AI Writing Tools

Explore the best AI Writing Tools — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

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  Online service provider

  An online service provider (OSP) can, for example, be an Internet service provider, an email provider, a news provider (press), an entertainment provider (music, movies), a search engine, an e-commerce site, an online banking site, a health site, an official government site, social media, a wiki, or a Usenet newsgroup. In its original more limited definition, it referred only to a commercial computer communication service in which paid members could dial via a computer modem the service's private computer network and access various services and information resources such as bulletin board systems, downloadable files and programs, news articles, chat rooms, and electronic mail services. The term "online service" was also used in references to these dial-up services. The traditional dial-up online service differed from the modern Internet service provider in that they provided a large degree of content that was only accessible by those who subscribed to the online service, while ISP mostly serves to provide access to the Internet and generally provides little if any exclusive content of its own. In the U.S., the Online Copyright Infringement Liability Limitation Act (OCILLA) portion of the U.S. Digital Millennium Copyright Act has expanded the legal definition of online service in two different ways for different portions of the law. It states in section 512(k)(1): (A) As used in subsection (a), the term "service provider" means an entity offering the transmission, routing, or providing of connections for digital online communications, between or among points specified by a user, of material of the user's choosing, without modification to the content of the material as sent or received. (B) As used in this section, other than subsection (a), the term "service provider" means a provider of online services or network access, or the operator of facilities therefore, and includes an entity described in subparagraph (A). These broad definitions make it possible for numerous web businesses to benefit from the OCILLA. == History == The first commercial online services went live in 1969. CompuServe (owned in the 1980s and 1990s by H&R Block) and The Source (for a time owned by The Reader's Digest) are considered the first major online services created to serve the market of personal computer users. Utilizing text-based interfaces and menus, these services allowed anyone with a modem and communications software to use email, chat, news, financial and stock information, bulletin boards, special interest groups (SIGs), forums and general information. Subscribers could exchange email only with other subscribers of the same service. (For a time a service called DASnet carried mail among several online services, and CompuServe, MCI Mail, and other services experimented with X.400 protocols to exchange email until the Internet rendered these outmoded.) Other text-based online services followed such as Delphi, GEnie and MCI Mail. The 1980s also saw the rise of independent Computer Bulletin Boards, or BBSes. (Online services are not BBSes. An online service may contain an electronic bulletin board, but the term "BBS" is reserved for independent dialup, microcomputer-based services that are usually single-user systems.) The commercial services used pre-existing packet-switched (X.25) data communications networks, or the services' own networks (as with CompuServe). In either case, users dialed into local access points and were connected to remote computer centers where information and services were located. As with telephone service, subscribers paid by the minute, with separate day-time and evening/weekend rates. As the use of computers that supported color and graphics, such the Atari 8-bit computers, Commodore 64, TI-99/4A, Apple II, and early IBM PC compatibles, increased, online services gradually developed framed or partially graphical information displays. Early services such as CompuServe added increasingly sophisticated graphics-based front end software to present their information, though they continued to offer text-based access for those who needed or preferred it. In 1985 Viewtron, which began as a Videotex service requiring a dedicated terminal, introduced software allowing home computer owners access. Beginning in the mid-1980s graphics based online services such as PlayNET, Prodigy, and Quantum Link (aka Q-Link) were developed. Quantum Link, which was based on Commodore-only Playnet software, later developed AppleLink Personal Edition, PC-Link (based on Tandy's DeskMate), and Promenade (for IBM), all of which (including Q-Link) were later combined as America Online. These online services presaged the web browser that would change global online life 10 years later. Before Quantum Link, Apple computer had developed its own service, called AppleLink, which was mostly a support network targeted at Apple dealers and developers. Later, Apple offered the short-lived eWorld, targeted at Mac consumers and based on the Mac version of the America Online software. Beginning in 1992, the Internet, which had previously been limited to government, academic, and corporate research settings, was opened to commercial entities. The first online service to offer Internet access was DELPHI, which had developed TCP/IP access much earlier, in connection with an environmental group that rated Internet access. The explosion of popularity of the World Wide Web in 1994 accelerated the development of the Internet as an information and communication resource for consumers and businesses. The sudden availability of low- to no-cost email and appearance of free independent web sites broke the business model that had supported the rise of the early online service industry. CompuServe, BIX, AOL, DELPHI, and Prodigy gradually added access to Internet e-mail, Usenet newsgroups, ftp, and to web sites. At the same time, they moved from usage-based billing to monthly subscriptions. Similarly, companies that paid to have AOL host their information or early online stores began to develop their own web sites, putting further stress on the economics of the online industry. Only the largest services like AOL (which later acquired CompuServe, just as CompuServe acquired The Source) were able to make the transition to the Internet-centric world. A new class of online service provider arose to provide access to the Internet, the internet service provider or ISP. Internet-only service providers like UUNET, The Pipeline, Panix, Netcom, the World, EarthLink, and MindSpring provided no content of their own, concentrating their efforts on making it easy for nontechnical users to install the various software required to "get online" before consumer operating systems came internet-enabled out of the box. In contrast to the online services' multitiered per-minute or per-hour rates, many ISPs offered flat-fee, unlimited access plans. Independent companies sprang up to offer access and packages to compete with the big networks (eg, the-wire.com, 1994 in Toronto and bway.net 1995 in New York). These providers first offered access through telephone and modem, just as did the early online services providers. By the early 2000s, these independent ISPs had largely been supplanted by high speed and broadband access through cable and phone companies, as well as wireless access. The importance of the online services industry was vital in "paving the road" for the information superhighway. When Mosaic and Netscape were released in 1994, they had a ready audience of more than 10 million people who were able to download their first web browser through an online service. Though ISPs quickly began offering software packages with setup to their customers, this brief period gave many users their first online experience. Two online services in particular, Prodigy and AOL, are often confused with the Internet, or the origins of the Internet. Prodigy's Chief Technical Officer said in 1999: "Eleven years ago, the Internet was just an intangible dream that Prodigy brought to life. Now it is a force to be reckoned with." Despite that statement, neither service provided the back bone for the Internet, nor did either start the Internet. == Online service interfaces == The first online service used a simple text-based interface in which content was largely text only and users made choices via a command prompt. This allowed just about any computer with a modem and terminal communications program the ability to access these text-based online services. CompuServe would later offer, with the advent of the Apple Macintosh and Microsoft Windows-based PCs, a GUI interface program for their service. This provided a very rudimentary GUI interface. CompuServe continued to offer text-only access for those needing it. Online services like Prodigy and AOL developed their online service around a GUI and thus unlike CompuServe's early GUI-based software, these online services provided a more robust GUI interface. Early GUI-base

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  LMArena

  Arena (formerly LMArena and Chatbot Arena) is a public, web-based platform that evaluates large language models (LLMs). Users enter prompts for two anonymous models to respond to and vote on the model that gave the better response, after which the models' identities are revealed. Users can also choose models to test themselves via the "Direct" selection. Companies which have supplied the company with their large language models include OpenAI, Google DeepMind, and Anthropic. The website has been used for preview releases of upcoming models. Chinese company DeepSeek tested its prototype models in the Arena months before its R1 model gained attention in Western media. Other notable pre-release models include OpenAI's GPT-5 under the codename "summit" and Google DeepMind's Gemini 2.5 Flash Image (an image-generation and editing model) under the codename "Nano Banana". Research has identified specific limitations in Arena's methodology. == History == Chatbot Arena was released on April 24, 2023. In June 2024, Chatbot Arena added image support. In September 2024, Chatbot Arena moved to its own dedicated domain name, lmarena.ai (or LMArena). In April 2025, Meta released Llama 4. Llama 4 Maverick beat GPT-4o and Gemini 2.0 Flash on LMArena, but the version of Maverick on LMArena unfairly differed from the publicly available version. LMArena updated their policies in response. In April 2025, LMArena incorporated as an independent company. That May, LMArena raised $100 million in a seed funding round, valuing the company at $600 million. Participants in the seed funding round included Andreessen Horowitz, UC Investments, Lightspeed Venture Partners, Felicis Ventures, and Kleiner Perkins. On January 6, 2026, LMArena announced the closing of a $150 million Series A funding round, bringing the company’s post-money valuation to approximately $1.7 billion. The round was led by Felicis and UC Investments (University of California), with participation from Andreessen Horowitz, The House Fund, LDVP, Kleiner Perkins, Lightspeed Venture Partners, and Laude Ventures. In January 2026, LMArena added video support. On January 28, 2026, LMArena rebranded to "Arena".

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  Virtual Woman

  Virtual Woman is a software program that has elements of a chatbot, virtual reality, artificial intelligence, a video game, and a virtual human. It claims to be the oldest form of virtual life in existence, as it has been distributed since the late 1980s. Recent releases of the program can update their intelligence by connecting online and downloading newer personalities and histories. == Program play == When Virtual Woman starts, the user is presented with a list of options and then may choose their Virtual Woman's ethnic type, personality, location, clothing, etc. or load a pre-built Virtual Woman from a Digital DNA file. Once the options are determined, the user is presented with a 3-D animated Virtual Woman of their selection and then can engage them in conversation, progressing in a manner similar to that of its predecessor, ELIZA and its successors, the chatbots. In most versions of Virtual Woman, this is done through the keyboard, but some versions also support voice input. == In popular culture == Software sales and usage statistics from private companies are difficult to verify. WinSite, an independent Internet shareware distribution site that does publish public download counts, has for some time now listed some version of Virtual Woman in their top three shareware downloads of all time with well over seven hundred thousand downloads. == Compadre == The group of beta testers and advisers for Virtual Woman are referred to as Compadre and have their own beta testing site and forum. == Criticisms == As Virtual Woman has developed the ability to conduct longer and more realistic interactions, particularly in recent beta releases, criticism has arisen that this may lead some users to social isolation, or to use the program as a substitute for real human interaction. However, these are criticisms that have been leveled at all video games and at the use of the Internet itself. == Release history == Versions of Virtual Woman with rough release dates and PC platforms for which they were designed: Virtual Woman (????) (DOS) Virtual Woman for Windows (1991) (Windows 3.0) Virtual Woman 95 (1995) (Windows 3X, Windows 95) Virtual Woman 98 (1998) (Windows 3X, Windows 95) Virtual Woman 2000 (2000) (Windows 95+) Virtual Woman Millennium (Windows 95, XP) Virtual Woman Net ( Windows XP/Vista specific)

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  Local ternary patterns

  Local ternary patterns (LTP) are an extension of local binary patterns (LBP). Unlike LBP, it does not threshold the pixels into 0 and 1, rather it uses a threshold constant to threshold pixels into three values. Considering k as the threshold constant, c as the value of the center pixel, a neighboring pixel p, the result of threshold is: { 1 , if p > c + k 0 , if p > c − k and p < c + k − 1 if p < c − k {\displaystyle {\begin{cases}1,&{\text{if }}p>c+k\\0,&{\text{if }}p>c-k{\text{ and }}p Read more →

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  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

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  Augmented Analytics

  Augmented Analytics is an approach of data analytics that employs the use of machine learning and natural language processing to automate analysis processes normally done by a specialist or data scientist. The term was introduced in 2017 by Rita Sallam, Cindi Howson, and Carlie Idoine in a Gartner research paper. Augmented analytics is based on business intelligence and analytics. In the graph extraction step, data from different sources are investigated. == Defining Augmented Analytics == Machine Learning – a systematic computing method that uses algorithms to sift through data to identify relationships, trends, and patterns. It is a process that allows algorithms to dynamically learn from data instead of having a set base of programmed rules. Natural language generation (NLG) – a software capability that takes unstructured data and translates it into plain-English, readable, language. Automating Insights – using machine learning algorithms to automate data analysis processes. Natural Language Query – enabling users to query data using business terms that are either typed onto a search box or spoken. == Data Democratization == Data Democratization is the democratizing data access in order to relieve data congestion and get rid of any sense of data "gatekeepers". This process must be implemented alongside a method for users to make sense of the data. This process is used in hopes of speeding up company decision making and uncovering opportunities hidden in data. There are three aspects to democratising data: Data Parameterisation and Characterisation. Data Decentralisation using an OS of blockchain and DLT technologies, as well as an independently governed secure data exchange to enable trust. Consent Market-driven Data Monetisation. When it comes to connecting assets, there are two features that will accelerate the adoption and usage of data democratisation: decentralized identity management and business data object monetization of data ownership. It enables multiple individuals and organizations to identify, authenticate, and authorize participants and organizations, enabling them to access services, data or systems across multiple networks, organizations, environments, and use cases. It empowers users and enables a personalized, self-service digital onboarding system so that users can self-authenticate without relying on a central administration function to process their information. Simultaneously, decentralized identity management ensures the user is authorized to perform actions subject to the system’s policies based on their attributes (role, department, organization, etc.) and/ or physical location. == Use cases == Agriculture – Farmers collect data on water use, soil temperature, moisture content and crop growth, augmented analytics can be used to make sense of this data and possibly identify insights that the user can then use to make business decisions. Smart Cities – Many cities across the United States, known as Smart Cities collect large amounts of data on a daily basis. Augmented analytics can be used to simplify this data in order to increase effectiveness in city management (transportation, natural disasters, etc.). Analytic Dashboards – Augmented analytics has the ability to take large data sets and create highly interactive and informative analytical dashboards that assist in many organizational decisions. Augmented Data Discovery – Using an augmented analytics process can assist organizations in automatically finding, visualizing and narrating potentially important data correlations and trends. Data Preparation – Augmented analytics platforms have the ability to take large amounts of data and organize and "clean" the data in order for it to be usable for future analyses. Business – Businesses collect large amounts of data, daily. Some examples of types of data collected in business operations include; sales data, consumer behavior data, distribution data. An augmented analytics platform provides access to analysis of this data, which could be used in making business decisions.

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  Brill tagger

  The Brill tagger is an inductive method for part-of-speech tagging. It was described and invented by Eric Brill in his 1993 PhD thesis. It can be summarized as an "error-driven transformation-based tagger". It is: a form of supervised learning, which aims to minimize error; and, a transformation-based process, in the sense that a tag is assigned to each word and changed using a set of predefined rules. In the transformation process, if the word is known, it first assigns the most frequent tag, or if the word is unknown, it naively assigns the tag "noun" to it. High accuracy is eventually achieved by applying these rules iteratively and changing the incorrect tags. This approach ensures that valuable information such as the morphosyntactic construction of words is employed in an automatic tagging process. == Algorithm == The algorithm starts with initialization, which is the assignment of tags based on their probability for each word (for example, "dog" is more often a noun than a verb). Then "patches" are determined via rules that correct (probable) tagging errors made in the initialization phase: Initialization: Known words (in vocabulary): assigning the most frequent tag associated to a form of the word Unknown word == Rules and processing == The input text is first tokenized, or broken into words. Typically in natural language processing, contractions such as "'s", "n't", and the like are considered separate word tokens, as are punctuation marks. A dictionary and some morphological rules then provide an initial tag for each word token. For example, a simple lookup would reveal that "dog" may be a noun or a verb (the most frequent tag is simply chosen), while an unknown word will be assigned some tag(s) based on capitalization, various prefix or suffix strings, etc. (such morphological analyses, which Brill calls Lexical Rules, may vary between implementations). After all word tokens have (provisional) tags, contextual rules apply iteratively, to correct the tags by examining small amounts of context. This is where the Brill method differs from other part of speech tagging methods such as those using Hidden Markov Models. Rules are reapplied repeatedly, until a threshold is reached, or no more rules can apply. Brill rules are of the general form: tag1 → tag2 IF Condition where the Condition tests the preceding and/or following word tokens, or their tags (the notation for such rules differs between implementations). For example, in Brill's notation: IN NN WDPREVTAG DT while would change the tag of a word from IN (preposition) to NN (common noun), if the preceding word's tag is DT (determiner) and the word itself is "while". This covers cases like "all the while" or "in a while", where "while" should be tagged as a noun rather than its more common use as a conjunction (many rules are more general). Rules should only operate if the tag being changed is also known to be permissible, for the word in question or in principle (for example, most adjectives in English can also be used as nouns). Rules of this kind can be implemented by simple Finite-state machines. See Part of speech tagging for more general information including descriptions of the Penn Treebank and other sets of tags. Typical Brill taggers use a few hundred rules, which may be developed by linguistic intuition or by machine learning on a pre-tagged corpus. == Code == Brill's code pages at Johns Hopkins University are no longer on the web. An archived version of a mirror of the Brill tagger at its latest version as it was available at Plymouth Tech can be found on Archive.org. The software uses the MIT License.

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  Hard sigmoid

  In artificial intelligence, especially computer vision and artificial neural networks, a hard sigmoid is non-smooth function used in place of a sigmoid function. These retain the basic shape of a sigmoid, rising from 0 to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of computation is more important than precision. == Examples == The most extreme examples are the sign function or Heaviside step function, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0. Other examples include the Theano library, which provides two approximations: ultra_fast_sigmoid, which is a multi-part piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1).

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  Umoove

  Umoove is a high tech startup company that has developed and patented a software-only face and eye tracking technology. The idea was first conceived as an attempt to aid people with disabilities but has since evolved. The only compatibility qualification for tablet computers and smartphones to run Umoove software is a front-facing camera. Umoove headquarters are in Israel on Jerusalem’s Har Hotzvim. Umoove has 15 employees and received two million dollars in financing in 2012. The company's original founders invested around $800,000 to start the business in 2010. In 2013 Umoove was named one of the top three most promising Israeli start ups by Newsgeeks magazine. The company also participated in the 2013 LeWeb conference in Paris, France, where innovative technology startups are showcased. == Technology == The technology uses information extracted from previous frames, such as the angle of the user's head to predict where to look for facial targets in the next frame. This anticipation minimizes the amount of computation needed to scan each image. Umoove accounts for variances in environment, lighting conditions and user hand shake/movement. The technology is designed to provide a consistent experience, whether you're in a brightly lit area or a darkened basement, and to work fluidly between them by adapting its processing when it detects color and brightness shifts. It uses an active stabilization technique to filter out natural body movements from an unstable camera in order to minimize false-positive motion detection. Running the Umoove software on a Samsung Galaxy S3 is said to take up only 2% CPU. Umoove works exclusively with software and there is no hardware add-on necessary. It can be run on any smartphone or tablet computer that has a front-facing camera. Umoove claims that even a low-quality camera on an old device will run their software flawlessly. == Umoove Experience == In January 2014 Umoove released its first game onto the app store. The Umoove Experience game lets users control where they are 'flying' in the game through simple gestures and motions with their head. The avatar will basically go toward wherever the user looks. The game was created to showcase the technology for game developers but that did not stop some from criticizing its simplicity. Umoove also announced that they raised another one million dollars and that they are opening offices in Silicon Valley, California. In February 2014, Umoove announced that their face-tracking software development kit is available for Android developers as well as iOS. == Reviews == The Umoove Experience garnered mostly positive reviews from bloggers and mainstream media with some predicting that it could be the future of mobile gaming. Mashable wrote that Umoove's technology could be the emergence of gesture recognition technology in the mobile space, similar to Kinect with console gaming and what Leap Motion has done with desktop computers. Some, however, remain skeptical. CNET, for example, did not give the game a positive review and called the eye tracking technology 'freaky but cool'. They also noted that pioneering technologies have been known to fall short of expectations, citing Apple Inc’s Siri as an example. The technology blog GigaOM said that the Umoove Experience is ’awesome’ and technology evangelist Robert Scoble has called Umoove "brilliant". == uHealth == In January 2015, Umoove released uHealth, a mobile application that uses eye tracking game-like exercise to challenge the user's ability to be attentive, continuously focus, follow commands and avoid distractions. The app is designed in the form of two games, one to improve attention and another that hones focus. uHealth is a training tool, not a diagnostic. Umoove has stated that they want to use their technology for diagnosing neurological disorders but this will depend on clinical tests and FDA approval. The company cites the direct relationship between eye movements and brain activity as well as various vision-based therapies have been backed by many scientific studies conducted over the past decades. uHealth is the first time this type of therapy is delivered right to the end user through a simple download. == Collaboration rumors == In March 2013 there were rumors on the internet that Umoove would be the functioning software embedded into the Samsung Galaxy S4, which was due to launch that month. This rumor was perpetrated by, among others, New York Times, Techcrunch and Yahoo. Once Samsung launched without the Umoove technology rumors about a potential collaboration with Apple Inc hit the web. It has been said that due to the fact that Apple Inc is losing market share and stock value to Samsung they will be more aggressive and eye tracking is a logical place to make that move.

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  Image fusion

  The image fusion process is defined as gathering all the important information from multiple images, and their inclusion into fewer images, usually a single one. This single image is more informative and accurate than any single source image, and it consists of all the necessary information. The purpose of image fusion is not only to reduce the amount of data but also to construct images that are more appropriate and understandable for the human and machine perception. In computer vision, multisensor image fusion is the process of combining relevant information from two or more images into a single image. The resulting image will be more informative than any of the input images. In remote sensing applications, the increasing availability of space borne sensors gives a motivation for different image fusion algorithms. Several situations in image processing require high spatial and high spectral resolution in a single image. Most of the available equipment is not capable of providing such data convincingly. Image fusion techniques allow the integration of different information sources. The fused image can have complementary spatial and spectral resolution characteristics. However, the standard image fusion techniques can distort the spectral information of the multispectral data while merging. In satellite imaging, two types of images are available. The panchromatic image acquired by satellites is transmitted with the maximum resolution available and the multispectral data are transmitted with coarser resolution. This will usually be two or four times lower. At the receiver station, the panchromatic image is merged with the multispectral data to convey more information. Many methods exist to perform image fusion. The very basic one is the high-pass filtering technique. Later techniques are based on Discrete Wavelet Transform, uniform rational filter bank, and Laplacian pyramid. == Motivation == Multi sensor data fusion has become a discipline which demands more general formal solutions to a number of application cases. Several situations in image processing require both high spatial and high spectral information in a single image. This is important in remote sensing. However, the instruments are not capable of providing such information either by design or because of observational constraints. One possible solution for this is data fusion. == Methods == Image fusion methods can be broadly classified into two groups – spatial domain fusion and transform domain fusion. The fusion methods such as averaging, Brovey method, principal component analysis (PCA) and IHS based methods fall under spatial domain approaches. Another important spatial domain fusion method is the high-pass filtering based technique. Here the high frequency details are injected into upsampled version of MS images. The disadvantage of spatial domain approaches is that they produce spatial distortion in the fused image. Spectral distortion becomes a negative factor while we go for further processing, such as classification problem. Spatial distortion can be very well handled by frequency-domain approaches on image fusion. The multiresolution analysis has become a very useful tool for analysing remote sensing images. The discrete wavelet transform has become a very useful tool for fusion. Some other fusion methods are also there, such as Laplacian pyramid based, curvelet transform based etc. These methods show a better performance in spatial and spectral quality of the fused image compared to other spatial methods of fusion. The images used in image fusion should already be registered. Misregistration is a major source of error in image fusion. Some well-known image fusion methods are: High-pass filtering technique IHS transform based image fusion PCA-based image fusion Wavelet transform image fusion Pair-wise spatial frequency matching Comparative analysis of image fusion methods demonstrates that different metrics support different user needs, sensitive to different image fusion methods, and need to be tailored to the application. Categories of image fusion metrics are based on information theory features, structural similarity, or human perception. === Multi-focus image fusion === Multi-focus image fusion is used to collect useful and necessary information from input images with different focus depths in order to create an output image that ideally has all information from input images. In visual sensor network (VSN), sensors are cameras which record images and video sequences. In many applications of VSN, a camera can’t give a perfect illustration including all details of the scene. This is because of the limited depth of focus exists in the optical lens of cameras. Therefore, just the object located in the focal length of camera is focused and cleared and the other parts of image are blurred. VSN has an ability to capture images with different depth of focuses in the scene using several cameras. Due to the large amount of data generated by camera compared to other sensors such as pressure and temperature sensors and some limitation such as limited band width, energy consumption and processing time, it is essential to process the local input images to decrease the amount of transmission data. The aforementioned reasons emphasize the necessary of multi-focus images fusion. Multi-focus image fusion is a process which combines the input multi-focus images into a single image including all important information of the input images and it’s more accurate explanation of the scene than every single input image. == Applications == === In remote sensing === Image fusion in remote sensing has several application domains. An important domain is the multi-resolution image fusion (commonly referred to pan-sharpening). In satellite imagery we can have two types of images: Panchromatic images – An image collected in the broad visual wavelength range but rendered in black and white. Multispectral images – Images optically acquired in more than one spectral or wavelength interval. Each individual image is usually of the same physical area and scale but of a different spectral band. The SPOT PAN satellite provides high resolution (10m pixel) panchromatic data. While the LANDSAT TM satellite provides low resolution (30m pixel) multispectral images. Image fusion attempts to merge these images and produce a single high resolution multispectral image. The standard merging methods of image fusion are based on Red–Green–Blue (RGB) to Intensity–Hue–Saturation (IHS) transformation. The usual steps involved in satellite image fusion are as follows: Resize the low resolution multispectral images to the same size as the panchromatic image. Transform the R, G and B bands of the multispectral image into IHS components. Modify the panchromatic image with respect to the multispectral image. This is usually performed by histogram matching of the panchromatic image with Intensity component of the multispectral images as reference. Replace the intensity component by the panchromatic image and perform inverse transformation to obtain a high resolution multispectral image. Pan-sharpening can be done with Photoshop. Other applications of image fusion in remote sensing are available. === In medical imaging === Image fusion has become a common term used within medical diagnostics and treatment. The term is used when multiple images of a patient are registered and overlaid or merged to provide additional information. Fused images may be created from multiple images from the same imaging modality, or by combining information from multiple modalities, such as magnetic resonance image (MRI), computed tomography (CT), positron emission tomography (PET), and single-photon emission computed tomography (SPECT). In radiology and radiation oncology, these images serve different purposes. For example, CT images are used more often to ascertain differences in tissue density while MRI images are typically used to diagnose brain tumors. For accurate diagnosis, radiologists must integrate information from multiple image formats. Fused, anatomically consistent images are especially beneficial in diagnosing and treating cancer. With the advent of these new technologies, radiation oncologists can take full advantage of intensity modulated radiation therapy (IMRT). Being able to overlay diagnostic images into radiation planning images results in more accurate IMRT target tumor volumes.

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  Spleak

  Spleak was an IM platform where users could publish and rate content. It existed in the form of six bots covering as many subject areas: CelebSpleak, SportSpleak, VoteSpleak, TVSpleak, GameSpleak, and StyleSpleak. == Overview == Users can add a "multi-Spleak" (which contains all of the different Spleak bots in one) or add the separate bots to their IM buddy lists on MSN and AIM. Users are also allowed access to Spleak online by using a CelebSpleak, SportSpleak, or VoteSpleak widget, or through the CelebSpleak and SportSpleak applications with Facebook. Spleak was an alternate reality game and is moving to its own company, Spleak Media Network. "Celebrate Spleak" was introduced throughout 2007, launched in 2008, and was forced to retire in 2009. == Key people == Spleak was co-founded by Morten Lund and Nicolaj Reffstrup. The company's chief executive officer is Morrie Eisenburg; Josh Scott is Vice President in Product and Tyler Wells is Vice President in Engineering.

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  Jaggaer

  JAGGAER, formerly SciQuest, is a provider of cloud-based business automation technology for Business Spend Management. Its headquarters is in Durham, North Carolina. == Company history == SciQuest was established in 1995 as a B2B eCommerce exchange.The company went public with an IPO in 1999. In 2001, SciQuest transitioned from a B2B exchange company into eProcurement software and supplier enablement platforms. SciQuest was taken private in 2004 and continued to move into eProcurement, inventory management and accounts payable automation. SciQuest completed an IPO in September 2010, raising approximately $57 million. SciQuest, and its 510 person workforce, was taken private in June 2016 as part of a $509 million acquisition by Accel-KKR, a private equity firm headquartered in Menlo Park, CA. In 2017 SciQuest was rebranded as JAGGAER and announced increased focus on offering a complete, integrated source-to-pay suite. Along with the name change, the company expanded its market focus to manufacturing, healthcare, consumer packaged goods, retail, education, life sciences, logistics and the public sector. JAGGAER acquired the European direct materials procurement specialist Pool4Tool in June 2017 giving it end-to-end direct as well as indirect materials procurement coverage. JAGGAER acquired spend management company BravoSolution in 2017, and entered into a joint venture with United Arab Emirates-based Tejari. In February 2019 JAGGAER launched JAGGAER One, which unifies its full product suite on a single platform. In 2019 the UK-based private equity firm Cinven acquired a majority holding in the company. Jim Bureau was subsequently named JAGGAER's Chief Executive Officer. Bureau left the firm in March 2023, and Andy Hovancik was announced as the company's CEO in June. In 2024, JAGGAER was acquired by Vista Equity Partners, a private equity firm specializing in enterprise software investments. == Current positioning == As of April 2025, JAGGAER positions itself as "an enterprise procurement and supplier collaboration SaaS provider." Its core technology platform, which is called JAGGAER One, serves "direct and indirect procurement with specializations in Higher Education, Discrete and Process Manufacturing, and Public Sector." == Product Categories == The JAGGAER One platform supports the following products: Spend Analytics Category Management Supplier Management Sourcing Contracts eProcurement Invoicing Inventory Management Supply Chain Collaboration Quality Management == Acquisitions == SciQuest acquired the following companies: AECsoft - January 2011. Provider of supplier management and sourcing technology. Upside Software, Inc. - August 2012. Provider of contract lifecycle management (CLM) solutions. Spend Radar, LLC - October 2012, Provider of spend analysis software. CombineNet - September 2013, Provider of advanced sourcing software JAGGAER acquired the following companies: POOL4TOOL - June 2017, Provider of direct sourcing and supply chain management software BravoSolution - December 2017, Provider of global platform spend management solutions

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  Geofence warrant

  A geofence warrant or a reverse location warrant is a search warrant issued by a court to allow law enforcement to search a database to find all active mobile devices within a particular geo-fence area. Courts have granted law enforcement geo-fence warrants to obtain information from databases such as Google's Sensorvault, which collects users' historical geolocation data. Geo-fence warrants are a part of a category of warrants known as reverse search warrants. == History == Geofence warrants were first used in 2016. Google reported that it had received 982 such warrants in 2018, 8,396 in 2019, and 11,554 in 2020. A 2021 transparency report showed that 25% of data requests from law enforcement to Google were geo-fence data requests. Google is the most common recipient of geo-fence warrants and the main provider of such data, although companies including Apple, Snapchat, Lyft, and Uber have also received such warrants. == Legality == === United States === Some lawyers and privacy experts believe reverse search warrants are unconstitutional under the Fourth Amendment to the United States Constitution, which protects people from unreasonable searches and seizures, and requires any search warrants be specific to what and to whom they apply. The Fourth Amendment specifies that warrants may only be issued "upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." Some lawyers, legal scholars, and privacy experts have likened reverse search warrants to general warrants, which were made illegal by the Fourth Amendment. Groups including the Electronic Frontier Foundation have opposed geo-fence warrants in amicus briefs filed in motions to quash such orders to disclose geo-fence data. In 2024, a panel of the United States Fourth Circuit Court of Appeals considered data acquired from Google’s Sensorvault not to be a search, but non-private business records when users opt-in to Google’s location history. However, upon a rehearing en banc, the Court vacated that decision. In April 2025, the full Court affirmed the judgment solely on the 'good faith' exception, leaving the underlying constitutional question of whether geofence warrants constitute a search unsettled in the Circuit. However, the United States Fifth Circuit Court of Appeals found that geofence warrants are "categorically prohibited by the Fourth Amendment." The split in Circuits prompted the United States Supreme Court to agree to hear Chatrie v. United States in January 2026.

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  Neural operators

  Neural operators are a class of deep learning architectures designed to learn maps between infinite-dimensional function spaces. Neural operators represent an extension of traditional artificial neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets. Neural operators directly learn operators between function spaces; they can receive input functions, and the output function can be evaluated at any discretization. The primary application of neural operators is in learning surrogate maps for the solution operators of partial differential equations (PDEs), which are critical tools in modeling the natural environment. Standard PDE solvers can be time-consuming and computationally intensive, especially for complex systems. Neural operators have demonstrated improved performance in solving PDEs compared to existing machine learning methodologies while being significantly faster than numerical solvers. Neural operators have also been applied to various scientific and engineering disciplines such as turbulent flow modeling, computational mechanics, graph-structured data, and the geosciences. In particular, they have been applied to learning stress-strain fields in materials, classifying complex data like spatial transcriptomics, predicting multiphase flow in porous media, and carbon dioxide migration simulations. Finally, the operator learning paradigm allows learning maps between function spaces, and is different from parallel ideas of learning maps from finite-dimensional spaces to function spaces, and subsumes these settings as special cases when limited to a fixed input resolution. == Operator learning == Understanding and mapping relationships between function spaces has many applications in engineering and the sciences. In particular, one can cast the problem of solving partial differential equations as identifying a map between function spaces, such as from an initial condition to a time-evolved state. In other PDEs this map takes an input coefficient function and outputs a solution function. Operator learning is a machine learning paradigm to learn solution operators mapping the input function to the output function . Using traditional machine learning methods, addressing this problem would involve discretizing the infinite-dimensional input and output function spaces into finite-dimensional grids and applying standard learning models, such as neural networks. This approach reduces the operator learning to finite-dimensional function learning and has some limitations, such as generalizing to discretizations beyond the grid used in training. The primary properties of neural operators that differentiate them from traditional neural networks is discretization invariance and discretization convergence. Unlike conventional neural networks, which are fixed on the discretization of training data, neural operators can adapt to various discretizations without re-training. This property improves the robustness and applicability of neural operators in different scenarios, providing consistent performance across different resolutions and grids. == Definition and formulation == Architecturally, neural operators are similar to feed-forward neural networks in the sense that they are composed of alternating linear maps and non-linearities. Since neural operators act on and output functions, neural operators have been instead formulated as a sequence of alternating linear integral operators on function spaces and point-wise non-linearities. Using an analogous architecture to finite-dimensional neural networks, similar universal approximation theorems have been proven for neural operators. In particular, it has been shown that neural operators can approximate any continuous operator on a compact set. Neural operators seek to approximate some operator G : A → U {\displaystyle {\mathcal {G}}:{\mathcal {A}}\to {\mathcal {U}}} between function spaces A {\displaystyle {\mathcal {A}}} and U {\displaystyle {\mathcal {U}}} by building a parametric map G ϕ : A → U {\displaystyle {\mathcal {G}}_{\phi }:{\mathcal {A}}\to {\mathcal {U}}} . Such parametric maps G ϕ {\displaystyle {\mathcal {G}}_{\phi }} can generally be defined in the form G ϕ := Q ∘ σ ( W T + K T + b T ) ∘ ⋯ ∘ σ ( W 1 + K 1 + b 1 ) ∘ P , {\displaystyle {\mathcal {G}}_{\phi }:={\mathcal {Q}}\circ \sigma (W_{T}+{\mathcal {K}}_{T}+b_{T})\circ \cdots \circ \sigma (W_{1}+{\mathcal {K}}_{1}+b_{1})\circ {\mathcal {P}},} where P , Q {\displaystyle {\mathcal {P}},{\mathcal {Q}}} are the lifting (lifting the codomain of the input function to a higher dimensional space) and projection (projecting the codomain of the intermediate function to the output dimension) operators, respectively. These operators act pointwise on functions and are typically parametrized as multilayer perceptrons. σ {\displaystyle \sigma } is a pointwise nonlinearity, such as a rectified linear unit (ReLU), or a Gaussian error linear unit (GeLU). Each layer t = 1 , … , T {\displaystyle t=1,\dots ,T} has a respective local operator W t {\displaystyle W_{t}} (usually parameterized by a pointwise neural network), a kernel integral operator K t {\displaystyle {\mathcal {K}}_{t}} , and a bias function b t {\displaystyle b_{t}} . Given some intermediate functional representation v t {\displaystyle v_{t}} with domain D {\displaystyle D} in the t {\displaystyle t} -th hidden layer, a kernel integral operator K ϕ {\displaystyle {\mathcal {K}}_{\phi }} is defined as ( K ϕ v t ) ( x ) := ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x):=\int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy,} where the kernel κ ϕ {\displaystyle \kappa _{\phi }} is a learnable implicit neural network, parametrized by ϕ {\displaystyle \phi } . In practice, one is often given the input function to the neural operator at a specific resolution. For instance, consider the setting where one is given the evaluation of v t {\displaystyle v_{t}} at n {\displaystyle n} points { y j } j n {\displaystyle \{y_{j}\}_{j}^{n}} . Borrowing from Nyström integral approximation methods such as Riemann sum integration and Gaussian quadrature, the above integral operation can be computed as follows: ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y ≈ ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j , {\displaystyle \int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy\approx \sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}},} where Δ y j {\displaystyle \Delta _{y_{j}}} is the sub-area volume or quadrature weight associated to the point y j {\displaystyle y_{j}} . Thus, a simplified layer can be computed as v t + 1 ( x ) ≈ σ ( ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j + W t ( v t ( y j ) ) + b t ( x ) ) . {\displaystyle v_{t+1}(x)\approx \sigma \left(\sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}}+W_{t}(v_{t}(y_{j}))+b_{t}(x)\right).} The above approximation, along with parametrizing κ ϕ {\displaystyle \kappa _{\phi }} as an implicit neural network, results in the graph neural operator (GNO). There have been various parameterizations of neural operators for different applications. These typically differ in their parameterization of κ {\displaystyle \kappa } . The most popular instantiation is the Fourier neural operator (FNO). FNO takes κ ϕ ( x , y , v t ( x ) , v t ( y ) ) := κ ϕ ( x − y ) {\displaystyle \kappa _{\phi }(x,y,v_{t}(x),v_{t}(y)):=\kappa _{\phi }(x-y)} and by applying the convolution theorem, arrives at the following parameterization of the kernel integral operator: ( K ϕ v t ) ( x ) = F − 1 ( R ϕ ⋅ ( F v t ) ) ( x ) , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x)={\mathcal {F}}^{-1}(R_{\phi }\cdot ({\mathcal {F}}v_{t}))(x),} where F {\displaystyle {\mathcal {F}}} represents the Fourier transform and R ϕ {\displaystyle R_{\phi }} represents the Fourier transform of some periodic function κ ϕ {\displaystyle \kappa _{\phi }} . That is, FNO parameterizes the kernel integration directly in Fourier space, using a prescribed number of Fourier modes. When the grid at which the input function is presented is uniform, the Fourier transform can be approximated using the discrete Fourier transform (DFT) with frequencies below some specified threshold. The discrete Fourier transform can be computed using a fast Fourier transform (FFT) implementation. == Training == Training neural operators is similar to the training process for a traditional neural network. Neural operators are typically trained in some Lp norm or Sobolev norm. In particular, for a dataset { ( a i , u i ) } i = 1 N {\displaystyle \{(a_{i},u_{i})\}_{i=1}^{N}} of size N {\displaystyle N} , neural operators minimize (a discretization of) L U ( { ( a i , u i ) } i = 1 N ) := ∑ i = 1 N ‖ u i − G θ ( a i ) ‖ U 2 {\displaystyle {\mathcal {L}}_{\mathca

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  Deep learning

  In machine learning, deep learning (DL) focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and revolves around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Early forms of neural networks were inspired by information processing and distributed communication nodes in biological systems, particularly the human brain. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose. == Overview == Most modern deep learning models are based on multi-layered neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines. Fundamentally, deep learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an image recognition model, the raw input may be an image (represented as a tensor of pixels). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face. Importantly, a deep learning process can learn which features to optimally place at which level on its own. Prior to deep learning, machine learning techniques often involved hand-crafted feature engineering to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model discovers useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction. The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited. No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function. Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively. Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks. The term deep learning was introduced to the machine learning community by Rina Dechter in 1986, and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons. The etymology of the term is more complicated. == Interpretations == Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference. The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit. The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop. == History == === Before 1980 === There are two types of artificial neural network (ANN): feedforward neural network (FNN) or multilayer perceptron (MLP) and recurrent neural networks (RNN). RNNs have cycles in their connectivity structure, whereas FNNs do not. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was republished by John Hopfield in 1982. Other early recurrent neural networks were published by Kaoru Nakano in 1971. Already in 1948, Alan Turing produced work on "Intelligent Machinery" that was not published in his lifetime, containing "ideas related to artificial evolution and learning RNNs". Frank Rosenblatt (1958) proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight). The book cites an earlier network by R. D. Joseph (1960) "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive multilayer perceptrons with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion. The first working deep learning algorithm was the Group method of data handling, a method to train arbitrarily deep neural networks, published by Alexey Ivakhnenko and Lapa in 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron to handle more complex, nonlinear, and hierarchical relationships. A 1971 paper described a deep network with eight layers trained by this method, which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates". The first deep learning multilayer perceptron trained by stochastic gradient descent was published in 1967 by Shun'ichi

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