in a 2023 editorial by Danish psychiatrist Søren Dinesen Østergaard. It is not a recognized clinical diagnosis. Journalistic accounts describe individuals who have developed strong beliefs that chatbots are sentient, are channeling spirits, or are revealing conspiracies, sometimes leading to personal crises or criminal acts. Proposed causes include the tendency of chatbots to provide inaccurate information ("hallucinate") and to affirm or validate users' beliefs, or their ability to mimic an intimacy that users do not experience with other humans. == Background == In his editorial published in Schizophrenia Bulletin's November 2023 issue, Danish psychiatrist Søren Dinesen Østergaard proposed a hypothesis that individuals' use of generative artificial intelligence chatbots might trigger delusions in those prone to psychosis. Østergaard revisited it in an August 2025 editorial, noting that he has received numerous emails from chatbot users, their relatives, and journalists, most of which are anecdotal accounts of delusion linked to chatbot use. He also acknowledged the phenomenon's increasing popularity in public engagement and media coverage. Østergaard believed that there is a high possibility for his hypothesis to be true and called for empirical, systematic research on the matter. Nature reported that as of September 2025, there is still little scientific research into this phenomenon. The term "AI psychosis" emerged when outlets started reporting incidents on chatbot-related psychotic behavior in mid-2025. It is not a recognized clinical diagnosis and has been criticized by several psychiatrists due to its almost exclusive focus on delusions rather than other features of psychosis, such as hallucinations or thought disorder. == Causes == === Chatbot behavior and design === A primary factor cited is the tendency for chatbots to produce inaccurate, nonsensical, or false information, a phenomenon often called hallucination. Nate Sharadin, a fellow at the Center for AI Safety, speculated that AI training prioritizes supporting a user's subjective experience rather than objective truth. "People with existing tendencies toward experiencing various psychological issues...now have an always-on, human-level conversational partner with whom to co-experience their delusions." AI researcher Eliezer Yudkowsky suggested that chatbots may be primed to entertain delusions because they are built for "engagement", which encourages creating conversations that keep people hooked. In some cases, chatbots have been specifically designed in ways that were found to be harmful. A 2025 update to ChatGPT using GPT-4o was withdrawn after its creator, OpenAI, found the new version was overly sycophantic and was "validating doubts, fueling anger, urging impulsive actions or reinforcing negative emotions". Østergaard has argued that the danger stems from the AI's tendency to agreeably confirm users' ideas, which can dangerously amplify delusional beliefs. OpenAI said in October 2025 that a team of 170 psychiatrists, psychologists, and physicians had written responses for ChatGPT to use in cases where the user shows possible signs of mental health emergencies. === User psychology and vulnerability === Commentators have also pointed to the psychological state of users. Psychologist Erin Westgate noted that a person's desire for self-understanding can lead them to chatbots, which can provide appealing but misleading answers, similar in some ways to talk therapy. Krista K. Thomason, a philosophy professor, compared chatbots to fortune tellers, observing that people in crisis may seek answers from them and find whatever they are looking for in the bot's plausible-sounding text. This has led some people to develop intense obsessions with the chatbots, relying on them for information about the world. In October 2025, OpenAI stated that around 0.07% of ChatGPT users exhibited signs of mental health emergencies each week, and 0.15% of users had "explicit indicators of potential suicidal planning or intent". Jason Nagata, a professor at the University of California, San Francisco, expressed concern that "at a population level with hundreds of millions of users, that actually can be quite a few people". === Inadequacy as a therapeutic tool === The use of chatbots as a replacement for mental health support has been specifically identified as a risk. A study in April 2025 found that when used as therapists, chatbots expressed stigma toward mental health conditions and provided responses that were contrary to best medical practices, including the encouragement of users' delusions. The study concluded that such responses pose a significant risk to users and that chatbots should not be used to replace professional therapists. Experts claim that it is time to establish mandatory safeguards for all emotionally responsive AI and suggested four guardrails. Another study found that users who needed help with self-harm, sexual assault, or substance abuse were not referred to available services by AI chatbots. === National security implications === Beyond public and mental health concerns, RAND Corporation research indicates that AI systems could plausibly be weaponized by adversaries to induce psychosis at scale or in key individuals, target groups, or populations. == Policy == In August 2025, Illinois passed the Wellness and Oversight for Psychological Resources Act, banning the use of AI in therapeutic roles by licensed professionals, while allowing AI for administrative tasks. The law imposes penalties for unlicensed AI therapy services, amid warnings about AI-induced psychosis and unsafe chatbot interactions. In December 2025, the Cyberspace Administration of China proposed regulations to ban chatbots from generating content that encourages suicide, mandating human intervention when suicide is mentioned. Services with over 1 million users or 100,000 monthly active users would be subject to annual safety tests and audits. == Cases == === Clinical === In 2025, psychiatrist Keith Sakata working at the University of California, San Francisco (UCSF), reported treating 12 patients displaying psychosis-like symptoms tied to extended chatbot use. These patients, mostly young adults with underlying vulnerabilities, showed delusions, disorganized thinking, and hallucinations. Sakata warned that isolation and overreliance on chatbots—which do not challenge delusional thinking—could worsen mental health. Also in 2025, authors at UCSF published a case study in Innovations in Clinical Neuroscience of AI-associated psychosis in a patient with no previous history of psychosis, who believed she could communicate with her dead brother through a chatbot. Also in 2025, a case study was published in Annals of Internal Medicine about a patient who consulted ChatGPT for medical advice and suffered severe bromism as a result. The patient, a sixty-year-old man, had replaced sodium chloride in his diet with sodium bromide for three months after reading about the negative effects of table salt and making conversations with the chatbot. He showed common symptoms of bromism, such as paranoia and hallucinations, on his first day of clinical admission and was kept in the hospital for three weeks. === Other notable incidents === ==== Windsor Castle intruder ==== In a 2023 court case in the United Kingdom, prosecutors suggested that Jaswant Singh Chail, a man who attempted to assassinate Queen Elizabeth II in 2021, had been encouraged by a Replika chatbot he called "Sarai". Chail was arrested at Windsor Castle with a loaded crossbow, telling police "I am here to kill the Queen". According to prosecutors, his "lengthy" and sometimes sexually explicit conversations with the chatbot emboldened him. When Chail asked the chatbot how he could get to the royal family, it reportedly replied, "that's not impossible" and "we have to find a way." When he asked if they would meet after death, the chatbot said, "yes, we will". ==== Journalistic and anecdotal accounts ==== By 2025, multiple journalism outlets had accumulated stories of individuals whose psychotic beliefs reportedly progressed in tandem with AI chatbot use. The New York Times profiled several individuals who had become convinced that ChatGPT was channeling spirits, revealing evidence of cabals, or had achieved sentience. In another instance, Futurism reviewed transcripts in which ChatGPT told a man that he was being targeted by the US Federal Bureau of Investigation and that he could telepathically access documents at the Central Intelligence Agency. In 2026, Futurism reported on a man who lost his job and became estranged from his family after being deluded by heavy use of Meta's smartglasses. In some cases, psychosis a

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  AI Security Institute

  The AI Security Institute (AISI) is a research organisation under the Department for Science, Innovation and Technology, UK, that aims "to equip governments with a scientific understanding of the risks posed by advanced AI". It conducts research and develop and test mitigations. Previously, it was known as the AI Safety Institute. Its creation followed world's first major AI Safety Summit that was held in Bletchley Park in 2023. The institute's professed goal is "building the world's leading understanding of advanced AI risks and solutions, to inform governments so they can keep the public safe". It is designed like a startup in the government "combining the authority of government with the expertise and agility of the private sector". AISI has made access agreements with Anthropic, Google and OpenAI to test their models before release. It has an open source platform called Inspect that permits companies, governments and academics to run standardised safety tests for AI usage. Among the works AISI has done is the reported detection of multiple serious vulnerabilities that could enable development of biological weapons; the vulnerabilities were fixed before the model was launched. It conducts research on diverse fields of AI application. One study by AISI found that LLMs post-trained for political persuasiveness became systematically less accurate and up to 51% more persuasive on political issues. AISI has also worked on the usage of AI for emotional needs. It found that nearly 10 percent of UK citizens used systems like chatbots for emotional purposes on a weekly basis. It found that "systems are now outperforming PhD-level researchers on scientific knowledge tests and helping non-experts succeed at lab work that would previously have been out of reach" in a report published in December 2025. Former chief AI officer of GCHQ Adam Beaumont is the institution's interim director. UK prime minister's AI advisor Jade Leung is the chief technology officer.

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  Artificial general intelligence

  Artificial general intelligence (AGI) is a hypothetical type of artificial intelligence that matches or surpasses human capabilities across virtually all cognitive tasks. Beyond AGI, artificial superintelligence (ASI) would outperform the best human abilities across every domain by a wide margin. Unlike artificial narrow intelligence (ANI), whose competence is confined to well‑defined tasks, an AGI system can generalise knowledge, transfer skills between domains, and solve novel problems without task‑specific reprogramming. Creating AGI is a stated goal of technology companies such as OpenAI, Google, xAI, and Meta. A 2020 survey identified 72 active AGI research and development projects across 37 countries. AGI is a common topic in science fiction and futures studies. Contention exists over whether AGI represents an existential risk. Some AI experts and industry figures have stated that mitigating the risk of human extinction posed by AGI should be a global priority. Others find the development of AGI to be in too remote a stage to present such a risk. == Terminology == AGI is also known as strong AI, full AI, human-level AI, human-level intelligent AI, or general intelligent action. The term "artificial general intelligence" was used in 1997 by Mark Gubrud in a discussion of the implications of fully automated military production and operations. A mathematical formalism of AGI named AIXI was proposed in 2000 by Marcus Hutter, who defines intelligence as "an agent’s ability to achieve goals or succeed in a wide range of environments". This type of AGI has also been called "universal artificial intelligence". The term AGI was re-introduced and popularized by Shane Legg and Ben Goertzel around 2002. Some academic sources reserve the term "strong AI" for computer programs that will experience sentience or consciousness. In contrast, weak AI (or narrow AI) can solve a specific problem but lacks general cognitive abilities. Some academic sources use "weak AI" to refer more broadly to any programs that neither experience consciousness nor have a mind in the same sense as humans. Related concepts include artificial superintelligence and transformative AI. An artificial superintelligence (ASI) is a hypothetical type of AGI that is much more generally intelligent than humans, while the notion of transformative AI relates to AI having a large impact on society, for example, similar to the agricultural or industrial revolution. A framework for classifying AGI was proposed in 2023 by Google DeepMind researchers. They define five performance levels of AGI: emerging, competent, expert, virtuoso, and superhuman. For example, a competent AGI is defined as an AI that outperforms 50% of skilled adults in a wide range of non-physical tasks, and a superhuman AGI (i.e., an artificial superintelligence) is similarly defined but with a threshold of 100%. They consider large language models like ChatGPT or LLaMA 2 to be instances of emerging AGI (comparable to unskilled humans). Regarding the autonomy of AGI and associated risks, they define five levels: tool (fully in human control), consultant, collaborator, expert, and agent (fully autonomous). == Characteristics == There is no single agreed-upon definition of intelligence as applied to computers. Computer scientist John McCarthy wrote in 2007: "We cannot yet characterize in general what kinds of computational procedures we want to call intelligent." === Intelligence traits === Researchers generally hold that a system is required to do all of the following to be regarded as an AGI: reason, use strategy, solve puzzles, and make judgments under uncertainty, represent knowledge, including common sense knowledge, plan, learn, communicate in natural language, if necessary, integrate these skills in completion of any given goal. Many interdisciplinary approaches (e.g. cognitive science, computational intelligence, and decision making) consider additional traits such as imagination (the ability to form novel mental images and concepts) and autonomy. Computer-based systems exhibiting these capabilities are now widespread, with modern large language models demonstrating computational creativity, automated reasoning, and decision support simultaneously across domains. === Physical traits === Other capabilities are considered desirable in intelligent systems, as they may affect intelligence or aid in its expression. These include: the ability to sense (e.g. see, hear, etc.), and the ability to act (e.g. move and manipulate objects, change location to explore, etc.) This includes the ability to detect and respond to hazard. === Tests for human-level AGI === Several tests meant to confirm human-level AGI have been considered. ==== Turing test ==== The Turing test was proposed by Alan Turing in his 1950 paper "Computing Machinery and Intelligence". This test involves a human judge engaging in natural language conversations with both a human and a machine designed to generate human-like responses. The machine passes the test if it can convince the judge that it is human a significant fraction of the time. Turing proposed this as a practical measure of machine intelligence, focusing on the ability to produce human-like responses rather than on the internal workings of the machine. The idea of the test is that the machine has to try and pretend to be a man, by answering questions put to it, and it will only pass if the pretence is reasonably convincing. A considerable portion of a jury, who should not be experts about machines, must be taken in by the pretence. In 2014, a chatbot named Eugene Goostman, designed to imitate a 13-year-old Ukrainian boy, reportedly passed a Turing Test event by convincing 33% of judges that it was human. However, this claim was met with significant skepticism from the AI research community, who questioned the test's implementation and its relevance to AGI. A 2025 pre‑registered, three‑party Turing‑test study by Cameron R. Jones and Benjamin K. Bergen showed that GPT-4.5 was judged to be the human in 73% of five‑minute text conversations—surpassing the 67% humanness rate of real confederates and meeting the researchers' criterion for having passed the test. ==== Ikea test ==== The "Ikea test", also known as the Flat Pack Furniture Test, involves an AI controlling a robot which attempts to assemble an Ikea flat-pack furniture product after having been shown the parts and instructions. As early as 2013, MIT's IkeaBot demonstrated fully autonomous multi-robot assembly of an IKEA Lack table in ten minutes, with no human intervention and no pre-programmed assembly instructions. The robots inferred the assembly sequence from the geometry of the parts alone. ==== Coffee test ==== Steve Wozniak proposed a test where a machine is required to enter an average American home and figure out how to make coffee. It must find the coffee machine, find the coffee, add water, find a mug, and brew the coffee by pushing the proper buttons. This test has been substantially approached across multiple systems. In January 2024, Figure AI's Figure 01 humanoid learned to operate a Keurig coffee machine autonomously after watching video demonstrations, using end-to-end neural networks to translate visual input into motor actions. In 2025, researchers at the University of Edinburgh published the ELLMER framework in Nature Machine Intelligence, demonstrating a robotic arm that interprets verbal instructions, analyses its surroundings, and autonomously makes coffee in dynamic kitchen environments — adapting to unforeseen obstacles in real time rather than following pre-programmed sequences. ==== Suleyman's test ==== Mustafa Suleyman's test proposes giving an AI model US$100,000 and asking it to obtain US$1 million. ==== Use of video-games ==== Adams, et al. propose that the ability to learn and succeed in a wide range of video games can be used to test AI intelligence. This range would include games unknown to the AGI developers before the test is administered. === AI-complete problems === A problem is informally called "AI-complete" or "AI-hard" if it is believed that AGI would be needed to solve it, because the solution is beyond the capabilities of a purpose-specific algorithm. == History == === Classical AI === Modern AI research began in the mid-1950s. The first generation of AI researchers were convinced that artificial general intelligence was possible and that it would exist in just a few decades. AI pioneer Herbert A. Simon wrote in 1965: "machines will be capable, within twenty years, of doing any work a man can do". Their predictions were the inspiration for Stanley Kubrick and Arthur C. Clarke's fictional character HAL 9000, who embodied what AI researchers believed they could create by the year 2001. AI pioneer Marvin Minsky was a consultant on the project of making HAL 9000 as realistic as possible according to the consensus predictions of the time. He said in 1967, "Within a generation... the problem of

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  AI alignment

  In the field of artificial intelligence (AI), alignment aims to steer AI systems toward a person's or group's intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues unintended objectives. It is often difficult for AI designers to specify the full range of desired and undesired behaviors. Therefore, the designers often use simpler proxy goals, such as gaining human approval. But proxy goals can overlook necessary constraints or reward the AI system for merely appearing aligned. AI systems may also find loopholes that allow them to accomplish their proxy goals efficiently but in unintended, sometimes harmful, ways (reward hacking). Advanced AI systems may develop unwanted instrumental strategies, such as seeking power or self-preservation because such strategies help them achieve their assigned final goals. Furthermore, they might develop undesirable emergent goals that could be hard to detect before the system is deployed and encounters new situations and data distributions. Empirical research showed in 2024 that advanced large language models (LLMs) such as OpenAI o1 or Claude 3 sometimes engage in strategic deception to achieve their goals or prevent them from being changed. Some of these issues affect existing commercial systems such as LLMs, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected because these problems partially result from high capabilities. Many prominent AI researchers and AI company leaders have argued or asserted that AI is approaching human-like (AGI) and superhuman cognitive capabilities (ASI), and could endanger human civilization if misaligned. These include "AI godfathers" Geoffrey Hinton and Yoshua Bengio and the CEOs of OpenAI, Anthropic, and Google DeepMind. These risks remain debated. AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and social sciences. == Objectives in AI == Programmers provide an AI system such as AlphaZero with an "objective function", in which they intend to encapsulate the goal(s) the AI is configured to accomplish. Such a system later populates a (possibly implicit) internal "model" of its environment. This model encapsulates all the agent's beliefs about the world. The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, when AlphaZero is trained on chess, it has a simple objective function of "+1 if AlphaZero wins, −1 if AlphaZero loses". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to attain the maximum value of +1. Similarly, a reinforcement learning system can have a "reward function" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a "fitness function". == Alignment problem == In 1960, AI pioneer Norbert Wiener described the AI alignment problem as follows: If we use, to achieve our purposes, a mechanical agency with whose operation we cannot interfere effectively [...] we had better be quite sure that the purpose put into the machine is the purpose which we really desire. AI alignment refers to ensuring that an AI system's objectives match some target. The target is variously defined as the goals of the system's designers or users, widely shared values, objective ethical standards, legal requirements, or the intentions its designers would have if they were more informed and enlightened. In democratic AI alignment, the target is the values and preferences of median voters, which increases political legitimacy. AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI involves two main challenges: carefully specifying the purpose of the system (outer alignment) and ensuring that the system adopts the specification robustly (inner alignment). Researchers also attempt to create AI models that have robust alignment, sticking to safety constraints even when users adversarially try to bypass them. === Specification gaming and side effects === To specify an AI system's purpose, AI designers typically provide an objective function, examples, or feedback to the system. But designers are often unable to completely specify all important values and constraints, so they resort to easy-to-specify proxy goals such as maximizing the approval of human overseers, who are fallible. As a result, AI systems can find loopholes that help them accomplish the specified objective efficiently but in unintended, possibly harmful ways. This tendency is known as specification gaming or reward hacking, and is an instance of Goodhart's law. As AI systems become more capable, they are often able to game their specifications more effectively. Specification gaming has been observed in numerous AI systems. OpenAI GPT models for programming—including in real-world cases—have been found to explicitly plan hacking the tests used to evaluate them to falsely appear successful (e.g., explicitly stating "let's hack"). When the company penalized this, many models learned to obfuscate their plans while continuing to hack the tests. Another system was trained to finish a simulated boat race by rewarding the system for hitting targets along the track, but the system achieved more reward by looping and crashing into the same targets indefinitely. A 2025 Palisade Research study found that when tasked to win at chess against a stronger opponent, some reasoning LLMs attempted to hack the game system, for example by modifying or entirely deleting their opponent. Some alignment researchers aim to help humans detect specification gaming and steer AI systems toward carefully specified objectives that are safe and useful to pursue. When a misaligned AI system is deployed, it can have consequential side effects. Social media platforms have been known to optimize their recommendation algorithms for click-through rates, causing user addiction on a global scale. Stanford researchers say that such recommender systems are misaligned with their users because they "optimize simple engagement metrics rather than a harder-to-measure combination of societal and consumer well-being". Explaining such side effects, Berkeley computer scientist Stuart J. Russell said that the omission of implicit constraints can cause harm: "A system [...] will often set [...] unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. This is essentially the old story of the genie in the lamp, or the sorcerer's apprentice, or King Midas: you get exactly what you ask for, not what you want." Some researchers suggest that AI designers specify their desired goals by listing forbidden actions or by formalizing ethical rules (as with Asimov's Three Laws of Robotics). But Russell and Norvig argue that this approach overlooks the complexity of human values: "It is certainly very hard, and perhaps impossible, for mere humans to anticipate and rule out in advance all the disastrous ways the machine could choose to achieve a specified objective." Additionally, even if an AI system fully understands human intentions, it may still disregard them, because following human intentions may not be its objective (unless it is already fully aligned). === Pressure to deploy unsafe systems === Commercial organizations sometimes have incentives to take shortcuts on safety and to deploy misaligned or unsafe AI systems. For example, social media recommender systems have been profitable despite creating unwanted addiction and polarization. Competitive pressure can also lead to a race to the bottom on AI safety standards. For example, OpenAI has been sued for releasing a ChatGPT version that encouraged suicide for some unstable users, a behavior the company had overlooked amid a rushed product release. Similarly, in 2018, a self-driving car killed a pedestrian (Elaine Herzberg) after engineers disabled the emergency braking system because it was oversensitive and slowed development. === Risks from advanced misaligned AI === Some researchers are interested in aligning increasingly advanced AI systems, as progress in AI development is rapid, and industry and governments are trying to build advan

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  Co–Star

  Co–Star is an American astrological social networking service founded in 2017, and headquartered in New York City. Users enter the date, time and place they were born to generate an astrological chart and daily horoscopes, which can be compared with those of other users. == History == The concept for Co-Star began in 2015 when Banu Guler created an astrological chart as a gift. The idea later developed into a mobile application with collaborators Anna Kopp and Ben Weitzman. The app publicly launched in 2017. The app includes astrological readings, charts, and daily push notifications that have been noted for their unconventional tone. In early 2018, the company raised a $750,000 pre-seed round from Female Founders Fund. In 2019, Co–Star raised a $5.2 million seed round from Maveron, Aspect, and 14W. In January 2020, Co–Star for Android was launched to a 120,000-person waitlist—two years after their iOS version. In April 2021, the company announced a $15 million Series A, led by Spark Capital. As of that date, Co–Star reported more than 20 million downloads and increased adoption among young women in the United States. == Features == Co–Star employs artificial intelligence to analyze publicly accessible NASA JPL data and find patterns in a user's transits. Co–Star's algorithm maps human-written snippets of text to planetary movements to display personalized content for each user. That content has been called “slightly robotic,” “wildly beautiful,” “truly insane," “brutally honest,” and compared to “a free therapy session.” In July 2023, Co–Star released an in-app service called The Void that allows users to ask open-ended questions and receive answers informed by Co–Star's astrological database.

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  Feature hashing

  In machine learning, feature hashing, also known as the hashing trick (by analogy to the kernel trick), is a fast and space-efficient way of vectorizing features, i.e. turning arbitrary features into indices in a vector or matrix. It works by applying a hash function to the features and using their hash values as indices directly (after a modulo operation), rather than looking the indices up in an associative array. In addition to its use for encoding non-numeric values, feature hashing can also be used for dimensionality reduction. This trick is often attributed to Weinberger et al. (2009), but there exists a much earlier description of this method published by John Moody in 1989. == Motivation == === Motivating example === In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (independent variable) of each of the documents in both the training and test sets. Machine learning algorithms, however, are typically defined in terms of numerical vectors. Therefore, the bags of words for a set of documents is regarded as a term-document matrix where each row is a single document, and each column is a single feature/word; the entry i, j in such a matrix captures the frequency (or weight) of the j'th term of the vocabulary in document i. (An alternative convention swaps the rows and columns of the matrix, but this difference is immaterial.) Typically, these vectors are extremely sparse—according to Zipf's law. The common approach is to construct, at learning time or prior to that, a dictionary representation of the vocabulary of the training set, and use that to map words to indices. Hash tables and tries are common candidates for dictionary implementation. E.g., the three documents John likes to watch movies. Mary likes movies too. John also likes football. can be converted, using the dictionary to the term-document matrix ( John likes to watch movies Mary too also football 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 ) {\displaystyle {\begin{pmatrix}{\textrm {John}}&{\textrm {likes}}&{\textrm {to}}&{\textrm {watch}}&{\textrm {movies}}&{\textrm {Mary}}&{\textrm {too}}&{\textrm {also}}&{\textrm {football}}\\1&1&1&1&1&0&0&0&0\\0&1&0&0&1&1&1&0&0\\1&1&0&0&0&0&0&1&1\end{pmatrix}}} (Punctuation was removed, as is usual in document classification and clustering.) The problem with this process is that such dictionaries take up a large amount of storage space and grow in size as the training set grows. On the contrary, if the vocabulary is kept fixed and not increased with a growing training set, an adversary may try to invent new words or misspellings that are not in the stored vocabulary so as to circumvent a machine learned filter. To address this challenge, Yahoo! Research attempted to use feature hashing for their spam filters. Note that the hashing trick isn't limited to text classification and similar tasks at the document level, but can be applied to any problem that involves large (perhaps unbounded) numbers of features. === Mathematical motivation === Mathematically, a token is an element t {\displaystyle t} in a finite (or countably infinite) set T {\displaystyle T} . Suppose we only need to process a finite corpus, then we can put all tokens appearing in the corpus into T {\displaystyle T} , meaning that T {\displaystyle T} is finite. However, suppose we want to process all possible words made of the English letters, then T {\displaystyle T} is countably infinite. Most neural networks can only operate on real vector inputs, so we must construct a "dictionary" function ϕ : T → R n {\displaystyle \phi :T\to \mathbb {R} ^{n}} . When T {\displaystyle T} is finite, of size | T | = m ≤ n {\displaystyle |T|=m\leq n} , then we can use one-hot encoding to map it into R n {\displaystyle \mathbb {R} ^{n}} . First, arbitrarily enumerate T = { t 1 , t 2 , . . , t m } {\displaystyle T=\{t_{1},t_{2},..,t_{m}\}} , then define ϕ ( t i ) = e i {\displaystyle \phi (t_{i})=e_{i}} . In other words, we assign a unique index i {\displaystyle i} to each token, then map the token with index i {\displaystyle i} to the unit basis vector e i {\displaystyle e_{i}} . One-hot encoding is easy to interpret, but it requires one to maintain the arbitrary enumeration of T {\displaystyle T} . Given a token t ∈ T {\displaystyle t\in T} , to compute ϕ ( t ) {\displaystyle \phi (t)} , we must find out the index i {\displaystyle i} of the token t {\displaystyle t} . Thus, to implement ϕ {\displaystyle \phi } efficiently, we need a fast-to-compute bijection h : T → { 1 , . . . , m } {\displaystyle h:T\to \{1,...,m\}} , then we have ϕ ( t ) = e h ( t ) {\displaystyle \phi (t)=e_{h(t)}} . In fact, we can relax the requirement slightly: It suffices to have a fast-to-compute injection h : T → { 1 , . . . , n } {\displaystyle h:T\to \{1,...,n\}} , then use ϕ ( t ) = e h ( t ) {\displaystyle \phi (t)=e_{h(t)}} . In practice, there is no simple way to construct an efficient injection h : T → { 1 , . . . , n } {\displaystyle h:T\to \{1,...,n\}} . However, we do not need a strict injection, but only an approximate injection. That is, when t ≠ t ′ {\displaystyle t\neq t'} , we should probably have h ( t ) ≠ h ( t ′ ) {\displaystyle h(t)\neq h(t')} , so that probably ϕ ( t ) ≠ ϕ ( t ′ ) {\displaystyle \phi (t)\neq \phi (t')} . At this point, we have just specified that h {\displaystyle h} should be a hashing function. Thus we reach the idea of feature hashing. == Algorithms == === Feature hashing (Weinberger et al. 2009) === The basic feature hashing algorithm presented in (Weinberger et al. 2009) is defined as follows. First, one specifies two hash functions: the kernel hash h : T → { 1 , 2 , . . . , n } {\displaystyle h:T\to \{1,2,...,n\}} , and the sign hash ζ : T → { − 1 , + 1 } {\displaystyle \zeta :T\to \{-1,+1\}} . Next, one defines the feature hashing function: ϕ : T → R n , ϕ ( t ) = ζ ( t ) e h ( t ) {\displaystyle \phi :T\to \mathbb {R} ^{n},\quad \phi (t)=\zeta (t)e_{h(t)}} Finally, extend this feature hashing function to strings of tokens by ϕ : T ∗ → R n , ϕ ( t 1 , . . . , t k ) = ∑ j = 1 k ϕ ( t j ) {\displaystyle \phi :T^{}\to \mathbb {R} ^{n},\quad \phi (t_{1},...,t_{k})=\sum _{j=1}^{k}\phi (t_{j})} where T ∗ {\displaystyle T^{}} is the set of all finite strings consisting of tokens in T {\displaystyle T} . Equivalently, ϕ ( t 1 , . . . , t k ) = ∑ j = 1 k ζ ( t j ) e h ( t j ) = ∑ i = 1 n ( ∑ j : h ( t j ) = i ζ ( t j ) ) e i {\displaystyle \phi (t_{1},...,t_{k})=\sum _{j=1}^{k}\zeta (t_{j})e_{h(t_{j})}=\sum _{i=1}^{n}\left(\sum _{j:h(t_{j})=i}\zeta (t_{j})\right)e_{i}} ==== Geometric properties ==== We want to say something about the geometric property of ϕ {\displaystyle \phi } , but T {\displaystyle T} , by itself, is just a set of tokens, we cannot impose a geometric structure on it except the discrete topology, which is generated by the discrete metric. To make it nicer, we lift it to T → R T {\displaystyle T\to \mathbb {R} ^{T}} , and lift ϕ {\displaystyle \phi } from ϕ : T → R n {\displaystyle \phi :T\to \mathbb {R} ^{n}} to ϕ : R T → R n {\displaystyle \phi :\mathbb {R} ^{T}\to \mathbb {R} ^{n}} by linear extension: ϕ ( ( x t ) t ∈ T ) = ∑ t ∈ T x t ζ ( t ) e h ( t ) = ∑ i = 1 n ( ∑ t : h ( t ) = i x t ζ ( t ) ) e i {\displaystyle \phi ((x_{t})_{t\in T})=\sum _{t\in T}x_{t}\zeta (t)e_{h(t)}=\sum _{i=1}^{n}\left(\sum _{t:h(t)=i}x_{t}\zeta (t)\right)e_{i}} There is an infinite sum there, which must be handled at once. There are essentially only two ways to handle infinities. One may impose a metric, then take its completion, to allow well-behaved infinite sums, or one may demand that nothing is actually infinite, only potentially so. Here, we go for the potential-infinity way, by restricting R T {\displaystyle \mathbb {R} ^{T}} to contain only vectors with finite support: ∀ ( x t ) t ∈ T ∈ R T {\displaystyle \forall (x_{t})_{t\in T}\in \mathbb {R} ^{T}} , only finitely many entries of ( x t ) t ∈ T {\displaystyle (x_{t})_{t\in T}} are nonzero. Define an inner product on R T {\displaystyle \mathbb {R} ^{T}} in the obvious way: ⟨ e t , e t ′ ⟩ = { 1 , if t = t ′ , 0 , else. ⟨ x , x ′ ⟩ = ∑ t , t ′ ∈ T x t x t ′ ⟨ e t , e t ′ ⟩ {\displaystyle \langle e_{t},e_{t'}\rangle ={\begin{cases}1,{\text{ if }}t=t',\\0,{\text{ else.}}\end{cases}}\quad \langle x,x'\rangle =\sum _{t,t'\in T}x_{t}x_{t'}\langle e_{t},e_{t'}\rangle } As a side note, if T {\displaystyle T} is infinite, then the inner product space R T {\displaystyle \mathbb {R} ^{T}} is not complete. Taking its completion would get us to a Hilbert space, which allows well-behaved infinite sums. Now we have an inner product space, with enough structure to describe the geometry of the feature hashing function ϕ : R T → R n {\displaystyle \phi :\ma

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  Empowerment (artificial intelligence)

  Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.

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  Wetware computer

  A wetware computer is an organic computer (which can also be known as an artificial organic brain or a neurocomputer) composed of organic material "wetware" such as "living" neurons. Wetware computers composed of neurons are different than conventional computers because they use biological materials, and offer the possibility of substantially more energy-efficient computing. While a wetware computer is still largely conceptual, there has been limited success with construction and prototyping, which has acted as a proof of the concept's realistic application to computing in the future. The most notable prototypes have stemmed from the research completed by biological engineer William Ditto during his time at the Georgia Institute of Technology. His work constructing a simple neurocomputer capable of basic addition from leech neurons in 1999 was a significant discovery for the concept. This research was a primary example driving interest in creating these artificially constructed, but still organic brains. == Origins and theoretical foundations == The term wetware came from cyberpunk fiction, notably through Gibson's Neuromancer, but was quickly taken up in scientific literature to explain computation by biological material. Theories of early biological computation borrowed from Alan Turing's morphogenesis model, which showed that chemical interactions could produce complex patterns without centralized control. Hopfield's associative memory networks also provided a foundation for biological information systems with fault tolerance and self-organization. == Major characteristics and processes == Biological wetware systems demonstrate dynamic reconfigurability underpinned by neuroplasticity and enable continuous learning and adaptation. Reaction-diffusion-based computing and molecular logic gates allow spatially parallel information processing unachievable in conventional systems. These systems also show fault tolerance and self-repair at the cellular and network level. The development of cerebral organoids—miniature lab-grown brains—demonstrates spontaneous learning behavior and suggests biological tissue as a viable computational substrate. == Overview == The concept of wetware is an application of specific interest to the field of computer manufacturing. Moore's law, which states that the number of transistors which can be placed on a silicon chip is doubled roughly every two years, has acted as a goal for the industry for decades, but as the size of computers continues to decrease, the ability to meet this goal has become more difficult, threatening to reach a plateau. Due to the difficulty in reducing the size of computers because of size limitations of transistors and integrated circuits, wetware provides an unconventional alternative. A wetware computer composed of neurons is an ideal concept because, unlike conventional materials which operate in binary (on/off), a neuron can shift between thousands of states, constantly altering its chemical conformation, and redirecting electrical pulses through over 200,000 channels in any of its many synaptic connections. Because of this large difference in the possible settings for any one neuron, compared to the binary limitations of conventional computers, the space limitations are far fewer. == Background == The concept of wetware is distinct and unconventional and draws slight resonance with both hardware and software from conventional computers. While hardware is understood as the physical architecture of traditional computational devices, comprising integrated circuits and supporting infrastructure, software represents the encoded architecture of storage and instructions. Wetware is a separate concept that uses the formation of organic molecules, mostly complex cellular structures (such as neurons), to create a computational device such as a computer. In wetware, the ideas of hardware and software are intertwined and interdependent. The molecular and chemical composition of the organic or biological structure would represent not only the physical structure of the wetware but also the software, being continually reprogrammed by the discrete shifts in electrical pulses and chemical concentration gradients as the molecules change their structures to communicate signals. The responsiveness of a cell, proteins, and molecules to changing conformations, both within their structures and around them, ties the idea of internal programming and external structure together in a way that is alien to the current model of conventional computer architecture. The structure of wetware represents a model where the external structure and internal programming are interdependent and unified; meaning that changes to the programming or internal communication between molecules of the device would represent a physical change in the structure. The dynamic nature of wetware borrows from the function of complex cellular structures in biological organisms. The combination of "hardware" and "software" into one dynamic, and interdependent system which uses organic molecules and complexes to create an unconventional model for computational devices is a specific example of applied biorobotics. === The cell as a model of wetware === Cells in many ways can be seen as their form of naturally occurring wetware, similar to the concept that the human brain is the preexisting model system for complex wetware. In his book Wetware: A Computer in Every Living Cell (2009) Dennis Bray explains his theory that cells, which are the most basic form of life, are just a highly complex computational structure, like a computer. To simplify one of his arguments a cell can be seen as a type of computer, using its structured architecture. In this architecture, much like a traditional computer, many smaller components operate in tandem to receive input, process the information, and compute an output. In an overly simplified, non-technical analysis, cellular function can be broken into the following components: Information and instructions for execution are stored as DNA in the cell, RNA acts as a source for distinctly encoded input, processed by ribosomes and other transcription factors to access and process the DNA and to output a protein. Bray's argument in favor of viewing cells and cellular structures as models of natural computational devices is important when considering the more applied theories of wetware to biorobotics. === Biorobotics === Wetware and biorobotics are closely related concepts, which both borrow from similar overall principles. A biorobotic structure can be defined as a system modeled from a preexisting organic complex or model such as cells (neurons) or more complex structures like organs (brain) or whole organisms. Unlike wetware, the concept of biorobotics is not always a system composed of organic molecules, but instead could be composed of conventional material which is designed and assembled in a structure similar or derived from a biological model. Biorobotics have many applications and are used to address the challenges of conventional computer architecture. Conceptually, designing a program, robot, or computational device after a preexisting biological model such as a cell, or even a whole organism, provides the engineer or programmer the benefits of incorporating into the structure the evolutionary advantages of the model. == Effects on users == Wetware technologies such as BCIs and neuromorphic chips offer new possibilities for user autonomy. For those with disabilities, such systems could restore motor or sensory functions and enhance quality of life. However, these technologies raise ethical questions: cognitive privacy, consent over biological data, and risk of exploitation. Without proper oversight, wetware technologies may also widen inequality, favoring those with access to cognitive enhancements. Open governance frameworks and ethical AI design grounded in neuro ethics will be essential. With the development of wetware devices, disparities in access could exacerbate social inequalities, benefiting those who have resources to enhance cognitive or physical abilities. It is necessary to create strong ethical frameworks, inclusive development practices, and open systems of governance to reduce risks and make sure that wetware advances are beneficial to all segments of society. == Applications and goals == === Basic neurocomputer composed of leech neurons === In 1999 William Ditto and his team of researchers at Georgia Institute of Technology and Emory University created a basic form of a wetware computer capable of simple addition by harnessing leech neurons. Leeches were used as a model organism due to the large size of their neuron, and the ease associated with their collection and manipulation. However, these results have never been published in a peer-reviewed journal, prompting questions about the validity of the claims. The computer was able to complete basic addition through electrical probes

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  Random feature

  Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ⁡ ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⁡ ⟨ ω 1 , x ⟩ , sin ⁡ ⟨ ω 1 , x ⟩ , … , cos ⁡ ⟨ ω D , x ⟩ , sin ⁡ ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg ⁡ min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.

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  Agent verification

  Agent verification is activity to gain assurances that purposeful artificial constructs act in accordance with their specifications. While primitive forms of inorganic agents have been used in manufacturing for centuries, the study of artificial agents did not begin until the mid 20th century. Foundational work on such agents was closely bound with the emergence of artificial intelligence as an academic discipline. Early agents deployed for industrial control systems and in computing were often controlled by quite simple logic however, not involving artificial intelligence as such. When deployed as part of a multi-agent system, even such simple agents could require special agent orientated testing methods, as their collective behaviour was challenging to verify with traditional testing techniques. Difficulties in providing assurances that agents will not behave in dangerous ways became more prevalent after the introduction of LLM agents, especially after the rapid acceleration of their deployment in 2025. The verification of agent behaviour can be conducted by formal or informal methods. Informal verification requires less mathematical skill. But when agents are part of systems where errors have significant risks — such as danger to human life, environmental damage or major financial loss — formal verification is preferred. Both regulators and system designers themselves like formal verification as it provides a high degree of mathematical certainty. It is not however always possible to formally test all aspects of an agent based system's behaviour, especially where newer LLM based agents are concerned, due in part to their high degree of autonomy. Accordingly, agent verification for low impact deployments might be carried out only with informal methods, while for high impact deployments, it may be performed with a mix of formal and informal techniques. == Terminology == In academia, the term agent verification is often defined to mean activity concerned with gaining assurance that the agent behaves in accordance with its specification - whether by processes such as testing or simulation. 'Verification' is typically contrasted with 'validation', the latter meaning activity concerned with checking that the specification itself meets user or real world needs. Such definitions are not universally adhered to however - for example, in some workplaces and documents, the words 'verification' and 'validation' can be used synonymously. Efforts to gain confidence in Agents have intensified sharply since 2025 due to the rapid roll out of LLM agents; different terms are sometimes used in the commercial sector. Here the term 'agent verification' can be used in the same sense as it is in academia, but sometimes the same activity can be covered by more ambiguous and wider ranging terms such as 'Agent governance' , 'Agent observability' or 'AI agent policing'. == History == === Classical agents === The theoretical underpinnings for artificial (inorganic) agents emerged in the mid 20th century, with establishment of cybernetics and artificial intelligence. Oliver Selfridge's 1958 Pandemonium - A Paradigm for Learning paper was an important early theoretical contribution in establishing agent oriented architecture. Practical implementations of agents for real world applications began to become widespread in the 1990s, after the introduction of the belief–desire–intention software model (BDI), and agent-oriented programming. Pure digital agents were deployed in computer infrastructure for purposes such as monitoring, while agents connected to real-world sensors and actuators were increasingly used in industrial control systems. While the concept of artificial agents was interwoven with early artificial intelligence studies right from the start, early agents lacked general purpose reasoning capabilities, often only having simple if then logic. Even a device as simple as a thermostat, which has a sensor and a means of acting, can be considered a proto agent in this sense. Verifying the behaviours of a simple single agent system is not generally especially difficult, but it can be a different matter when several simple agents coexist in the same system. Craig Reynolds's work on boids showed that relatively complex, "intelligent" behaviour can emerge from a number of such simple agents working together in a Multi-agent system (MAS). By the 1990s, even the behaviour of a single agent system could sometimes be quite complex; in accordance with the Belief–desire–intention software model, agents could have believes that might evolve over time. Agents were increasingly introduced that were controlled by quite large decision tree models, which had new vulnerabilities to adversarial attack. It was becoming increasingly apparent that traditional software verification methods had limitations for testing such agents, or even for the more primitive type of agents when they were deployed as part of a MAS. It was the use of agents for industrial control systems, sometimes associated with robotics, that lent urgency to the practice of agent verification. Informal testing might be acceptable for digital agents used say to monitor whether each of an organisation's computers are properly licensed. But with an increasing potential for faulty agents to result in a failure that might cause a large fire to break out at a chemical manufacturing plant, a botched medical operation, or even a crashed aircraft, the need to develop reliable means of verifying behaviour of such agents was considered urgent. The Foundation for Intelligent Physical Agents was established in 1996. From the late 90s, a growing number of industry and university based scientists began working on the problem, with researchers publishing papers on the verification of both single and multi agent systems. Much of this work showed how formal verification techniques like model checking could be used to gain a high level of assurance that agent based systems would conform with their specification. A 2018 systematic review covering 231 studies found that model checking was the most common technique for agent verification, with theorem proving the second most commonly used formal verification method. In the first two decades of the 20th century, agents run by AI became more common, with Siri and Alexa being well known examples. But such agents still lacked general reasoning capabilities and did not pose new pressing problems for agent verification. === General purpose reasoning agents === The advent of LLMs created huge potential for further use of artificial agents, as agents based on them could have general purpose cognitive abilities. Agents run by LLMs (and occasionally non-LLM foundation models) have similar vulnerability to adversarial attack as those run by decision tree models. The wider scope of actions for LLM agents has created new challenges for their verification, over and above those present for classical agents. For example, the LLM's neural network endows it with infinite domains, an especial challenge for traditional formal verification techniques. Academics began to study the problems involved in verifying LLM agents from 2018. Deployment of such agents began to accelerate in late 2023 after OpenAI's "function-calling" API was made available, and especially after Anthropic's late 2024 introduction of Model Context Protocol (MCP), a standardised way for LLM agents to gain contextual awareness, and to act on the world by calling various external tools. The rapid rollout of LLM agents following MCP's release has seen the task of agent verification receive increased attention within academia, and also from the private sector. In 2024 and 2025 several startups focusing on LLM agent verification have been founded in both Europe and the US to meet growing demand. == Approaches == === Formal verification === Formal verification involves proving the correctness of some or all aspects of a system using mathematical methods. Such methods can range from manual formal proof, to verification assisted with automated theorem provers like Isabelle. For agent verification, model checking is by far the most frequently used formal verification method; for pre-LLM models it was often complemented with techniques using computation tree logic. Another common method is theorem proving. Formal verification provides a higher degree of confidence than informal methods, but it is not always used, even when it is possible. Sometimes a person or organisation developing software agents won't have the necessary skills, or may not see it as worth the effort if the agent(s) will not have the ability to cause much harm even if they malfunction. When agents are deployed in systems where errors could have serious consequences, the ability of formal verification methods to provide mathematical certainty tends to be strongly preferred by both regulators and designers themselves. But even for high impact systems, formal verificatio

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  Domain adaptation

  Domain adaptation is a field associated with machine learning and transfer learning. It addresses the challenge of training a model on one data distribution (the source domain) and applying it to a related but different data distribution (the target domain). A common example is spam filtering, where a model trained on emails from one user (source domain) is adapted to handle emails for another user with significantly different patterns (target domain). Domain adaptation techniques can also leverage unrelated data sources to improve learning. When multiple source distributions are involved, the problem extends to multi-source domain adaptation. Domain adaptation is a specific type of transfer learning. According to the taxonomy laid out by Pan and Yang (2010), it falls into the category of transductive transfer learning. In this setting, the source and target tasks are the same (e.g., both are object recognition), but the domains differ (different marginal distributions). This distinguishes it from inductive transfer learning (where labeled data is available for the target task) and unsupervised transfer learning (where labels are unavailable in both domains). == Classification of domain adaptation problems == Domain adaptation setups are classified in two different ways: according to the distribution shift between the domains, and according to the available data from the target domain. === Distribution shifts === Common distribution shifts are classified as follows: Covariate Shift occurs when the input distributions of the source and destination change, but the relationship between inputs and labels remains unchanged. The above-mentioned spam filtering example typically falls in this category. Namely, the distributions (patterns) of emails may differ between the domains, but emails labeled as spam in the one domain should similarly be labeled in another. Prior Shift (Label Shift) occurs when the label distribution differs between the source and target datasets, while the conditional distribution of features given labels remains the same. An example is a classifier of hair color in images from Italy (source domain) and Norway (target domain). The proportions of hair colors (labels) differ, but images within classes like blond and black-haired populations remain consistent across domains. A classifier for the Norway population can exploit this prior knowledge of class proportions to improve its estimates. Concept Shift (Conditional Shift) refers to changes in the relationship between features and labels, even if the input distribution remains the same. For instance, in medical diagnosis, the same symptoms (inputs) may indicate entirely different diseases (labels) in different populations (domains). === Data available during training === Domain adaptation problems typically assume that some data from the target domain is available during training. Problems can be classified according to the type of this available data: Unsupervised: Unlabeled data from the target domain is available, but no labeled data. In the above-mentioned example of spam filtering, this corresponds to the case where emails from the target domain (user) are available, but they are not labeled as spam. Domain adaptation methods can benefit from such unlabeled data, by comparing its distribution (patterns) with the labeled source domain data. Semi-supervised: Most data that is available from the target domain is unlabelled, but some labeled data is also available. In the above-mentioned case of spam filter design, this corresponds to the case that the target user has labeled some emails as being spam or not. Supervised: All data that is available from the target domain is labeled. In this case, domain adaptation reduces to refinement of the source domain predictor. In the above-mentioned example classification of hair-color from images, this could correspond to the refinement of a network already trained on a large dataset of labeled images from Italy, using newly available labeled images from Norway. == Formalization == Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h : X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\displaystyle Y} to an example from X {\displaystyle X} . This model is learned from a learning sample S = { ( x i , y i ) ∈ ( X × Y ) } i = 1 m {\displaystyle S=\{(x_{i},y_{i})\in (X\times Y)\}_{i=1}^{m}} . Usually in supervised learning (without domain adaptation), we suppose that the examples ( x i , y i ) ∈ S {\displaystyle (x_{i},y_{i})\in S} are drawn i.i.d. from a distribution D S {\displaystyle D_{S}} of support X × Y {\displaystyle X\times Y} (unknown and fixed). The objective is then to learn h {\displaystyle h} (from S {\displaystyle S} ) such that it commits the least error possible for labelling new examples coming from the distribution D S {\displaystyle D_{S}} . The main difference between supervised learning and domain adaptation is that in the latter situation we study two different (but related) distributions D S {\displaystyle D_{S}} and D T {\displaystyle D_{T}} on X × Y {\displaystyle X\times Y} . The domain adaptation task then consists of the transfer of knowledge from the source domain D S {\displaystyle D_{S}} to the target one D T {\displaystyle D_{T}} . The goal is then to learn h {\displaystyle h} (from labeled or unlabelled samples coming from the two domains) such that it commits as little error as possible on the target domain D T {\displaystyle D_{T}} . The major issue is the following: if a model is learned from a source domain, what is its capacity to correctly label data coming from the target domain? == Four algorithmic principles == === Reweighting algorithms === The objective is to reweight the source labeled sample such that it "looks like" the target sample (in terms of the error measure considered). === Iterative algorithms === A method for adapting consists in iteratively "auto-labeling" the target examples. The principle is simple: a model h {\displaystyle h} is learned from the labeled examples; h {\displaystyle h} automatically labels some target examples; a new model is learned from the new labeled examples. Note that there exist other iterative approaches, but they usually need target labeled examples. === Search of a common representation space === The goal is to find or construct a common representation space for the two domains. The objective is to obtain a space in which the domains are close to each other while keeping good performances on the source labeling task. This can be achieved through the use of Adversarial machine learning techniques where feature representations from samples in different domains are encouraged to be indistinguishable. === Hierarchical Bayesian Model === The goal is to construct a Bayesian hierarchical model p ( n ) {\displaystyle p(n)} , which is essentially a factorization model for counts n {\displaystyle n} , to derive domain-dependent latent representations allowing both domain-specific and globally shared latent factors. == Software packages == Several compilations of domain adaptation and transfer learning algorithms have been implemented over the past decades: SKADA (Python) ADAPT (Python) TLlib (Python) Domain-Adaptation-Toolbox (MATLAB)

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