ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
Image formation
The study of image formation encompasses the radiometric and geometric processes by which 2D images of 3D objects are formed. In the case of digital images, the image formation process also includes analog to digital conversion and sampling. == Imaging == The imaging process is a mapping of an object to an image plane. Each point on the image corresponds to a point on the object. An illuminated object will scatter light toward a lens and the lens will collect and focus the light to create the image. The ratio of the height of the image to the height of the object is the magnification. The spatial extent of the image surface and the focal length of the lens determines the field of view of the lens. Image formation of mirror these have a center of curvature and its focal length of the mirror is half of the center of curvature. == Illumination == An object may be illuminated by the light from an emitting source such as the sun, a light bulb or a Light Emitting Diode. The light incident on the object is reflected in a manner dependent on the surface properties of the object. For rough surfaces, the reflected light is scattered in a manner described by the Bi-directional Reflectance Distribution Function (BRDF) of the surface. The BRDF of a surface is the ratio of the exiting power per square meter per steradian (radiance) to the incident power per square meter (irradiance). The BRDF typically varies with angle and may vary with wavelength, but a specific important case is a surface that has constant BRDF. This surface type is referred to as Lambertian and the magnitude of the BRDF is R/π, where R is the reflectivity of the surface. The portion of scattered light that propagates toward the lens is collected by the entrance pupil of the imaging lens over the field of view. == Field of view and imagery == The Field of view of a lens is limited by the size of the image plane and the focal length of the lens. The relationship between a location on the image and a location on the object is y = ftan(θ), where y is the max extent of the image plane, f is the focal length of the lens and θ is the field of view. If y is the max radial size of the image then θ is the field of view of the lens. While the image created by a lens is continuous, it can be modeled as a set of discrete field points, each representing a point on the object. The quality of the image is limited by the aberrations in the lens and the diffraction created by the finite aperture stop. == Pupils and stops == The aperture stop of a lens is a mechanical aperture which limits the light collection for each field point. The entrance pupil is the image of the aperture stop created by the optical elements on the object side of the lens. The light scattered by an object is collected by the entrance pupil and focused onto the image plane via a series of refractive elements. The cone of the focused light at the image plane is set by the size of the entrance pupil and the focal length of the lens. This is often referred to as the f-stop or f-number of the lens. f/# = f/D where D is the diameter of the entrance pupil. == Pixelation and color vs. monochrome == In typical digital imaging systems, a sensor is placed at the image plane. The light is focused on to the sensor and the continuous image is pixelated. The light incident on each pixel in the sensor will be integrated within the pixel and a proportional electronic signal will be generated. The angular geometric resolution of a pixel is given by atan(p/f), where p is the pitch of the pixel. This is also called the pixel field of view. The sensor may be monochrome or color. In the case of a monochrome sensor, the light incident on each pixel is integrated and the resulting image is a grayscale like picture. For color images, a mosaic color filter is typically placed over the pixels to create a color image. An example is a Bayer filter. The signal incident on each pixel is then digitized to a bit stream. == Image quality == The quality of an image is dependent upon both geometric and physical items. Geometrically, higher density of pixels across an image will give less blocky pixelation and thus a better geometric image quality. Lens aberrations also contribute to the quality of the image. Physically, diffraction due to the aperture stop will limit the resolvable spatial frequencies as a function of f-number. In the frequency domain, Modulation Transfer Function (MTF) is a measure of the quality of the imaging system. The MTF is a measure of the visibility of a sinusoidal variation in irradiance on the image plane as a function of the frequency of the sinusoid. It includes the effects of diffraction, aberrations and pixelation. For the lens, the MTF is the autocorrelation of the pupil function, so it accounts for the finite pupil extent and the lens aberrations. The sensor MTF is the Fourier Transform of the pixel geometry. For a square pixel, MTF(ξ) = sin(πξp)/πξp where p is the pixel width and ξ is the spatial frequency. The MTF of the combination of the lens and detector is the product of the two component MTFs. == Perception == Color images can be perceived via two means. In the case of computer vision the light incident on the sensor comprises the image. In the case of visual perception, the human eye has a color dependent response to light so this must be accounted for. This is important consideration when converting to grayscale. == Image formation in eye == The principal difference between the lens of the eye and an ordinary optical lens is that the former is flexible. The radius of the curvature of the anterior surface of the lens is greater than the radius of its posterior surface. The shape of the lens is controlled by tension in the fibers of the ciliary body. To focus on distant objects, the controlling muscles cause the lens to be relatively flattened. Similarly, these muscles allow the lens to become thicker in order to focus on objects near the eye. The distance between the center of the lens and the retina (focal length) varies from approximately 17 mm to about 14 mm, as the refractive power of the lens increases from its minimum to its maximum. When the eye focuses on an object farther away than about 3 m, the lens exhibits its lowest refractive power. When the eye focuses on a close object, the lens is most strongly refractive.
Adobe Presenter
Adobe Presenter is eLearning software released by Adobe Systems available on the Microsoft Windows platform as a Microsoft PowerPoint plug-in, and on both Windows and OS X as the screencasting and video editing tool Adobe Presenter Video Express. It is mainly targeted towards learning professionals and trainers. In addition to recording one's computer desktop and speech, it also provides the option to add quizzes and track performance by integrating with learning management systems. Adobe Presenter was designed to replace the discontinued Adobe Ovation software, which had similar functions. == Predecessor == Adobe Ovation was originally released by Serious Magic. It converted PowerPoint slides into visual presentations with additional effects. Ovation included themes called PowerLooks that could add motion and polish the presentations. They were available in a variety of color variations complete with animated backgrounds and dynamic text effects. Ovation could make text with jagged edges more readable. TimeKeeper could be used to set the period of the presentation, and the PointPrompter scrolled down the notes. Ovation's development has been discontinued, nor does it support PowerPoint 2007. == Features == The main purpose of Adobe Presenter is to capture on-screen presentations and convert them into more interactive and engaging videos. Support is given to convert Microsoft PowerPoint 2010 and 2013 presentations into videos. It also allows for content authoring on PowerPoint and ActionScript 3, and offers integration with Adobe Captivate. Slide branching enables users to control slide navigation and titles and create complex slide branching to guide viewers through the content of the presentation. Video editing tools are also provided, and offer the ability to upload to video-sharing platforms such as YouTube, Vimeo and other sites. Multimedia features such as annotations, eLearning templates, actors, audio narration and drag-and-drop elements enrich users' presentations. Quizzes and surveys is another highlighted feature, which include generating question pools, importing questions from existing quizzes and in-course collaboration which allows presenters to receive feedback by allowing them to comment on specific content within a course or ask questions for more clarity. Presenters could opt to receive feedback from viewers through video analytics and create Experience API, SCORM and AICC-compliant content. Options to publish to Adobe Connect are provided. Other unique features include universal standards support, file size control, navigational restrictions among others.
Nuance Communications
Nuance Communications, Inc. was an American multinational computer software technology corporation, headquartered in Burlington, Massachusetts, that markets speech recognition and artificial intelligence software. Nuance merged with its competitor in the commercial large-scale speech application business, ScanSoft, in October 2005. ScanSoft was a Xerox spin-off that was bought in 1999 by Visioneer, a hardware and software scanner company, which adopted ScanSoft as the new merged company name. The original ScanSoft had its roots in Kurzweil Computer Products. In April 2021, Microsoft announced it would buy Nuance Communications. The deal is an all-cash transaction of $19.7 billion, including company debt, or $56 per share. The acquisition was completed in March 2022. == History == The Speech Technology and Research (STAR) Laboratory at SRI International began the journey that, in 1994, resulted in a spin-off company; Corona Corporation (later renamed to Nuance Communications ). Nuance Communications (NUAN) went public on the Nasdaq Stock Market in 1995. Nuance focused on commercializing advanced speech recognition technologies. Nuance was an early spinoff of SRI's Speech Technology and Research (STAR) Laboratory, a world leader in audio processing, speech and speaker analytics and spoken language research. The technology that served as the foundation of Nuance's speech recognition solution started at the STAR Lab and helped launch Nuance more than 20 years ago. In 1995, The SRI Language Modeling Toolkit (SRILM) was developed. This provides the tools to build and apply statistical language models (LMs), primarily for use in speech recognition, statistical tagging and segmentation, and machine translation. In terms of commercialization of natural automated speech recognition, SRI's natural language speech recognition software was the first to be deployed by a major corporation. In 1996, Charles Schwab & Co., Inc., used Nuance's speech recognition technology to allow customers to receive stock quotes over the telephone. One of the key features of the ‘Schwab Discount Brokerage system’, was the ability to recognize English words even when spoken by customers with accents. In 1997, Nuance Communications developed the first large scale commercial dialog system for United Parcel Services (UPS). UPS used the voice recognition platform to handle very large numbers of inquiries about package status. The company that would later merge with Nuance Communications started life as Visioneer, incorporated in 1992. In 1999, Visioneer acquired ScanSoft, Inc. (SSFT), and the combined company became known as ScanSoft. In September 2005, ScanSoft Inc. acquired and merged with Nuance Communications (NUAN), a natural language DOD-project spinoff from SRI International. The resulting company adopted the Nuance name. During the prior decade, the two companies competed in the commercial large-scale speech application business. === Data breach === Between 2014 and 2017, Nuance exposed over 45,000 patient records. == Solutions == Customer service virtual assistants Speech recognition — for people Speech recognition — for business Speech recognition — for physicians Accessibility Power PDF Managed Print Services Transcription === ScanSoft origins === In 1974, Raymond Kurzweil founded Kurzweil Computer Products, Inc. to develop the first omni-font optical character-recognition system – a computer program capable of recognizing text written in any normal font. In 1980, Kurzweil sold his company to Xerox. The company became known as Xerox Imaging Systems (XIS), and later ScanSoft. In March 1992, a new company called Visioneer, Inc. was founded to develop scanner hardware and software products, such as a sheetfed scanner called PaperMax and the document management software PaperPort. Visioneer eventually sold its hardware division to Primax Electronics, Ltd. in January 1999. Two months later, in March, Visioneer acquired ScanSoft from Xerox to form a new public company with ScanSoft as the new company-wide name. Prior to 2001, ScanSoft focused primarily on desktop imaging software such as TextBridge, PaperPort and OmniPage. Beginning with the December 2001 acquisition of Lernout & Hauspie assets, the company moved into the speech recognition business and began to compete with Nuance. Lernout & Hauspie had acquired speech recognition company Dragon Systems in June 2001, shortly before becoming bankrupt in October. Scansoft acquired speech recognition company SpeechWorks in 2003. === Partnership with Siri and Apple Inc. === In 2013, Nuance confirmed that its natural language processing algorithms supported Apple's Siri voice assistant. === Focus on health care === In 2019, Nuance spun off its automotive division as the company Cerence, allowing it to focus on health care applications. === Acquisition by Microsoft === On April 12, 2021, Microsoft announced that it would buy Nuance Communications for $19.7 billion, or $56 a share, a 22% increase over the previous closing price. Nuance's CEO, Mark Benjamin, stayed with the company. This was Microsoft's second-biggest acquisition up to that point, after its purchase of LinkedIn for $24 billion (~$30.7 billion in 2024) in 2016. Shortly after the deal, the Competition and Markets Authority, a UK regulatory body, stated it was looking into the deal on the basis of antitrust concerns. In December 2021, it was reported that the deal would be approved by the European Union. The acquisition was completed on March 4, 2022. In May 2023, Nuance announced an unspecified number of layoffs.
Free Studio
Free Studio is a freeware set of multimedia computer programs developed by DVDVideoSoft. The programs are available in one integrated package and also as separate downloads (Free Studio Manager is included in both). == Overview == The Free Studio software bundle consists of about 48 programs, grouped into several sections: YouTube, MP3 & Audio, CD-DVD-BD, DVD & Video, Photo & Images, Mobiles, Apple Devices, and 3D. The largest group is the DVD & Video section containing 14 different applications. Mobiles section is the second largest group with 13 programs. However, the YouTube section, particularly YouTube downloading programs, has gained more popularity among users. The programs have been tested and endorsed by a dozen of software portals and have won awards from these sites. Free Studio is most popular in Germany, Greece, Italy, and the United States. It is also popular in Japan, France, and the United Kingdom. Some of the programs in the package are free and open-source software. == History == DVDVideoSoft project was launched in 2006 by company Digital Wave Ltd., for software development to produce multimedia application software. The founders distributed paid software as an affiliate at the start, later their own products appeared on the site. Free YouTube Download was the first successful program, then DVDVideoSoft created and launched several other 'Free YouTube' applications. Later on upon users' requests DVDVideoSoft started developing other kinds of applications including media converters etc. Today DVDVideoSoft offers up to 49 different programs for video, audio and image processing individually or integrated into the Free Studio package. == Features == DVDVideoSoft YouTube programs can be used to download YouTube videos in their original format and convert them to AVI, DVD, MP4, WMV etc. or different audio formats. YouTube section contains Free Video Call Recorder for Skype button, but the program itself is not included into FS installation (it has to be downloaded and installed separately). The "MP3 & Audio" section consists of the programs which convert audio files between different formats, convert audio files to Flash for web, extract audio from video files, edit audio files (Free Audio Dub), rip and burn CDs. Enclosed in the CD-DVD-BD section are the applications that enable users to burn files and folders to discs, to convert videos to a DVD format and vice versa, to burn CDs, and to copy music from audio CDs into files. The "DVD and Video" section contains several desktop video and DVD converters. Some of the programs can flip, rotate and cut (Free Video Dub) videos. One of the most popular programs from the section is Free Video Dub. Converted videos are now, contrary to previous versions, watermarked if no paid membership is present. Free Studio includes several applications for Apple phones, iPods and other devices. The Mobiles section contains a dozen video converters for various mobile devices such as cell phones, Tablets and Game consoles. They convert videos to play them on (BlackBerry, HTC, LG phones, Sony/Sony Ericsson, Nintendo, Xbox, Motorola phones, etc.) The "Photo & Images" section incorporates the programs for image conversion and resizing, extracting JPEG frames from videos (Free Video To JPEG Converter), recording screen activities, making screenshots (Free Screen Recorder). The 3D section is composed of the programs to make 3D videos and 3D images. There are several algorithms which allow to create different types of 3D images. == Supported formats == === Video formats === Input: .avi; .ivf; .div; .divx; .mpg; .mpeg; .mpe; .mp4; .m4v; .wmv; .asf; .webm; .mkv; .mov; .qt; .ts; .mts; .m2t; .m2ts; .mod; .tod; .vro; .dat; .3gp2; .3gpp; .3gp; .3g2; .dvr-ms; .flv; .f4v; .amv; .rm; .rmm; .rv; .rmvb; .ogv; DVD video Output: .mp4; .wmv; .avi; .mkv; .webm; .flv; .swf; .mov; .3gp; .m2ts; DVD video === Audio formats === Input: .mp3 .wav; .aac; .m4a; .m4b; .wma; .ogg; .flac; .ra; .ram; .amr; .ape; .mka; .tta; .aiff; .au; .mpc; .spx; .ac3; audio cd Output: .mp3; .m4a; .aac; .wav; .wma; .ogg; .flac; .ape; audio CD === Image formats === Input: .jpg, .png, .bmp, .gif, .tga Output: .jpg, .png, .bmp, .gif, .tga, .pdf == Reception == The programs have been tested and endorsed by Chip Online, Tucows, SnapFiles, Brothersoft, and Softonic and have won awards from these sites. Free Studio is most popular in Germany, United States and Italy. It is also popular in Japan, France and the United Kingdom. The most popular applications, according to CNET statistics, include Free YouTube to MP3 Converter, Free Video to MP3 Converter, Free MP4 Video Converter and Free YouTube Download. Other programs with high rank: Free AVI Video Converter, Free Video Editor, Free Audio Converter and Free Studio in a whole. == Criticism == Free Studio (as can be common for freeware packages) is criticized for toolbar and Web search engine installation. Older versions have also included OpenCandy, which is loaded automatically, with no request for user approval. There can be difficulties installing only the programs needed without installing bundled extra programs. In March 2017, DVDVideoSoft announced that it had stopped showing other products' ads during installation and removed all toolbars, search engines, and OpenCandy.
Hyperparameter optimization
In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a
Alexis Spectral Data
Alexis Spectral Data is a software developed for colour matching processes that calculates from available spectral data the colour numbers used by computers to display colours on screen. It displays the colour for each spectral reflectance curve and records the calculated trichromatic values and colour numbers along with the spectral curves. This eliminates the need to scan the samples separately with a truecolour Scanner while creating the database. The spectral data can be introduced manually as a series of reflectance values at wavelengths measured in different standard illuminants with an arbitrary but fixed increment that must be kept for each spectral curve throughout the creation of the whole database. Therefore, older UV-VIS Spectrophotometers that can't be interfaced with computers can also be used for creating the database needed for colour matching. Alexis Spectral Data determines the whiteness degree in a less time-consuming method, which permits storage and easier handling of the obtained data. Alexis Spectral Data can export the trichromatic values, calculated from the spectral curves, to Alexis Analyser, software that handles only trichromatic data. The earliest information about the development of this software comes from a paper published by a student at the University Politehnica Bucharest in 1993. The software runs on Windows based computers but not on other operating systems.