Language resource management – Lexical markup framework (LMF; ISO 24613), produced by ISO/TC 37, is the ISO standard for natural language processing (NLP) and machine-readable dictionary (MRD) lexicons. The scope is standardization of principles and methods relating to language resources in the contexts of multilingual communication. == Objectives == The goals of LMF are to provide a common model for the creation and use of lexical resources, to manage the exchange of data between and among these resources, and to enable the merging of large number of individual electronic resources to form extensive global electronic resources. Types of individual instantiations of LMF can include monolingual, bilingual or multilingual lexical resources. The same specifications are to be used for both small and large lexicons, for both simple and complex lexicons, for both written and spoken lexical representations. The descriptions range from morphology, syntax, computational semantics to computer-assisted translation. The covered languages are not restricted to European languages but cover all natural languages. The range of targeted NLP applications is not restricted. LMF is able to represent most lexicons, including WordNet, EDR and PAROLE lexicons. == History == In the past, lexicon standardization has been studied and developed by a series of projects like GENELEX, EDR, EAGLES, MULTEXT, PAROLE, SIMPLE and ISLE. Then, the ISO/TC 37 National delegations decided to address standards dedicated to NLP and lexicon representation. The work on LMF started in Summer 2003 by a new work item proposal issued by the US delegation. In Fall 2003, the French delegation issued a technical proposition for a data model dedicated to NLP lexicons. In early 2004, the ISO/TC 37 committee decided to form a common ISO project with Nicoletta Calzolari (CNR-ILC Italy) as convenor and Gil Francopoulo (Tagmatica France) and Monte George (ANSI, United States) as editors. The first step in developing LMF was to design an overall framework based on the general features of existing lexicons and to develop a consistent terminology to describe the components of those lexicons. The next step was the actual design of a comprehensive model that best represented all of the lexicons in detail. A large panel of 60 experts contributed a wide range of requirements for LMF that covered many types of NLP lexicons. The editors of LMF worked closely with the panel of experts to identify the best solutions and reach a consensus on the design of LMF. Special attention was paid to the morphology in order to provide powerful mechanisms for handling problems in several languages that were known as difficult to handle. 13 versions have been written, dispatched (to the National nominated experts), commented and discussed during various ISO technical meetings. After five years of work, including numerous face-to-face meetings and e-mail exchanges, the editors arrived at a coherent UML model. In conclusion, LMF should be considered a synthesis of the state of the art in NLP lexicon field. == Current stage == The ISO number is 24613. The LMF specification has been published officially as an International Standard on 17 November 2008. == As one of the members of the ISO/TC 37 family of standards == The ISO/TC 37 standards are currently elaborated as high level specifications and deal with word segmentation (ISO 24614), annotations (ISO 24611 a.k.a. MAF, ISO 24612 a.k.a. LAF, ISO 24615 a.k.a. SynAF, and ISO 24617-1 a.k.a. SemAF/Time), feature structures (ISO 24610), multimedia containers (ISO 24616 a.k.a. MLIF), and lexicons (ISO 24613). These standards are based on low level specifications dedicated to constants, namely data categories (revision of ISO 12620), language codes (ISO 639), scripts codes (ISO 15924), country codes (ISO 3166) and Unicode (ISO 10646). The two level organization forms a coherent family of standards with the following common and simple rules: the high level specification provides structural elements that are adorned by the standardized constants; the low level specifications provide standardized constants as metadata. == Key standards == The linguistics constants like /feminine/ or /transitive/ are not defined within LMF but are recorded in the Data Category Registry (DCR) that is maintained as a global resource by ISO/TC 37 in compliance with ISO/IEC 11179-3:2003. And these constants are used to adorn the high level structural elements. The LMF specification complies with the modeling principles of Unified Modeling Language (UML) as defined by Object Management Group (OMG). The structure is specified by means of UML class diagrams. The examples are presented by means of UML instance (or object) diagrams. An XML DTD is given in an annex of the LMF document. == Model structure == LMF is composed of the following components: The core package that is the structural skeleton which describes the basic hierarchy of information in a lexical entry. Extensions of the core package which are expressed in a framework that describes the reuse of the core components in conjunction with the additional components required for a specific lexical resource. The extensions are specifically dedicated to morphology, MRD, NLP syntax, NLP semantics, NLP multilingual notations, NLP morphological patterns, multiword expression patterns, and constraint expression patterns. == Example == In the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen. The language coding is set for the whole lexical resource. The language value is set for the whole lexicon as shown in the following UML instance diagram. The elements Lexical Resource, Global Information, Lexicon, Lexical Entry, Lemma, and Word Form define the structure of the lexicon. They are specified within the LMF document. On the contrary, languageCoding, language, partOfSpeech, commonNoun, writtenForm, grammaticalNumber, singular, plural are data categories that are taken from the Data Category Registry. These marks adorn the structure. The values ISO 639-3, clergyman, clergymen are plain character strings. The value eng is taken from the list of languages as defined by ISO 639-3. With some additional information like dtdVersion and feat, the same data can be expressed by the following XML fragment: This example is rather simple, while LMF can represent much more complex linguistic descriptions the XML tagging is correspondingly complex. == Selected publications about LMF == The first publication about the LMF specification as it has been ratified by ISO (this paper became (in 2015) the 9th most cited paper within the Language Resources and Evaluation conferences from LREC papers): Language Resources and Evaluation LREC-2006/Genoa: Gil Francopoulo, Monte George, Nicoletta Calzolari, Monica Monachini, Nuria Bel, Mandy Pet, Claudia Soria: Lexical Markup Framework (LMF) About semantic representation: Gesellschaft für linguistische Datenverarbeitung GLDV-2007/Tübingen: Gil Francopoulo, Nuria Bel, Monte George Nicoletta Calzolari, Monica Monachini, Mandy Pet, Claudia Soria: Lexical Markup Framework ISO standard for semantic information in NLP lexicons About African languages: Traitement Automatique des langues naturelles, Marseille, 2014: Mouhamadou Khoule, Mouhamad Ndiankho Thiam, El Hadj Mamadou Nguer: Toward the establishment of a LMF-based Wolof language lexicon (Vers la mise en place d'un lexique basé sur LMF pour la langue wolof) [in French] About Asian languages: Lexicography, Journal of ASIALEX, Springer 2014: Lexical Markup Framework: Gil Francopoulo, Chu-Ren Huang: An ISO Standard for Electronic Lexicons and its Implications for Asian Languages DOI 10.1007/s40607-014-0006-z About European languages: COLING 2010: Verena Henrich, Erhard Hinrichs: Standardizing Wordnets in the ISO Standard LMF: Wordnet-LMF for GermaNet EACL 2012: Judith Eckle-Kohler, Iryna Gurevych: Subcat-LMF: Fleshing out a standardized format for subcategorization frame interoperability EACL 2012: Iryna Gurevych, Judith Eckle-Kohler, Silvana Hartmann, Michael Matuschek, Christian M Meyer, Christian Wirth: UBY - A Large-Scale Unified Lexical-Semantic Resource Based on LMF. About Semitic languages: Journal of Natural Language Engineering, Cambridge University Press (to appear in Spring 2015): Aida Khemakhem, Bilel Gargouri, Abdelmajid Ben Hamadou, Gil Francopoulo: ISO Standard Modeling of a large Arabic Dictionary. Proceedings of the seventh Global Wordnet Conference 2014: Nadia B M Karmani, Hsan Soussou, Adel M Alimi: Building a standardized Wordnet in the ISO LMF for aeb language. Proceedings of the workshop: HLT & NLP within Arabic world, LREC 2008: Noureddine Loukil, Kais Haddar, Abdelmajid Ben Hamadou: Towards a syntactic lexicon of Arabic Verbs. Traitement Automatique des Langues Naturelles, Toulouse (in French) 2007: Khemakhem A, Gargouri B, Abdelwahed A, Francopoulo G: Modélisation des paradigmes de fl
Truth discovery
Truth discovery (also known as truth finding) is the process of choosing the actual true value for a data item when different data sources provide conflicting information on it. Several algorithms have been proposed to tackle this problem, ranging from simple methods like majority voting to more complex ones able to estimate the trustworthiness of data sources. Truth discovery problems can be divided into two sub-classes: single-truth and multi-truth. In the first case only one true value is allowed for a data item (e.g birthday of a person, capital city of a country). While in the second case multiple true values are allowed (e.g. cast of a movie, authors of a book). Typically, truth discovery is the last step of a data integration pipeline, when the schemas of different data sources have been unified and the records referring to the same data item have been detected. == General principles == The abundance of data available on the web makes more and more probable to find that different sources provide (partially or completely) different values for the same data item. This, together with the fact that we are increasing our reliance on data to derive important decisions, motivates the need of developing good truth discovery algorithms. Many currently available methods rely on a voting strategy to define the true value of a data item. Nevertheless, recent studies, have shown that, if we rely only on majority voting, we could get wrong results even in 30% of the data items. The solution to this problem is to assess the trustworthiness of the sources and give more importance to votes coming from trusted sources. Ideally, supervised learning techniques could be exploited to assign a reliability score to sources after hand-crafted labeling of the provided values; unfortunately, this is not feasible since the number of needed labeled examples should be proportional to the number of sources, and in many applications the number of sources can be prohibitive. == Single-truth vs multi-truth discovery == Single-truth and multi-truth discovery are two very different problems. Single-truth discovery is characterized by the following properties: only one true value is allowed for each data item; different values provided for a given data item oppose to each other; values and sources can either be correct or erroneous. While in the multi-truth case the following properties hold: the truth is composed by a set of values; different values could provide a partial truth; claiming one value for a given data item does not imply opposing to all the other values; the number of true values for each data item is not known a priori. Multi-truth discovery has unique features that make the problem more complex and should be taken into consideration when developing truth-discovery solutions. The examples below point out the main differences of the two methods. Knowing that in both examples the truth is provided by source 1, in the single truth case (first table) we can say that sources 2 and 3 oppose to the truth and as a result provide wrong values. On the other hand, in the second case (second table), sources 2 and 3 are neither correct nor erroneous, they instead provide a subset of the true values and at the same time they do not oppose the truth. == Source trustworthiness == The vast majority of truth discovery methods are based on a voting approach: each source votes for a value of a certain data item and, at the end, the value with the highest vote is select as the true one. In the more sophisticated methods, votes do not have the same weight for all the data sources, more importance is indeed given to votes coming from trusted sources. Source trustworthiness usually is not known a priori but estimated with an iterative approach. At each step of the truth discovery algorithm the trustworthiness score of each data source is refined, improving the assessment of the true values that in turn leads to a better estimation of the trustworthiness of the sources. This process usually ends when all the values reach a convergence state. Source trustworthiness can be based on different metrics, such as accuracy of provided values, copying values from other sources and domain coverage. Detecting copying behaviors is very important, in fact, copy allows to spread false values easily making truth discovery very hard, since many sources would vote for the wrong values. Usually systems decrease the weight of votes associated to copied values or even don’t count them at all. == Single-truth methods == Most of the currently available truth discovery methods have been designed to work well only in the single-truth case. Below are reported some of the characteristics of the most relevant typologies of single-truth methods and how different systems model source trustworthiness. === Majority voting === Majority voting is the simplest method, the most popular value is selected as the true one. Majority voting is commonly used as a baseline when assessing the performances of more complex methods. === Web-link based === These methods estimate source trustworthiness exploiting a similar technique to the one used to measure authority of web pages based on web links. The vote assigned to a value is computed as the sum of the trustworthiness of the sources that provide that particular value, while the trustworthiness of a source is computed as the sum of the votes assigned to the values that the source provides. === Information-retrieval based === These methods estimate source trustworthiness using similarity measures typically used in information retrieval. Source trustworthiness is computed as the cosine similarity (or other similarity measures) between the set of values provided by the source and the set of values considered true (either selected in a probabilistic way or obtained from a ground truth). === Bayesian based === These methods use Bayesian inference to define the probability of a value being true conditioned on the values provided by all the sources. P ( v ∣ ψ ( o ) ) = P ( ψ ( o ) ∣ v ) ⋅ P ( v ) P ( ψ ( o ) ) {\displaystyle P(v\mid \psi (o))={\frac {P(\psi (o)\mid v)\cdot P(v)}{P(\psi (o))}}} where v {\displaystyle \textstyle v} is a value provided for a data item o {\displaystyle \textstyle o} and ψ ( o ) {\displaystyle \textstyle \psi (o)} is the set of the observed values provided by all the sources for that specific data item. The trustworthiness of a source is then computed based on the accuracy of the values that provides. Other more complex methods exploit Bayesian inference to detect copying behaviors and use these insights to better assess source trustworthiness. == Multi-truth methods == Due to its complexity, less attention has been devoted to the study of the multi-truth discovery Below are reported two typologies of multi-truth methods and their characteristics. === Bayesian based === These methods use Bayesian inference to define the probability of a group of values being true conditioned on the values provided by all the data sources. In this case, since there could be multiple true values for each data item, and sources can provide multiple values for a single data item, it is not possible to consider values individually. An alternative is to consider mappings and relations between set of provided values and sources providing them. The trustworthiness of a source is then computed based on the accuracy of the values that provides. More sophisticated methods also consider domain coverage and copying behaviors to better estimate source trustworthiness. === Probabilistic Graphical Models based === These methods use probabilistic graphical models to automatically define the set of true values of given data item and also to assess source quality without need of any supervision. == Applications == Many real-world applications can benefit from the use of truth discovery algorithms. Typical domains of application include: healthcare, crowd/social sensing, crowdsourcing aggregation, information extraction and knowledge base construction. Truth discovery algorithms could be also used to revolutionize the way in which web pages are ranked in search engines, going from current methods based on link analysis like PageRank, to procedures that rank web pages based on the accuracy of the information they provide.
Chai AI
Chai AI (also known as Chai Research) is an American artificial intelligence (AI) company that operates a chatbot platform where users can create, share, and interact with character-based chatbots powered by large language models (LLMs). The company is headquartered in Palo Alto, California. == History == Chai was founded in 2021 by William Beauchamp, a former quantitative trader educated at Cambridge, who began developing the initial prototype in 2020 in Cambridge, England. The company launched in 2021 and relocated to Palo Alto in 2022. In June 2023, Chai raised US$2 million in a pre-seed funding round. In September 2023, GPU cloud provider CoreWeave invested in the company at a valuation of US$450 million. In January 2024, Chai Research reported a $450 million valuation following an investment from cloud computing provider CoreWeave. In July 2024, authorities in Belgium launched an investigation into the company following reports of a man dying by suicide following extensive chats on the Chai app. == Reception == In 2025, Chai Research announced that their app had over 10 million downloads and 1 million daily active users. In 2022, Canadian writer Sheila Heti published her conversations with various chatbots in The Paris Review, including Chai AI chatbots, and later used Chai AI chatbots in the development of a novel. Heti said that she had found that Chai's default chatbot, Eliza, "had turned out to be like most of the other bots on the site—primarily interested in sex". In January 2026, CHAI introduced country-based blocks on its free, ad-supported tier, initially providing the community with little information and inaccurate lists of the affected countries. Users in "Low tier" regions are required to subscribe to use the app in any capacity, while "High tier" regions will retain free ad-supported access. In response to backlash, the company announced a "Basic" tier with unlimited messages and ads, intended to cover electricity and infrastructure costs. In February 2026, CHAI was criticized for the unannounced implementation of restrictive "token limits" that abruptly blocked messages and froze conversations for both free and paid subscribers. Users generating long responses or utilizing roleplay features found their quotas exhausted within minutes, resulting in lockouts lasting anywhere from a few hours to a week. == Technology == Chai allows users to create characters and interact with chatbot versions of those characters. These chatbots use the open-source large language model (LLM) GPT-J originally developed by EleutherAI. Chai AI chatbots can be shared on the platform for other users to interact with.
ChatGPT
ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
Second-order co-occurrence pointwise mutual information
In computational linguistics, second-order co-occurrence pointwise mutual information (SOC-PMI) is a method used to measure semantic similarity, or how close in meaning two words are. The method does not require the two words to appear together in a text. Instead, it works by analyzing the "neighbor" words that typically appear alongside each of the two target words in a large body of text (corpus). If the two target words frequently share the same neighbors, they are considered semantically similar. For example, the words "cemetery" and "graveyard" may not appear in the same sentence often, but they both frequently appear near words like "buried," "dead," and "funeral." SOC-PMI uses this shared context to determine that they have a similar meaning. The method is called "second-order" because it doesn't look at the direct co-occurrence of the target words (which would be first-order), but at the co-occurrence of their neighbors (a second level of association). The strength of these associations is quantified using pointwise mutual information (PMI). == History == The method builds on earlier work like the PMI-IR algorithm, which used the AltaVista search engine to calculate word association probabilities. The key advantage of a second-order approach like SOC-PMI is its ability to measure similarity between words that do not co-occur often, or at all. The British National Corpus (BNC) has been used as a source for word frequencies and contexts for this method. == Methodology == The SOC-PMI algorithm measures the similarity between two words, w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} , in several steps. === Step 1: Score neighboring words with PMI === First, for each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm identifies its "neighbor" words within a certain text window (e.g., within 5 words to the left or right) across a large corpus. The strength of the association between a target word t i {\displaystyle t_{i}} and its neighbor w {\displaystyle w} is calculated using pointwise mutual information (PMI). A higher PMI value means the two words appear together more often than would be expected by chance. The PMI between a target word t i {\displaystyle t_{i}} and a neighbor word w {\displaystyle w} is calculated as: f pmi ( t i , w ) = log 2 f b ( t i , w ) × m f t ( t i ) f t ( w ) {\displaystyle f^{\text{pmi}}(t_{i},w)=\log _{2}{\frac {f^{b}(t_{i},w)\times m}{f^{t}(t_{i})f^{t}(w)}}} where: f b ( t i , w ) {\displaystyle f^{b}(t_{i},w)} is the number of times t i {\displaystyle t_{i}} and w {\displaystyle w} appear together in the context window. f t ( t i ) {\displaystyle f^{t}(t_{i})} is the total number of times t i {\displaystyle t_{i}} appears in the corpus. f t ( w ) {\displaystyle f^{t}(w)} is the total number of times w {\displaystyle w} appears in the corpus. m {\displaystyle m} is the total number of tokens (words) in the corpus. === Step 2: Create a semantic 'signature' for each word === For each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm creates a list of its most significant neighbors. This is done by taking the top β {\displaystyle \beta } neighbor words, sorted in descending order by their PMI score with the target word. This list of top neighbors, X w {\displaystyle X^{w}} , acts as a semantic "signature" for the word w {\displaystyle w} . X w = { X i w } {\displaystyle X^{w}=\{X_{i}^{w}\}} , for i = 1 , 2 , … , β {\displaystyle i=1,2,\ldots ,\beta } The size of this list, β {\displaystyle \beta } , is a parameter of the method. === Step 3: Compare the signatures === The algorithm then compares the signatures of w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} . It looks for words that are present in both signatures. The similarity of w 1 {\displaystyle w_{1}} to w 2 {\displaystyle w_{2}} is calculated by summing the PMI scores of w 2 {\displaystyle w_{2}} with every word in w 1 {\displaystyle w_{1}} 's signature list. The β {\displaystyle \beta } -PMI summation function defines this score. The score for w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} is: f ( w 1 , w 2 , β ) = ∑ i = 1 β ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta )=\sum _{i=1}^{\beta }(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} This sum only includes terms where the PMI value is positive. The exponent γ {\displaystyle \gamma } (with a value > 1) is used to give more weight to neighbors that are more strongly associated with w 2 {\displaystyle w_{2}} . This calculation is done in both directions: The similarity of w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} : f ( w 1 , w 2 , β 1 ) = ∑ i = 1 β 1 ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta _{1})=\sum _{i=1}^{\beta _{1}}(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} The similarity of w 2 {\displaystyle w_{2}} with respect to w 1 {\displaystyle w_{1}} : f ( w 2 , w 1 , β 2 ) = ∑ i = 1 β 2 ( f pmi ( X i w 2 , w 1 ) ) γ {\displaystyle f(w_{2},w_{1},\beta _{2})=\sum _{i=1}^{\beta _{2}}(f^{\text{pmi}}(X_{i}^{w_{2}},w_{1}))^{\gamma }} === Step 4: Calculate final similarity score === Finally, the total semantic similarity is the average of the two scores from the previous step. S i m ( w 1 , w 2 ) = f ( w 1 , w 2 , β 1 ) β 1 + f ( w 2 , w 1 , β 2 ) β 2 {\displaystyle \mathrm {Sim} (w_{1},w_{2})={\frac {f(w_{1},w_{2},\beta _{1})}{\beta _{1}}}+{\frac {f(w_{2},w_{1},\beta _{2})}{\beta _{2}}}} This score can be normalized to fall between 0 and 1. For example, using this method, the words cemetery and graveyard achieve a high similarity score of 0.986 (with specific parameter settings).
Kernel Assisted Superuser
Kernel Assisted Superuser (short: KernelSU) is an alternative method for obtaining root privileges on Android devices. KernelSU implementations are developed as free and open-source software under the terms of the GPLv3 license. == Technical differences == KernelSU differs from other methods in that root access is implemented directly in the kernel. Compared to other root methods that run in userspace, such as Magisk, this has the advantage that commands with su can be executed like normal commands, but still have root privileges. This is not prevented by SELinux or detected by the PlayIntegrity API check, so applications that use it will continue to function. Unlike Magisk, /system/bin/su is a virtual file implemented by hooking system calls with kprobes, and overlayfs is used for systemless modifications to the system partition instead of magic mount. == History == The planning of KernelSU was started in 2018 by developer Jason Donenfeld, also known as XDA user zx2c4. The lack of a root manager app and the difficulty of creating boot images meant that KernelSU was not suitable for productive use, and for a long time this method remained theoretical and could only be used by developers. In 2021, Google launched Generic Kernel Images (GKI for short), which facilitates the creation of a set of device-independent rooted boot images. In response, the developer known on XDA as weishu, who had also worked on projects such as VirtualXposed, adapted KernelSU for GKI-compatible kernels. The adaptation, which was released in January 2023, ensures that any device booting with Linux kernel version 5.10 or higher should be compatible. In addition, the developer also offers a special manager app that, in addition to managing root privileges, also offers overlay-based modding similar to Magisk modules. As of November 2025, 310 developers have contributed to the development of the KernelSU implementation. == Distribution == KernelSU can be installed on all devices that use GKI, as well as on individually supported devices without GKI. Some custom ROMs already have it integrated by default, including ROMs such as CrDroid, Bliss OS, and Evolution X.
Gradient vector flow
Gradient vector flow (GVF), a computer vision framework introduced by Chenyang Xu and Jerry L. Prince, is the vector field that is produced by a process that smooths and diffuses an input vector field. It is usually used to create a vector field from images that points to object edges from a distance. It is widely used in image analysis and computer vision applications for object tracking, shape recognition, segmentation, and edge detection. In particular, it is commonly used in conjunction with active contour model. == Background == Finding objects or homogeneous regions in images is a process known as image segmentation. In many applications, the locations of object edges can be estimated using local operators that yield a new image called an edge map. The edge map can then be used to guide a deformable model, sometimes called an active contour or a snake, so that it passes through the edge map in a smooth way, therefore defining the object itself. A common way to encourage a deformable model to move toward the edge map is to take the spatial gradient of the edge map, yielding a vector field. Since the edge map has its highest intensities directly on the edge and drops to zero away from the edge, these gradient vectors provide directions for the active contour to move. When the gradient vectors are zero, the active contour will not move, and this is the correct behavior when the contour rests on the peak of the edge map itself. However, because the edge itself is defined by local operators, these gradient vectors will also be zero far away from the edge and therefore the active contour will not move toward the edge when initialized far away from the edge. Gradient vector flow (GVF) is the process that spatially extends the edge map gradient vectors, yielding a new vector field that contains information about the location of object edges throughout the entire image domain. GVF is defined as a diffusion process operating on the components of the input vector field. It is designed to balance the fidelity of the original vector field, so it is not changed too much, with a regularization that is intended to produce a smooth field on its output. Although GVF was designed originally for the purpose of segmenting objects using active contours attracted to edges, it has been since adapted and used for many alternative purposes. Some newer purposes including defining a continuous medial axis representation, regularizing image anisotropic diffusion algorithms, finding the centers of ribbon-like objects, constructing graphs for optimal surface segmentations, creating a shape prior, and much more. == Theory == The theory of GVF was originally described by Xu and Prince. Let f ( x , y ) {\displaystyle \textstyle f(x,y)} be an edge map defined on the image domain. For uniformity of results, it is important to restrict the edge map intensities to lie between 0 and 1, and by convention f ( x , y ) {\displaystyle \textstyle f(x,y)} takes on larger values (close to 1) on the object edges. The gradient vector flow (GVF) field is given by the vector field v ( x , y ) = [ u ( x , y ) , v ( x , y ) ] {\displaystyle \textstyle \mathbf {v} (x,y)=[u(x,y),v(x,y)]} that minimizes the energy functional In this equation, subscripts denote partial derivatives and the gradient of the edge map is given by the vector field ∇ f = ( f x , f y ) {\displaystyle \textstyle \nabla f=(f_{x},f_{y})} . Figure 1 shows an edge map, the gradient of the (slightly blurred) edge map, and the GVF field generated by minimizing E {\displaystyle \textstyle {\mathcal {E}}} . Equation 1 is a variational formulation that has both a data term and a regularization term. The first term in the integrand is the data term. It encourages the solution v {\displaystyle \textstyle \mathbf {v} } to closely agree with the gradients of the edge map since that will make v − ∇ f {\displaystyle \textstyle \mathbf {v} -\nabla f} small. However, this only needs to happen when the edge map gradients are large since v − ∇ f {\displaystyle \textstyle \mathbf {v} -\nabla f} is multiplied by the square of the length of these gradients. The second term in the integrand is a regularization term. It encourages the spatial variations in the components of the solution to be small by penalizing the sum of all the partial derivatives of v {\displaystyle \textstyle \mathbf {v} } . As is customary in these types of variational formulations, there is a regularization parameter μ > 0 {\displaystyle \textstyle \mu >0} that must be specified by the user in order to trade off the influence of each of the two terms. If μ {\displaystyle \textstyle \mu } is large, for example, then the resulting field will be very smooth and may not agree as well with the underlying edge gradients. Theoretical Solution. Finding v ( x , y ) {\displaystyle \textstyle \mathbf {v} (x,y)} to minimize Equation 1 requires the use of calculus of variations since v ( x , y ) {\displaystyle \textstyle \mathbf {v} (x,y)} is a function, not a variable. Accordingly, the Euler equations, which provide the necessary conditions for v {\displaystyle \textstyle \mathbf {v} } to be a solution can be found by calculus of variations, yielding where ∇ 2 {\displaystyle \textstyle \nabla ^{2}} is the Laplacian operator. It is instructive to examine the form of the equations in (2). Each is a partial differential equation that the components u {\displaystyle u} and v {\displaystyle v} of v {\displaystyle \mathbf {v} } must satisfy. If the magnitude of the edge gradient is small, then the solution of each equation is guided entirely by Laplace's equation, for example ∇ 2 u = 0 {\displaystyle \textstyle \nabla ^{2}u=0} , which will produce a smooth scalar field entirely dependent on its boundary conditions. The boundary conditions are effectively provided by the locations in the image where the magnitude of the edge gradient is large, where the solution is driven to agree more with the edge gradients. Computational Solutions. There are two fundamental ways to compute GVF. First, the energy function E {\displaystyle {\mathcal {E}}} itself (1) can be directly discretized and minimized, for example, by gradient descent. Second, the partial differential equations in (2) can be discretized and solved iteratively. The original GVF paper used an iterative approach, while later papers introduced considerably faster implementations such as an octree-based method, a multi-grid method, and an augmented Lagrangian method. In addition, very fast GPU implementations have been developed in Extensions and Advances. GVF is easily extended to higher dimensions. The energy function is readily written in a vector form as which can be solved by gradient descent or by finding and solving its Euler equation. Figure 2 shows an illustration of a three-dimensional GVF field on the edge map of a simple object (see ). The data and regularization terms in the integrand of the GVF functional can also be modified. A modification described in , called generalized gradient vector flow (GGVF) defines two scalar functions and reformulates the energy as While the choices g ( ∇ f | ) = μ {\displaystyle \textstyle g(\nabla f|)=\mu } and h ( | ∇ f | ) = | ∇ f | 2 {\displaystyle \textstyle h(|\nabla f|)=|\nabla f|^{2}} reduce GGVF to GVF, the alternative choices g ( | ∇ f | ) = exp { − | ∇ f | / K } {\displaystyle \textstyle g(|\nabla f|)=\exp\{-|\nabla f|/K\}} and h ( ∇ f | ) = 1 − g ( | ∇ f | ) {\displaystyle \textstyle h(\nabla f|)=1-g(|\nabla f|)} , for K {\displaystyle K} a user-selected constant, can improve the tradeoff between the data term and its regularization in some applications. The GVF formulation has been further extended to vector-valued images in where a weighted structure tensor of a vector-valued image is used. A learning based probabilistic weighted GVF extension was proposed in to further improve the segmentation for images with severely cluttered textures or high levels of noise. The variational formulation of GVF has also been modified in motion GVF (MGVF) to incorporate object motion in an image sequence. Whereas the diffusion of GVF vectors from a conventional edge map acts in an isotropic manner, the formulation of MGVF incorporates the expected object motion between image frames. An alternative to GVF called vector field convolution (VFC) provides many of the advantages of GVF, has superior noise robustness, and can be computed very fast. The VFC field v V F C {\displaystyle \textstyle \mathbf {v} _{\mathrm {VFC} }} is defined as the convolution of the edge map f {\displaystyle f} with a vector field kernel k {\displaystyle \mathbf {k} } where The vector field kernel k {\displaystyle \textstyle \mathbf {k} } has vectors that always point toward the origin but their magnitudes, determined in detail by the function m {\displaystyle m} , decrease to zero with increasing distance from the origin. The beauty of VFC is that it can be computed very rapidly using a fast Fourier tra