A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to update its internal values. From a historical perspective, the first fuzzy relation was mentioned in the year 1971 by Lotfi A. Zadeh. A practical approach to describe a fuzzy relation is based on a 2d table. At first, a table is created which consists of fuzzy values from 0..1. The next step is to apply the if-then-rules to the values. The resulting numbers are stored in the table as an array. Fuzzy relations can be utilized in fuzzy databases.
Example-based machine translation
Example-based machine translation (EBMT) is a method of machine translation often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base at run-time. It is essentially a translation by analogy and can be viewed as an implementation of a case-based reasoning approach to machine learning. == Translation by analogy == At the foundation of example-based machine translation is the idea of translation by analogy. When applied to the process of human translation, the idea that translation takes place by analogy is a rejection of the idea that people translate sentences by doing deep linguistic analysis. Instead, it is founded on the belief that people translate by first decomposing a sentence into certain phrases, then by translating these phrases, and finally by properly composing these fragments into one long sentence. Phrasal translations are translated by analogy to previous translations. The principle of translation by analogy is encoded to example-based machine translation through the example translations that are used to train such a system. Other approaches to machine translation, including statistical machine translation, also use bilingual corpora to learn the process of translation. == History == Example-based machine translation was first suggested by Makoto Nagao in 1984. He pointed out that it is especially adapted to translation between two totally different languages, such as English and Japanese. In this case, one sentence can be translated into several well-structured sentences in another language, therefore, it is no use to do the deep linguistic analysis characteristic of rule-based machine translation. == Example == Example-based machine translation systems are trained from bilingual parallel corpora containing sentence pairs like the example shown in the table above. Sentence pairs contain sentences in one language with their translations into another. The particular example shows an example of a minimal pair, meaning that the sentences vary by just one element. These sentences make it simple to learn translations of portions of a sentence. For example, an example-based machine translation system would learn three units of translation from the above example: How much is that X ? corresponds to Ano X wa ikura desu ka. red umbrella corresponds to akai kasa small camera corresponds to chiisai kamera Composing these units can be used to produce novel translations in the future. For example, if we have been trained using some text containing the sentences: President Kennedy was shot dead during the parade. and The convict escaped on July 15th., then we could translate the sentence The convict was shot dead during the parade. by substituting the appropriate parts of the sentences. == Phrasal verbs == Example-based machine translation is best suited for sub-language phenomena like phrasal verbs. Phrasal verbs have highly context-dependent meanings. They are common in English, where they comprise a verb followed by an adverb and/or a preposition, which are called the particle to the verb. Phrasal verbs produce specialized context-specific meanings that may not be derived from the meaning of the constituents. There is almost always an ambiguity during word-to-word translation from source to the target language. As an example, consider the phrasal verb "put on" and its Hindustani translation. It may be used in any of the following ways: Ram put on the lights. (Switched on) (Hindustani translation: Jalana) Ram put on a cap. (Wear) (Hindustani translation: Pahenna)
Texas Senate Bill 20
Texas Senate Bill 20 (S.B. 20), also known as the "Stopping AI-Generated Child Pornography Act", is a 2025 law in the state of Texas that creates new criminal offenses for those who possess, promote, or view visual material deemed obscene, which is said to depict a child, whether it is an actual person, animated or cartoon depiction, or an image of someone created through computer software or artificial intelligence. It was passed by the Texas Legislature on May 28, 2025, unanimously in both chambers. It was signed into law by Governor Greg Abbott on June 20, 2025. It went into effect on September 1, 2025. It was authored by Pete Flores and co-sponsored by Brent Hagenbuch, Juan Hinojosa, Joan Huffman, Phil King, and Tan Parker, as part of a package of legislation in the Texas House and Senate about A.I. and child pornography. Some supporters called it "common-sense" legislation falling within the "proper role" of government, protecting children and the "common good" within the state, with Heidi Ruiz, a police sergeant in Houston, describing the bill as "fantastic" and "fabulous." The bill drew comparisons to language, within Texas state legislation, which aimed to institute state-level book bans. Critics described the law as unconstitutional, saying it violated the Free Speech Clause of the First Amendment which prohibits abridgement of freedom of speech and the press, including the legal precedent set in Ashcroft v. Free Speech Coalition. The Comic Book Legal Defense Fund vowed to support those wrongly accused under the law. Much of the controversy regarding S.B. 20 involves the broad language pertaining to "obscene" pornographic images as including A.I.-created, animated, and cartoon depictions, with some critics arguing it could have a chilling effect on anime, manga, graphic novels, and other media produced, distributed, or created within Texas. == Provisions == S.B. 20 gives Texas police more provisions to restrict artificial intelligence-created child pornography, creating new criminal charge for possessing material depicting an underage person, under age 18, whether this child is an actual person or not. Those charged with this felony offense could go to state jail, but this could be elevated if the person charged has a prior conviction, of a $10,000 fine and two years in prison. == Reactions == === Support === Lieutenant Governor Dan Patrick applauded the unanimous passage of the law in the Texas Senate and called it "a priority" to protect children in Texas, and Texas citizens and thanked Pete Flores for his work on "this important issue". He later described the bill as part of the "bold, conservative agenda" that the Texas legislature passed during the 2025 legislative session. Phil King, one of the bill's co-sponsors, said that issue of child pornography had "infiltrated" the state's schools and said he was proud that the Texas legislature had "taken decisive action to protect our vulnerable Texans". Another co-sponsor of the legislation, Tan Parker described the law as "decisive action" to protect the children within Texas, and said he looked "forward to advancing this critical legislation" onward from the Texas Senate Criminal Justice Committee. He also described the legislation as "critical" action to protect the state's children from A.I.-generated child pornography and an "effective tool for law enforcement" to crack down on child porn perpetrators. Other supporters, such as police, and prosecutors, called the legislation an "important step" to ensure that images generated with A.I., along with deepfakes, "can't be shared with impunity" and necessary to ensure children's protection. Flores told senators that technology which enabled the production of "offensive" material by child predators had "no redeeming value whatsoever" and asserted that the materials had often been "used to groom and abuse children". John Leigh, a co-founder of Anime Matsuri, one of the largest conventions for anime within Texas, reassured those who contacted him, saying that the law is not targeted at anime and manga fans, stated that he supported the legislation, describing it as a step "in the right direction," and said that he did not believe it would "negatively impact" anime or related art in the state. Also, State Representative Dade Phelan emphasized the legislation's urgency to deal with A.I. and child pornography, adding that they need to "put some guardrails on it to where the public is being taken care of". The Texas Policy Research Foundation supported the legislation, saying that although it may lead to increased demands on state and local governmental resources, higher costs for local governments, and possible "civil liberty concerns" around online censorship, it represents a "necessary legal update" to address exploitation of children online, while "modernizing enforcement mechanisms" and recommended that lawmakers vote in favor of the law. Additionally, the group Texans for Fiscal Responsibility supported the law, arguing that it strengthened state law, upheld public safety, protected minors, and called it a "common-sense bill" protecting and promoting the "common good", children, and fell within the "proper role" of government. The Texas Public Policy Foundation also expressed their support for the law. A policy director for aforementioned conservative think tank, Zach Whiting, told the Texas Senate Committee on Criminal Justice, on March 4, 2025, that the foundation would assist legislators ans staff to "advance any and all measures to protect kids online" and shared an excerpt from of research paper about threats posed by A.I. in creating "sexually explicit deepfakes of children". === Opposition === Although the bill passed both chambers unanimously, there were some reports that the bill stalled due to opposition from Democratic lawmakers. Additionally, some individuals expressed concerns about the broad nature of the law's provisions. Anime Matsuri co-founder Deneice Leigh called for the law's wording to be clarified because "artists are anxious about displaying or selling fan art" even if the intention is "not be to penalize creators". She also described the bill as "vague and open to interpretation" as to what would be considered obscene and offensive while noting that the bill is not aiming to "target artists". Benjamin Napier, owner of Mansfield Comics and Manga in Mansfield, Texas, said that at first he felt the law was "ridiculous" and "kind of frivolous" at first, part of a "misguided puritanical onslaught", and noted that he would not cow "to the puritanical regime" if it was enacted. Kirsten Cather, an Asian Studies scholar at University of Texas, expressed concern at the law's misinterpretation because "many anime characters appear youthful, regardless of their actual age", said that the law could "stifle creative expression", and noted that the law's scope is broad enough to have manga and anime under scrutiny, a "real slippery slope here that's being breached". Marcel Green of Screen Rant said that the law's ambiguity led to concerns from manga and anime fans, and theorized that the law's application to a fan within Texas, who downloaded the 368th chapter of My Hero Academia, which has a "sexualized depiction" of an "underage high school student", would result in a criminal offense of "180 days to two years in state jail, along with a fine of up to $10,000". Green also said the law is problematic because many anime and manga characters are young, with many protagonists as minors and argued that the law could apply in limited cases, if state officials deemed an anime or manga under scrutiny as lacking "artistic value". Evan D. Mullicane, on the same site, said the vague wording of the legislation made it "dangerous" for anime such as Dragon Ball and Naruto, and could impact more than hentai, predicting it will be used against more than its "intended target" and be used to censor stories with "young LGBTQIA characters". Another critic on the same site, Carlyle Edmundson, called for anime fans to step up and prevent the law's enactment "for the good of artists and fans everywhere", saying that the legislation was "draconian" and claimed it was the most extreme case of anime and manga censorship in U.S. history. Nick Valdez of ComicBook.com said that the legislation could lead to censorship of "many anime and manga projects," like Kill la Kill and The 100 Girlfriends Who Really, Really, Really, Really, Really Love You, becoming a crime, and said that even if the law is enforced in a case-by-case basis, it could lead to a "much larger ban of materials in the state" itself due to the content of certain manga and anime. Vanessa Esguerra of The Mary Sue argued that possession of manga like Berserk and Vagabond, or viewing Dandadan, could be deemed illegal under the law, due to various parts of each of these media, and asserted that viewing and owning certain anime and other media, falling under the law's provisions,
AlphaEvolve
AlphaEvolve is an evolutionary coding agent for designing advanced algorithms based on large language models such as Gemini. It was developed by Google DeepMind and unveiled in May 2025. == Design == AlphaEvolve aims to autonomously discover and refine algorithms through a combination of large language models (LLMs) and evolutionary computation. AlphaEvolve needs an evaluation function with metrics to optimize, and an initial algorithm. At each step, AlphaEvolve uses the LLM to produce variants of the existing algorithms, and then selects the most effective ones. Unlike domain-specific predecessors like AlphaFold or AlphaTensor, AlphaEvolve is designed as a general-purpose system. It can operate across a wide array of scientific and engineering tasks by automatically modifying code and optimizing for multiple objectives. Its architecture allows it to evaluate code programmatically, reducing reliance on human input and mitigating risks such as hallucinations common in standard LLM outputs. == Achievements == According to Google, across a selection of 50 open mathematical problems, the model was able to rediscover state-of-the-art solutions 75% of the time and discovered improved solutions 20% of the time, for example advancing the kissing number problem. AlphaEvolve was also used to optimize Google's computing ecosystem. Improved data center scheduling heuristics, enabled the recovery of 0.7% of stranded resources. It was also used to optimize TPU circuit design and Gemini's training matrix multiplication kernel. == Open source implementations == Following the publication of AlphaEvolve, several open source implementations have been developed by the research community. One such implementation is OpenEvolve, which implements distributed evolutionary algorithms, multi-language support, integration with various large language model providers, and automated discovery of high-performance GPU kernels that outperform expert-engineered baselines.
Tractable (company)
Tractable is a technology company specializing in the development of Artificial Intelligence (AI) to assess damage to property and vehicles. The AI allows users to appraise damage digitally. == Technology == Tractable's technology uses computer vision and deep learning to automate the appraisal of visual damage in accident and disaster recovery, for example to a vehicle. Drivers can be directed to use the application by their insurer after an accident, with the aim of settling their claim more quickly. The AI evaluates the damage from images, and therefore doesn't assess what isn't visible (such as, for example, interior damage to a vehicle or property). == History == Alexandre Dalyac and Razvan Ranca founded Tractable in 2014, and Adrien Cohen joined as co-founder in 2015. The company employs more than 300 staff members, largely in the United Kingdom. Tractable was named one of the 100 leading AI companies in the world in 2020 and 2021 by CB Insights. It won the Best Technology Award in the 2020 British Insurance Awards. In June 2021, Tractable announced a venture round that valued the company at $1 billion. Tractable was the UK's 100th billion-dollar tech company, or unicorn. In July 2023, the company received a $65 million investment from SoftBank Group, through its Vision Fund 2.
Compute (machine learning)
In machine learning and deep learning, compute is the amount of computing power or computational resources required to train machine learning models and large language models. More broadly, compute is the computational power or resources necessary for a computer or computer program to function. == Definition == Compute is commonly defined as the amount of computing power or computational resources required to train machine learning and large language models. The term "compute" has also been more broadly applied to cloud computing, referencing processing power, memory, networking, storage, and other resources required for the computation of any program. Compute is measured in petaflop/s-days and is used to document AI training. A petaflop/s-day (pfs-day) consists of performing 1015 neural net operations per second for one day, or a total of about 1020 operations. The compute-time product serves as a mental convenience, similar to kilowatt-hour for energy. An amount of compute is meant to give an idea of the number of actual operations performed. == History == In a 2018 analysis titled "AI and compute", artificial intelligence company OpenAI introduced the concept of compute. OpenAI identified two eras of training AI systems in terms of compute-usage. From 1959 to 2012, compute roughly followed Moore’s law. Between 2012 and 2018, the amount of compute used in the largest AI training runs increased exponentially, growing by more than 300,000 times — roughly doubling every 3.4 months. By comparison, Moore’s Law doubled every two years over the same period. One of the largest models, released in 2020, used 600,000 times more computing power than the 2012 model. After 2020, compute growth began to slow down, with the compute needed for the largest AI models continuing to slow down in 2023. The notion of compute has become increasingly used from the mid-2020s onwards. == Compute growth and AI progress == Larger AI models trained on more data and using more computational resources, tend to perform better. This happens even if the algorithms themselves remain unchanged. As early as 2018, OpenAI noted the exponential increase in compute to be have a key role in AI progress. OpenAI considers three factors drive the advance of AI: algorithmic innovation, data, and the amount of compute available for training. AI models with more compute not only improve in the tasks they were trained on but can develop emergent abilities. Incremental improvements can lead to more abrupt leaps in capabilities. AI provider SpaceXAI said in 2026 that their AI progress is driven by compute and used it a key metric in the AI training of its supercomputer Colossus, the which contains 1 million GPUs. Anthropic has a contract of $1.25 billion per month with SpaceXAI to buy all the compute capacity at Colossus 1 data center. === Criticism and policy === Increasing, promoting or constraining progress in artificial intelligence has often be done via controlling the amount of compute. Policymarkers have enacted policies and provided support to make compute resources more accessible to domestic AI researchers. In a January 2022 report, the Center for Security and Emerging Technology (CSET) suggested to institutions that increasingly powerful and generalizable AI (AGI) will likely require other strategies than maximizing compute. Some AI researchers are also concerned that government might exclusively focus on scaling compute instead of other strategies. The CSET has reported on the various bottlenecks which could explain why deep learning needs for compute have slow down: training is expensive and training extremely large models generates traffic jams across many processors that are difficult to manage. there is a limited supply of AI chips (see AI chip memory shortage). CSET advances that the main resource is human capital, specifically talented researchers — according to a 2023 published survey of more than 400 AI researchers, academic and private sector workers. The survey found that AI researchers are not primarily or exclusively constrained by compute access. However, both academic and industry AI researchers equally report concerns that insufficient compute could prevent them from contributing meaningfully to AI research in the future. High compute users are more concerned about compute access. When asked about which resource provided by the government would be the most useful to them, some AI researchers select compute, other prefer grant funding. For this goal, CSET advised policymakers to ensure that even researchers with smaller budgets could effectively contribute to AI research. Other proposed strategies include using contemporary AI algorithms, managing modern AI infrastructure or focusing on interdisciplinary work between the AI field and other fields of computer science. A 2024 study on compute access found that academic-only AI research teams often have less compute intensive research topics, especially foundation models, compared to industry AI labs. As a consequence, academia is likely to play a smaller role in advancing such techniques. The researchers suggest nationally-sponsored computing infrastructure as well as open science initiatives to boost academic compute access. === Data === A 2022 study found that current large language models are significantly under-trained, a consequence of focusing on scaling language models whilst keeping the amount of training data constant. By training over 400 language models of various parameter and token size, they found that "for compute-optimal training", the model size and the number of training tokens should ideally be scaled equally: for every doubling of model size the number of training tokens should also be doubled.
Norm (artificial intelligence)
Norms can be considered from different perspectives in artificial intelligence to create computers and computer software that are capable of intelligent behaviour. In artificial intelligence and law, legal norms are considered in computational tools to automatically reason upon them. In multi-agent systems (MAS), a branch of artificial intelligence (AI), a norm is a guide for the common conduct of agents, thereby easing their decision-making, coordination and organization. Since most problems concerning regulation of the interaction of autonomous agents are linked to issues traditionally addressed by legal studies, and since law is the most pervasive and developed normative system, efforts to account for norms in artificial intelligence and law and in normative multi-agent systems often overlap. == Artificial intelligence and law == With the arrival of computer applications into the legal domain, and especially artificial intelligence applied to it, logic has been used as the major tool to formalize legal reasoning and has been developed in many directions, ranging from deontic logics to formal systems of argumentation. The knowledge base of legal reasoning systems usually includes legal norms (such as governmental regulations and contracts), and as a consequence, legal rules are the focus of knowledge representation and reasoning approaches to automatize and solve complex legal tasks. Legal norms are typically represented into a logic-based formalism, such as deontic logic. Artificial intelligence and law applications using an explicit representation of norms range from checking the compliance of business processes and the automatic execution of smart contracts to legal expert systems advising people on legal matters. == Multi-agent systems == Norms in multi-agent systems may appear with different degrees of explicitness ranging from fully unambiguous written prescriptions to implicit unwritten norms or tacit emerging patterns. Computer scientists’ studies mirror this polarity. Explicit norms are typically investigated in formal logics (e.g. deontic logics and argumentation) to represent and reason upon them, leading eventually to architecture for cognitive agents, while implicit norms are accounted as patterns emerging from repeated interactions amongst agents (typically reinforced learning agents). Explicit and implicit norms can be used together to coordinate agents. Explicit norms are typically represented as a deontic statement that aims at regulating the life of software agents and the interactions among them. It can be an obligation, a permission or a prohibition, and is often represented with some dialect or extension of Deontic logic. At the opposite, implicit norms are social norms that are not written, and they usually emerge from the repetitive interactions of agents.