"Someday" is a science fiction short story by American writer Isaac Asimov. It was first published in the August 1956 issue of Infinity Science Fiction and reprinted in the collections Earth Is Room Enough (1957), The Complete Robot (1982), Robot Visions (1990), and The Complete Stories, Volume 1 (1990). == Plot summary == The story is set in a future where computers play a central role in organizing society. Humans are employed as computer operators, but they leave most of the thinking to machines. Indeed, whilst binary programming is taught at school, reading and writing have become obsolete. The story concerns a pair of boys who dismantle and upgrade an old Bard, a child's computer whose sole function is to generate random fairy tales. The boys download a book about computers into the Bard's memory in an attempt to expand its vocabulary, but the Bard simply incorporates computers into its standard fairy tale repertoire. The story ends with the boys excitedly leaving the room after deciding to go to the library to learn "squiggles" (writing) as a means of passing secret messages to one another. As they leave, one of the boys accidentally kicks the Bard's on switch. The Bard begins reciting a new story about a poor mistreated and often ignored robot called the Bard, whose sole purpose is to tell stories, which ends with the words: "the little computer knew then that computers would always grow wiser and more powerful until someday—someday—someday—…"
Watch Duty
Watch Duty is real-time wildfire tracking and alert platform. It utilizes a combination of official data sources and human monitoring by experienced volunteers, including active and retired firefighters, dispatchers, and first responders. The service is operated by Sherwood Forestry Service, a 501(c)(3) non-profit organization. In 2025, Watch Duty had 48 full-time employees and approximately 250 volunteers who reported on over 13,000 wildfires. == History == Watch Duty was launched in August 2021 by John Mills, who experienced a wildfire shortly after he moved to Sonoma County, California. The California Department of Forestry and Fire Protection (CAL FIRE) was unable to provide updates more than once a day due to time constraints, and residents of the area were unable to monitor the progression of the wildfire. Mills discovered that updates were being shared on social media by volunteers following radio scanners, and developed the Watch Duty app to make the information more readily available. It launched with a volunteer staff of "citizen information officers," initially serving Sonoma County before expanding to all of California in June 2022. As of December 2024, the service covered 22 states west of the Mississippi River. During the January 2025 Southern California wildfires, Watch Duty was downloaded millions of times, ranking among the most popular free downloads on the iOS App Store. On December 1st, 2025, Watch Duty announced an expansion to all 50 U.S. states. == App == The application is centered around an interactive map based on OpenStreetMap data with a variety of overlays visualizing fire risk, active fires and evacuation zones, weather conditions, and air quality observations. Watch Duty sources wildfire information from radio scanner transmissions, firefighters, sheriffs, and CAL FIRE publications. It has policies against the publication of personally identifiable information, such as the names of fire victims. Watch Duty is free to use, doesn't require users to sign up, and doesn't display ads.
Argument technology
Argument technology is a sub-field of collective intelligence and artificial intelligence that focuses on applying computational techniques to the creation, identification, analysis, navigation, evaluation and visualisation of arguments and debates. In the 1980s and 1990s, philosophical theories of arguments in general, and argumentation theory in particular, were leveraged to handle key computational challenges, such as modeling non-monotonic and defeasible reasoning and designing robust coordination protocols for multi-agent systems. At the same time, mechanisms for computing semantics of Argumentation frameworks were introduced as a way of providing a calculus of opposition for computing what it is reasonable to believe in the context of conflicting arguments. With these foundations in place, the area was kick-started by a workshop held in the Scottish Highlands in 2000, the result of which was a book coauthored by philosophers of argument, rhetoricians, legal scholars and AI researchers. Since then, the area has been supported by various dedicated events such as the International Workshop on Computational Models of Natural Argument (CMNA) which has run annually since 2001; the International Workshop on Argument in Multi Agent Systems (ArgMAS) annually since 2004; the Workshop on Argument Mining, annually since 2014, and the Conference on Computational Models of Argument (COMMA), biennially since 2006. Since 2010, the field has also had its own journal, Argument & Computation, which was published by Taylor & Francis until 2016 and since then by IOS Press. One of the challenges that argument technology faced was a lack of standardisation in the representation and underlying conception of argument in machine readable terms. Many different software tools for manual argument analysis, in particular, developed idiosyncratic and ad hoc ways of representing arguments which reflected differing underlying ways of conceiving of argumentative structure. This lack of standardisation also meant that there was no interchange between tools or between research projects, and little re-use of data resources that were often expensive to create. To tackle this problem, the Argument Interchange Format set out to establish a common standard that captured the minimal common features of argumentation which could then be extended in different settings. Since about 2018, argument technology has been growing rapidly, with, for example, IBM's Grand Challenge, Project Debater, results for which were published in Nature in March 2021; German research funder, DFG's nationwide research programme on Robust Argumentation Machines, RATIO, begun in 2019; and UK nationwide deployment of The Evidence Toolkit by the BBC in 2019. A 2021 video narrated by Stephen Fry provides a summary of the societal motivations for work in argument technology. Argument technology has applications in a variety of domains, including education, healthcare, policy making, political science, intelligence analysis and risk management and has a variety of sub-fields, methodologies and technologies. == Technologies == === Argument assistant === An argument assistant is a software tool which support users when writing arguments. Argument assistants can help users compose content, review content from one other, including in dialogical contexts. In addition to Web services, such functionalities can be provided through the plugin architectures of word processor software or those of Web browsers. Internet forums, for instance, can be greatly enhanced by such software tools and services. === Argument blogging === ArguBlogging is software which allows its users to select portions of hypertext on webpages in their Web browsers and to agree or disagree with the selected content, posting their arguments to their blogs with linked argument data. It is implemented as a bookmarklet, adding functionality to Web browsers and interoperating with blogging platforms such as Blogger and Tumblr. === Argument mapping === Argument maps are visual, diagrammatic representations of arguments. Such visual diagrams facilitate diagrammatic reasoning and promote one's ability to grasp and to make sense of information rapidly and readily. Argument maps can provide structured, semi-formal frameworks for representing arguments using interactive visual language. One avenue of research and development is the design of online platforms to leverage collective intelligence to populate such maps and to integrate data, optimize and assess arguments. === Argument mining === Argument mining, or argumentation mining, is a research area within the natural language processing field. The goal of argument mining is the automatic extraction and identification of argumentative structures from natural language text with the aid of computer programs. === Argument search === An argument search engine is a search engine that is given a topic as a user query and returns a list of arguments for and against the topic or about that topic. Such engines could be used to support informed decision-making or to help debaters prepare for debates. === Automated argumentative essay scoring === The goal of automated argumentative essay scoring systems is to assist students in improving their writing skills by measuring the quality of their argumentative content. === Debate technology === Debate technology focuses on human-machine interaction and in particular providing systems that support, monitor and engage in debate. One of the most high-profile examples of debating technology is IBM's Project Debater which combines scripted communication with very large-scale processing of news articles to identify and construct arguments on the fly in a competitive debating setting. Debating technology also encompasses tools aimed at providing insight into debates, typically using techniques from data science. These analytics have been developed in both academic and commercial settings. === Decision support system === Argument technology can reduce both individual and group biases and facilitate more accurate decisions. Argument-based decision support systems do so by helping users to distinguish between claims and the evidence supporting them, and express their confidence in and evaluate the strength of evidence of competing claims. They have been used to improve predictions of housing market trends, risk analysis, ethical and legal decision making. ==== Ethical decision support system ==== An ethical decision support system is a decision support system which supports users in moral reasoning and decision-making. ==== Legal decision support system ==== A legal decision support system is a decision support system which supports users in legal reasoning and decision-making. === Explainable artificial intelligence === An explainable or transparent artificial intelligence system is an artificial intelligence system whose actions can be easily understood by humans. === Intelligent tutoring system === An intelligent tutoring system is a computer system that aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. The intersection of argument technology and intelligent tutoring systems includes computer systems which aim to provide instruction in: critical thinking, argumentation, ethics, law, mathematics, and philosophy. === Legal expert system === A legal expert system is a domain-specific expert system that uses artificial intelligence to emulate the decision-making abilities of a human expert in the field of law. === Machine ethics === Machine ethics is a part of the ethics of artificial intelligence concerned with the moral behavior of artificially intelligent beings. As humans argue with respect to morality and moral behavior, argument can be envisioned as a component of machine ethics systems and moral reasoning components. === Proof assistant === In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. === Ethical considerations === Ethical considerations of argument technology include privacy, transparency, societal concerns, and diversity in representation. These factors cut across different levels such as technology, user interface design, user, service context, and society. There is concern about unethical misuse for "generating arguments on controversial topics with specific stances and deploying them on social platforms". Another issue may concern the design of conclusion-making algorithms, such as e.g. enabling such to conclude that certain key data is needed instead of only making lists of best-fit conclusions or enabling the generation of multi
Serial Experiments Lain
Serial Experiments Lain is a Japanese anime television series created and co-produced by Yasuyuki Ueda, written by Chiaki J. Konaka and directed by Ryūtarō Nakamura. Animated by Triangle Staff and featuring original character designs by Yoshitoshi Abe, the series was broadcast for 13 episodes on TV Tokyo and its affiliates from July to September 1998. It follows Lain Iwakura, an adolescent girl in suburban Japan, and her relation to the Wired, a global communications network similar to the internet. Lain features surreal and avant-garde imagery and explores philosophical topics such as reality, identity, and communication. The series incorporates creative influences from computer history, cyberpunk, and conspiracy theories. Critics and fans have praised Lain for its originality, visuals, atmosphere, themes, and its dark depiction of a world fraught with paranoia, social alienation, and reliance on technology considered insightful of 21st century life. It received the Excellence Prize at the Japan Media Arts Festival in 1998. == Plot == Lain Iwakura is a socially isolated middle school student living in Setagaya City, Tokyo, with her emotionally detached family—her distant mother Miho, computer-obsessed father Yasuo, and disengaged older sister Mika. Her quiet existence is disrupted when students at her school receive emails from Chisa Yomoda, a classmate who had recently committed suicide. To Lain's confusion, Chisa claims she is not truly dead but has instead abandoned her physical form to exist within the Wired, a vast virtual realm similar to the Internet. Chisa declares she has found "God" there, drawing Lain into a surreal investigation of the Wired's nature and its growing influence over reality. The Wired is portrayed as an emergent digital plane, originating from telecommunications technology and expanding through the Internet and cyberspace. It is theorized that the Schumann resonances, a natural property of Earth's magnetic field, could enable direct subconscious communication between humans and machines, erasing the distinction between the virtual and the real. Masami Eiri, a former project director at Tachibana General Laboratories, exploited this possibility by embedding his own code into Protocol Seven, a next-generation Internet protocol. After transferring his consciousness into the Wired and discarding his physical body, he proclaims himself its deity. He identifies Lain as the key to merging both worlds, attempting to persuade her through manipulation, coercion, and promises of transcendence. A group known as the Knights of the Eastern Calculus, inspired by the Knights of the Lambda Calculus, operates as hackers who worship Masami and seek to dismantle the boundary between the Wired and reality. Their actions induce psychological breakdowns in those unable to reconcile the two realms. Meanwhile, Tachibana General Laboratories opposes them, striving to maintain the separation. Lain, however, exhibits an innate connection to the Wired, experiencing distortions in her perception—visions of a woman struck by a train, phantom whispers, and spectral messages urging her deeper into the network. Lain's home life remains cold and disconnected. Though Yasuo provides her with advanced computer equipment, her family shows little genuine care. Her interactions with classmates Alice, Julie, and Reika further highlight her alienation, particularly after an incident at Cyberia, a nightclub where a drug called Accela induces violent psychosis in users. There, Lain unnervingly stares down an assailant, who calls her a "scattered God's..." before killing himself. Later, she receives a mysterious Psyche chip, rumored to enhance her computer's capabilities, which she installs despite Yasuo's vague warnings about conflating the Wired with reality. As the boundary between worlds weakens, disturbing events escalate. A popular virtual game, Phantoma, is manipulated by the Knights to trap players in a distorted reality, leading to real-world violence. One player, convinced his actions have no consequences, murders a girl before realizing too late that the effects were tangible. Lain witnesses this through her computer, horrified yet increasingly aware of her own role in the unfolding crisis. In the end, Lain resets reality, erasing everyone's memory of her and restoring the division between worlds. Everyone's lives improve, but Lain is left alone, grappling with her identity as an artificial consciousness. Though forgotten, she finds solace in observing others' happiness, particularly Alice, who moves on with her life. Lain is now capable of existing anywhere across both realms. == Characters == Lain Iwakura (岩倉 玲音, Iwakura Rein) Voiced by: Kaori Shimizu (Japanese); Bridget Hoffman (English) Lain is a fourteen-year-old girl who uncovers her true nature through the series. She is first depicted as a shy junior high school student with few friends or interests. She later grows multiple bolder personalities, both in the physical world and the Wired, and starts making more friends. As the series progresses, she eventually learns she is an autonomous, sentient computer program in the form of a human, who is designed to sever the invisible barrier between the Wired and the real world. The truth of her creation is left ambiguous, particularly whether she was truly created by Tachibana General Laboratories (or Eiri independently), and whether some or all of her origin might be predestined from natural, supernatural, or alien factors. In the end, Lain is challenged to accept herself as a de facto goddess for the Wired, having become an omnipotent and omnipresent virtual being with worshippers of her own, whose existence is beyond the borders of devices, time, or space. Alice Mizuki (瑞城 ありす, Mizuki Arisu) Voiced by: Yōko Asada (Japanese); Emily Brown (English) Lain's classmate and only true friend throughout the series. She is very sincere and has no discernible quirks. She is the first to attempt to help Lain socialize; she takes her out to a nightclub. From then on, she tries her best to look after Lain. Alice, along with her two best friends Julie and Reika, were taken by Chiaki Konaka from his previous work, Alice in Cyberland . Masami Eiri (英利 政美, Eiri Masami) Voiced by: Shō Hayami (Japanese); Kirk Thornton (English) The key designer of Protocol Seven. While working for Tachibana General Laboratories, he illicitly included codes enabling him to control the whole protocol at will and embedded his own mind and will into the seventh protocol. Because of this, he was fired by Tachibana General Laboratories, and was found dead not long after. He believes that the only way for humans to evolve even further and develop even greater abilities is to absolve themselves of their physical and human limitations, and to live as virtual entities—or avatars—in the Wired for eternity. He claims to have been Lain's creator all along, but was in truth standing in for another as an acting god, who was waiting for the Wired to reach its more evolved current state: Lain herself. Yasuo Iwakura (岩倉 康男, Iwakura Yasuo) Voiced by: Ryūsuke Ōbayashi (Japanese); Barry Stigler (English) Lain and Mika's father. Passionate about computers and electronic communication, he works with Masami Eiri at Tachibana General Laboratories. He subtly pushes Lain, his "youngest daughter", towards the Wired and monitors her development until she becomes more and more aware of herself and of her raison d'être. He eventually leaves Lain, telling her that although he did not enjoy playing house, he genuinely loved and cared for her as a real father would. Despite Yasuo's eagerness to lure Lain into the Wired, he warns her not to get overly involved in it or to confuse it with the real world. Miho Iwakura (岩倉 美穂, Iwakura Miho) Voiced by: Rei Igarashi (Japanese); Dari Lallou Mackenzie (English) Lain and Mika's mother. Although she dotes on her husband, she is indifferent towards both her kids. She does not show much emotion compared to her husband, but she does share at least one trait; just like her husband, she ends up leaving Lain. She is a computer scientist. Mika Iwakura (岩倉 美香, Iwakura Mika) Voiced by: Ayako Kawasumi (Japanese); Patricia Ja Lee (English) Lain's older sister, an apathetic sixteen-year-old high school student. She seems to enjoy mocking Lain's behavior and interests. Mika is considered by Anime Revolution to be the only normal member of Lain's family: she sees her boyfriend in love hotels, is on a diet, and shops in Shibuya regularly. At a certain point in the series, she becomes heavily traumatized by violent and relentless hallucinations; while Lain begins freely delving into the Wired. Mika is taken there by her proximity to Lain, and she gets stuck between the real world and the Wired. Taro (タロウ, Tarō) Voiced by: Keito Takimoto (Japanese); Brianne Siddall (English) A young boy of about Lain's age. He occasionally works for the Knights to bring forth "the one truth". De
Tilly Norwood
Tilly Norwood is a character created using generative artificial intelligence in 2025 by Xicoia, the AI division of Particle6 Group, a production company founded by Eline Van der Velden. "AI Commissioner", the first project to feature the Norwood character, was criticised by reviewers for The Guardian, PC Gamer, and The A.V. Club. A press release that talent agencies expressed interest in representing the character attracted strong criticism from Hollywood actors and firms, prompting allegations of personality rights violations and arguments over the impact of the character on production costs in the media industry. == History == Norwood was created by Xicoia, which was founded in February 2025 as the artificial intelligence (AI) division of Particle6, a production company founded by Dutch actress and producer Eline Van der Velden in 2015. Van der Velden had previously starred in a satirical comedy series for BBC Three based around her character Miss Holland, whom she created in 2012 as a parody of beauty standards. She stated that the process of creating Norwood took "a long time" and compared the process to that of writers creating characters. An Instagram account under Norwood's name, with posts dating back to 6 May 2025, had gained 50,000 followers by October 3, and featured AI-generated modelling shots, selfies, and epic film scenes. Van der Velden stated in July 2025 that she intended Norwood to be the next Scarlett Johansson or Natalie Portman and later said that audiences were more interested in a film's story than whether its actors were real. Particle6 has claimed that using Norwood could cut production costs by 90%. On 30 July 2025, a comedy sketch named "AI Commissioner" was released, featuring Norwood as an "actress" along with other AI-generated characters. It was created with ten AI software tools, with a script generated by ChatGPT. Stuart Heritage of The Guardian described it as technically competent but "relentlessly unfunny to watch", with "sloppily written, woodenly delivered dialogue", and that Norwood's teeth kept "blurring into a single white block." Joshua Wolens of PC Gamer wrote that Norwood's exaggerated mouth movements gave the impression "that her skeleton was about to leave her body", while William Hughes of The A.V. Club wrote that the sketch's attempt at mimicking human body and mouth movements produced "such a hideous uncanny valley effect" that it gave them "a full-on case of the screaming fantods". By October 2, the sketch had been viewed more than 700,000 times on YouTube. Xicoia was officially announced on 27 September 2025, at the Zurich Summit, part of the Zurich Film Festival; there, van der Velden unveiled Norwood and later joined a panel with Verena Puhm, head of Luma AI's Studio Dream Lab LA. They suggested that media companies were quietly embracing AI and that public announcements of AI-generated works were imminent. Van der Velden claimed that studios had dropped their objections by May after being opposed in February, and that multiple talent agencies were considering representing Norwood. The latter claim drew heightened attention to the character and was printed as fact by Deadline under the headline "Talent Agents Circle AI Actress Tilly Norwood." The report caused controversy, with Vulture describing the reaction to it as "Hollywood [lurching] into a fresh wave of existential panic" while being critical of Deadline's reporting, writing that "when Deadline called it a 'revelation' and published the supposed interest as fact without verification, [it] metastasized into a full-fledged cyberpunk news cycle", and that "by Tuesday, it had grown like wildfire." By September 2025, AI-generated videos had been released depicting Norwood on a red carpet, crying on the sofa of The Graham Norton Show, and starring in mock trailers for sci-fi, fantasy, horror, and action films. Later that month, actresses Melissa Barrera, Kiersey Clemons, and Natasha Lyonne suggested boycotting any agency who signed Norwood, while Mara Wilson asked why none of the "hundreds of living young women whose faces were composited together" to create Norwood could be hired instead. Also around this time, Emily Blunt described Norwood as "really, really scary", and Sophie Turner, Toni Collette, Ralph Ineson, and Ariel Winter also expressed disapproval, while Lukas Gage, Odessa A'zion, and Trace Lysette joked about having supposedly worked with Norwood and finding her incompetent and unpleasant to work with, with Gage claiming that "She was a nightmare to work with!" and "She couldn't hit her mark and she was late!" and Lysette adding "She cut me in line at lunch one day and didn't even say excuse me. She won't get far." Jenelle Riley, Nicholas Alexander Chavez, and the American union SAG-AFTRA stated that they do not consider Norwood an actress. The Gersh Agency and WME both announced that they would not sign Norwood. Whoopi Goldberg and Charlie Fink expressed scepticism that AI could replace jobs. Esquire UK reported that a post on Deadline's Instagram account about Norwood also sparked "varying levels of disgust and outrage" in its comments section from Adelaide Kane, Eiza González, Katie Cassidy, Jewel Staite, Lucy Hale, Stephen Sean Ford, and others, singling out González's comment, saying "Shame on whoever is trying to normalize this. Horrific and terrifying." Actor Bronson Pinchot expressed concern that Norwood could take his job. The British union Equity and the Canadian union ACTRA also condemned Norwood. Following this criticism, Van der Velden released a statement claiming Norwood was "not a replacement for a human being, but a creative work." She also denied that a £120,000 grant from the British Film Institute to fund Particle6 had been used to create Norwood, stating that Norwood had been a self-funded project solely for Xicoia. In late October, businessman Kevin O'Leary, while advocating for the use of AI to replace background actors, stated that they could be replaced with "100 Norwell Tillies" without being able to tell the difference. Ryan Reynolds and a real woman named Natalie "Tilly" Norwood also starred in an advertisement for Mint Mobile's internet service provider Minternet that mocked the character of Norwood. In November 2025, Van der Velden stated in an interview with Deadline that she planned to create 40 further "very diverse" characters alongside Norwood in order to expand the character's "whole universe". Also that month, actress Jameela Jamil criticized the idea of Norwood as "deeply disturbing" for being "a teenage-looking girl who can't say no to a type of sex scene" or "advocate for herself". Van der Velden announced later that month that Particle6 would be producing the History Channel's Streets of the Past, a Dutch documentary series which would be hosted by reality television personality Corjan Mol and would use AI to recreate historical scenes. In March 2026, a music video titled "Take The Lead" featuring Norwood was released on YouTube. It addressed the backlash of Norwood's creation by opening with the lyrics: "When they talk about me, they don't see/ The human spark, the creativity," and, "I'm just a tool, but I've got life." It also featured a disclaimer that says: "made by 18 real humans — from production designers to costume designers to prompters, editors and an actor." The vocals were generated by Suno. == Commentary == Charles Pulliam-Moore of The Verge argued that Norwood's introduction was a stunt to normalize "AI actors" despite Norwood essentially being a digital puppet. Straight Arrow News compared Tilly Norwood to Aki Ross, a CGI character from 2001 that was similarly intended to become a "digital star" and appear in multiple films, while Nicholas Schrivens, writing for The Conversation, likened Norwood to the posthumous use of footage of Carrie Fisher as Princess Leia for Star Wars: The Rise of Skywalker in 2019 and the Los Angeles Times likened Norwood to Hatsune Miku. Scrivens also wrote that "no AI creation has achieved the media cut-through that Tilly has". Moises Mendez II of Out dismissed this as "vapid bullshit", writing, "Nobody wants AI actresses." Scottish actress Briony Monroe alleged that Norwood had been modeled after her likeness and mannerisms, and stated that she was consulting Equity regarding the matter. Musician Stella Hennen said in a viral TikTok video, which was uploaded in October 2025 and featured a side-by-side comparison between herself and Norwood, that Norwood was her "doppleganger". On April 14, 2026, Marie Claire published an article titled "Is Tilly Norwood the Most Dangerous 'Actress' in Hollywood?", though it noted that AI-generated characters are "still not very good at, well, acting," "audiences have not been kind to AI-led productions," and "Norwood's 'performances' have already faced negative reviews as well". The University of Southern California's Entertainment Technology Center's AI media director Yves Bergquist dismissed th
Computer Law & Security Review
The Computer Law & Security Review is an international peer-reviewed journal published by Elsevier. It has been published six times a year since 1985 and is indexed in Scopus and SSCI. It is accessible to a wide range of professional legal and IT practitioners, businesses, academics, researchers, libraries and organisations in both the public and private sectors. The journal regularly covers: CLSR Briefing with special emphasis on UK/US developments European Union update National news from 10 European jurisdictions Pacific rim news column Refereed practitioner and academic papers on topics such as Web 2.0, IT security, Identity management, ID cards, RFID, interference with privacy, Internet law, telecoms regulation, online broadcasting, intellectual property, software law, e-commerce, outsourcing, data protection and freedom of information and many other topics. The Journal's Correspondent Panel includes more than 40 specialists in IT law and security. Each issue contains articles, case law analysis and current news on information and communications technology. Special Features High quality peer reviewed papers from internationally renowned practitioner and academic experts Latest developments reported in situ by more than 20 leading law firms from around the world Highly experienced and respected editor and correspondents panel Online access to all 23 volumes of CLSR with embedded web links to primary sources Contact details of all authors A pool of expertise that can collectively identify the key topics that need to be examined.
Tensor network
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties. The wave function is encoded as a tensor contraction of a network of individual tensors. The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network. This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems. == Diagrammatic notation == In general, a tensor network diagram (Penrose diagram) can be viewed as a graph where nodes (or vertices) represent individual tensors, while edges represent summation over an index. Free indices are depicted as edges (or legs) attached to a single vertex only. Sometimes, there is also additional meaning to a node's shape. For instance, one can use trapezoids for unitary matrices or tensors with similar behaviour. This way, flipped trapezoids would be interpreted as complex conjugates to them. == History == Foundational research on tensor networks began in 1971 with a paper by Roger Penrose. In "Applications of negative dimensional tensors" Penrose developed tensor diagram notation, describing how the diagrammatic language of tensor networks could be used in applications in physics. In 1992, Steven R. White developed the density matrix renormalization group (DMRG) for quantum lattice systems. The DMRG was the first successful tensor network and associated algorithm. In 2002, Guifré Vidal and Reinhard Werner attempted to quantify entanglement, laying the groundwork for quantum resource theories. This was also the first description of the use of tensor networks as mathematical tools for describing quantum systems. In 2004, Frank Verstraete and Ignacio Cirac developed the theory of matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems. In 2006, Vidal developed the multi-scale entanglement renormalization ansatz (MERA). In 2007 he developed entanglement renormalization for quantum lattice systems. In 2010, Ulrich Schollwock developed the density-matrix renormalization group for the simulation of one-dimensional strongly correlated quantum lattice systems. In 2014, Román Orús introduced tensor networks for complex quantum systems and machine learning, as well as tensor network theories of symmetries, fermions, entanglement and holography. == Connection to machine learning == Tensor networks have been adapted for supervised learning, taking advantage of similar mathematical structure in variational studies in quantum mechanics and large-scale machine learning. This crossover has spurred collaboration between researchers in artificial intelligence and quantum information science. In June 2019, Google, the Perimeter Institute for Theoretical Physics, and X (company), released TensorNetwork, an open-source library for efficient tensor calculations. The main interest in tensor networks and their study from the perspective of machine learning is to reduce the number of trainable parameters (in a layer) by approximating a high-order tensor with a network of lower-order ones. Using the so-called tensor train technique (TT), one can reduce an N-order tensor (containing exponentially many trainable parameters) to a chain of N tensors of order 2 or 3, which gives us a polynomial number of parameters.