AI App Builder Free

AI App Builder Free — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Exercism

Exercism is an online, open-source, free coding platform that offers code practice and mentorship on 77 different programming languages. == History == Software developer Katrina Owen created Exercism while she was teaching programming at Jumpstart Labs. The platform was developed as an internal tool to solve the problem of her own students not receiving feedback on the coding problems they were practicing. Katrina put the site publicly online and found that people were sharing it with their friends, practicing together and giving each other feedback. Within 12 months, the site had organically grown to see over 6,000 users had submitted code or feedback, and hundreds of volunteers contribute to the languages or tooling on the platform. In 2016, Jeremy Walker joined as co-founder and CEO. In July 2018, the site was relaunched with a new design and centered around a formal mentoring mode, at which point Katrina stepped back from day-to-day involvement. == Product == In the past, the website differed from other coding platforms by requiring students to download exercises through a command line client, solve the code on their own computers then submit the solution for feedback, at which point they can also view other's solutions to the same problem. Since its second relaunch in 2021, solutions can be edited and submitted through a web editor, though the command line client remains available. Exercism has tracks for 74 programming languages. Among the notable languages taught: ABAP, C, C#, C++, CoffeeScript, Delphi, Elm, Erlang, F#, Gleam, Go, Java, JavaScript, Julia, Kotlin, Objective-C, PHP, Python, Raku, Red, Ruby, Rust, Scala, Swift, and V (Vlang). In 2023, the site launched a "12 in 23" challenge for users to learn the basics of 12 different languages - one per month in 2023. == Open source == The Exercism codebase is open source. In April 2016, it consisted of 50 repositories including website code, API code, command-line code and, most of all, over 40 stand-alone repositories for different language tracks. As of February 2024 Exercism has 14,344 contributors, maintains 366 repositories, and 19,603 mentors.
Read more →
Computational semantics

Computational semantics is a subfield of computational linguistics. Its goal is to elucidate the cognitive mechanisms supporting the generation and interpretation of meaning in humans. It usually involves the creation of computational models that simulate particular semantic phenomena, and the evaluation of those models against data from human participants. While computational semantics is a scientific field, it has many applications in real-world settings and substantially overlaps with Artificial Intelligence. Broadly speaking, the discipline can be subdivided into areas that mirror the internal organization of linguistics. For example, lexical semantics and frame semantics have active research communities within computational linguistics. Some popular methodologies are also strongly inspired by traditional linguistics. Most prominently, the area of distributional semantics, which underpins investigations into embeddings and the internals of Large Language Models, has roots in the work of Zellig Harris. Some traditional topics of interest in computational semantics are: construction of meaning representations, semantic underspecification, anaphora resolution, presupposition projection, and quantifier scope resolution. Methods employed usually draw from formal semantics or statistical semantics. Computational semantics has points of contact with the areas of lexical semantics (word-sense disambiguation and semantic role labeling), discourse semantics, knowledge representation and automated reasoning (in particular, automated theorem proving). Since 1999 there has been an ACL special interest group on computational semantics, SIGSEM.
Read more →
Microsoft Whiteboard

Microsoft Whiteboard is a free multi-platform application, as well as an online service and a feature in Microsoft Teams, which simulates a virtual whiteboard and enables real-time collaboration between users. == Overview and features == Microsoft Whiteboard allows users to draw on a virtual whiteboard using input methods such as a stylus pen or a mouse and keyboard, and write down notes, draw connections between shareable ideas, and interact in real time. Microsoft Whiteboard is available to download on the following platforms and devices: Microsoft Windows (on Windows 10 or above) Android Apple iOS Surface Hub devices It is also available on the web and as a feature in Microsoft Teams. Microsoft Whiteboard allows users with Microsoft accounts to view, edit, and share whiteboards using the provided tools and options. The feature set includes tools for drawing, shapes, and media. Drawing in Microsoft Whiteboard is called inking. It works both on mobile devices and computers. The inking toolbar has customizable pencils, a ruler, a highlighter, an eraser, and an object selector. Whiteboard can recognize shapes drawn by hand and straighten them. Holding the Shift key on a computer while inking draws straight lines. Microsoft Whiteboard has keyboard shortcuts for some functions. Additional features include inserting sticky notes, text boxes, stickers, as well as images. Grid lines and colors are adjustable. Different templates can be inserted into the whiteboard. Users can also share their reactions. A feature limited to boards created in Microsoft Teams, is the ability to make them read-only; other participants from the meeting cannot edit them. == Reviews == PC Magazine gave Microsoft Whiteboard a score of 3.5 out of 5, praising the app's free availability and plentiful templates. It compared it to other, paid whiteboarding solutions, and concluded that Microsoft offers the best free one. Some of the cons, described by PCMag, include the inability to view boards without a Microsoft account and the inability to create custom templates.
Read more →
DBGallery

DBGallery, short for Database Gallery, is a cloud-based Software as a Service (SaaS) and on-prem webserver for teams of various sizes. DBGallery enables users to centrally store, manage, catalog, archive, and securely share image, video, and document files. It facilitates version control, detects duplicates, and offers an intuitive and advanced search functionality, making assets easily accessible to all users. It takes advantage of current AI technologies to automatically add significant metadata to images, facilitates custom-trained AI models, and offers bespoke AI features. Additionally, DBGallery provides team management tools, workflow management, an activity audit trail, and other collaborative features that foster a productive environment for both internal and external stakeholders. == History == DBGallery's first public release was December 2007. Since then each year has seen continuous enhancements. 2013 added support for additional non-English languages in its meta-data. 2014 added support for creating custom data fields for tagging and search. In 2015 included the ability to auto-tag images using Reverse Geocoding. 2018 added artificial intelligence (AI) image recognition as a further addition to auto-tagging. March 2020 added complete image collection management via the web (e.g. file and folder drag and drop), a new collection dashboard, custom data layouts, and an improved audit trail. 2021 saw user experience improvements provided by improved styling and performance enhancements. Version 12 was released in October 2021. It added the ability to upload unlimited file sizes and made significant performance improvements for very large collections. June 2022 saw the release of a global duplicate images search. In late 2022, DBGallery began offering significantly reduced cloud storage cost, at a third of its previous prices, which played into its recent high-volume/high-capacity capabilities and its clients' subsequent demand for additional storage. 2023 saw improvements in user and role management, introduced it's mobile app (PWA), and improved custom-trained object detection. Release 14.0 in the spring of 2024 had large sharing improvements and a new find related images feature. Winter 2025's v15 release introduced AI-generated image descriptions, image-to-text, and facial recognition.
Read more →
Isotropic position

In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is proportional to the identity matrix. == Formal definitions == Let D {\textstyle D} be a distribution over vectors in the vector space R n {\textstyle \mathbb {R} ^{n}} . Then D {\textstyle D} is in isotropic position if, for vector v {\textstyle v} sampled from the distribution, E v v T = I d . {\displaystyle \mathbb {E} \,vv^{\mathsf {T}}=\mathrm {Id} .} A set of vectors is said to be in isotropic position if the uniform distribution over that set is in isotropic position. In particular, every orthonormal set of vectors is isotropic. As a related definition, a convex body K {\textstyle K} in R n {\textstyle \mathbb {R} ^{n}} is called isotropic if it has volume | K | = 1 {\textstyle |K|=1} , center of mass at the origin, and there is a constant α > 0 {\textstyle \alpha >0} such that ∫ K ⟨ x , y ⟩ 2 d x = α 2 | y | 2 , {\displaystyle \int _{K}\langle x,y\rangle ^{2}dx=\alpha ^{2}|y|^{2},} for all vectors y {\textstyle y} in R n {\textstyle \mathbb {R} ^{n}} ; here | ⋅ | {\textstyle |\cdot |} stands for the standard Euclidean norm.
Read more →
Automatic acquisition of lexicon

Automatic acquisition of lexicon is a computerized process used for the development of a complex morphological lexicon of a language. The lexicon is essential for the NLP (Natural language processing), as well as a prerequisite to any wide-coverage parser. The two main requirements represent raw corpus and the morphological description of the language. The aim is to provide lemmas that will serve to the explanation of all the words that occur within the corpus. For the achievement of a quality lexicon it is necessary to manually validate the generated lemmas and iterate the whole process several times. The process is focused on the open word classes (e.g. nouns, adjectives, verbs). Closed classes (e.g. prepositions, pronouns, numerals) are excluded. This method is applicable to the languages with a rich morphology, such as Slovak, Russian or Croatian. Applied to Slovak, being an inflectional language, the automatic acquisition focuses on the inflectional morphology as well as on the derivational morphology. This fact enables the users to find out the information about derivational relations (e.g. adjectivizations, prefixes) in the lexicon. For example, Slovak word korpusový is an adjectivization of korpus (eng. corpus). == Three-step loop == Conformably to Benoît Sagot, there are three stages involved in the acquisition of lemmas: Generation and inflection Ranking Manual validation The more iteration will be performed, the more accurate lexicon will be obtained. For each iteration are essential the information given by a manual validator. === Generation and inflection === Firstly, all words which represent the closed word classes (pronouns, prepositions, numerals) are manually excluded from the given corpus. Number of their occurrences in the corpus is provided. Then the automatic generation comes, when the hypothetical lemmas according to the morphological description of a language are created. Generated lemmas are consequently being inflected, so that all of their inflected forms are built. Obtained forms are associated with the corresponding lemma and a morphological tag. === Ranking === There was created a probabilistic model, represented by a fix-point algorithm, to rank the hypothetical lemmas generated in the first step. Best ranked lemmas are expected to be ideally all correct, whereas the least ranked tend to be incorrect. === Manual validation === Correctness of the best- ranked lemmas created in the previous step are checked by the manual validator, who should be a native speaker. Lemmas are at this stage divided into three categories: valid lemmas, appended to lexicon erroneous lemmas generated by valid forms (later associated to another lemmas) erroneous lemmas generated by invalid forms (these need to be excluded) == Future development == Automatic acquisition, in comparison to a purely manual development of the lexicons, seems to be promising, considering the future development, because of the short validation time needed and the relatively small amount of human labor involved.
Read more →
Attensity

Attensity was an American company that provided social analytics and engagement applications for social customer relationship management (social CRM). Attensity's text analytics software applications extracted facts, relationships and sentiment from unstructured data. == History == Attensity was founded in 2000. An early investor in Attensity was In-Q-Tel, which funds technology to support the missions of the US Government and the broader DOD. InTTENSITY, an independent company that has combined Inxight with Attensity Software (the only joint development project that combines two InQTel funded software packages), was the exclusive distributor and outlet for Attensity in the Federal Market. In 2009, Attensity Corp., then based in Palo Alto, merged with Germany's Empolis and Living-e AG to form Attensity Group. In 2010, Attensity Group acquired Biz360, a provider of social media monitoring and market intelligence solutions. In early 2012, Attensity Group divested itself of the Empolis business unit via a management buyout; that unit currently conducts business under its pre-merger name. Attensity Group was a closely held private company. Its majority shareholder was Aeris Capital, a private Swiss investment office advising a high-net-worth individual and his charitable foundation. Foundation Capital, Granite Ventures, and Scale Venture Partners were among Biz360's investors and thus became shareholders in Attensity Group. In February 2016, Attensity's IP assets were acquired by InContact, and Attensity closed.
Read more →
Calais (Reuters product)

Calais is a service created by Thomson Reuters that automatically extracts semantic information from web pages in a format that can be used on the semantic web. Calais was launched in January 2008, and is free to use. The technology is now available via the website of Refinitiv, a provider of financial market data and infrastructure founded in 2018, that is a subsidiary of London Stock Exchange Group. The Calais Web service reads unstructured text and returns Resource Description Framework formatted results identifying entities, facts and events within the text. The service appears to be based on technology acquired when Reuters purchased ClearForest in 2007. The technology has also been used to automatically tag blog articles, and organize museum collections. Calais uses natural language processing technologies delivered via a web service interface.
Read more →
List & Label

List & Label is a professional reporting tool for software developers. It provides comprehensive design, print and export functions. The software component runs on Microsoft Windows and can be implemented in desktop, cloud and web applications. List & Label can be used to create user-defined dashboards, lists, invoices, forms and labels. It supports many development environments, frameworks and programming languages such as Microsoft Visual Studio, Embarcadero RAD Studio, .NET Framework, .NET Core, ASP.NET, C++, Delphi, Java, C Sharp and some more. List & Label either retrieves data from various sources via data binding, or works database independent. Reports are designed and created in the so-called List & Label Designer and then exported into a multitude of formats like PDF, Excel, XHTML and RTF. Since version 27 a web report designer for ASP.NET MVC is available. == History == The product was first released in 1992 by combit. The current version is 30. A new major version of List & Label is released every fall, usually in October. Updates are available several times a year via Service Pack. == Features == === Report Designer === The Designer enables users to graphically layout the report. It offers report objects such as tables, charts, crosstabs, gauges, HTML, conditionally formatted text, barcodes, matrix codes, and graphics, and is extensible using third-party add-ons. User applications can interact with the report via the programmable object model of the report. The real-time preview functionality allows users to view changes instantly. Usability features include layer and appearance management, enabling conditional logic to dynamically control the visibility of objects in reports. The Designer also supports the inclusion of multiple report containers in a single project, accommodating complex layouts such as parallel tables and charts. A formula wizard and support for scripting languages such as C# facilitate advanced calculations and logic. The Designer's object model (DOM) provides developers with the ability to modify layouts and behaviors programmatically. === Web Report Designer === The web report designer works browser-based and independent from printer drivers and spoolers - that makes deployments to the cloud easier. Just like the use of the Visual Studio deployment pipeline. === Data Sources === Depending on the programming language, the product offers automatic support for data sources: Databases such as Microsoft SQL Server, Oracle, MySQL, PostgreSQL, IBM Db2, SQLite, MariaDB, MongoDB, Cosmos DB XML data, CSV Business objects Data sources that can be accessed via OLE DB, ODBC or ADO.NET LINQ data and data from web services GraphQL Additionally, the product offers support for unbound data and can be extended to support other data sources via interfaces. === Output Options === Printer Image Formats (JPEG, BMP, EMF, TIFF, PNG, SVG, HEIF, WebP) Document Formats: PDF, PDF/A, Word (DOCX), Excel (XLS), PowerPoint (PPTX) HTML, XHTML, MHTML Barcodes Plain Text, RTF, CSV, JSON XML, ZIP, Email, JSON List & Label preview file === Target Audience === List & Label can be used in Windows development environments. While it competes most notably on the Microsoft .NET platform with other products such as Crystal Reports, SQL Server Reporting Services, ActiveReports, there are few competing products for other programming languages (e.g. Progress, Alaska Xbase++, Visual DataFlex). == Awards == Reader's Choice Award 2005–2008 Stevie Awards 2021: Best Technology for Data Visualization Top 100 Publisher Award Component Source 2013-2014, 2014-2015,2016, 2018, 2019, 2020, 2021, 2022
Read more →
Chai AI

Chai AI (also known as Chai Research) is an American artificial intelligence (AI) company that operates a chatbot platform where users can create, share, and interact with character-based chatbots powered by large language models (LLMs). The company is headquartered in Palo Alto, California. == History == Chai was founded in 2021 by William Beauchamp, a former quantitative trader educated at Cambridge, who began developing the initial prototype in 2020 in Cambridge, England. The company launched in 2021 and relocated to Palo Alto in 2022. In June 2023, Chai raised US$2 million in a pre-seed funding round. In September 2023, GPU cloud provider CoreWeave invested in the company at a valuation of US$450 million. In January 2024, Chai Research reported a $450 million valuation following an investment from cloud computing provider CoreWeave. In July 2024, authorities in Belgium launched an investigation into the company following reports of a man dying by suicide following extensive chats on the Chai app. == Reception == In 2025, Chai Research announced that their app had over 10 million downloads and 1 million daily active users. In 2022, Canadian writer Sheila Heti published her conversations with various chatbots in The Paris Review, including Chai AI chatbots, and later used Chai AI chatbots in the development of a novel. Heti said that she had found that Chai's default chatbot, Eliza, "had turned out to be like most of the other bots on the site—primarily interested in sex". In January 2026, CHAI introduced country-based blocks on its free, ad-supported tier, initially providing the community with little information and inaccurate lists of the affected countries. Users in "Low tier" regions are required to subscribe to use the app in any capacity, while "High tier" regions will retain free ad-supported access. In response to backlash, the company announced a "Basic" tier with unlimited messages and ads, intended to cover electricity and infrastructure costs. In February 2026, CHAI was criticized for the unannounced implementation of restrictive "token limits" that abruptly blocked messages and froze conversations for both free and paid subscribers. Users generating long responses or utilizing roleplay features found their quotas exhausted within minutes, resulting in lockouts lasting anywhere from a few hours to a week. == Technology == Chai allows users to create characters and interact with chatbot versions of those characters. These chatbots use the open-source large language model (LLM) GPT-J originally developed by EleutherAI. Chai AI chatbots can be shared on the platform for other users to interact with.
Read more →
Multi-scale approaches

The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of "multi-scale approaches" in the areas of computer vision, image processing and signal processing, in particular the notion of wavelets. The purpose of this article is to describe a few of these approaches: == Scale-space theory for one-dimensional signals == For one-dimensional signals, there exists quite a well-developed theory for continuous and discrete kernels that guarantee that new local extrema or zero-crossings cannot be created by a convolution operation. For continuous signals, it holds that all scale-space kernels can be decomposed into the following sets of primitive smoothing kernels: the Gaussian kernel : g ( x , t ) = 1 2 π t exp ⁡ ( − x 2 / 2 t ) {\displaystyle g(x,t)={\frac {1}{\sqrt {2\pi t}}}\exp({-x^{2}/2t})} where t > 0 {\displaystyle t>0} , truncated exponential kernels (filters with one real pole in the s-plane): h ( x ) = exp ⁡ ( − a x ) {\displaystyle h(x)=\exp({-ax})} if x ≥ 0 {\displaystyle x\geq 0} and 0 otherwise where a > 0 {\displaystyle a>0} h ( x ) = exp ⁡ ( b x ) {\displaystyle h(x)=\exp({bx})} if x ≤ 0 {\displaystyle x\leq 0} and 0 otherwise where b > 0 {\displaystyle b>0} , translations, rescalings. For discrete signals, we can, up to trivial translations and rescalings, decompose any discrete scale-space kernel into the following primitive operations: the discrete Gaussian kernel T ( n , t ) = I n ( α t ) {\displaystyle T(n,t)=I_{n}(\alpha t)} where α , t > 0 {\displaystyle \alpha ,t>0} where I n {\displaystyle I_{n}} are the modified Bessel functions of integer order, generalized binomial kernels corresponding to linear smoothing of the form f o u t ( x ) = p f i n ( x ) + q f i n ( x − 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x-1)} where p , q > 0 {\displaystyle p,q>0} f o u t ( x ) = p f i n ( x ) + q f i n ( x + 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x+1)} where p , q > 0 {\displaystyle p,q>0} , first-order recursive filters corresponding to linear smoothing of the form f o u t ( x ) = f i n ( x ) + α f o u t ( x − 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\alpha f_{out}(x-1)} where α > 0 {\displaystyle \alpha >0} f o u t ( x ) = f i n ( x ) + β f o u t ( x + 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\beta f_{out}(x+1)} where β > 0 {\displaystyle \beta >0} , the one-sided Poisson kernel p ( n , t ) = e − t t n n ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{n}}{n!}}} for n ≥ 0 {\displaystyle n\geq 0} where t ≥ 0 {\displaystyle t\geq 0} p ( n , t ) = e − t t − n ( − n ) ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{-n}}{(-n)!}}} for n ≤ 0 {\displaystyle n\leq 0} where t ≥ 0 {\displaystyle t\geq 0} . From this classification, it is apparent that we require a continuous semi-group structure, there are only three classes of scale-space kernels with a continuous scale parameter; the Gaussian kernel which forms the scale-space of continuous signals, the discrete Gaussian kernel which forms the scale-space of discrete signals and the time-causal Poisson kernel that forms a temporal scale-space over discrete time. If we on the other hand sacrifice the continuous semi-group structure, there are more options: For discrete signals, the use of generalized binomial kernels provides a formal basis for defining the smoothing operation in a pyramid. For temporal data, the one-sided truncated exponential kernels and the first-order recursive filters provide a way to define time-causal scale-spaces that allow for efficient numerical implementation and respect causality over time without access to the future. The first-order recursive filters also provide a framework for defining recursive approximations to the Gaussian kernel that in a weaker sense preserve some of the scale-space properties.
Read more →
VLLM

vLLM is an open-source software framework for inference and serving of large language models and related multimodal models. Originally developed at the University of California, Berkeley's Sky Computing Lab, the project is centered on PagedAttention, a memory-management method for transformer key–value caches, and supports features such as continuous batching, distributed inference, quantization, and OpenAI-compatible APIs. According to a project maintainer, the "v" in vLLM originally referred to "virtual", inspired by virtual memory. == History == vLLM was introduced in 2023 by researchers affiliated with the Sky Computing Lab at UC Berkeley. Its core ideas were described in the 2023 paper Efficient Memory Management for Large Language Model Serving with PagedAttention, which presented the system as a high-throughput and memory-efficient serving engine for large language models. In 2025, the PyTorch Foundation announced that vLLM had become a Foundation-hosted project. PyTorch's project page states that the University of California, Berkeley contributed vLLM to the Linux Foundation in July 2024. In January 2026, TechCrunch reported that the creators of vLLM had launched the startup Inferact to commercialize the project, raising $150 million in seed funding. == Architecture == According to its 2023 paper, vLLM was designed to improve the efficiency of large language model serving by reducing memory waste in the key–value cache used during transformer inference. The paper introduced PagedAttention, an algorithm inspired by virtual memory and paging techniques in operating systems, and described vLLM as using block-level memory management and request scheduling to increase throughput while maintaining similar latency. The project documentation and repository describe support for continuous batching, chunked prefill, speculative decoding, prefix caching, quantization, and multiple forms of distributed inference and serving. PyTorch has described vLLM as a high-throughput, memory-efficient inference and serving engine that supports a range of hardware back ends, including NVIDIA and AMD GPUs, Google TPUs, AWS Trainium, and Intel processors.
Read more →
GamePigeon

GamePigeon is a mobile app for iOS devices, developed by Vitalii Zlotskii and released on September 13, 2016. The game takes advantage of the iOS 10 update, which expanded how users could interact with Apple's Messages app. GamePigeon is only available through the Messages app, which allows players to start and respond to different party games in conversations. == Release == The app was first released on September 13, 2016, coinciding with the launch of iOS 10. The app was released for free, although it includes in-app purchases to unlock additional items, such as cosmetic skins, avatar items, new game modes, and an option to remove ads. == Games in the app == The following is a list of games that users can play within GamePigeon: Sources: Poker was one of the games included in GamePigeon at launch, although it has since been removed and is no longer listed on the game's App Store description. == Reception == GamePigeon has enjoyed commercial success, with VentureBeat noting that GamePigeon was ranked number-one in the "Top Free" category of the iMessage App Store, six months after its release. Critically, GamePigeon has been generally well received, being highlighted by online media publications early on shortly after the iOS 10 launch. It has since been included on many "best iMessage apps" lists. Based on over 162,000 ratings, the game holds a 4.0 out of 5 rating on the App Store. Julian Chokkattu of Digital Trends wrote "GamePigeon should be like the pre-installed versions of Solitaire and Minesweeper that used to come with older iterations of Windows." On its launch day, Boy Genius Report included it on a list of "10 of the best iMessage apps, games and stickers for iOS 10 on launch day." The Daily Dot wrote, "GamePigeon is easily the best current gaming option within iMessages." 8-ball and cup pong have been particularly well received by media outlets. The Daily Dot had specific praise for the app's billiards game: "8-Ball controls shockingly smoothly with your fingers, and there’s nothing quite like destroying a dear friend in poker." During his 2020 U.S. presidential campaign, Cory Booker was cited as playing the game with his family. In 2017, CNBC cited one teenager who expressed that GamePigeon was one of just a few reasons that those in her age range use the iMessage app. The game has received particular positive reception for allowing introverted individuals to exercise a form social activity; similarly, the game was highlighted as a way to maintain social distancing guidelines during the COVID-19 pandemic. As an April Fools' Day joke in 2020, The Chronicle, a Duke University newspaper, published that Duke's athletic program adopted GamePigeon's Cup Pong as an official varsity sport.
Read more →
Superquadrics

In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ⁡ ( sin ⁡ ω ) | sin ⁡ ω | m g ( ω , m ) = sgn ⁡ ( cos ⁡ ω ) | cos ⁡ ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ⁡ ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin ⁡ θ cos ⁡ φ y = y 0 + r sin ⁡ θ sin ⁡ φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos ⁡ θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:
Read more →
Chinchilla (language model)

Chinchilla is a family of large language models (LLMs) developed by the research team at Google DeepMind, presented in March 2022. == Models == It is named "chinchilla" because it is a further development over a previous model family named Gopher. Both model families were trained in order to investigate the scaling laws of large language models. It claimed to outperform GPT-3. It considerably simplifies downstream utilization because it requires much less computer power for inference and fine-tuning. Based on the training of previously employed language models, it has been determined that if one doubles the model size, one must also have twice the number of training tokens. This hypothesis has been used to train Chinchilla by DeepMind. Similar to Gopher in terms of cost, Chinchilla has 70B parameters and four times as much data. Chinchilla has an average accuracy of 67.5% on the Measuring Massive Multitask Language Understanding (MMLU) benchmark, which is 7% higher than Gopher's performance. Chinchilla was still in the testing phase as of January 12, 2023. Chinchilla contributes to developing an effective training paradigm for large autoregressive language models with limited compute resources. The Chinchilla team recommends that the number of training tokens is twice for every model size doubling, meaning that using larger, higher-quality training datasets can lead to better results on downstream tasks. It has been used for the Flamingo vision-language model. == Architecture == Both the Gopher family and Chinchilla family are families of transformer models. In particular, they are essentially the same as GPT-2, with different sizes and minor modifications. Gopher family uses RMSNorm instead of LayerNorm; relative positional encoding rather than absolute positional encoding. The Chinchilla family is the same as the Gopher family, but trained with AdamW instead of Adam optimizer. The Gopher family contains six models of increasing size, from 44 million parameters to 280 billion parameters. They refer to the largest one as "Gopher" by default. Similar naming conventions apply for the Chinchilla family. Table 1 of shows the entire Gopher family: Table 4 of compares the 70-billion-parameter Chinchilla with Gopher 280B.
Read more →