Self-supervised learning (SSL) is a paradigm in machine learning where a model is trained on a task using the data itself to generate supervisory signals, rather than relying on externally-provided labels. In the context of neural networks, self-supervised learning aims to leverage inherent structures or relationships within the input data to create meaningful training signals. SSL tasks are designed so that solving them requires capturing essential features or relationships in the data. The input data is typically augmented or transformed in a way that creates pairs of related samples, where one sample serves as the input, and the other is used to formulate the supervisory signal. This augmentation can involve introducing noise, cropping, rotation, or other transformations. Self-supervised learning more closely imitates the way humans learn to classify objects. During SSL, the model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels, which help to initialize the model parameters. Next, the actual task is performed with supervised or unsupervised learning. Self-supervised learning has produced promising results in recent years, and has found practical application in fields such as audio processing, and is being used by Facebook and others for speech recognition. == Pseudo-labels == Pseudo-labels are automatically generated labels that a model assigns to unlabeled data based on its own predictions. They are widely used in self-supervised and semi-supervised learning, where ground-truth annotations are limited or unavailable. By treating predicted labels as surrogate ground truth, learning algorithms can make use of large quantities of unlabeled data in the training process. Pseudo-labeling also plays an important role in systems that must adapt to concept drift, where the statistical properties of the data change over time. In these scenarios, the model may detect that an incoming instance deviates from previously learned behavior. The system then generates a classification result for that instance, and this predicted class is used as a pseudo-label for updating or retraining model components that are becoming outdated. This approach enables continuous adaptation in dynamic environments without requiring manual annotation. In many adaptive learning pipelines, pseudo-labels are chosen when the classifier produces sufficiently confident predictions, reducing the risk of propagating errors. These pseudo-labeled instances are then incorporated into training to refresh or evolve the model's understanding of emerging data patterns, particularly when existing components show signs of “aging” due to drift or distributional shifts. This strategy reduces reliance on manual labeling while helping maintain long-term model performance. == Types == === Autoassociative self-supervised learning === Autoassociative self-supervised learning is a specific category of self-supervised learning where a neural network is trained to reproduce or reconstruct its own input data. In other words, the model is tasked with learning a representation of the data that captures its essential features or structure, allowing it to regenerate the original input. The term "autoassociative" comes from the fact that the model is essentially associating the input data with itself. This is often achieved using autoencoders, which are a type of neural network architecture used for representation learning. Autoencoders consist of an encoder network that maps the input data to a lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error). By minimizing this reconstruction error, the autoencoder learns a meaningful representation of the data in its latent space. === Contrastive self-supervised learning === For a binary classification task, training data can be divided into positive examples and negative examples. Positive examples are those that match the target. For example, if training a classifier to identify birds, the positive training data would include images that contain birds. Negative examples would be images that do not. Contrastive self-supervised learning uses both positive and negative examples. The loss function in contrastive learning is used to minimize the distance between positive sample pairs, while maximizing the distance between negative sample pairs. An early example uses a pair of 1-dimensional convolutional neural networks to process a pair of images and maximize their agreement. Contrastive Language-Image Pre-training (CLIP) allows joint pretraining of a text encoder and an image encoder, such that a matching image-text pair have image encoding vector and text encoding vector that span a small angle (having a large cosine similarity). InfoNCE (Noise-Contrastive Estimation) is a method to optimize two models jointly, based on Noise Contrastive Estimation (NCE). Given a set X = { x 1 , … x N } {\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle p\left(x_{t+k}\mid c_{t}\right)} and N − 1 {\displaystyle N-1} negative samples from the 'proposal' distribution p ( x t + k ) {\displaystyle p\left(x_{t+k}\right)} , it minimizes the following loss function: L N = − E X [ log f k ( x t + k , c t ) ∑ x j ∈ X f k ( x j , c t ) ] {\displaystyle {\mathcal {L}}_{\mathrm {N} }=-\mathbb {E} _{X}\left[\log {\frac {f_{k}\left(x_{t+k},c_{t}\right)}{\sum _{x_{j}\in X}f_{k}\left(x_{j},c_{t}\right)}}\right]} === Non-contrastive self-supervised learning === Non-contrastive self-supervised learning (NCSSL) uses only positive examples. Counterintuitively, NCSSL converges on a useful local minimum rather than reaching a trivial solution, with zero loss. For the example of binary classification, it would trivially learn to classify each example as positive. Effective NCSSL requires an extra predictor on the online side that does not back-propagate on the target side. === Joint-Embedding and Predictive Architectures === A major class of self-supervised learning moves beyond contrastive pairs, instead maximizing the agreement between views while preventing collapse through statistical constraints. Rooted in Deep Canonical Correlation Analysis (Deep CCA), this approach includes Joint-Embedding Architectures (JEA) like Barlow Twins and VICReg, which enforce covariance constraints to learn invariant representations without negative sampling. Deep Latent Variable Path Modelling (DLVPM) generalizes this to multimodal systems, using path models to enforce correlation and orthogonality across diverse data types. In 2022 Yann LeCun introduced Joint-Embedding Predictive Architectures (JEPA) as a step towards decision making, reasoning, and autonomous human intelligence in machines, including self-improvement through autonomous learning. Founded in representation learning, LeCun included the concept of a “world model” in JEPA which aims to enable machines to replicate human intellect by providing machines with a concept for the world in which they exist. Unlike autoencoders, JEPAs operate entirely in latent space, avoiding pixel-level noise to focus on semantic structure. Rather than just learning invariance, JEPAs learn by predicting masked latent representations from visible context. JEPA has been applied to domains such as image analysis, audio processing, and motion in images and video. == Comparison with other forms of machine learning == SSL belongs to supervised learning methods insofar as the goal is to generate a classified output from the input. At the same time, however, it does not require the explicit use of labeled input-output pairs. Instead, correlations, metadata embedded in the data, or domain knowledge present in the input are implicitly and autonomously extracted from the data. These supervisory signals, extracted from the data, can then be used for training. SSL is similar to unsupervised learning in that it does not require labels in the sample data. Unlike unsupervised learning, however, learning is not done using inherent data structures. Semi-supervised learning combines supervised and unsupervised learning, requiring only a small portion of the learning data be labeled. In transfer learning, a model designed for one task is reused on a different task. Training an autoencoder intrinsically constitutes a self-supervised process, because the output pattern needs to become an optimal reconstruction of the input pattern itself. However, in current jargon, the term 'self-supervised' often refers to tasks based on a pretext-task training setup
CityEngine
ArcGIS CityEngine is a commercial 3D modeling program. Developed by Esri R&D Center Zurich (formerly Procedural Inc.), it specializes in the generation of 3D urban environments to support the creation of detailed large-scale 3D city models. Unlike traditional 3D modeling methodology, which uses computer-aided design (CAD) tools and techniques, CityEngine takes a procedural modeling approach which shapes generation via a rules-based system. Due to its integration with the wider ArcGIS platform, CityEngine can also be used with geographic information system (GIS) datasets. CityEngine can be used for urban planning and architecture, graphics visualization, game development, entertainment, and archeology. CityEngine can be used to visualize the building information modeling (BIM) data of buildings in a larger urban context, making for more realistic construction projects. == History and releases == === Software history === ArcGIS CityEngine, originally named Esri CityEngine, was developed at Swiss technology university ETH Zurich by Pascal Mueller, the co-founder and CEO of Procedural Inc. While researching for his PhD at the ETH Computer Vision Lab, Mueller invented a number of techniques for procedural modeling of 3D architecture that make up the foundation of CityEngine. CityEngine publically debuted at the 2001 SIGGRAPH conference; since then, additional research papers have been published that have contributed to CityEngine and its features. The first commercial version of CityEngine was released in 2008. In 2007, Procedural Inc. was founded and separated from ETH Zurich, the top-ranking technology university in Switzerland. In the summer of 2011, Procedural Inc. was acquired by Esri Inc., becoming Esri R&D Center Zurich. Esri CityEngine was renamed to ArcGIS CityEngine in June 2020 to offically make it a part of the ArcGIS software suite. === Releases === === Licensing and pricing === ArcGIS CityEngine is included in the Professional and Professional Plus tiers of ArcGIS Online. Pricing may vary by region and distributors. In the US, the professional tier costs US$2,200 per year; in the UK, it is £4,200 per year (excluding VAT). CityEngine can be purchased elsewhere via a local Esri partner. . Once purchased, users can download and obtain license details from the MyEsri portal. == Features == CGA (computer generated architecture) parametric modeling rules to control mass, geometry assets, proportions, or texturing of buildings or streets on a citywide scale Select a target location and import geo-referenced satellite imagery and 3D terrain of the location to more quickly build accurate urban environments through OpenStreetMap integration Interactively control specific street or building parameters, such as height or age Import/export geo-spatial/vector data with industry-standard formats such as Esri Shapefile, File Geodatabase, and OpenStreetMap, as well as file formats for WebGL, KMZ, Collada, Autodesk FBX, Autodesk Maya, 3DS, Wavefront OBJ, RenderMan RIB, Alembic, e-on software's Vue, Universal Scene Description USD, Khronos Group GLTF, Unreal Engine, and Unreal Datasmith Script and generate rules-based reports to show socioeconomic figures (e.g., Gross Floor Area (GFA) and Floor Area Ratio (FAR)) to analyze their urban design proposals. VR viewing of modeled environments with Samsung Gear VR Use a variety of materials through the Esri materials library == Procedural modeling == ArcGIS CityEngine uses a procedural modeling approach to automatically generate models through a predefined rule set. The rules are defined through a CGA shape grammar system, enabling the creation of complex parametric models. Users can change or add the shape grammar as needed. Urban environments can be modeled within CityEngine by starting with creating a street network (either from the street drawing tool or with data imported from map data). Then, lots may be subdivided as many times as specified, resulting in a map of multiple lots and streets. CityEngine can then be instructed to start generating the buildings using defined procedural modeling rules. At this point, the city model can be re-designed and adjusted by changing the parameters or the shape grammar. === Geodesign === Though CityEngine is not an analytical tool like GIS, discussions about geodesign often mention the use of ArcGIS CityEngine. As it can be used to enhance 3D shape generation in ArcGIS, ArcGIS CityEngine is a critical product to improve the applicability of geodesign by using geospatial information to design or analyze a city. == Applications == === Urban design and planning === Garsdale Design used ArcGIS CityEngine in the creation of city master plans in Iraq before 2013, both to model existing historic areas and also model future plans. Larger companies like Foster+Partners and HOK Architects have also used CityEngine in their urban planning projects. === Urban and environmental studies === Because its primary feature is building informative city models, some urban researchers use CityEngine to compare land-use planning schemes, for example in very dense global cities such as Hong Kong and Seoul. Environmental scientists can also utilize the instant 3D model generation in CityEngine, which can make for more convenient informative research than modeling a city by creating each building individually. === Game development === CityEngine can be used as a tool in the creation of video games that require detailed 3D environments to assign interactive scripts. === Movie industry === Zootopia (also known outside of the US as Zootopolis), which won the 2016 Academy Award for Best Animated Feature Film, used CityEngine to model the city in its movie. multi-scaling city, the designers used CityEngine due to its rule-based system. CityEngine was also used to create Big Hero 6's San-Fransokyo. === Military === Due to its integration with the Esri product suite and its ability to process geospatial data to create 3D scenes/maps, CityEngine can be used within military/defense organizations. == List of movies and TV shows using CityEngine == Studios and companies rarely state what software they use in their pipelines. When CityEngine is mentioned as a tool in production, it's often in a small reference in a larger article. Movies only claimed to use CityEngine by a single Esri employee Presented at FMX 2025 workshop == Ports == ArcGIS CityEngine is built on top of Eclipse IDE, and has therefore able to be used on Windows and Linux operating systems. Support for macOS was stopped in March 2021. == Plugins and extensions == ArcGIS CityEngine currently works with a number of third party 3D modeling, rendering, and analytical software products via its SDK and API; these currently are: ArcGIS CityEngine for ArcGIS Urban: ArcGIS Urban Suite Puma: ArcGIS CityEngine for Rhinoceros 3D Palladio: ArcGIS CityEngine for Houdini Serlio: ArcGIS CityEngine for Maya PyPRT: ArcGIS CityEngine for Python ArcGIS CityEngine provides a Python scripting interface built on Jython (current version 2.7.0) which allows users to create their own tools and functionality. == Publications ==
PitchYaGame
PitchYaGame or #PitchYaGame (sometimes abbreviated to PYG) is a volunteer movement hosted on the social media platform Twitter to showcase, and present awards for, independent video games from around the world. == Description == PitchYaGame is hosted on the social media platform Twitter to showcase independent video games from around the world. Video pitches are presented by developers in June and November each year, and use the hashtag #PitchYaGame to identify and reference news about the showcase and the individual pitches, and the presentation of awards. The showcase was founded in May 2020 by Liam Twose, with the mission of recognising independent video games, and "focused on empowering indie game developers to strengthen their position in the industry." Twose has made clear that PitchYaGame is a showcase and not a hardcore competition, with "[j]ust enough of a push to make sure people put their best pitch forward." The team now comprises Twose (@LiamTwose at Twitter), operations manager "Indie Game Lover" (@IndieGameLover), and host Sarah Clancy (@ImSarahNow). The pitches were originally made monthly, with entries split into a number of categories, but this proved unmanageable. PitchYaGame collaborator, Sarah Clancy reported that judging the many entries on a monthly basis was "difficult and unwieldy." Therefore, pitches were later switched to six monthly, "feature creep" was reduced, and awards streamlined into gold, silver, bronze, runners-up, and most viral. == Sponsorship == In June 2021, PitchYaGame prizes were sponsored by Xsolla, and in November 2021 by Aurora Punks and Cold Pixel. No cash prizes were available in 2022, as the organisers moved PitchYaGame into a less-competitive, "more showcase centric format". == Reception == In October 2020, Elijah Beahm at The Escapist wrote that "One of the greatest challenges for any game is landing a solid pitch. You have to sell people, maybe even a publisher, to take your idea seriously. Most of the time, it's an obfuscated process that leaves the average developer scratching their heads, but Liam Twose and his team behind #PitchYaGame, 'PYG' for short, are looking to change all that with some clever social engineering." In March 2021, Cameron Koch at GameSpot wrote that "Using the #PitchYaGame, thousands of indie developers tweeted out pitches for their games on November 2 as part of a social media contest, and the results are astounding." He went on to say that "There is no arguing with the results. According to Twose, around 1100-1300 games were shared with the hashtag, and some real gems look to have shined through." In November 2021, Stafano "Stef" Castelli at IGN Italia wrote that "I myself enjoyed 'browsing through' the competitors, discovering a handful of intriguing video games in development." (translated from Italian). In November 2022, Eric Bartelson at Premortem Games wrote that "It's a great way to get games noticed by fellow developers, but also publishers, investors and press." In June 2023, Mark Plunkett in Kotaku wrote about the impossibility of keeping up with all the video game releases, and described PitchYaGame, which has attracted over 10,000 pitches since 2020, as an "astoundingly simple idea" that has "become an increasingly useful spot to catch up on some excellent-looking games that we may have otherwise completely slept on."
Social media use in health awareness
Social media is being increasingly used for health awareness. It is not only used to promote health and wellness but also to motivate and guide public for various disease and ailments. Use of social media was proven to be cornerstone for awareness during COVID-19 management. In recent times, it is one of the most cost effective tool for cardiovascular health awareness since it can be used to motivate people for adoption of healthy lifestyle practices. Over the span of a decade, and Doctor Mike utilized social media to significantly impact the public about cardiovascular health awareness. == Background == Social media is proven to be useful for various chronic and incurable diseases where patients form groups and connect for sharing of knowledge. Similarly, health professionals, health institutions, and various other individuals and organizations have their own social media accounts for health information, awareness, guidance, or motivation for their patients. The utilization of social media for health awareness campaigns has become increasingly prevalent in recent years. The history of utilizing social media in health campaigns can be traced back to the early 2000s with the rise of platforms such as Facebook, Twitter, and YouTube. == Health campaigns == Health campaigns especially for chronic diseases like cancer and heart diseases are increasingly common on different social media platforms because social media serves as a cost-effective medium for launching and promoting health campaigns. Many organizations and governmental bodies use platforms like Twitter and Instagram to reach a wide audience. This wide outreach gives health campaigns more attention and support while raising awareness of their specific cause. Recently, there have been increasing calls for health organizations to involve the public and consumer groups in their social media health campaigns to ensure their acceptability with the target audience, encouraging use of collaborations and co-design of messages. == Research == When incorporating social media into health research recruitment, there is potential for a greater number of individuals to participate. Social media allows researchers to reach a wide range of participants while also allowing for recruitment 24 hours a day. There are many health organizations with large social media followings to allow them to reach a large amount of individuals. If these organizations pair with researchers and post flyers or make posts about a study they may be able to find the population that they are looking for. Although there are positives to using social media for health research recruitment, looking at the issues is important. Using this method in recruitment may cause competition between companies for the attention of the users. Another important point is that this is dependent on the type of health condition that is being researched. For chronic conditions, there are many organizations and platforms for support while for acute illnesses, there are not as many organizations that would be able to promote these studies and post for outreach. == Patient education == Patients increasingly turn to social media for health communication and health-related information. Online health communities, forums and blogs enable individuals to share their experiences, offer support, and seek advice from peers. Healthcare professionals also use social media to provide valuable insights and address common health concerns. The use of social media for patient education allows individuals to gain more information for their illness or disease along with gaining support from individuals who may be experiencing the same. Many health organizations such as cancer organizations or organizations for chronic health conditions often have social media platforms that allow individuals to connect and even share their own stories. Peer support is beneficial to patients emotionally and even for them to understand their condition and how to cope. Another way that social media allows individuals to gain more information is the improvement of health literacy. Medical jargon can be confusing for individuals especially when they are newly diagnosed with an illness or disease. Social media has been able to create platforms that explain the information that individuals may need when they are newly diagnosed or if they just want to learn more about their illness. Medical conditions can be confusing but using social media may allow for individuals to develop a better understanding in a manner that they understand. When patients have a better understanding of their health there will be a result of better health outcomes. == Misinformation == While social media is a powerful tool for health awareness, it comes with challenges. Misinformation can spread rapidly, potentially leading to incorrect or harmful health practices. Ensuring the accuracy of health-related information on social media is an ongoing concern. Health misinformation can be easily spread through social media to large amounts of individuals which can make this dangerous. Often, critics will question whether health-related information that is shared online is credible. Social media does not require the amount of regulation that could prevent false medical information from being disseminated online. According to The Influencer Effect: Exploring the persuasive communication tactics of social media influencers in the health and wellness industry by Deborah Deutsch, "the information shared is often lacking accepted scientific evidence or is contrary to industry standards, and, at times, deceptive, unethical, and misleading." One example of this was in 2020, when President Donald Trump said in speeches and on Twitter that hydroxychloroquine and chloroquine could be used to treat COVID-19. While these drugs are antimalaria, it was being spread that they could be used for COVID-19. This resulted in increased deaths and individuals falling ill from taking this drug and the misinformation that was spread about this drug. Spreading misinformation regarding health is one of the biggest concerns when using social media for health awareness. When spreading misinformation about health there is an increase in confusion about what is true and what is false regardless of who is saying this information. Along with the confusion of the public, there is a sense of mistrust that is a consequence of misinformation. Individuals are seeing different opinions which leads people to a situation where they do not know who to trust. While health misinformation is one of the largest issues, there are ways to help prevent it. As individuals, it is important to know where you are getting your information from and learn how to identify what is misinformation and avoid the spread of it. == Privacy and ethical issues == The sharing of personal health information on social media raises privacy and ethical concerns. Striking a balance between raising awareness and respecting individuals' privacy remains a delicate issue.
SPKAC
SPKAC (Signed Public Key and Challenge, also known as Netscape SPKI) is a format for sending a certificate signing request (CSR): it encodes a public key, that can be manipulated using OpenSSL. It is created using the little documented HTML keygen element inside a number of Netscape compatible browsers. == Standardisation == There exists an ongoing effort to standardise SPKAC through an Internet Draft in the Internet Engineering Task Force (IETF). The purpose of this work has been to formally define what has existed prior as a de facto standard, and to address security deficiencies, particular with respect to historic insecure use of MD5 that has since been declared unsafe for use with digital signatures. == Implementations == HTML5 originally specified the
Random feature
Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⟨ ω 1 , x ⟩ , sin ⟨ ω 1 , x ⟩ , … , cos ⟨ ω D , x ⟩ , sin ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.
Social media and identity
Social media can have both positive and negative impacts on a user's identity. Scholars within the fields of psychology and communication study the relationship between social media and identity in order to understand individual behavior, psychological impacts, and social patterns. Communication within political or social groups online can result in practice application, real-world implementation of a concept, of those found identities or the adoption of them as a whole. Young people, defined as emerging adults in or entering college, are especially found to have their identities shaped through social media. Sometimes it seems as though social media is taking over and changing us for the worse. Social media is always changing and can be hard to keep up with. Platforms come and go trends change everyday. What was cool yesterday is lame today. The biggest change from recent years that users are still adjusting to is the name change of Twitter now called X. Since Elon Musk purchased the platform he changed the name but nothing else about the app. Users now feel the need to explain when talking about X. Now it is often referred to as ‘X(Twitter)’ to clarify. == Social Media Usage and Demographics == We know what social media is and how it is used but who uses it? The Pew Research center conducted a 10 year study from 2005-2015 about the demographics of social media usage. While this article is 10 years old the statistics in it are from a very formative time in social media. This is when most people joined and were consistently using social media. Age: While it is no surprise that 90% of young adults use social media they are the main demographic of users. Older adults (65 and older) really hit a boom on social media. In 2005 only 2% of older adults used any form of social media. By 2015 35% of older adults used social media. We can infer that that percentage has grown even more since 2015. Gender: It is known that women tend to use social media more than men. In 2015 it was noted that 65% of women used social media. Men were not far behind, 62% of men were reported to use social media. There are no notable differences of users from various races and ethnicities. The research also shows that more suburban and urban residents use social media over those who live in rural areas. == Young adults == Young adults are especially influenced by social media, where they find social groups to belong to. Research shows that nearly half of teens believe social media platforms has a negative impact on people their age. Psychologists believe that at a time when young adults are coming into adolescence, they are more likely to be influenced by what they see on sites like Instagram or Twitter. Most young adults will widely share, with varying degrees of accuracy, honesty, and openness, information that in the past would have been private or reserved for select individuals. Key questions include whether they accurately portray their identities online and whether the use of social media might impact young adults' identity development. Media Imagery, in particular, is said to be a major influence on the minds of young men and women. Studies have shown that it is even more relevant when it comes to the issue of body image. Social media, in part, has been created to host a safe haven for those who do not claim a solid identity in the material world, but past identities are not easy to escape from since the Internet preserves much of the information that was shared. Social media is an essential part of the social lives of young adults. They rely on it to maintain relationships, create new relationships, and stay up to date with the world around them. Adolescents find social media to be extremely helpful when changing environments, like moving off to university for example. Social media provides students, especially first year students, the opportunity to create the identity they want the world to see. However, it has been seen that these students create online personas that may not reflect their true selves bringing up the issues of impression management. Social media provides young adults with the opportunity to present themselves as something other than their authentic self. Social media providers can help build relationships and community on their platforms. This is something that will create a more positive impact from social media. When young adults interact with each other using social media they are creating something called a social self-identity. Social self identity is what individuals create when they assimilate to being in a group. Social media has gained the reputation of being isolating. If these platforms encourage community then they can help grow users' social self-identity. == Media literacy == The definition of media literacy has evolved over time to encompass a range of experiences that can occur in social media or other digital spaces. The definition of media literacy is also broad and wide ranging in its context. Currently, media literacy is the idea that one is able to analyze, evaluate, and interact with media content in a meaningful way. Educators teach media literacy skills because of the vulnerable relationship that young adults can have with social media. Some examples of media literacy practices, particularly on Twitter, include using hashtags, live tweeting, and sharing information. One of the overall goals of media literacy within the context of social media is to keep young adults aware of potentially violent, graphic, or dangerous content that they may come across on the internet, and how to determine if the content is credible while engaging responsibly with it. In order to be considered media-literate, a person must be able to take in media from online and social platforms and have the correct competencies and context to be able to organize the information. In order to be considered media-literate, the digital information must be given to the user in a way that it can be put into the correct perspective and analyzed, deducted and synthesized.Teenagers and young adults can be vulnerable to specific content online outside of their age-range. Media literacy campaigns and education research shows that targeting those who fall into this age category would be the best way to understand and target their needs as young online users. There are multiple individual studies investigating social media identity relating to media literacy online, however there is a need for much more conclusive information that analyzes multiple studies at a time. Social media literacy is still considered an under-researched topic. Many scholars in media literacy research emphasize the impact of training young adults to consume media in a safe way is the major solution for furthering internet education in children and young adults. The more information the young adults are given on media literacy, the better prepared they are to enter the digital world confidently. One scientific model that has been proposed, known as The Social Media Literacy (SMILE) model is a framework that hypothesizes that at the core of this model it is helping young adults truly know the meaning and display the actions of media literacy online. SMILE is also meant to inspire more research on the subject of media literacy as it relates to social media effects and young adult learning abilities. The model was applied through the lens of a social media positivity bias among adolescents and puts forth five different assumptions about social media and media literacy; Social media literacy as a moderator (what is seen on social media) Social media literacy as a predictor (what is seen for specific individuals on social media) Media literacy within social media is a reciprocal process The development of social media literacy depends on a conditional process of variables affecting other variables Media literacy within social media is a differential learning process, and who teaches it is highly affective of the outcome This model also stresses that human beings learn media literacy (and social media literacy) naturally as they go through life. Research suggests that having young adults taught media literacy from an educator may make them less interested (and therefore less careful) of threats on social media. == Self Presentation == People create images of themselves to present to the public, a process called self presentation. Depending on the demographic, presenting oneself as authentic can result in identity clarity. Methods of self presentation can also be influenced by geography. The framework for this relationship between a user's location and their social media presentation is called the spatial self. Users depict their spatial self in order to include their physical space as a part of their self presentation to an audience. According to a 2018 research paper, patients of plastic surgeons have gone in and asked for specific snapchat "filter" features. This led to a theory of Snap