NNDB

The Notable Names Database (NNDB) is an online database of biographical details of over 40,000 people. Soylent Communications, a sole proprietorship that also hosted the later defunct Rotten.com, describes NNDB as an "intelligence aggregator" of noteworthy persons, highlighting their interpersonal connections. The Rotten.com domain was registered in 1996 by former Apple and Netscape software engineer Thomas E. Dell, who was also known by his internet alias, "Soylent". == Entries == Each entry has an executive summary followed by a brief narrative about their life. It also lists date and cause of death if deceased. Businesspeople and government officials are listed with chronologies of their posts, positions, and board memberships. As of 2022, the site is no longer updated. == NNDB Mapper == The NNDB Mapper, a visual tool for exploring connections between people, was made available in May 2008. It required Adobe Flash 7.

List of JavaScript libraries

This is a list of notable JavaScript libraries. == Constraint programming == Cassowary (software) CHR.js == DOM (manipulation) oriented == Google Polymer Dojo Toolkit jQuery MooTools Prototype JavaScript Framework == Graphical/visualization (canvas, SVG, or WebGL related) == AnyChart Apache ECharts Babylon.js Chart.js Cytoscape D3.js Dojo Toolkit FusionCharts Google Charts JointJS p5.js Plotly.js Processing.js Raphaël RGraph SWFObject Teechart Three.js Velocity.js Verge3D Webix == GUI (Graphical user interface) and widget related == Angular (application platform) by Google AngularJS by Google Bootstrap Dojo Widgets Ext JS by Sencha Foundation by ZURB jQuery UI jQWidgets OpenUI5 by SAP Polymer (library) by Google qooxdoo React.js by Meta/Facebook Vue.js Webix WinJS Svelte === No longer actively developed === Glow Lively Kernel Script.aculo.us YUI Library == Pure JavaScript/Ajax == Google Closure Library JsPHP Microsoft's Ajax library MochiKit PDF.js Socket.IO Spry framework Underscore.js == Template systems == jQuery Mobile Mustache Jinja-JS Twig.js == Unit testing == Jasmine Mocha QUnit == Test automation == Playwright Cypress == Web-application related (MVC, MVVM) == Angular (application platform) by Google AngularJS by Google Backbone.js Echo Ember.js Enyo Express.js Ext JS Google Web Toolkit JsRender/JsViews Knockout Meteor Mojito MooTools Next.js Nuxt.js OpenUI5 by SAP Polymer (library) by Google Prototype JavaScript Framework qooxdoo React.js SproutCore svelte Vue.js == Other == Blockly Cannon.js MathJax Modernizr TensorFlow Brain.js

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.

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

Deep learning in photoacoustic imaging

Photoacoustic imaging (PA) is based on the photoacoustic effect, in which optical absorption causes a rise in temperature, which causes a subsequent rise in pressure via thermo-elastic expansion. This pressure rise propagates through the tissue and is sensed via ultrasonic transducers. Due to the proportionality between the optical absorption, the rise in temperature, and the rise in pressure, the ultrasound pressure wave signal can be used to quantify the original optical energy deposition within the tissue. Photoacoustic imaging has applications of deep learning in both photoacoustic computed tomography (PACT) and photoacoustic microscopy (PAM). PACT utilizes wide-field optical excitation and an array of unfocused ultrasound transducers. Similar to other computed tomography methods, the sample is imaged at multiple view angles, which are then used to perform an inverse reconstruction algorithm based on the detection geometry (typically through universal backprojection, modified delay-and-sum, or time reversal ) to elicit the initial pressure distribution within the tissue. PAM on the other hand uses focused ultrasound detection combined with weakly focused optical excitation (acoustic resolution PAM or AR-PAM) or tightly focused optical excitation (optical resolution PAM or OR-PAM). PAM typically captures images point-by-point via a mechanical raster scanning pattern. At each scanned point, the acoustic time-of-flight provides axial resolution while the acoustic focusing yields lateral resolution. == Applications of deep learning in PACT == The first application of deep learning in PACT was by Reiter et al. in which a deep neural network was trained to learn spatial impulse responses and locate photoacoustic point sources. The resulting mean axial and lateral point location errors on 2,412 of their randomly selected test images were 0.28 mm and 0.37 mm respectively. After this initial implementation, the applications of deep learning in PACT have branched out primarily into removing artifacts from acoustic reflections, sparse sampling, limited-view, and limited-bandwidth. There has also been some recent work in PACT toward using deep learning for wavefront localization. There have been networks based on fusion of information from two different reconstructions to improve the reconstruction using deep learning fusion based networks. === Using deep learning to locate photoacoustic point sources === Traditional photoacoustic beamforming techniques modeled photoacoustic wave propagation by using detector array geometry and the time-of-flight to account for differences in the PA signal arrival time. However, this technique failed to account for reverberant acoustic signals caused by acoustic reflection, resulting in acoustic reflection artifacts that corrupt the true photoacoustic point source location information. In Reiter et al., a convolutional neural network (similar to a simple VGG-16 style architecture) was used that took pre-beamformed photoacoustic data as input and outputted a classification result specifying the 2-D point source location. ==== Deep learning for PA wavefront localization ==== Johnstonbaugh et al. was able to localize the source of photoacoustic wavefronts with a deep neural network. The network used was an encoder-decoder style convolutional neural network. The encoder-decoder network was made of residual convolution, upsampling, and high field-of-view convolution modules. A Nyquist convolution layer and differentiable spatial-to-numerical transform layer were also used within the architecture. Simulated PA wavefronts served as the input for training the model. To create the wavefronts, the forward simulation of light propagation was done with the NIRFast toolbox and the light-diffusion approximation, while the forward simulation of sound propagation was done with the K-Wave toolbox. The simulated wavefronts were subjected to different scattering mediums and Gaussian noise. The output for the network was an artifact free heat map of the targets axial and lateral position. The network had a mean error rate of less than 30 microns when localizing target below 40 mm and had a mean error rate of 1.06 mm for localizing targets between 40 mm and 60 mm. With a slight modification to the network, the model was able to accommodate multi target localization. A validation experiment was performed in which pencil lead was submerged into an intralipid solution at a depth of 32 mm. The network was able to localize the lead's position when the solution had a reduced scattering coefficient of 0, 5, 10, and 15 cm−1. The results of the network show improvements over standard delay-and-sum or frequency-domain beamforming algorithms and Johnstonbaugh proposes that this technology could be used for optical wavefront shaping, circulating melanoma cell detection, and real-time vascular surgeries. === Removing acoustic reflection artifacts (in the presence of multiple sources and channel noise) === Building on the work of Reiter et al., Allman et al. utilized a full VGG-16 architecture to locate point sources and remove reflection artifacts within raw photoacoustic channel data (in the presence of multiple sources and channel noise). This utilization of deep learning trained on simulated data produced in the MATLAB k-wave library, and then later reaffirmed their results on experimental data. === Ill-posed PACT reconstruction === In PACT, tomographic reconstruction is performed, in which the projections from multiple solid angles are combined to form an image. When reconstruction methods like filtered backprojection or time reversal, are ill-posed inverse problems due to sampling under the Nyquist-Shannon's sampling requirement or with limited-bandwidth/view, the resulting reconstruction contains image artifacts. Traditionally these artifacts were removed with slow iterative methods like total variation minimization, but the advent of deep learning approaches has opened a new avenue that utilizes a priori knowledge from network training to remove artifacts. In the deep learning methods that seek to remove these sparse sampling, limited-bandwidth, and limited-view artifacts, the typical workflow involves first performing the ill-posed reconstruction technique to transform the pre-beamformed data into a 2-D representation of the initial pressure distribution that contains artifacts. Then, a convolutional neural network (CNN) is trained to remove the artifacts, in order to produce an artifact-free representation of the ground truth initial pressure distribution. ==== Using deep learning to remove sparse sampling artifacts ==== When the density of uniform tomographic view angles is under what is prescribed by the Nyquist-Shannon's sampling theorem, it is said that the imaging system is performing sparse sampling. Sparse sampling typically occurs as a way of keeping production costs low and improving image acquisition speed. The typical network architectures used to remove these sparse sampling artifacts are U-net and Fully Dense (FD) U-net. Both of these architectures contain a compression and decompression phase. The compression phase learns to compress the image to a latent representation that lacks the imaging artifacts and other details. The decompression phase then combines with information passed by the residual connections in order to add back image details without adding in the details associated with the artifacts. FD U-net modifies the original U-net architecture by including dense blocks that allow layers to utilize information learned by previous layers within the dense block. Another technique was proposed using a simple CNN based architecture for removal of artifacts and improving the k-wave image reconstruction. ==== Removing limited-view artifacts with deep learning ==== When a region of partial solid angles are not captured, generally due to geometric limitations, the image acquisition is said to have limited-view. As illustrated by the experiments of Davoudi et al., limited-view corruptions can be directly observed as missing information in the frequency domain of the reconstructed image. Limited-view, similar to sparse sampling, makes the initial reconstruction algorithm ill-posed. Prior to deep learning, the limited-view problem was addressed with complex hardware such as acoustic deflectors and full ring-shaped transducer arrays, as well as solutions like compressed sensing, weighted factor, and iterative filtered backprojection. The result of this ill-posed reconstruction is imaging artifacts that can be removed by CNNs. The deep learning algorithms used to remove limited-view artifacts include U-net and FD U-net, as well as generative adversarial networks (GANs) and volumetric versions of U-net. One GAN implementation of note improved upon U-net by using U-net as a generator and VGG as a discriminator, with the Wasserstein metric and gradient penalty to stabilize training (WGAN-GP). ==== Pixel-wise interpolation

PeduliLindungi

SatuSehat (Indonesian for "one health"), formerly PeduliLindungi (roughly "care to protect"), is a national integrated health data exchange platform, jointly developed by the Indonesian Ministry of Communication and Information Technology (Kemenkominfo), in partnership with Committee for COVID-19 Response and National Economic Recovery (KPCPEN), Ministry of Health (Kemenkes), Ministry of State-Owned Enterprises (KemenBUMN), and Telkom Indonesia. The SatuSehat platform aims to facilitate data accessibility and service efficiency for health providers and the government, and assist the public as a tool to access their own electronic medical record data. This app was the official COVID-19 contact tracing app used for digital contact tracing in Indonesia, and originally known as TraceTogether but later changed because Singapore had its app using the same name. == Implementation == On 23 August 2021, Coordinating Minister for Maritime and Investments Affairs, Luhut Binsar Panjaitan, encouraged the government to make this app a mandatory requirement before using public transportations, such as train, bus, ferry, and plane. Furthermore, citizen must have installed the app before entering shopping malls, factories, and sport venues. Every person who have received at least a dose of vaccine will receive a vaccine card and vaccination certificate which can be downloaded from the app. In December 2022, with the revocation of PPKM (Community Activities Restrictions Enforcement) starting from 1 January 2023, Ministry of Health issued a statement that the usage of the app is not a governmental mandatory requirement as it used to be. === Transition into a citizen health app === On 7 September 2022, it was announced that the app would be modified to become a citizen health app, capitalising on the reach of the app and the existing work done around the app. On 28 February 2023, the authorities announced that the app was rebranded to SATUSEHAT Mobile (lit. 'OneHealth Mobile'), with existing users needing to update the PeduliLindungi app and re-synchronise their COVID-19 related health information. The re-branded app would eventually be an all-in-one health service and records retrieval app for Indonesians. == Controversy == It was reported that the app requires continuous access to the phone's files, media, and GPS, which quickly drains the battery. Allowing location access only during use or denying it altogether will render the app unusable. This stands in stark contrast to COVID-19 apps used in other countries that only utilize Bluetooth and do not require any additional permissions. In September 2021, stored personal data of at least 1.3 million Indonesian residents were leaked online, including the vaccine certificate of President Joko Widodo. The data leak was also reported on eHAC (electronic Health Alert Card), a mandatory app used for air passengers.

Pooling layer

In neural networks, a pooling layer is a kind of network layer that downsamples and aggregates information that is dispersed among many vectors into fewer vectors. It has several uses. It removes redundant information, thus reducing the amount of computation and memory required, which makes the model more robust to small variations in the input; and it increases the receptive field of neurons in later layers in the network. == Convolutional neural network pooling == Pooling is most commonly used in convolutional neural networks (CNN). Below is a description of pooling in 2-dimensional CNNs. The generalization to n-dimensions is immediate. As notation, we consider a tensor x ∈ R H × W × C {\displaystyle x\in \mathbb {R} ^{H\times W\times C}} , where H {\displaystyle H} is height, W {\displaystyle W} is width, and C {\displaystyle C} is the number of channels. A pooling layer outputs a tensor y ∈ R H ′ × W ′ × C ′ {\displaystyle y\in \mathbb {R} ^{H'\times W'\times C'}} . We define two variables f , s {\displaystyle f,s} called "filter size" (aka "kernel size") and "stride". Sometimes, it is necessary to use a different filter size and stride for horizontal and vertical directions. In such cases, we define 4 variables: f H , f W , s H , s W {\displaystyle f_{H},f_{W},s_{H},s_{W}} . The receptive field of an entry in the output tensor, y {\displaystyle y} , are all the entries in x {\displaystyle x} that can affect that entry. === Max pooling === Max Pooling (MaxPool) is commonly used in CNNs to reduce the spatial dimensions of feature maps. Define M a x P o o l ( x | f , s ) 0 , 0 , 0 = max ( x 0 : f − 1 , 0 : f − 1 , 0 ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{0,0,0}=\max(x_{0:f-1,0:f-1,0})} where 0 : f − 1 {\displaystyle 0:f-1} means the range 0 , 1 , … , f − 1 {\displaystyle 0,1,\dots ,f-1} . Note that we need to avoid the off-by-one error. The next input is M a x P o o l ( x | f , s ) 1 , 0 , 0 = max ( x s : s + f − 1 , 0 : f − 1 , 0 ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{1,0,0}=\max(x_{s:s+f-1,0:f-1,0})} and so on. The receptive field of y i , j , c {\displaystyle y_{i,j,c}} is x i s + f − 1 , j s + f − 1 , c {\displaystyle x_{is+f-1,js+f-1,c}} , so in general, M a x P o o l ( x | f , s ) i , j , c = m a x ( x i s : i s + f − 1 , j s : j s + f − 1 , c ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{i,j,c}=\mathrm {max} (x_{is:is+f-1,js:js+f-1,c})} If the horizontal and vertical filter size and strides differ, then in general, M a x P o o l ( x | f , s ) i , j , c = m a x ( x i s H : i s H + f H − 1 , j s W : j s W + f W − 1 , c ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{i,j,c}=\mathrm {max} (x_{is_{H}:is_{H}+f_{H}-1,js_{W}:js_{W}+f_{W}-1,c})} More succinctly, we can write y k = max ( { x k ′ | k ′ in the receptive field of k } ) {\displaystyle y_{k}=\max(\{x_{k'}|k'{\text{ in the receptive field of }}k\})} . If H {\displaystyle H} is not expressible as k s + f {\displaystyle ks+f} where k {\displaystyle k} is an integer, then for computing the entries of the output tensor on the boundaries, max pooling would attempt to take as inputs variables off the tensor. In this case, how those non-existent variables are handled depends on the padding conditions, illustrated on the right. Global Max Pooling (GMP) is a specific kind of max pooling where the output tensor has shape R C {\displaystyle \mathbb {R} ^{C}} and the receptive field of y c {\displaystyle y_{c}} is all of x 0 : H , 0 : W , c {\displaystyle x_{0:H,0:W,c}} . That is, it takes the maximum over each entire channel. It is often used just before the final fully connected layers in a CNN classification head. === Average pooling === Average pooling (AvgPool) is similarly defined A v g P o o l ( x | f , s ) i , j , c = a v e r a g e ( x i s : i s + f − 1 , j s : j s + f − 1 , c ) = 1 f 2 ∑ k ∈ i s : i s + f − 1 ∑ l ∈ j s : j s + f − 1 x k , l , c {\displaystyle \mathrm {AvgPool} (x|f,s)_{i,j,c}=\mathrm {average} (x_{is:is+f-1,js:js+f-1,c})={\frac {1}{f^{2}}}\sum _{k\in is:is+f-1}\sum _{l\in js:js+f-1}x_{k,l,c}} Global Average Pooling (GAP) is defined similarly to GMP. It was first proposed in Network-in-Network. Similarly to GMP, it is often used just before the final fully connected layers in a CNN classification head. === Interpolations === There are some interpolations of max pooling and average pooling. Mixed Pooling is a linear sum of max pooling and average pooling. That is, M i x e d P o o l ( x | f , s , w ) = w M a x P o o l ( x | f , s ) + ( 1 − w ) A v g P o o l ( x | f , s ) {\displaystyle \mathrm {MixedPool} (x|f,s,w)=w\mathrm {MaxPool} (x|f,s)+(1-w)\mathrm {AvgPool} (x|f,s)} where w ∈ [ 0 , 1 ] {\displaystyle w\in [0,1]} is either a hyperparameter, a learnable parameter, or randomly sampled anew every time. Lp Pooling is similar to average pooling, but uses Lp norm average instead of average: y k = ( 1 N ∑ k ′ in the receptive field of k | x k ′ | p ) 1 / p {\displaystyle y_{k}=\left({\frac {1}{N}}\sum _{k'{\text{ in the receptive field of }}k}|x_{k'}|^{p}\right)^{1/p}} where N {\displaystyle N} is the size of receptive field, and p ≥ 1 {\displaystyle p\geq 1} is a hyperparameter. If all activations are non-negative, then average pooling is the case of p = 1 {\displaystyle p=1} , and max pooling is the case of p → ∞ {\displaystyle p\to \infty } . Square-root pooling is the case of p = 2 {\displaystyle p=2} . Stochastic pooling samples a random activation x k ′ {\displaystyle x_{k'}} from the receptive field with probability x k ′ ∑ k ″ x k ″ {\displaystyle {\frac {x_{k'}}{\sum _{k''}x_{k''}}}} . It is the same as average pooling in expectation. Softmax pooling is like max pooling, but uses softmax, i.e. ∑ k ′ e β x k ′ x k ′ ∑ k ″ e β x k ″ {\displaystyle {\frac {\sum _{k'}e^{\beta x_{k'}}x_{k'}}{\sum _{k''}e^{\beta x_{k''}}}}} where β > 0 {\displaystyle \beta >0} . Average pooling is the case of β ↓ 0 {\displaystyle \beta \downarrow 0} , and max pooling is the case of β ↑ ∞ {\displaystyle \beta \uparrow \infty } Local Importance-based Pooling generalizes softmax pooling by ∑ k ′ e g ( x k ′ ) x k ′ ∑ k ″ e g ( x k ″ ) {\displaystyle {\frac {\sum _{k'}e^{g(x_{k'})}x_{k'}}{\sum _{k''}e^{g(x_{k''})}}}} where g {\displaystyle g} is a learnable function. === Other poolings === Spatial pyramidal pooling applies max pooling (or any other form of pooling) in a pyramid structure. That is, it applies global max pooling, then applies max pooling to the image divided into 4 equal parts, then 16, etc. The results are then concatenated. It is a hierarchical form of global pooling, and similar to global pooling, it is often used just before a classification head. Region of Interest Pooling (also known as RoI pooling) is a variant of max pooling used in R-CNNs for object detection. It is designed to take an arbitrarily-sized input matrix, and output a fixed-sized output matrix. Covariance pooling computes the covariance matrix of the vectors { x k , l , 0 : C − 1 } k ∈ i s : i s + f − 1 , l ∈ j s : j s + f − 1 {\displaystyle \{x_{k,l,0:C-1}\}_{k\in is:is+f-1,l\in js:js+f-1}} which is then flattened to a C 2 {\displaystyle C^{2}} -dimensional vector y i , j , 0 : C 2 − 1 {\displaystyle y_{i,j,0:C^{2}-1}} . Global covariance pooling is used similarly to global max pooling. As average pooling computes the average, which is a first-degree statistic, and covariance is a second-degree statistic, covariance pooling is also called "second-order pooling". It can be generalized to higher-order poolings. Blur Pooling means applying a blurring method before downsampling. For example, the Rect-2 blur pooling means taking an average pooling at f = 2 , s = 1 {\displaystyle f=2,s=1} , then taking every second pixel (identity with s = 2 {\displaystyle s=2} ). == Vision Transformer pooling == In Vision Transformers (ViT), there are the following common kinds of poolings. BERT-like pooling uses a dummy [CLS] token, "classification". For classification, the output at [CLS] is the classification token, which is then processed by a LayerNorm-feedforward-softmax module into a probability distribution, which is the network's prediction of class probability distribution. This is the one used by the original ViT and Masked Autoencoder. Global average pooling (GAP) does not use the dummy token, but simply takes the average of all output tokens as the classification token. It was mentioned in the original ViT as being equally good. Multihead attention pooling (MAP) applies a multi headed attention block to pooling. Specifically, it takes as input a list of vectors x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} , which might be thought of as the output vectors of a layer of a ViT. It then applies a feedforward layer F F N {\displaystyle \mathrm {FFN} } on each vector, resulting in a matrix V = [ F F N ( v 1 ) , … , F F N ( v n ) ] {\displaystyle V=[\mathrm {FFN} (v_{1}),\dots ,\mathrm {FFN} (v_{n})]} . This is then sent to a multi-headed attention, resulting in M u l t i h e a d e d A