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  Lexical Markup Framework

  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

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  Top 10 AI Video Editors Compared (2026)

  Looking for the best AI video editor? An AI video editor is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI video editor slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  DALL-E

  DALL-E, DALL-E 2, and DALL-E 3 (stylised DALL·E) are text-to-image models developed by OpenAI using deep learning methodologies to generate digital images from natural language descriptions known as prompts. The first version of DALL-E was announced in January 2021. In the following year, its successor DALL-E 2 was released. DALL-E 3 was released natively into ChatGPT for ChatGPT Plus and ChatGPT Enterprise customers in October 2023, with availability via OpenAI's API and "Labs" platform provided in early November. Microsoft implemented the model in Bing's Image Creator tool and plans to implement it into their Designer app. With Bing's Image Creator tool, Microsoft Copilot runs on DALL-E 3. In March 2025, DALL-E-3 was replaced in ChatGPT by GPT Image's native image-generation capabilities. == History and background == DALL-E was revealed by OpenAI in a blog post on 5 January 2021, and uses a version of GPT-3 modified to generate images. On 6 April 2022, OpenAI announced DALL-E 2, a successor designed to generate more realistic images at higher resolutions that "can combine concepts, attributes, and styles". On 20 July 2022, DALL-E 2 entered into a beta phase with invitations sent to 1 million waitlisted individuals; users could generate a certain number of images for free every month and may purchase more. Access had previously been restricted to pre-selected users for a research preview due to concerns about ethics and safety. On 28 September 2022, DALL-E 2 was opened to everyone and the waitlist requirement was removed. In September 2023, OpenAI announced their latest image model, DALL-E 3, capable of understanding "significantly more nuance and detail" than previous iterations. In early November 2022, OpenAI released DALL-E 2 as an API, allowing developers to integrate the model into their own applications. Microsoft unveiled their implementation of DALL-E 2 in their Designer app and Image Creator tool included in Bing and Microsoft Edge. The API operates on a cost-per-image basis, with prices varying depending on image resolution. Volume discounts are available to companies working with OpenAI's enterprise team. The software's name is a portmanteau of the names of animated robot Pixar character WALL-E and the Spanish surrealist artist Salvador Dalí. In February 2024, OpenAI began adding watermarks to DALL-E generated images, containing metadata in the C2PA (Coalition for Content Provenance and Authenticity) standard promoted by the Content Authenticity Initiative. == Technology == The first generative pre-trained transformer (GPT) model was initially developed by OpenAI in 2018, using a Transformer architecture. The first iteration, GPT-1, was scaled up to produce GPT-2 in 2019; in 2020, it was scaled up again to produce GPT-3, with 175 billion parameters. === DALL-E === DALL-E has three components: a discrete VAE, an autoregressive decoder-only Transformer model (12 billion parameters) similar to GPT-3, and a CLIP pair of image encoder and text encoder. The discrete VAE can convert an image to a sequence of tokens, and conversely, convert a sequence of tokens back to an image. This is necessary as the Transformer model does not directly process image data. The input to the Transformer model is a sequence of tokenised image caption followed by tokenised image patches. The image caption is in English, tokenised by byte pair encoding (vocabulary size 16384), and can be up to 256 tokens long. Each image is a 256×256 RGB image, divided into 32×32 patches of 4×4 each. Each patch is then converted by a discrete variational autoencoder to a token (vocabulary size 8192). DALL-E was developed and announced to the public in conjunction with CLIP (Contrastive Language-Image Pre-training). CLIP is a separate model based on contrastive learning that was trained on 400 million pairs of images with text captions scraped from the Internet. Its role is to "understand and rank" DALL-E's output by predicting which caption from a list of 32,768 captions randomly selected from the dataset (of which one was the correct answer) is most appropriate for an image. A trained CLIP pair is used to filter a larger initial list of images generated by DALL-E to select the image that is closest to the text prompt. === DALL-E 2 === DALL-E 2 uses 3.5 billion parameters, a smaller number than its predecessor. Instead of an autoregressive Transformer, DALL-E 2 uses a diffusion model conditioned on CLIP image embeddings, which, during inference, are generated from CLIP text embeddings by a prior model. This is the same architecture as that of Stable Diffusion, released a few months later. === DALL-E 3 === While a technical report was written for DALL-E 3, it does not include training or implementation details of the model, instead focusing on the improved prompt following capabilities developed for DALL-E 3. == Capabilities == DALL-E can generate imagery in multiple styles, including photorealistic imagery, paintings, and emoji. It can "manipulate and rearrange" objects in its images, and can correctly place design elements in novel compositions without explicit instruction. Thom Dunn writing for BoingBoing remarked that "For example, when asked to draw a daikon radish blowing its nose, sipping a latte, or riding a unicycle, DALL-E often draws the handkerchief, hands, and feet in plausible locations." DALL-E showed the ability to "fill in the blanks" to infer appropriate details without specific prompts, such as adding Christmas imagery to prompts commonly associated with the celebration, and appropriately placed shadows to images that did not mention them. Furthermore, DALL-E exhibits a broad understanding of visual and design trends. DALL-E can produce images for a wide variety of arbitrary descriptions from various viewpoints with only rare failures. Mark Riedl, an associate professor at the Georgia Tech School of Interactive Computing, found that DALL-E could blend concepts (described as a key element of human creativity). Its visual reasoning ability is sufficient to solve Raven's Matrices (visual tests often administered to humans to measure intelligence). DALL-E 3 follows complex prompts with more accuracy and detail than its predecessors, and is able to generate more coherent and accurate text. DALL-E 3 is integrated into ChatGPT Plus. === Image modification === Given an existing image, DALL-E 2 and DALL-E 3 can produce "variations" of the image as individual outputs based on the original, as well as edit the image to modify or expand upon it. The "inpainting" and "outpainting" abilities of these models use context from an image to fill in missing areas using a medium consistent with the original, following a given prompt. For example, this can be used to insert a new subject into an image, or expand an image beyond its original borders. According to OpenAI, "Outpainting takes into account the image’s existing visual elements — including shadows, reflections, and textures — to maintain the context of the original image." === Technical limitations === DALL-E 2's language understanding has limits. It is sometimes unable to distinguish "A yellow book and a red vase" from "A red book and a yellow vase" or "A panda making latte art" from "Latte art of a panda". It generates images of an astronaut riding a horse when presented with the prompt "a horse riding an astronaut". It also fails to generate the correct images in a variety of circumstances. Requesting more than three objects, negation, numbers, and connected sentences may result in mistakes, and object features may appear on the wrong object. Additional limitations include generating text, ambigrams and other forms of typography, which often results in dream-like gibberish. The model also has a limited capacity to address scientific information, such as astronomy or medical imagery. == Ethical concerns == DALL-E 2's reliance on public datasets influences its results and leads to algorithmic bias in some cases, such as generating higher numbers of men than women for requests that do not mention gender. DALL-E 2's training data was filtered to remove violent and sexual imagery, but this was found to increase bias in some cases such as reducing the frequency of women being generated. OpenAI hypothesise that this may be because women were more likely to be sexualised in training data which caused the filter to influence results. In September 2022, OpenAI confirmed to The Verge that DALL-E invisibly inserts phrases into user prompts to address bias in results; for instance, "black man" and "Asian woman" are inserted into prompts that do not specify gender or race. OpenAI claims to address concerns for potential "racy content" – containing nudity or sexual content generation, with DALL-E 3 through input/output filters, blocklists, ChatGPT refusals, and model level interventions. However, DALL-E 3 continues to disproportionally represent people as White, female, and youthful. Users are able to somewhat remedy

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  Madhan Karky

  Madhan Karky Vairamuthu is an Indian lyricist, screenwriter, research associate, software engineer, and entrepreneur. A holder of a doctorate in computer science from the University of Queensland, Karky began his professional career as an assistant professor at the College of Engineering, Guindy, and soon after ventured into the Tamil cinema, working as a lyricist and dialogue writer. He resigned from his teaching profession in early 2013 and began working full-time in the film industry, while also launching the Karky Research Foundation (KaReFo), an educational research organization which primarily focuses on language computing and language literacy. He also founded the Mellinam Education, which develops educational games and story books designed to propagate learning among children, and DooPaaDoo, an online music platform which promotes independent music and serves a distributor for film soundtracks. == Early life == Karky is the eldest son of seven-time National Award winning lyricist Vairamuthu and Ponmani, a Tamil scholar and veteran professor at the Meenakshi College for Women. He has a younger brother, Kabilan, who is a novelist and also works as a lyricist and dialogue writer for Tamil films. === Education === He grew up in Chennai and was educated at the Loyala Matriculation School in Kodambakkam. By his own admission, he was not a good student, excelling primarily only in Tamil and English. During his time in high school, he gained an interest in computer science He got admission in College of Engineering, Guindy which is affiliated with the Anna University. He began his undergraduate education in the field of Computer engineering in the year 1997. While in CEG, as part of his final year project, Karky developed a program called the Tamil Voice Engine, under the supervision of Professor T.V. Geetha. The goal of the project was construction of a text to speech engine for the Tamil language. The research paper on the project was officially selected at the Tamil Internet Conference in Kuala Lumpur, Malaysia. Other projects during his tenure include the Name Generator, which was part of his course on Creativity, Innovation and New Product Development (the objective being to generate random names that are pronounceable with respect to Indian phonetics) and Compiler Design, for which a high level programming language was conceived, with the goal of proper specification and interpretation of lexical rules and grammar rules. For Chennai Kavigal, he created a Spell Checker for a Tamil Word Processor. The project involved a lot of Natural Language Processing elements, based on a root dictionary built as a part of the morphological analyzer for the Tamil Language. The endgame being determining the correctness of words. Following the completion of his bachelor's degree in 2001, Karky began his master's degree at the University of Queensland in the year 2003. In that particular stint, he developed a project based on the theory of computation and strong mathematics (under the supervision of Dr. George Havas). It aimed at analyzing an existing algorithm of reducing any kind of matrix format to a standard format called 'Hermite Normal form', which is a unit upper triangular matrix. Some of his other projects during this course include the Disciplined Software Process Project (whose objective was to introduce and practice the software development process for individuals called Personal Software Process), the On-Line Art Store Website (which involved the creation of a website that trades paintings through the Internet) and the Text Based Voice Chat (for which a Proxy Voice Chat system was designed and developed in Visual Basic that incorporated the predominant computing aspects). In addition to his academics, Karky also served as Academic tutor at the university. He conducted class room tutorials and laboratory sessions on subjects such as Relational Database Systems and Programming Languages. As part of his PhD program on information technology, he developed a Java-based simulation platform called SENSE (Simulated Environment of Networked Sensor Experiments), to test different heuristics. This project was done under the guidance of Dr. Maria Orlowska and Dr. Shazia Sadiq. His thesis is titled "Design considerations for query dissemination in wireless sensor networks". === Teaching career === Upon his return to India following the completion of his post-graduation, Karky returned to CEG Anna University in December 2007. He was a Senior Research Fellow for the next six months, managing research projects as well as multiple student projects at an undergrad and postgrad levels. In addition to those, he handled courses and labs for students who pursued their master's degrees. He also served as a Project Scientist between July 2008 and July 2009, managing projects of research groups as well as ME & MBA students. Starting from August 2009, he began his role as an assistant professor. He lectured Computer Science students who were pursuing their Bachelors and master's degrees as well as coordinated the Tamil Computing Lab at the university. He also served as counsellor for NRI and foreign national students, as well as the Staff treasurer of Computer Science Engineering Association. Some of the subjects he taught include Advanced Databases, Ethics for Engineers, Principles of Programming Languages, Environmental Science and Tamil Computing (for PhD students). === Family and personal life === Karky's been married to Nandini Eswaramoorthy, a fellow alum at Anna University, since June 22, 2008. Nandini Karky now works in the Tamil film industry as a subtitler for feature films and documentaries. They have a son named Haiku Karky, who was born in 2009. == Film career == === Debut === During his teaching stint at Anna University, Karky also began his career in the Tamil film industry with the science-fiction film Enthiran (2010), the magnum opus of director Shankar. Karky had approached the director in 2008 with some of the songs he had written, and was brought him on board to help with the dialogues of the film, especially assisting with technical terminology. He stated that there were three sets of dialogues written for almost every scene of the film; one by Shankar, one by Karky, and the other by the late Sujatha, a frequent collaborator with the director who had died during the early stages of the film's pre-production. Shankar would go through all the three drafts and implement those that fit best. The climax was the only portion that didn't have multiple hands, as it was written solely by Karky. In addition to the dialogue, Karky wrote 2 songs for the film, as well: "Irumbile oru Irudhaiyam" (the first song of his career, which was partially crooned by A.R. Rahman) and "Boom Boom Robo Da". However, Kanden Kadhalai (2009), in which he had written the song "Ododi Poren" (composed by Vidyasagar), became his first release. For his work on Enthiran, Karky was named Best Find of the Year at the 2011 Vijay Awards. === Lyric writer === Following his work on Enthiran, Karky became one of the most sought after lyricists in the Tamil film industry, having multiple collaborations with A.R. Rahman, Harris Jayaraj, G. V. Prakash Kumar, D. Imman, M.M. Keeravani, Yuvan Shankar Raja, S. Thaman, Sanjay Leela Bhansali, Anirudh Ravichander and Sam CS. In addition to his native Tamil, he is known for penning songs in multiple languages; some of which include "Asku Laska" from Nanban (which features 16 different languages), "The Rise of Damo" from 7 Aum Arivu (written in Mandarin) and "Continua" from Nootrenbadhu (in Portuguese). His work is also characterized by infusing uncommon Tamil words that aren't normally used in everyday lexicon, as part of lyrics (like "Kuviyamillaa Kaatchi Paezhai" from Ko and "Panikoozh" from I). He also wrote the first palindrome song in Tamil cinema for the film Vinodhan. As of the end of 2025, he has over one thousand songs to his credit. Some of Karky's most popular songs include "Irumbile oru Irudhaiyam" (Enthiran), "Enamo Edho" (Ko), "Nee Koorinal" (Nootrenbadhu), "Asku Laska" (Nanban), "Google Google" (Thuppakki), "Elay Keechaan" (Kadal), "Osakka" (Vanakkam Chennai), "Selfie Pulla" (Kaththi), "Pookkalae Sattru Oyivedungal" (I), "Mei Nigara" (24), "Azhagiye" (Kaatru Veliyidai), "Endhira Logathu Sundariye" (2.0) and "Kurumba" (Tik Tik Tik). === Dialogue writer === On the heels of the success with Enthiran, Karky once again collaborated as a dialogue writer with director Shankar for Nanban. An adaptation of the Hindi blockbuster 3 Idiots, he infused a twang to the dialogue that aimed to showcase college life in a different manner. He also collaborated as a technical advisor with Shankar with 2.0 (the sequel to Enthiran). Karky's also known for his successful collaboration with Telugu director S.S. Rajamouli, on his two-part magnum opus Baahubali; the second part being the most profitable South Indian film of all time, and RRR. His o

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  Keyword extraction

  Keyword extraction is tasked with the automatic identification of terms that best describe the subject of a document. Key phrases, key terms, key segments or just keywords are the terminology which is used for defining the terms that represent the most relevant information contained in the document. Although the terminology is different, function is the same: characterization of the topic discussed in a document. The task of keyword extraction is an important problem in text mining, information extraction, information retrieval and natural language processing (NLP). == Keyword assignment vs. extraction == Keyword assignment methods can be roughly divided into: keyword assignment (keywords are chosen from controlled vocabulary or taxonomy) and keyword extraction (keywords are chosen from words that are explicitly mentioned in original text). Methods for automatic keyword extraction can be supervised, semi-supervised, or unsupervised. Unsupervised methods can be further divided into simple statistics, linguistics or graph-based, or ensemble methods that combine some or most of these methods.

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  Tamara Berg

  Tamara Lee Berg is a tenured associate professor at the University of North Carolina at Chapel Hill and a research scientist manager at Facebook AML/FAIR. == Education == Berg obtained her PhD in computer science from the University of California, Berkeley in 2007 as a member of the Berkeley Computer Vision Group. She was an assistant professor at Stony Brook University from 2008 to 2013 before joining University of North Carolina Chapel Hill in 2013. == Research == Berg's research interests are at the boundary of computer vision and natural language processing. In particular, she focuses on understanding the connections between vision and language, for example, to automatically identify people in news photographs, for generating natural language descriptions for images, or for recognising clothing and style. == Selected awards and honours == 2019 Mark Everingham Prize 2013 Marr Prize at the International Conference on Computer Vision 2011 National Science Foundation Career Award == Personal life == Berg is married to fellow computer vision researcher Alexander Berg.

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  Kaiming He

  Kaiming He (Chinese: 何恺明; pinyin: Hé Kǎimíng) is a Chinese computer scientist who primarily researches computer vision and deep learning. He is an associate professor at Massachusetts Institute of Technology and works part-time as a Distinguished Scientist at Google DeepMind. He is known as one of the creators of the residual neural network (ResNet) architecture. == Early life and education == He attended the public Guangzhou Zhixin High School in Guangzhou, Guangdong, China. He scored first place for the total scores in the 2003 Guangdong provincial undergraduate admissions exam. He went to Tsinghua University for undergraduate education and received a Bachelor of Science degree in 2007. In 2007 to 2011, he pursued doctoral studies in information engineering at the Chinese University of Hong Kong at its Multimedia Laboratory, receiving a PhD degree in 2011. His doctoral dissertation was titled Single image haze removal using dark channel prior (2011), and his doctoral adviser was Tang Xiao'ou. == Career == He worked at Microsoft Research Asia from 2011 to 2016 and at Facebook Artificial Intelligence Research from 2016 to 2024. In 2024, he became an associate professor at the Department of Electrical Engineering and Computer Science of the Massachusetts Institute of Technology. His 2016 paper Deep Residual Learning for Image Recognition is the most cited research paper in 5 years according to Google Scholar's reports in 2020 and 2021. == Awards and recognitions == He won ICCV's best paper award (Marr Prize) in 2017 and CVPR's best paper award in 2009 and 2016. He was awarded the 2023 Future Science Prize along with 3 collaborators for "fundamental contribution to artificial intelligence by introducing deep residual learning".

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  Is an AI Marketing Tool Worth It in 2026?

  Trying to pick the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  Metigo

  metigo is a software application that performs image-based modelling and close range photogrammetry. It produces rectified imagery plans, true ortho-projections on planar, cylindric and conic surfaces, 3D photorealistic models, measurements from photography and mappings on a photographic base for uses in the cultural heritage sector, mainly conservation. == Products == The metigo product line currently consists of the mapping software metigo MAP, the stereo-photogrammetry modeling software metigo 3D, the free viewer metigo VIEW. These products are all standalone and are not depending on other software, such as AutoCAD. === metigo MAP === metigo MAP is mainly used to map findings and conservation measured on a uniform metric photographic base. Therefore, photos of planar surfaces can be rectified based on geometrical informations, e.g. height and width of a rectangle, or cartesian coordinates measured by total station. Beside rectified imagery several other metric mapping bases can be imported and used: true ortho-projections; scaled scans of plans and plots; CAD-files; 3D models, such as digital surface models (DSM) produced by stereo-photogrammetry, SfM or 3D scanning. metigo MAP 's strong point is that rectified imagery taken with different techniques (visual light, sided light, IR, UV, UV-fluorescence, X-ray), historic images and photos taken at various stages of the conservation process can be superimposed and evaluated mutually. The user can allocate several attributes, such as different conservation measures and damage classes, to the mapped geometries. The mappings can be analysed by geometries as well as by user-defined attributes at any stage of the project. metigo MAP targets mainly conservators in different cultural heritage fields. Using it no specialist knowledge of surveying and photogrammetric techniques are needed. === metigo 3D === metigo 3D is a stereo-photogrammetric kit that allows to calculate bundle adjustments (axios3D), create high-quality 3D point clouds using multiple stereo photo pairs combined with metric survey data, mesh these point clouds, texture the meshes with high-resolution image data to create photo-realistic models, ortho-project orientated images on digital surface models (DSM) on planes and best-fit cylinders and cones, create unwrappings and developed views of curved surfaces, analyse deformations of 3D surfaces. metigo 3D targets metric survey specialists working in the cultural heritage sector. == Supported file formats == metigo has the ability to read the following formats: images: JPEG (.jpg), Tiff (.tif), Bitmaps (.bmp), CompuServ (.gif), Encapsualated Postscript (.eps), PCX (.pcx), Photo-CD (.pcd), PICT (.pcd), PNG (.png), Targa (.tga), RAW-format of several camera brands. CAD: DBX, DXF, DWG. 3D: many ASCII-formats (.stl, .wrl, etc.) point data: format editor for ASCII files. == Supported languages == Currently, an English and German version of the software is supported. For metigo MAP beside these a French and Polish GUI is offered for sale. == Applications == The main applications of metigo are: conservation in the cultural heritage context, e.g. stone conservation paintings tapestry etc. architecture, archaeology, many other are possible, e.g. forensics. == History == The first public release of metigo was in 2000.

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  Markov chain geostatistics

  Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability matrices are difficult to estimate from sparse sample data and are impractical in representing the complex spatial heterogeneity of states, the transiogram, which is defined as a transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.

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  Dan Jurafsky

  Daniel Jurafsky is a professor of linguistics and computer science at Stanford University, and also an author. With Daniel Gildea, he is known for developing the first automatic system for semantic role labeling (SRL). He is the author of The Language of Food: A Linguist Reads the Menu (2014) and a textbook on speech and language processing (2000). For the former, Jurafsky was named a finalist for the James Beard Award. Jurafsky was given a MacArthur Fellowship in 2002. == Education == Jurafsky received his B.A in linguistics (1983) and Ph.D. in computer science (1992), both at University of California, Berkeley; and then a postdoc at International Computer Science Institute, Berkeley (1992–1995). == Academic life == He is the author of The Language of Food: A Linguist Reads the Menu (W. W. Norton & Company, 2014). With James H. Martin, he wrote the textbook Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition (Prentice Hall, 2000). The first automatic system for semantic role labeling (SRL, sometimes also referred to as "shallow semantic parsing") was developed by Daniel Gildea and Daniel Jurafsky to automate the FrameNet annotation process in 2002; SRL has since become one of the standard tasks in natural language processing. == Personal life == Jurafsky is Jewish. He is married. They reside in San Francisco, California. == Selected works == 2009. Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition, 2nd Edition. (with James H. Martin) Prentice-Hall. ISBN 978-0131873216 2014. The Language of Food: A Linguist Reads the Menu. W. W. Norton & Company. ISBN 978-0393240832 2026. Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition, 3rd Edition draft. (with James H. Martin) == Honors and awards == 1998. NSF Career Award 2002. MacArthur Fellowship 2019. LSA Fellow 2022. Atkinson Prizes in Psychological and Cognitive Sciences

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  Weighted automaton

  In theoretical computer science and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state machines are only capable of answering decision problems; they take as input a string and produce a Boolean output, i.e. either "accept" or "reject". In contrast, weighted automata produce a quantitative output, for example a count of how many answers are possible on a given input string, or a probability of how likely the input string is according to a probability distribution. They are one of the simplest studied models of quantitative automata. The definition of a weighted automaton is generally given over an arbitrary semiring R {\displaystyle R} , an abstract set with an addition operation + {\displaystyle +} and a multiplication operation × {\displaystyle \times } . The automaton consists of a finite set of states, a finite input alphabet of characters Σ {\displaystyle \Sigma } and edges which are labeled with both a character in Σ {\displaystyle \Sigma } and a weight in R {\displaystyle R} . The weight of any path in the automaton is defined to be the product of weights along the path, and the weight of a string is the sum of the weights of all paths which are labeled with that string. The weighted automaton thus defines a function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} . Weighted automata generalize deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs), which correspond to weighted automata over the Boolean semiring, where addition is logical disjunction and multiplication is logical conjunction. In the DFA case, there is only one accepting path for any input string, so disjunction is not applied. When the weights are real numbers and the outgoing weights for each state add to one, weighted automata can be considered a probabilistic model and are also known as probabilistic automata. These machines define a probability distribution over all strings, and are related to other probabilistic models such as Markov decision processes and Markov chains. Weighted automata have applications in natural language processing where they are used to assign weights to words and sentences, as well as in image compression. They were first introduced by Marcel-Paul Schützenberger in his 1961 paper On the definition of a family of automata. Since their introduction, many extensions have been proposed, for example nested weighted automata, cost register automata, and weighted finite-state transducers. Researchers have studied weighted automata from the perspective of learning a machine from its input-output behavior (see computational learning theory) and studying decidability questions. == Definition == A commutative semiring (or rig) is a set R equipped with two distinguished elements 0 ≠ 1 {\displaystyle 0\neq 1} and addition and multiplication operations ⊕ {\displaystyle \oplus } and ⊗ {\displaystyle \otimes } such that ⊕ {\displaystyle \oplus } is commutative and associative with identity 0 {\displaystyle 0} , ⊗ {\displaystyle \otimes } is commutative and associative with identity 1 {\displaystyle 1} , ⊗ {\displaystyle \otimes } distributes over ⊕ {\displaystyle \oplus } , and 0 is an absorbing element for ⊗ {\displaystyle \otimes } . A weighted automaton over R {\displaystyle R} is a tuple A = ( Q , Σ , Δ , I , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\Delta ,I,F)} where: Q {\displaystyle Q} is a finite set of states. Σ {\displaystyle \Sigma } is a finite alphabet. Δ ⊆ Q × Σ × R × Q {\displaystyle \Delta \subseteq Q\times \Sigma \times R\times Q} is a finite set of transitions ( q , σ , w , q ′ ) {\displaystyle (q,\sigma ,w,q')} , where σ {\displaystyle \sigma } is called a character and w {\displaystyle w} is called a weight. I : Q → R {\displaystyle I:Q\to R} is an initial weight function. F : Q → R {\displaystyle F:Q\to R} is a final weight function. A path on input w ∈ Σ ∗ {\displaystyle w\in \Sigma ^{}} is a finite path in the graph, where the concatenation of the character labels equals w {\displaystyle w} . The weight of the path q 0 , q 1 , … , q n {\displaystyle q_{0},q_{1},\ldots ,q_{n}} is the product ( ⊗ {\displaystyle \otimes } ) of the weights along the path, additionally multiplied by the initial and final weights I ( q 0 ) ⊗ F ( q n ) {\displaystyle I(q_{0})\otimes F(q_{n})} . The weight of the word w {\displaystyle w} is the sum ( ⊕ {\displaystyle \oplus } ) of the weights of all paths on input w {\displaystyle w} (or 0 if there are no accepting paths). In this way the machine defines a function [ [ A ] ] : Σ ∗ → R {\displaystyle [\![{\mathcal {A}}]\!]:\Sigma ^{}\to R} . == Ambiguity and determinism == Since Δ {\displaystyle \Delta } is a set of transitions, weighted automata allow multiple transitions (or paths) on a single input string. Therefore a weighted automaton can be considered analogous to a nondeterministic finite automaton (NFA). As is the case with NFAs, restrictions of weighted automata are considered that correspond to the concepts of deterministic finite automaton and unambiguous finite automaton (deterministic weighted automata and unambiguous weighted automata, respectively). First, a preliminary definition: the underlying NFA of A {\displaystyle {\mathcal {A}}} is an NFA formed by removing all transitions with weight 0 {\displaystyle 0} and then erasing all of the weights on the transitions Δ {\displaystyle \Delta } , so that the new transition set lies in Q × Σ × Q {\displaystyle Q\times \Sigma \times Q} . The initial states and final states are the set of states q {\displaystyle q} such that I ( q ) ≠ 0 {\displaystyle I(q)\neq 0} and F ( q ) ≠ 0 {\displaystyle F(q)\neq 0} , respectively. A weighted automaton is deterministic if the underlying NFA is deterministic and unambiguous if the underlying NFA is unambiguous. Every deterministic weighted automaton is unambiguous. In both the deterministic and unambiguous cases, there is always at most one accepting path, so the ⊕ {\displaystyle \oplus } operation is never applied and can be omitted from the definition. == Variations == The requirement that there is a zero element for ⊕ {\displaystyle \oplus } is sometimes omitted; in this case the machine defines a partial function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} rather than a total function. It is possible to extend the definition to allow epsilon transitions ( q , ϵ , w , q ′ ) {\displaystyle (q,\epsilon ,w,q')} , where ϵ {\displaystyle \epsilon } is the empty string. In this case, one must then require that there are no cycles of epsilon transitions. This does not increase the expressiveness of weighted automata. If epsilon transitions are allowed, the initial weights and final weights can be replaced by initial and final sets of states without loss of expressiveness. Some authors omit the initial and final weight functions I {\displaystyle I} and F {\displaystyle F} . Instead, I {\displaystyle I} and F {\displaystyle F} are replaced by a set of initial and final states. If epsilon transitions are not present, this technically decreases expressiveness as it forces [ [ A ] ] ( ε ) {\displaystyle [\![{\mathcal {A}}]\!](\varepsilon )} to depend only on the number of states that are both initial and final. The transition function can be given as a matrix Δ σ ∈ R Q × Q {\displaystyle \Delta _{\sigma }\in R^{Q\times Q}} with entries in R {\displaystyle R} for each σ {\displaystyle \sigma } , rather than a set of transitions. The entry of the matrix at ( q , q ′ ) {\displaystyle (q,q')} is the sum of all transitions labeled ( q , σ , q ′ ) {\displaystyle (q,\sigma ,q')} . Some authors restrict to specific semirings, such as N {\displaystyle \mathbb {N} } or Z {\displaystyle \mathbb {Z} } , particularly when studying decidability results.

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  Glossary of robotics

  Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots. Robotics is related to the sciences of electronics, engineering, mechanics, and software. The following is a list of common definitions related to the Robotics field. == A == Actuator: a motor that translates control signals into mechanical movement. The control signals are usually electrical but may, more rarely, be pneumatic or hydraulic. The power supply may likewise be any of these. It is common for electrical control to be used to modulate a high-power pneumatic or hydraulic motor. Aerobot: a robot capable of independent flight on other planets. A type of aerial robot. Arduino: The current platform of choice for small-scale robotic experimentation and physical computing. Artificial intelligence: is the intelligence of machines and the branch of computer science that aims to create it. Aura (satellite): a robotic spacecraft launched by NASA in 2004 which collects atmospheric data from Earth. Automaton: an early self-operating robot, performing exactly the same actions, over and over. Autonomous vehicle: a vehicle equipped with an autopilot system, which is capable of driving from one point to another without input from a human operator. == B == Biomimetic: See Bionics. Bionics: also known as biomimetics, biognosis, biomimicry, or bionical creativity engineering is the application of biological methods and systems found in nature to the study and design of engineering systems and modern technology. == C == CAD/CAM (computer-aided design and computer-aided manufacturing): These systems and their data may be integrated into robotic operations. Čapek, Karel: Czech author who coined the term 'robot' in his 1921 play, Rossum's Universal Robots. Chandra X-ray Observatory: a robotic spacecraft launched by NASA in 1999 to collect astronomical data. Cloud robotics: robots empowered with more capacity and intelligence from cloud. Combat, robot: a hobby or sport event where two or more robots fight in an arena to disable each other. This has developed from a hobby in the 1990s to several TV series worldwide. Cruise missile: a robot-controlled guided missile that carries an explosive payload. Cyborg: also known as a cybernetic organism, a being with both biological and artificial (e.g. electronic, mechanical or robotic) parts. == D == Degrees of freedom: the extent to which a robot can move itself; expressed in terms of Cartesian coordinates (x, y, and z) and angular movements (yaw, pitch, and roll). Delta robot: a tripod linkage, used to construct fast-acting manipulators with a wide range of movement. Drive Power: The energy source or sources for the robot actuators. == E == Emergent behaviour, a complicated resultant behaviour that emerges from the repeated operation of simple underlying behaviours. Envelope (Space), Maximum The volume of space encompassing the maximum designed movements of all robot parts including the end-effector, workpiece, and attachments. Explosive ordnance disposal robot A mobile robot designed to assess whether an object contains explosives; some carry detonators that can be deposited at the object and activated after the robot withdraws. == F == FIRST(For Inspiration and Recognition of Science and Technology): an organization founded by inventor Dean Kamen in 1989 in order to develop ways to inspire students in engineering and technology fields. Forward chaining: a process in which events or received data are considered by an entity to intelligently adapt its behavior. == G == Gynoid: A humanoid robot designed to look like a human female. == H == Haptic: tactile feedback technology using the operator's sense of touch. Also sometimes applied to robot manipulators with their own touch sensitivity. Hexapod (platform): A movable platform using six linear actuators. Often used in flight simulators and fairground rides, they also have applications as a robotic manipulator. Hexapod (walker): A six-legged walking robot, using a simple insect-like locomotion. Human–computer interaction. Humanoid: A robotic entity designed to resemble a human being in form, function, or both. Hydraulics: the control of mechanical force and movement, generated by the application of liquid under pressure. cf. pneumatics. == I == Industrial robot: A reprogrammable, multifunctional manipulator designed to move material, parts, tools, or specialized devices through variable programmed motions for the performance of a variety of tasks. Insect robot: A small robot designed to imitate insect behaviors rather than complex human behaviors. == K == Kalman filter: a mathematical technique to estimate the value of a sensor measurement, from a series of intermittent and noisy values. Kinematics: the study of motion, as applied to robots. This includes both the design of linkages to perform motion, their power, control and stability; also their planning, such as choosing a sequence of movements to achieve a broader task. Inverse Kinematics: the process of determining joint angles required for a robot's end-effector to reach a desired position and orientation in space. Used in motion planning to calculate motor commands from target positions. == L == Linear actuator A form of motor that generates a linear movement directly. == M == Manipulator or gripper: A robotic 'hand'. Mobile robot: A self-propelled and self-contained robot that is capable of moving over a mechanically unconstrained course. Muting: The deactivation of a presence-sensing safeguarding device during a portion of the robot cycle. Mecanum wheel: A wheel fitted with angled rollers that enables a robot vehicle to move in multiple directions, including sideways. == O == Ornithopter – An aerial robot or drone that achieves flight through a flapping-wing mechanism rather than rotating blades or fixed wings, often utilized for highly maneuverable flight. == P == Parallel manipulator: an articulated robot or manipulator based on a number of kinematic chains, actuators and joints, in parallel. cf. serial manipulator. Pendant: Any portable control device that permits an operator to control the robot from within the restricted envelope (space) of the robot. Pneumatics: the control of mechanical force and movement, generated by the application of compressed gas. cf. hydraulics. Powered exoskeleton: is a wearable mobile machine that allow for limb movement with increased strength and endurance. Prosthetic robots: programmable manipulators or devices for missing human limbs. == R == Remote manipulator: A manipulator under direct human control, often used for work with hazardous materials. Robonaut: a development project conducted by NASA to create humanoid robots capable of using space tools and working in similar environments to suited astronauts. == S == Sensor fusion:The process of combining data from multiple sensors, such as LiDAR, cameras, global positioning systems (GPS), and inertial measurement units (IMUs), to produce a more accurate and reliable understanding of an environment than using a single sensor alone. It is widely used in robotics and autonomous systems to improve perception, localization, and decision-making. Serial manipulator: an articulated robot or manipulator with a single series kinematic chain of actuators. cf. parallel manipulator. Service robots are machines that extend human capabilities. Servo, a motor that moves to and maintains a set position under command, rather than continuously moving. Servomechanism An automatic device that uses error-sensing negative feedback to correct the performance of a mechanism. Single Point of Control The ability to operate the robot such that initiation or robot motion from one source of control is possible only from that source and cannot be overridden from another source. Slow Speed Control A mode of robot motion control where the velocity of the robot is limited to allow persons sufficient time either to withdraw the hazardous motion or stop the robot. Snake robot A robot component resembling a tentacle or elephant's trunk, where many small actuators are used to allow continuous curved motion of a robot component, with many degrees of freedom. This is usually applied to snake-arm robots, which use this as a flexible manipulator. A rarer application is the snakebot, where the entire robot is mobile and snake-like, so as to gain access through narrow spaces. Stepper motor Stewart platform A movable platform using six linear actuators, hence also known as a Hexapod. Subsumption architecture A robot architecture that uses a modular, bottom-up design beginning with the least complex behavioral tasks. Surgical robot, a remote manipulator used for keyhole surgery Swarm robotics involve large numbers of mostly simple physical robots. Their actions may seek to incorporate emergent behavior observed in social insects (swarm intelligence). Synchro == T == Teach Mode: The control state that al

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  Lingoes

  Lingoes is a dictionary and machine translation app. Lingoes was created in China. Lingoes is often compared to its competitor Babylon because of similarities in their GUI, functionalities and most importantly being freeware. == Features and expandability == Dictionaries and encyclopedias can be installed on Lingoes in the form of new add-ons to extend its functionality. Add-ons for Wikipedia, Baidu Baike, Longman Dictionary of Contemporary English, Merriam-Webster's Collegiate Dictionary, WordNet, MacMillan English Dictionary, Collins English Dictionary and other cross-English dictionaries (e.g. Arabic, French or German) are available in Lingoes' official website. The program has the ability to pronounce words and install additional text-to-speech engines available for download also through Lingoes' website. Lingoes also offers a whole-text translation ability using online translation service providers like Google Translate, Yahoo! Babel Fish Translation, SYSTRAN, Cross-Language, Click2Translate, and others. Lingoes offers to translate a text via a mouse-over popup, or by double-clicking the selected text. Additional tools, termed as appendices in the program, include a currency converter, weights and measure units converter and international time zones converter. Additional ones, such as the periodic table of elements, a scientific calculator, Traditional Chinese and Simplified Chinese conversion utility or a Base64 encoding utility, can be added through the website.

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  Baum–Welch algorithm

  In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to the forward recursions rapidly approaching values below machine precision. == History == The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One of the first major applications of HMMs was to the field of speech processing. In the 1980s, HMMs were emerging as a useful tool in the analysis of biological systems and information, and in particular genetic information. They have since become an important tool in the probabilistic modeling of genomic sequences. == Description == A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend only on the current hidden state. The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e. We assume there are N {\displaystyle N} states in total). We assume the P ( X t ∣ X t − 1 ) {\displaystyle P(X_{t}\mid X_{t-1})} is independent of time t {\displaystyle t} , which leads to the definition of the time-independent stochastic transition matrix A = { a i j } = P ( X t = j ∣ X t − 1 = i ) . {\displaystyle A=\{a_{ij}\}=P(X_{t}=j\mid X_{t-1}=i).} The initial state distribution (i.e. when t = 1 {\displaystyle t=1} ) is given by π i = P ( X 1 = i ) . {\displaystyle \pi _{i}=P(X_{1}=i).} The observation variables Y t {\displaystyle Y_{t}} can take one of K {\displaystyle K} possible values. We also assume the observation given the "hidden" state is time independent. The probability of a certain observation y i {\displaystyle y_{i}} at time t {\displaystyle t} for state X t = j {\displaystyle X_{t}=j} is given by b j ( y i ) = P ( Y t = y i ∣ X t = j ) . {\displaystyle b_{j}(y_{i})=P(Y_{t}=y_{i}\mid X_{t}=j).} Taking into account all the possible values of Y t {\displaystyle Y_{t}} and X t {\displaystyle X_{t}} , we obtain the N × K {\displaystyle N\times K} matrix B = { b j ( y i ) } {\displaystyle B=\{b_{j}(y_{i})\}} where b j {\displaystyle b_{j}} belongs to all the possible states and y i {\displaystyle y_{i}} belongs to all the observations. An observation sequence is given by Y = ( Y 1 = y 1 , Y 2 = y 2 , … , Y T = y T ) {\displaystyle Y=(Y_{1}=y_{1},Y_{2}=y_{2},\ldots ,Y_{T}=y_{T})} . Thus we can describe a hidden Markov chain by θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} . The Baum–Welch algorithm finds a local maximum for θ ∗ = a r g m a x θ ⁡ P ( Y ∣ θ ) {\displaystyle \theta ^{}=\operatorname {arg\,max} _{\theta }P(Y\mid \theta )} (i.e. the HMM parameters θ {\displaystyle \theta } that maximize the probability of the observation). === Algorithm === Set θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} with random initial conditions. They can also be set using prior information about the parameters if it is available; this can speed up the algorithm and also steer it toward the desired local maximum. ==== Forward procedure ==== Let α i ( t ) = P ( Y 1 = y 1 , … , Y t = y t , X t = i ∣ θ ) {\displaystyle \alpha _{i}(t)=P(Y_{1}=y_{1},\ldots ,Y_{t}=y_{t},X_{t}=i\mid \theta )} , the probability of seeing the observations y 1 , y 2 , … , y t {\displaystyle y_{1},y_{2},\ldots ,y_{t}} and being in state i {\displaystyle i} at time t {\displaystyle t} . This is found recursively: α i ( 1 ) = π i b i ( y 1 ) , {\displaystyle \alpha _{i}(1)=\pi _{i}b_{i}(y_{1}),} α i ( t + 1 ) = b i ( y t + 1 ) ∑ j = 1 N α j ( t ) a j i . {\displaystyle \alpha _{i}(t+1)=b_{i}(y_{t+1})\sum _{j=1}^{N}\alpha _{j}(t)a_{ji}.} Since this series converges exponentially to zero, the algorithm will numerically underflow for longer sequences. However, this can be avoided in a slightly modified algorithm by scaling α {\displaystyle \alpha } in the forward and β {\displaystyle \beta } in the backward procedure below. ==== Backward procedure ==== Let β i ( t ) = P ( Y t + 1 = y t + 1 , … , Y T = y T ∣ X t = i , θ ) {\displaystyle \beta _{i}(t)=P(Y_{t+1}=y_{t+1},\ldots ,Y_{T}=y_{T}\mid X_{t}=i,\theta )} that is the probability of the ending partial sequence y t + 1 , … , y T {\displaystyle y_{t+1},\ldots ,y_{T}} given starting state i {\displaystyle i} at time t {\displaystyle t} . We calculate β i ( t ) {\displaystyle \beta _{i}(t)} as, β i ( T ) = 1 , {\displaystyle \beta _{i}(T)=1,} β i ( t ) = ∑ j = 1 N β j ( t + 1 ) a i j b j ( y t + 1 ) . {\displaystyle \beta _{i}(t)=\sum _{j=1}^{N}\beta _{j}(t+1)a_{ij}b_{j}(y_{t+1}).} ==== Update ==== We can now calculate the temporary variables, according to Bayes' theorem: γ i ( t ) = P ( X t = i ∣ Y , θ ) = P ( X t = i , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) β i ( t ) ∑ j = 1 N α j ( t ) β j ( t ) , {\displaystyle \gamma _{i}(t)=P(X_{t}=i\mid Y,\theta )={\frac {P(X_{t}=i,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)\beta _{i}(t)}{\sum _{j=1}^{N}\alpha _{j}(t)\beta _{j}(t)}},} which is the probability of being in state i {\displaystyle i} at time t {\displaystyle t} given the observed sequence Y {\displaystyle Y} and the parameters θ {\displaystyle \theta } ξ i j ( t ) = P ( X t = i , X t + 1 = j ∣ Y , θ ) = P ( X t = i , X t + 1 = j , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) a i j β j ( t + 1 ) b j ( y t + 1 ) ∑ k = 1 N ∑ w = 1 N α k ( t ) a k w β w ( t + 1 ) b w ( y t + 1 ) , {\displaystyle \xi _{ij}(t)=P(X_{t}=i,X_{t+1}=j\mid Y,\theta )={\frac {P(X_{t}=i,X_{t+1}=j,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)a_{ij}\beta _{j}(t+1)b_{j}(y_{t+1})}{\sum _{k=1}^{N}\sum _{w=1}^{N}\alpha _{k}(t)a_{kw}\beta _{w}(t+1)b_{w}(y_{t+1})}},} which is the probability of being in state i {\displaystyle i} and j {\displaystyle j} at times t {\displaystyle t} and t + 1 {\displaystyle t+1} respectively given the observed sequence Y {\displaystyle Y} and parameters θ {\displaystyle \theta } . The denominators of γ i ( t ) {\displaystyle \gamma _{i}(t)} and ξ i j ( t ) {\displaystyle \xi _{ij}(t)} are the same ; they represent the probability of making the observation Y {\displaystyle Y} given the parameters θ {\displaystyle \theta } . The parameters of the hidden Markov model θ {\displaystyle \theta } can now be updated: π i ∗ = γ i ( 1 ) , {\displaystyle \pi _{i}^{}=\gamma _{i}(1),} which is the expected frequency spent in state i {\displaystyle i} at time 1 {\displaystyle 1} . a i j ∗ = ∑ t = 1 T − 1 ξ i j ( t ) ∑ t = 1 T − 1 γ i ( t ) , {\displaystyle a_{ij}^{}={\frac {\sum _{t=1}^{T-1}\xi _{ij}(t)}{\sum _{t=1}^{T-1}\gamma _{i}(t)}},} which is the expected number of transitions from state i to state j compared to the expected total number of transitions starting in state i, including from state i to itself. The number of transitions starting in state i is equivalent to the number of times state i is observed in the sequence from t = 1 to t = T − 1. b i ∗ ( v k ) = ∑ t = 1 T 1 y t = v k γ i ( t ) ∑ t = 1 T γ i ( t ) , {\displaystyle b_{i}^{}(v_{k})={\frac {\sum _{t=1}^{T}1_{y_{t}=v_{k}}\gamma _{i}(t)}{\sum _{t=1}^{T}\gamma _{i}(t)}},} where 1 y t = v k = { 1 if y t = v k , 0 otherwise {\displaystyle 1_{y_{t}=v_{k}}={\begin{cases}1&{\text{if }}y_{t}=v_{k},\\0&{\text{otherwise}}\end{cases}}} is an indicator function, and b i ∗ ( v k ) {\displaystyle b_{i}^{}(v_{k})} is the expected number of times the output observations have been equal to v k {\displaystyle v_{k}} while in state i {\displaystyle i} over the expected total number of times in state i {\displaystyle i} . These steps are now repeated iteratively until a desired level of convergence. Note: It is possible to over-fit a particular data set. That is, P ( Y ∣ θ final ) > P ( Y ∣ θ true ) {\displaystyle P(Y\mid \theta _{\text{final}})>P(Y\mid \theta _{\text{true}})} . The algorithm also does not guarantee a global maximum. ==== Multiple sequences ==== The algorithm described thus far assumes a single observed sequence Y = y 1 , … , y T {\displaystyle Y=y_{1},\ldots ,y_{T}} . However, in many situations, there are several sequences observed: Y 1 ,

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