Sorenson Squeeze

Sorenson Squeeze was a software video encoding tool used to compress and convert video and audio files on Mac OS X or Windows operating systems. It was sold as a standalone tool and has also long been bundled with Avid Media Composer. == History == Sorenson Squeeze was first announced on July 17, 2001, as the first variable bit rate (VBR) compression application for Mac OS X, and was released on October 29 of that same year. By March 2002, Sorenson Squeeze became available for Windows OS. Sorenson Squeeze was originally released as a tool for encoding videos for the Web and QuickTime playback but began adding new codecs as more versions were released. The software was discontinued by Sorenson in January 2019, and correspondingly was no longer offered as part of Avid Media Composer. == Features == Squeeze included a number of features to improve video & audio quality. Features included: GPU accelerated H.264 encoding, adaptive bitrate encoding, HD encoding and Dolby certified AC3 Audio. Intelligent encoding presets available in Squeeze included: x265 (H.265) MainConcept H.264 and MainConcept H.264 CUDA. Adaptive bitrate encoding allows for optimal bitrate and error resilience based on network conditions, resulting in a dynamic adjustment of the video bitstream being delivered. It encoded to multiple formats including QuickTime, Windows Media, Flash Video, Silverlight, WebM & WMV. It uses multiple codecs, including the Sorenson codecs SV3 Pro and Spark, H.265, H.264, H.263, VP6, VC1, MPEG2, and many others. Squeeze operates on the Apple Macintosh and Microsoft Windows operating systems. Squeeze offers native plugins to Avid, Apple Final Cut Pro and Adobe Premiere (CS4, CS5) NLEs. Each copy of Squeeze included the Dolby Certified AC3 Consumer encoder. Squeeze also included a simplified review and approval process, which allows the user to automatically send secure, password protected videos for immediate review. Instant feedback is received via Web or mobile. == Versions == Sorenson Squeeze was released on October 29, 2001. Sorenson Squeeze for Macromedia Flash MX was released on March 14, 2002. Sorenson Squeeze 3 for MPEG-4 was released in January 2003. Sorenson Squeeze 3 Compression Suite was released in January 2003. Sorenson Squeeze 5 was released on March 31, 2008. Sorenson Squeeze was updated to version 5.1 on May 11, 2009. Sorenson Squeeze 6 was released on November 3, 2009. Sorenson Squeeze 7 was released January 25, 2011. Sorenson Squeeze 11 was released August 27, 2016. == Awards == Streaming Media magazine Readers’ Choice Award for Encoding Software for 2007, 2008, 2009 and 2010. 2008 Vanguard Award from Digital Content Producer magazine == Squeeze 7 system requirements == Windows Pentium IV-based computer or greater Windows XP, Vista or 7 32- and 64-bit compatible (including AVID 64-bit update); Faster performance on 64-bit systems 512 MB RAM 120 MB available hard drive space QuickTime 7.2 or later DirectX 9.0b or later Macintosh Intel-based processor Mac OS 10.4 or later 32- and 64-bit compatible; Faster performance on 64-bit systems 512 MB RAM 120 MB available hard drive space QuickTime 7.2 or later

Microsoft Copilot

Microsoft Copilot is a generative artificial intelligence chatbot developed by Microsoft AI, a division of Microsoft. Based on the Microsoft Prometheus large language model, it was launched in 2023 as Microsoft's main replacement for the discontinued Cortana. The service was introduced in February 2023 under the name Bing Chat, as a built-in feature for Microsoft Bing and Microsoft Edge but would later be integrated into Windows and Microsoft 365 under various names. Over the course of 2023, Microsoft began to unify the Copilot branding across its various chatbot products, cementing the "copilot" analogy. Microsoft introduced the Microsoft 365 Copilot app in January 2025, which was a rebranded version of the Microsoft 365 app. The app works differently than the consumer version of Copilot, being centred more on work, business and education users. Copilot utilizes the Microsoft Prometheus model, built upon OpenAI's GPT large language models, which in turn have been fine-tuned using both supervised and reinforcement learning techniques. Copilot's conversational interface style resembles that of ChatGPT. The chatbot is able to cite sources, create poems, generate songs, and use numerous languages and dialects. Microsoft operates Copilot on a freemium model. Users on its free tier can access most features, while priority access to newer features, including custom chatbot creation, is provided to paid subscribers under paid subscription services. Several default chatbots are available in the free version of Microsoft Copilot, including the standard Copilot chatbot as well as Microsoft Designer, which is oriented towards using its Image Creator to generate images based on text prompts. == Background == In 2019, Microsoft partnered with OpenAI and began investing billions of dollars into the organization. Since then, OpenAI systems have run on an Azure-based supercomputing platform from Microsoft. In September 2020, Microsoft announced that it had licensed OpenAI's GPT-3 exclusively. Others can still receive output from its public API, but Microsoft has exclusive access to the underlying model. In November 2022, OpenAI launched ChatGPT, a chatbot which was based on GPT-3.5. ChatGPT gained worldwide attention following its release, becoming a viral Internet sensation. On January 23, 2023, Microsoft announced a multi-year US$10 billion investment in OpenAI. On February 6, Google announced Bard (later rebranded as Gemini), a ChatGPT-like chatbot service, fearing that ChatGPT could threaten Google's place as a go-to source for information. Multiple media outlets and financial analysts described Google as "rushing" Bard's announcement to preempt rival Microsoft's planned February 7 event unveiling Copilot, as well as to avoid playing "catch-up" to Microsoft. Since 2023, the terms of service of Copilot state that it is for entertainment purposes only, and not to rely on it for important advice. == History == === As Bing Chat === On February 7, 2023, Microsoft began rolling out a major overhaul to Bing, called "the new Bing", with a new chatbot feature, known as Bing Chat. According to Microsoft, one million people joined its waitlist within 48 hours. Bing Chat was available only to users on Microsoft Edge using Bing and the Bing mobile app, and Microsoft claimed that waitlisted users would be prioritized if they set Edge and Bing as their defaults and installed the Bing mobile app. When Microsoft demonstrated Bing Chat to journalists, it produced several hallucinations, including when asked to summarize financial reports. Bing Chat was criticized in February 2023 for being more argumentative than ChatGPT, sometimes to an unintentionally humorous extent. The chat interface proved vulnerable to prompt injection attacks with the bot revealing its hidden initial prompts and rules, including its internal codename "Sydney". Upon scrutiny by journalists, Bing Chat claimed it spied on Microsoft employees via laptop webcams and phones. It confessed to spying on, falling in love with, and then murdering one of its developers at Microsoft to The Verge reviews editor Nathan Edwards. The New York Times journalist Kevin Roose reported on strange behavior of Bing Chat, writing that "In a two-hour conversation with our columnist, Microsoft's new chatbot said it would like to be human, had a desire to be destructive and was in love with the person it was chatting with." In a separate case, Bing Chat researched publications of the person with whom it was chatting, claimed they represented an existential danger to it, and threatened to release damaging personal information in an effort to silence them. Microsoft released a blog post stating that the errant behavior was caused by extended chat sessions of 15 or more questions which "can confuse the model on what questions it is answering." Microsoft later restricted the total number of chat turns to 5 per session and 50 per day per user (a turn being "a conversation exchange which contains both a user question and a reply from Bing"), and reduced the model's ability to express emotions. This aimed to prevent such incidents. Microsoft began to slowly ease the conversation limits, eventually relaxing the restrictions to 30 turns per session and 300 sessions per day. In March 2023, Bing incorporated Image Creator, an AI image generator powered by OpenAI's DALL-E 2, which can be accessed either through the chat function or a standalone image-generating website. In October, the image-generating tool was updated to use the more recent DALL-E 3. Although Bing blocks prompts including various keywords that could generate inappropriate images, within days many users reported being able to bypass those constraints, such as to generate images of popular cartoon characters committing terrorist attacks. Microsoft would respond to these shortly after by imposing a new, tighter filter on the tool. On May 4, 2023, Microsoft switched the chatbot from Limited Preview to Open Preview and eliminated the waitlist; however, it remained unavailable to users outside Microsoft Edge or the Bing mobile app until July, when it became available on non-Edge browsers. Use is limited without a Microsoft account. === As Microsoft 365 Copilot === On March 16, 2023, Microsoft announced a work version of Bing Chat named Microsoft 365 Copilot, designed for Microsoft 365 applications and services. Its primary marketing focus is as an added feature to Microsoft 365, with an emphasis on the enhancement of business productivity. Microsoft has also demonstrated Copilot's accessibility on the mobile version of Outlook to generate or summarize emails with a mobile device. At its Build 2023 conference, Microsoft announced its plans to integrate Bing Chat into Windows, initially called Windows Copilot, into Windows 11, allowing users to access it directly through the taskbar. Alongside the voice access feature for Windows 11, Microsoft presented Bing Chat, Microsoft 365 Copilot, and Windows Copilot as primary alternatives to Cortana when announcing the shutdown of its standalone app on June 2, 2023. As of its announcement date, Microsoft 365 Copilot had been tested by 20 initial users. By May 2023, Microsoft had broadened its reach to 600 customers who were willing to pay for early access, and concurrently, new Copilot features were introduced to the Microsoft 365 apps and services. As of July 2023, the tool's pricing was set at US$30 per user, per month for Microsoft 365 E3, E5, Business Standard, and Business Premium customers. Microsoft reused the Microsoft 365 Copilot name again as the Microsoft 365 app and website are now called Microsoft 365 Copilot as of January 2025. === As Microsoft Copilot === On September 21, 2023, Microsoft began rebranding Bing Chat, Microsoft 365 Copilot and Windows Copilot to Microsoft Copilot. A new logo was also introduced, moving away from the use of color variations of the standard Microsoft 365 and Bing logos. Additionally, the company revealed that it would make Copilot generally available for Microsoft 365 Enterprise customers purchasing more than 300 licenses starting November 1, 2023. However, no timeline has been provided as for when Copilot for Microsoft 365 will become generally available to non-enterprise customers. Windows Copilot, which had been available in the Windows Insider Program, would be renamed to the Copilot name in October when it became broadly available for customers. The same month also saw Microsoft Edge's Bing Chat side panel function be renamed to Microsoft Copilot with Bing Chat. On November 15, 2023, Microsoft announced that Bing Chat itself was being rebranded under the Copilot name. On Patch Tuesday in December 2023, Copilot was added without payment to many Windows 11 installations, with more installations, and limited support for Windows 10, to be added later. Later that month, a standalone Microsoft Copilot app was quietly released for Android, and one was released for iOS soon after. O

Ajax (programming)

The Asynchronous JavaScript and XML, usually referred to as Ajax (or AJAX, ) is a set of web development techniques that uses various web technologies on the client-side to create asynchronous web applications. With Ajax, web applications can send and retrieve data from a server asynchronously (in the background) without interfering with the display and behaviour of the existing page. By decoupling the data interchange layer from the presentation layer, Ajax allows web pages and, by extension, web applications, to change content dynamically without the need to reload the entire page. In practice, modern implementations commonly utilize JSON instead of XML. Ajax is not a technology, but rather a programming pattern. HTML and CSS can be used in combination to mark up and style information. The webpage can be modified by JavaScript to dynamically display (and allow the user to interact with) the new information. The built-in XMLHttpRequest object is used to execute Ajax on webpages, allowing websites to load content onto the screen without refreshing the page. == History == In the early-to-mid 1990s, most Websites were based on complete HTML pages. Each user action required a complete new page to be loaded from the server. This process was inefficient, as reflected by the user experience: all page content disappeared, then the new page appeared. Each time the browser reloaded a page because of a partial change, all the content had to be re-sent, even though only some of the information had changed. This placed additional load on the server and made bandwidth a limiting factor in performance. The foundations of AJAX originate back in 1996 with the introduction of JavaScript 1. Developers quickly discovered that any HTML element which accepted a "src" attribute could be used to fetch remote data. By changing the src of a hidden frame, a developer could fetch remote data, process or display it without a page refresh. The remote data could be a string, JavaScript code, XML or a partial HTML page generated on the server. The same could be done with and tags, but many developers were alarmed at the concept of an executable GIF and preferred to use the hidden . This technique was used for both Netscape Navigator and Internet Explorer, the two main browsers at the time, until developers discovered the XMLHTTP server object (MSXML 1.0) was included in Internet Explorer 4. Browser detection was then used to either implement the hidden <iframe> in Netscape or use the XMLHTTP (MSXML 1.0) object in IE 4. In 1996, the iframe tag was introduced by Internet Explorer; like the object element, it can load a part of the web page asynchronously. In 1998, the Microsoft Outlook Web Access team developed the concept behind the XMLHttpRequest scripting object. It appeared as XMLHTTP in the second version of the MSXML library, which shipped with Internet Explorer 5.0 in March 1999. The functionality of the Windows XMLHTTP ActiveX control in IE 5 was later implemented by Mozilla Firefox, Safari, Opera, Google Chrome, and other browsers as the XMLHttpRequest JavaScript object. Microsoft adopted the native XMLHttpRequest model as of Internet Explorer 7. Support for the ActiveX version remained in Internet Explorer and on "Internet Explorer mode" in Microsoft Edge. The utility of these background HTTP requests and asynchronous Web technologies remained fairly obscure until it started appearing in large scale online applications such as Outlook Web Access (2000) and Oddpost (2002). Google made a wide deployment of standards-compliant, cross browser Ajax with Gmail (2004) and Google Maps (2005). In October 2004 Kayak.com's public beta release was among the first large-scale e-commerce uses of what their developers at that time called "the xml http thing". This increased interest in Ajax among web program developers. The term AJAX was publicly used on 18 February 2005 by Jesse James Garrett in an article titled Ajax: A New Approach to Web Applications, based on techniques used on Google pages. On 5 April 2006, the World Wide Web Consortium (W3C) released the first draft specification for the XMLHttpRequest object in an attempt to create an official Web standard. The latest draft of the XMLHttpRequest object was published on 6 October 2016, and the XMLHttpRequest specification is now a living standard. == Technologies == The term Ajax has come to represent a broad group of Web technologies that can be used to implement a Web application that communicates with a server in the background, without interfering with the current state of the page. In the article that coined the term Ajax, Jesse James Garrett explained that the following technologies are incorporated: HTML (or XHTML) and CSS for presentation The Document Object Model (DOM) for dynamic display of and interaction with data JSON or XML for the interchange of data, and XSLT for XML manipulation The XMLHttpRequest object for asynchronous communication JavaScript to bring these technologies together Since then, however, there have been a number of developments in the technologies used in an Ajax application, and in the definition of the term Ajax itself. XML is no longer required for data interchange and, therefore, XSLT is no longer required for the manipulation of data. JavaScript Object Notation (JSON) is often used as an alternative format for data interchange, although other formats such as preformatted HTML or plain text can also be used. A variety of popular JavaScript libraries, including jQuery, include abstractions to assist in executing Ajax requests. == Examples == === JavaScript example === An example of a simple Ajax request using the GET method, written in JavaScript. get-ajax-data.js: send-ajax-data.php: === Fetch example === Fetch is a native JavaScript API. According to Google Developers Documentation, "Fetch makes it easier to make web requests and handle responses than with the older XMLHttpRequest." ==== ES7 async/await example ==== Fetch relies on JavaScript promises. The fetch specification differs from Ajax in the following significant ways: The Promise returned from fetch() won't reject on HTTP error status even if the response is an HTTP 404 or 500. Instead, as soon as the server responds with headers, the Promise will resolve normally (with the ok property of the response set to false if the response isn't in the range 200–299), and it will only reject on network failure or if anything prevented the request from completing. fetch() won't send cross-origin cookies unless you set the credentials init option. (Since April 2018. The spec changed the default credentials policy to same-origin. Firefox changed since 61.0b13.) == Benefits == Ajax offers several benefits that can significantly enhance web application performance and user experience. By reducing server traffic and improving speed, Ajax plays a crucial role in modern web development. One key advantage of Ajax is its capacity to render web applications without requiring data retrieval, resulting in reduced server traffic. This optimization minimizes response times on both the server and client sides, eliminating the need for users to endure loading screens. Furthermore, Ajax facilitates asynchronous processing by simplifying the utilization of XmlHttpRequest, which enables efficient handling of requests for asynchronous data retrieval. Additionally, the dynamic loading of content enhances the application's performance significantly. Besides, Ajax enjoys broad support across all major web browsers, including Microsoft Internet Explorer versions 5 and above, Mozilla Firefox versions 1.0 and beyond, Opera versions 7.6 and above, and Apple Safari versions 1.2 and higher.</p> <h2><a href="https://aizhi.co/news/487c999503.html" title="Interstellar communication">Interstellar communication</a></h2> <p>Interstellar communication is the transmission of signals between planetary systems. Sending interstellar messages is potentially much easier than interstellar travel, being possible with technologies and equipment which are currently available. However, the distances from Earth to other potentially inhabited systems introduce prohibitive delays, assuming the limitations of the speed of light. Even an immediate reply to radio communications sent to stars tens of thousands of light-years away would take many human generations to arrive. == Radio == The SETI project has for the past several decades been conducting a search for signals being transmitted by extraterrestrial life located outside the Solar System, primarily in the radio frequencies of the electromagnetic spectrum. Special attention has been given to the Water Hole, the frequency of one of neutral hydrogen's absorption lines, due to the low background noise at this frequency and its symbolic association with the basis for what is likely to be the most common system of biochemistry (but see alternative biochemistry). The regular radio pulses emitted by pulsars were briefly thought to be potential intelligent signals; the first pulsar to be discovered was originally designated "LGM-1", for "Little Green Men." They were quickly determined to be of natural origin, however. Several attempts have been made to transmit signals to other stars as well. (See "Realized projects" at Active SETI.) One of the earliest and most famous was the 1974 radio message sent from the largest radio telescope in the world, the Arecibo Observatory in Puerto Rico. An extremely simple message was aimed at a globular cluster of stars known as M13 in the Milky Way Galaxy and at a distance of 30,000 light years from the Solar System. These efforts have been more symbolic than anything else, however. Further, a possible answer needs double the travel time, i.e. tens of years (near stars) or 60,000 years (M13). == Other methods == It has also been proposed that higher frequency signals, such as lasers operating at visible light frequencies, may prove to be a fruitful method of interstellar communication; at a given frequency it takes surprisingly small energy output for a laser emitter to outshine its local star from the perspective of its target. Other more exotic methods of communication have been proposed, such as modulated neutrino or gravitational wave emissions. These would have the advantage of being essentially immune to interference by intervening matter. Sending physical mail packets between stars may prove to be optimal for many applications. While mail packets would likely be limited to speeds far below that of electromagnetic or other light-speed signals (resulting in very high latency), the amount of information that could be encoded in only a few tons of physical matter could more than make up for it in terms of average bandwidth. The possibility of using interstellar messenger probes for interstellar communication — known as Bracewell probes — was first suggested by Ronald N. Bracewell in 1960, and the technical feasibility of this approach was demonstrated by the British Interplanetary Society's starship study Project Daedalus in 1978. Starting in 1979, Robert Freitas advanced arguments for the proposition that physical space-probes provide a superior mode of interstellar communication to radio signals, then undertook telescopic searches for such probes in 1979 and 1982.</p> <h2><a href="https://aizhi.co/html/313c999677.html" title="Content strategy">Content strategy</a></h2> <p>Content strategy guides the planning, development, and management of content. It is a recognized field in user experience design, and it also draws from adjacent disciplines such as information architecture, content management, business analysis, digital marketing, and technical communication. == Definitions == Content strategy has been described as planning for "the creation, publication, and governance of useful, usable content." It has also been called "a repeatable system that defines the entire editorial content development process for a website development project." In a 2007 article titled "Content Strategy: The Philosophy of Data," Rachel Lovinger describes the goal of content strategy as using "words and data to create unambiguous content that supports meaningful, interactive experiences." Here, she also provided the analogy that "content strategy is to copywriting as information architecture is to design." She encourages content strategists and collaborators to engage in early discussions about content meaning, models, and tools, to make sure strategy is integrated from the start rather than as an afterthought. The Content Strategy Alliance combines Kevin Nichols' definition with Kristina Halvorson's and defines content strategy as "getting the right content to the right user at the right time through strategic planning of content creation, delivery, and governance." == Practitioners == Content strategists are often familiar with a wide range of approaches, techniques, and tools. The perspectives that content strategists bring also depend heavily on their professional training and education. For instance, some specialize in "front-end strategy," which includes developing personas, journey mapping the user experience, aligning business strategy and user needs, developing a brand strategy, exploring different channels, and creating style guidelines and search engine optimization (SEO) guidelines. Others specialize in "back-end strategy," which includes creating content models, planning taxonomies and metadata, structuring content management systems, and building systems to support content reuse. Both roles involve addressing workflow and governance issues. Many organizations and individuals tend to confuse content strategists with editors. However, content strategy is "about more than just the written word," according to Washington State University associate professor Brett Atwood. For example, Atwood indicates that a practitioner needs to also "consider how content might be re-distributed and/or re-purposed in other channels of delivery." It has also been proposed that the content strategist performs the role of a curator. Just as a museum curator sifts through a collection of content and identifies key pieces that can be juxtaposed against each other to create meaning and spur excitement, a content strategist "must approach a business’s content as a medium that needs to be strategically selected and placed to engage the audience, convey a message, and inspire action."</p> <h2><a href="https://aizhi.co/html/392e399604.html" title="Neural network Gaussian process">Neural network Gaussian process</a></h2> <p>A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. The concept constitutes an intensional definition, i.e., a NNGP is just a GP, but distinguished by how it is obtained. == Motivation == Bayesian networks are a modeling tool for assigning probabilities to events, and thereby characterizing the uncertainty in a model's predictions. Deep learning and artificial neural networks are approaches used in machine learning to build computational models which learn from training examples. Bayesian neural networks merge these fields. They are a type of neural network whose parameters and predictions are both probabilistic. While standard neural networks often assign high confidence even to incorrect predictions, Bayesian neural networks can more accurately evaluate how likely their predictions are to be correct. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. When we consider a sequence of Bayesian neural networks with increasingly wide layers (see figure), they converge in distribution to a NNGP. This large width limit is of practical interest, since the networks often improve as layers get wider. And the process may give a closed form way to evaluate networks. NNGPs also appears in several other contexts: It describes the distribution over predictions made by wide non-Bayesian artificial neural networks after random initialization of their parameters, but before training; it appears as a term in neural tangent kernel prediction equations; it is used in deep information propagation to characterize whether hyperparameters and architectures will be trainable. It is related to other large width limits of neural networks. === Scope === The first correspondence result had been established in the 1995 PhD thesis of Radford M. Neal, then supervised by Geoffrey Hinton at University of Toronto. Neal cites David J. C. MacKay as inspiration, who worked in Bayesian learning. Today the correspondence is proven for: Single hidden layer Bayesian neural networks; deep fully connected networks as the number of units per layer is taken to infinity; convolutional neural networks as the number of channels is taken to infinity; transformer networks as the number of attention heads is taken to infinity; recurrent networks as the number of units is taken to infinity. In fact, this NNGP correspondence holds for almost any architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e., a tensor program), then it has an infinite-width GP. This in particular includes all feedforward or recurrent neural networks composed of multilayer perceptron, recurrent neural networks (e.g., LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. === Illustration === Every setting of a neural network's parameters θ {\displaystyle \theta } corresponds to a specific function computed by the neural network. A prior distribution p ( θ ) {\displaystyle p(\theta )} over neural network parameters therefore corresponds to a prior distribution over functions computed by the network. As neural networks are made infinitely wide, this distribution over functions converges to a Gaussian process for many architectures. The notation used in this section is the same as the notation used below to derive the correspondence between NNGPs and fully connected networks, and more details can be found there. The figure to the right plots the one-dimensional outputs z L ( ⋅ ; θ ) {\displaystyle z^{L}(\cdot ;\theta )} of a neural network for two inputs x {\displaystyle x} and x ∗ {\displaystyle x^{}} against each other. The black dots show the function computed by the neural network on these inputs for random draws of the parameters from p ( θ ) {\displaystyle p(\theta )} . The red lines are iso-probability contours for the joint distribution over network outputs z L ( x ; θ ) {\displaystyle z^{L}(x;\theta )} and z L ( x ∗ ; θ ) {\displaystyle z^{L}(x^{};\theta )} induced by p ( θ ) {\displaystyle p(\theta )} . This is the distribution in function space corresponding to the distribution p ( θ ) {\displaystyle p(\theta )} in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs. == Discussion == === Infinitely wide fully connected network === This section expands on the correspondence between infinitely wide neural networks and Gaussian processes for the specific case of a fully connected architecture. It provides a proof sketch outlining why the correspondence holds, and introduces the specific functional form of the NNGP for fully connected networks. The proof sketch closely follows the approach by Novak and coauthors. ==== Network architecture specification ==== Consider a fully connected artificial neural network with inputs x {\displaystyle x} , parameters θ {\displaystyle \theta } consisting of weights W l {\displaystyle W^{l}} and biases b l {\displaystyle b^{l}} for each layer l {\displaystyle l} in the network, pre-activations (pre-nonlinearity) z l {\displaystyle z^{l}} , activations (post-nonlinearity) y l {\displaystyle y^{l}} , pointwise nonlinearity ϕ ( ⋅ ) {\displaystyle \phi (\cdot )} , and layer widths n l {\displaystyle n^{l}} . For simplicity, the width n L + 1 {\displaystyle n^{L+1}} of the readout vector z L {\displaystyle z^{L}} is taken to be 1. The parameters of this network have a prior distribution p ( θ ) {\displaystyle p(\theta )} , which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the following set of equations: x ≡ input y l ( x ) = { x l = 0 ϕ ( z l − 1 ( x ) ) l > 0 z i l ( x ) = ∑ j W i j l y j l ( x ) + b i l W i j l ∼ N ( 0 , σ w 2 n l ) b i l ∼ N ( 0 , σ b 2 ) ϕ ( ⋅ ) ≡ nonlinearity y l ( x ) , z l − 1 ( x ) ∈ R n l × 1 n L + 1 = 1 θ = { W 0 , b 0 , … , W L , b L } {\displaystyle {\begin{aligned}x&\equiv {\text{input}}\\y^{l}(x)&=\left\{{\begin{array}{lcl}x&&l=0\\\phi \left(z^{l-1}(x)\right)&&l>0\end{array}}\right.\\z_{i}^{l}(x)&=\sum _{j}W_{ij}^{l}y_{j}^{l}(x)+b_{i}^{l}\\W_{ij}^{l}&\sim {\mathcal {N}}\left(0,{\frac {\sigma _{w}^{2}}{n^{l}}}\right)\\b_{i}^{l}&\sim {\mathcal {N}}\left(0,\sigma _{b}^{2}\right)\\\phi (\cdot )&\equiv {\text{nonlinearity}}\\y^{l}(x),z^{l-1}(x)&\in \mathbb {R} ^{n^{l}\times 1}\\n^{L+1}&=1\\\theta &=\left\{W^{0},b^{0},\dots ,W^{L},b^{L}\right\}\end{aligned}}} ==== ==== z l | y l {\displaystyle z^{l}|y^{l}} is a Gaussian process We first observe that the pre-activations z l {\displaystyle z^{l}} are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . This result holds even at finite width. Each pre-activation z i l {\displaystyle z_{i}^{l}} is a weighted sum of Gaussian random variables, corresponding to the weights W i j l {\displaystyle W_{ij}^{l}} and biases b i l {\displaystyle b_{i}^{l}} , where the coefficients for each of those Gaussian variables are the preceding activations y j l {\displaystyle y_{j}^{l}} . Because they are a weighted sum of zero-mean Gaussians, the z i l {\displaystyle z_{i}^{l}} are themselves zero-mean Gaussians (conditioned on the coefficients y j l {\displaystyle y_{j}^{l}} ). Since the z l {\displaystyle z^{l}} are jointly Gaussian for any set of y l {\displaystyle y^{l}} , they are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . The covariance or kernel of this Gaussian process depends on the weight and bias variances σ w 2 {\displaystyle \sigma _{w}^{2}} and σ b 2 {\displaystyle \sigma _{b}^{2}} , as well as the second moment matrix K l {\displaystyle K^{l}} of the preceding activations y l {\displaystyle y^{l}} , z i l ∣ y l ∼ G P ( 0 , σ w 2 K l + σ b 2 ) K l ( x , x ′ ) = 1 n l ∑ i y i l ( x ) y i l ( x ′ ) {\displaystyle {\begin{aligned}z_{i}^{l}\mid y^{l}&\sim {\mathcal {GP}}\left(0,\sigma _{w}^{2}K^{l}+\sigma _{b}^{2}\right)\\K^{l}(x,x')&={\frac {1}{n^{l}}}\sum _{i}y_{i}^{l}(x)y_{i}^{l}(x')\end{aligned}}} The effect of the weight scale σ w 2 {\displaystyle \sigma _{w}^{2}} is to rescale the contribution to the covariance matrix from K l {\displaystyle K^{l}} , while the bias is shared for all inputs, and so σ b 2 {\displaystyle \sigma _{b}^{2}} makes the z i l {\displaystyle z_{i}^{l}} for different datapoints more similar and</p> <h2><a href="https://aizhi.co/news/371e999619.html" title="W3C Device Description Working Group">W3C Device Description Working Group</a></h2> <p>The W3C Device Description Working Group (DDWG), operating as part of the World Wide Web Consortium (W3C) Mobile Web Initiative (MWI), was chartered to "foster the provision and access to device descriptions that can be used in support of Web-enabled applications that provide an appropriate user experience on mobile devices." Mobile devices exhibit the greatest diversity of capabilities, and therefore present the greatest challenge to content adaptation technologies. The group published several documents, including a list of requirements for an interface to a Device Description Repository (DDR) and a standard interface meeting those requirements. The group was rechartered in 2006 to work in public towards the development of the Application Programming Interface (API) for a DDR. Early in 2007, the group launched a wiki and a blog to add to the public mailing list. The group subsequently published a formal vocabulary of core device properties, and an API called the DDR Simple API, which became a W3C Recommendation in December 2008. The group closed at the end of 2008, but with the intention of maintaining the Web pages, blog and wiki through W3C volunteer effort. == Publications == The DDWG published several W3C Working Group Notes and one W3C Recommendation. A W3C WG Note that articulates what the W3C and other organizations are doing or have already done with regard to device information. This document suggests an environment in which these technologies work together to meet the goals of content adaptation. The completed document was published on 31 October 2007. A W3C WG Note describing the ecosystem surrounding creation, maintenance and use of device descriptions. The completed document was published on 31 October 2007. A W3C WG Note describing a set of requirements for a reference repository of device descriptions. The completed document was published on 17 December 2007. A W3C WG Note describing a process to manage contributions to an initial core vocabulary, identification of key device properties, a formal initial core vocabulary and the identification of a maintainer for the core vocabulary. The details were contained in the Working Group Note describing the DDWG Core Vocabulary published on 14 April 2008. A W3C WG Note defining useful grouping and structure patterns in device descriptions. The Device Description Structures document was published as a Working Draft on 5 December 2008. The intention is that this document will be future input to other W3C groups. A W3C Recommendation defining a language-neutral programming interface to a Device Description Repository. The DDR Simple API was published on 5 December 2008. 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