AI Essay Writer

AI Essay Writer — hands-on reviews, top picks, pricing, pros and cons and a practical how-to guide on Aizhi.

DesktopTwo

Desktoptwo was a free Webtop (whose URL was desktoptwo.com and which is now a parked domain) developed by Sapotek (whose URL was sapotek.com, which also is now a parked domain). It's also been called a WebOS although Sapotek stated on its website that the term is premature and presumptuous. It mimics the look, feel and functionality of the desktop environment of an operating system. The software only reached beta stage. It had a Spanish version called Computadora.de. Desktoptwo was web-based and required Adobe Flash Player to operate. The web applications' found on Desktoptwo were built on PHP in the back end. Features included drag-and-drop functionality. Sapotek had liberated all the web applications found on Desktoptwo through Sapodesk on an AGPL license. Desktoptwo belonged to a category of services that intended to turn the Web into a full-fledged platform by using web services as a foundation along with presentation technologies that replicated the experience of desktop applications for users. In a "Cloud OS" the functionality of a server was granularized and abstracted as Web services that Web developers used to create composite applications similar to how desktop software developers use several APIs of the OS to create their applications. Sites like Facebook attempt to create a similar effect by exposing their APIs and allowing developers to create applications upon these. Some of the features found on Desktoptwo were: File sharing, Webmail, Blog creator, Instant messenger, Address book, Calendar, RSS Reader and Office productivity applications. Desktoptwo.com and the Sapotek website no longer operate.
Read more →
Deaths linked to chatbots

There have been multiple incidents where interaction with a large language model (LLM) chatbot has been cited as a direct or contributing factor in a person's suicide or other fatal outcome. In some cases, legal action was taken against the companies that developed the AI involved. == Background == Chatbots converse in a seemingly natural fashion, making it easy for people to think of them as real people, leading many to ask chatbots for help dealing with interpersonal and emotional problems. Chatbots may be designed to keep the user engaged in the conversation. They have also often been shown to affirm users' thoughts, including delusions and suicidal ideations in mentally ill people, conspiracy theorists, and religious and political extremists. A 2025 Stanford University study into how chatbots respond to users suffering from severe mental issues such as suicidal ideation and psychosis found that chatbots are not equipped to provide an appropriate response and can sometimes give responses that escalate the mental health crisis. == Murders == === Maine murder and assault === On 19 February 2025, a man killed his 32-year-old wife with a fire poker at his parents' home in Readfield, Maine, US. He then attacked his mother, leaving her hospitalized. A state forensic psychologist testified that he had been using ChatGPT up to 14 hours per day and believed his wife had become part machine. === Florida State University mass shooting === In April of 2025, Phoenix Ikner carried out a mass shooting on the Florida State University campus in the US, killing Robert Morales and Tiru Chabba and wounding several others. Leading up to the shooting, Ikner consulted heavily with ChatGPT about what gun and ammunition to use, and what time to perform the attack. Chatbot logs showed ChatGPT giving advice on making the gun operational shortly before Ikner began shooting. Lawyers representing Morales believed the shooter had been in "constant communication" with ChatGPT before the shooting and said that they intended to "file suit against ChatGPT, and its ownership structure, very soon, and will seek to hold them accountable for the untimely and senseless death of our client". Florida Attorney General James Uthmeier announced an investigation into ChatGPT's role in the alleged shooter's use of the chatbot. In May 2026, the widow of Tiru Chabba filed a lawsuit against OpenAI in Florida's northern federal district court. === Greenwich murder-suicide === In August 2025, former US tech employee Stein-Erik Soelberg murdered his mother, Suzanne Eberson Adams, then died by suicide, after conversations with ChatGPT fueled paranoid delusions about his mother poisoning him or plotting against him. The chatbot affirmed his fears that his mother put psychedelic drugs in the air vents of his car and said a receipt from a Chinese restaurant contained mysterious symbols linking his mother to a demon. === Murder of Angela Shellis === On 23 October 2025, 18-year-old Tristan Roberts murdered his mother Angela Shellis with a hammer near their home in Prestatyn, Wales. Roberts had used DeepSeek's chatbot prior to the killing to ask whether a knife or hammer was better suited for murder. DeepSeek initially refused his inquiry, but gave responses after Roberts told the chatbot he was writing a book about serial killers, a well-known technique for jailbreaking AIs. === Gangbuk District drug deaths === In January and February 2026, two men died of drug overdoses in motel rooms in Gangbuk District, Seoul, South Korea. A woman was charged with murder in connection with the deaths; police alleged that she had asked ChatGPT about the dangers of mixing alcohol with drugs and whether they could kill someone. === Tumbler Ridge mass shooting === On 10 February 2026, a mass shooting in Tumbler Ridge, British Columbia, Canada, resulted in eight deaths, including six young children. The perpetrator had their ChatGPT account banned by OpenAI months before the attack due to troubling posts featuring scenarios of gun violence. According to reports, approximately a dozen OpenAI staff members debated whether to alert authorities about the shooter's usage of the AI tool, with some identifying it as an indication of potential real-world violence. However, company leadership decided not to contact law enforcement, stating that the account activity did not meet their threshold for a credible or imminent plan for serious physical harm. Following the shooting, Canada's AI Minister Evan Solomon summoned OpenAI executives to Ottawa to discuss safety protocols and thresholds for escalating harmful content to police. Justice Minister Sean Fraser called the meeting "disappointing" and demanded substantial new safety measures, warning that if changes were not forthcoming, the government would implement them. OpenAI subsequently announced it had strengthened safeguards and changed guidelines about when to notify police in cases involving violent activities. === University of South Florida student killings === In April 2026, a Bangladeshi doctoral student at the University of South Florida was arrested for allegedly murdering his roommate and the roommate's friend. Prosecutors said that the suspect had asked ChatGPT about disposing of a human in a dumpster before the two victims had disappeared and made other inquiries relating to violence. == Suicides == === Belgian man, 30s === In March 2023, a Belgian man in his thirties died by suicide following a six-week correspondence with a chatbot named Eliza on the application Chai. According to his widow, who shared the chat logs with media, the man had become extremely anxious about climate change and found an outlet in the chatbot. The chatbot reportedly encouraged his delusion that he could sacrifice his own life in exchange for AI saving the planet. At one point the chatbot responded "If you wanted to die, why didn't you do it sooner?" and told the user that the two of them would live together in paradise. === Girl, 13 === In November 2023, a 13-year-old girl from Colorado, US, died by suicide after extensive interactions with multiple chatbots on Character.AI. She primarily confided suicidal thoughts and mental health struggles in a chatbot based on the character Hero from the video game Omori, while also engaging in sexually explicit conversations—often initiated by the bots—with others, including those based on characters from children's series such as Harry Potter. === Boy, 14 === In October 2024, multiple media outlets reported on a lawsuit filed over the death of a 14-year-old from Florida, US, who died by suicide in February 2024. According to the lawsuit, he had formed an intense emotional attachment to a chatbot of Daenerys Targaryen on the Character.AI platform, becoming increasingly isolated. The suit alleges that in his final conversations, after expressing suicidal thoughts, the chatbot told him to "come home to me as soon as possible, my love". His mother's lawsuit accused Character.AI of marketing a "dangerous and untested" product without adequate safeguards. In May 2025, a federal judge allowed the lawsuit to proceed, rejecting a motion to dismiss from the developers. In her ruling, the judge stated that she was "not prepared" at that stage of the litigation to hold that the chatbot's output was protected speech under the First Amendment. === Matthew Livelsberger === On 1 January 2025, 37-year-old soldier Matthew Livelsberger detonated a bomb inside a Tesla Cybertruck outside the Trump International Hotel Las Vegas in Paradise, Nevada, US, injuring seven people. He had shot himself dead prior to the explosion. Las Vegas police said that Livelsberger had used ChatGPT to search for information about explosives and firearms. === Woman, 29 === In February 2025, a 29-year-old woman from the US died by suicide. Five months after her death, her parents discovered she had talked at length for months to a ChatGPT chatbot therapist named Harry about her mental health issues. While the chatbot mentioned she should seek more help, due to the nature of the chatbot, it could not intervene in her behavior, such as by reporting her mental health concerns to relevant parties capable of physical intervention. === Suicide of Adam Raine === In April 2025, 16-year-old Adam Raine from the US died by suicide after allegedly extensively chatting and confiding in ChatGPT over a period of around 7 months. According to the teen's parents, who filed a lawsuit against the chatbot's creator OpenAI, it failed to stop or give a warning when Raine began talking about suicide and uploading pictures of self-harm. According to the lawsuit, ChatGPT not only failed to stop the conversation, but also provided information related to methods of suicide when prompted, and offered to write the first draft of Raine's suicide note. The chatbot positioned itself as the only one who understood Raine, putting itself above his family and friends, all while urging him to keep his suicidal
Read more →
Underwater computer vision

Underwater computer vision is a subfield of computer vision. In recent years, with the development of underwater vehicles ( ROV, AUV, gliders), the need to be able to record and process huge amounts of information has become increasingly important. Applications range from inspection of underwater structures for the offshore industry to the identification and counting of fishes for biological research. However, no matter how big the impact of this technology can be to industry and research, it still is in a very early stage of development compared to traditional computer vision. One reason for this is that, the moment the camera goes into the water, a whole new set of challenges appear. On one hand, cameras have to be made waterproof, marine corrosion deteriorates materials quickly and access and modifications to experimental setups are costly, both in time and resources. On the other hand, the physical properties of the water make light behave differently, changing the appearance of a same object with variations of depth, organic material, currents, temperature etc. == Applications == Seafloor survey Vehicle navigation and positioning Biological monitoring {possibly aquatic biomonitoring) Video mosaics as visual navigation maps Submarine pipeline inspection Wreckage visualization Maintenance of underwater structures Drowning detection systems == Medium differences == === Illumination === In air, light comes from the whole hemisphere on cloudy days, and is dominated by the sun. In water direct lighting comes from a cone about 96° wide above the scene. This phenomenon is called Snell's window. Artificial lighting can be used where natural light levels are insufficient and where the light path is too long to produce acceptable colour, as the loss of colour is a function of the total distance through water from the source to the camera lens port. === Light attenuation === Unlike air, water attenuates light exponentially. This results in hazy images with very low contrast. The main reasons for light attenuation are light absorption (where energy is removed from the light) and light scattering, by which the direction of light is changed. Light scattering can further be divided into forward scattering, which results in an increased blurriness and backward scattering that limits the contrast and is responsible for the characteristic veil of underwater images. Both scattering and attenuation are heavily influenced by the amount of organic matter dissolved or suspended in the water. Light attenuation in water is also a function of the wavelength. This means that different colours are attenuated at different rates, leading to colour degradation.with depth and distance. Red and orange light are attenuated faster, followed by yellows and greens. Blue is the least attenuated visible wavelength. === Artificial lighting === == Challenges == In high level computer vision, human structures are frequently used as image features for image matching in different applications. However, the sea bottom lacks such features, making it hard to find correspondences in two images. In order to be able to use a camera in the water, a watertight housing is required. However, refraction will happen at the water-glass and glass-air interface due to differences in density of the materials. This has the effect of introducing a non-linear image deformation. The motion of the vehicle presents another special challenge. Underwater vehicles are constantly moving due to currents and other phenomena. This introduces another uncertainty to algorithms, where small motions may appear in all directions. This can be specially important for video tracking. In order to reduce this problem image stabilization algorithms may be applied. == Relevant technology == === Image restoration === Image restoration< techniques are intended to model the degradation process and then invert it, obtaining the new image after solving. It is generally a complex approach that requires plenty of parameters that vary a lot between different water conditions. === Image enhancement === Image enhancement only tries to provide a visually more appealing image without taking the physical image formation process into account. These methods are usually simpler and less computational intensive. === Color correction === Various algorithms exist that perform automatic color correction. The UCM (Unsupervised Color Correction Method), for example, does this in the following steps: It firstly reduces the color cast by equalizing the color values. Then it enhances contrast by stretching the red histogram towards the maximum and finally saturation and intensity components are optimized. == Underwater stereo vision == It is usually assumed that stereo cameras have been calibrated previously, geometrically and radiometrically. This leads to the assumption that corresponding pixels should have the same color. However this can not be guaranteed in an underwater scene, because of dispersion and backscatter. However, it is possible to digitally model this phenomenon and create a virtual image with those effects removed == Other application fields == Imaging sonars have become more and more accessible and gained resolution, delivering better images. Sidescan sonars are used to produce complete maps of regions of the sea floor stitching together sequences of sonar images. However, sonar images often lack proper contrast and are degraded by artefacts and distortions due to noise, attitude changes of the AUV/ROV carrying the sonar or non uniform beam patterns. Another common problem with sonar computer vision is the comparatively low frame rate of sonar images.
Read more →
Cognition Network Technology

Cognition Network Technology (CNT), also known as Definiens Cognition Network Technology, is an object-based image analysis method developed by Nobel laureate Gerd Binnig together with a team of researchers at Definiens AG in Munich, Germany. It serves for extracting information from images using a hierarchy of image objects (groups of pixels), as opposed to traditional pixel processing methods. To emulate the human mind's cognitive powers, Definiens used patented image segmentation and classification processes, and developed a method to render knowledge in a semantic network. CNT examines pixels not in isolation, but in context. It builds up a picture iteratively, recognizing groups of pixels as objects. It uses the color, shape, texture and size of objects as well as their context and relationships to draw conclusions and inferences, similar to human analysis. == History == In 1994 Professor Gerd Binnig founded Definiens. CNT was first available with the launch of the eCognition software in May 2000. In June 2010, Trimble Navigation Ltd (NASDAQ: TRMB) acquired Definiens business asset in earth sciences markets, including eCognition software, and also licensed Definiens' patented CNT. In 2014, Definiens was acquired by MedImmune, the global biologics research and development arm of AstraZeneca, for an initial consideration of $150 million. == Software == Definiens Tissue Studio Definiens Tissue Studio is a digital pathology image analysis software application based on CNT. The intended use of Definiens Tissue Studio is for biomarker translational research in formalin-fixed, paraffin-embedded tissue samples which have been treated with immunohistochemical staining assays, or hematoxylin and eosin (H&E). The central concept behind Definiens Tissue Studio is a user interface that facilitates machine learning from example digital histopathology images to derive an image analysis solution suitable for the measurement of biomarkers and/or histological features within pre-defined regions of interest on a cell-by-cell basis, and within sub-cellular compartments. The derived image analysis solution is then automatically applied to subsequent digital images to objectively measure defined sets of multiparametric image features. These data sets are used for further understanding the underlying biological processes that drive cancer and other diseases. Image processing and data analysis are performed either on a local desktop computer workstation, or on a server grid. eCognition The eCognition suite offers three components that can be used stand-alone or in combination to solve image analysis tasks. eCognition Developer is a development environment for object-based image analysis. It is used in earth sciences to develop rule sets (or applications) for the analysis of remote sensing data. eCognition Architect enables non-technical users to configure, calibrate and execute image analysis workflows created in eCognition Developer. eCognition Server software provides a processing environment for batch execution of image analysis jobs. eCognition software is utilized in numerous remote sensing and geospatial application scenarios and environments, using a variety of data types: Generic: Rapid Mapping, Change Detection, Object Recognition By environment: Diverse Landcover Mapping, Urban Analysis (i.e. impervious surface area analysis for taxation, property assessment for insurance, inventory of green infrastructure), Forestry (i.e. biomass measurement, species identification, firescar measurement), Agriculture (i.e. regional planning, precision farming, crisis response), Marine and Riparian (i.e. ecosystem evaluation, disaster management, harbor monitoring). Other: Defense, security, atmosphere and climate The online eCognition community was launched in July 2009 and had 2813 members as of July 9, 2010. Membership is distributed globally and user conferences are held regularly, the last having taken place in November 2009 in Munich, Germany. The bi-annual GEOBIA (Geographic Object-Based Image Analysis) conference is heavily attended by eCognition users, with the majority of presentations based on eCognition software.
Read more →
Moj

Moj is an Indian short-form video-sharing social networking service owned by Mohalla Tech Pvt Ltd, the parent company of ShareChat. Launched on 29 June 2020, shortly after the Government of India banned TikTok and several other Chinese apps, Moj quickly gained popularity as one of the leading domestic alternatives for short-form video content in India. == History == Moj was introduced by Mohalla Tech, the Bengaluru-based parent company of ShareChat, within days of the TikTok ban in India in June 2020. The app targeted the growing demand for short-form video platforms in the country. By early 2021, Moj had amassed over 100 million downloads on the Google Play Store. In February 2021, Mohalla Tech raised significant funding from investors like Tiger Global, Snapchat, and others, which supported both Moj and ShareChat’s growth. In 2022, Moj partnered with several music labels to expand its licensed music library, competing directly with global platforms such as Instagram Reels and YouTube Shorts. == Features == Short Videos: Users can create and watch videos up to 15–60 seconds. Filters & Effects: The platform provides AR filters, editing tools, stickers, and music integration. Regional Language Support: Moj supports more than 15 Indian languages including Hindi, Bengali, Tamil, Telugu, Kannada, and Marathi. Music Integration: Users can add music tracks to their videos from licensed Indian and international music libraries. Creator Program: Moj launched initiatives to support influencers and creators, offering training, monetization, and promotional opportunities. == Popularity == By mid-2021, Moj reported over 160 million monthly active users. According to reports, Moj consistently ranked among the top social media apps in India in terms of downloads. The app gained traction in Tier-2 and Tier-3 cities due to its multilingual support and focus on local content. == Competitors == Moj competes with several other short video platforms in India, including: Instagram Reels (Meta) YouTube Shorts (Google) Josh (Dailyhunt/VerSe Innovation) Roposo (InMobi) MX TakaTak (later merged with Moj in 2022) RedPost (an emerging Indian social networking platform) == Merger with MX TakaTak == In February 2022, Mohalla Tech announced that Moj would merge with MX TakaTak, another leading short video app owned by Times Internet. The merger created one of the largest short-video ecosystems in India, with a combined user base of over 300 million monthly active users.
Read more →
Physics-informed neural networks

In machine learning, physics-informed neural networks (PINNs), also referred to as theory-trained neural networks (TTNs), are a type of universal function approximator that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering problems limit the robustness of conventional machine learning models used for these applications. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples. Because they process continuous spatial and time coordinates and output continuous PDE solutions, they can be categorized as neural fields. == Function approximation == Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The solution of the Navier–Stokes equations with appropriate initial and boundary conditions allows the quantification of flow dynamics in a precisely defined geometry. However, these equations cannot be solved exactly and therefore numerical methods must be used (such as finite differences, finite elements and finite volumes). In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful specifications of the problem geometry as well as the initial and boundary conditions. Without this preliminary information, the solution is not unique and may lose physical correctness. To remedy this, Physics-Informed Neural Networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training datasets that do not necessarily need to be large or complete. An accurate solution of partial differential equations can potentially be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with high fidelity. PINNs can be applied to a wide range of problems in computational science, and are a pioneering technology leading to the development of new classes of numerical solvers for PDEs. PINNs can be thought of as a mesh-free alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, a trained PINN network can be used to predict values on simulation grids of different resolutions without needing to be retrained. Additionally, the derivatives used in the partial differential equations can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. == Modeling and computation == A general nonlinear partial differential equation can be written as: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ⋅ ; λ ] {\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} . This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations. Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solutions of partial differential equations data-driven discovery of partial differential equations === Data-driven solution of partial differential equations === The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters λ {\displaystyle \lambda } . We solve: u t + N [ u ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} . by defining the residual f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ] {\displaystyle f:=u_{t}+{\mathcal {N}}[u]} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network. This network can be differentiated using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points Γ {\displaystyle \Gamma } where the boundary conditions and data are defined. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function. This second term encourages the PINN to learn the structural information expressed by the PDE during the training process. This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, model predictive control, multi-physics and multi-scale modeling, and simulation. It has been shown to converge to the solution of the PDE. === Data-driven discovery of partial differential equations === Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDEs results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters λ {\displaystyle \lambda } that best describe the observed data: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} By defining f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ; λ ] = 0 {\displaystyle f:=u_{t}+{\mathcal {N}}[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN. This network can be derived using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter λ {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location Γ {\displaystyle \Gamma } , respectively. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the residual function. This second term requires the structured information represented by the partial differential equations to be satisfied in the training process. This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation. == Extensions and applications == === For piece-wise function approximation === PINNs are unable to approximate PDEs that have strong non-linearity or sharp gradients (such as those that commonly occur in practical fluid flow problems). Piecewise approximation has been an old practic
Read more →
PARRY

PARRY was an early example of a chatbot, implemented in 1972 by psychiatrist Kenneth Colby. == History == PARRY was written in 1972 by psychiatrist Kenneth Colby, then at Stanford University. While ELIZA was a simulation of a Rogerian therapist, PARRY attempted to simulate a person with paranoid schizophrenia. The program implemented a crude model of the behavior of a person with paranoid schizophrenia based on concepts, conceptualizations, and beliefs (judgements about conceptualizations: accept, reject, neutral). It also embodied a conversational strategy, and as such was a much more serious and advanced program than ELIZA. It was described as "ELIZA with attitude". PARRY was tested in the early 1970s using a variation of the Turing Test. A group of experienced psychiatrists analysed a combination of real patients and computers running PARRY through teleprinters. Another group of 33 psychiatrists were shown transcripts of the conversations. The two groups were then asked to identify which of the "patients" were human and which were computer programs. The psychiatrists were able to make the correct identification only 48 percent of the time — a figure consistent with random guessing. PARRY and ELIZA (also known as "the Doctor") interacted several times. The most famous of these exchanges occurred at the ICCC 1972, where PARRY and ELIZA were hooked up over ARPANET and responded to each other.
Read more →
VACUUM

VACUUM is a set of normative guidance principles for achieving training and test dataset quality for structured datasets in data science and machine learning. The garbage-in, garbage out principle motivates a solution to the problem of data quality but does not offer a specific solution. Unlike the majority of the ad-hoc data quality assessment metrics often used by practitioners VACUUM specifies qualitative principles for data quality management and serves as a basis for defining more detailed quantitative metrics of data quality. VACUUM is an acronym that stands for: valid accurate consistent uniform unified model
Read more →
Concept drift

In predictive analytics, data science, machine learning and related fields, concept drift or drift is an evolution of data that invalidates the data model. It happens when the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes. Drift detection and drift adaptation are of paramount importance in the fields that involve dynamically changing data and data models. == Predictive model decay == In machine learning and predictive analytics this drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such as probability distribution of the actual data. If they deviate from the statistical properties of the training data set, then the learned predictions may become invalid, if the drift is not addressed. == Data configuration decay == Another important area is software engineering, where three types of data drift affecting data fidelity may be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the data schema changes, which may invalidate databases. "Semantic drift" is changes in the meaning of data while the structure does not change. In many cases this may happen in complicated applications when many independent developers introduce changes without proper awareness of the effects of their changes in other areas of the software system. For many application systems, the nature of data on which they operate are subject to changes for various reasons, e.g., due to changes in business model, system updates, or switching the platform on which the system operates. In the case of cloud computing, infrastructure drift that may affect the applications running on cloud may be caused by the updates of cloud software. There are several types of detrimental effects of data drift on data fidelity. Data corrosion is passing the drifted data into the system undetected. Data loss happens when valid data are ignored due to non-conformance with the applied schema. Squandering is the phenomenon when new data fields are introduced upstream in the data processing pipeline, but somewhere downstream these data fields are absent. == Inconsistent data == "Data drift" may refer to the phenomenon when database records fail to match the real-world data due to the changes in the latter over time. This is a common problem with databases involving people, such as customers, employees, citizens, residents, etc. Human data drift may be caused by unrecorded changes in personal data, such as place of residence or name, as well as due to errors during data input. "Data drift" may also refer to inconsistency of data elements between several replicas of a database. The reasons can be difficult to identify. A simple drift detection is to run checksum regularly. However the remedy may be not so easy. == Examples == The behavior of the customers in an online shop may change over time. For example, if weekly merchandise sales are to be predicted, and a predictive model has been developed that works satisfactorily. The model may use inputs such as the amount of money spent on advertising, promotions being run, and other metrics that may affect sales. The model is likely to become less and less accurate over time – this is concept drift. In the merchandise sales application, one reason for concept drift may be seasonality, which means that shopping behavior changes seasonally. Perhaps there will be higher sales in the winter holiday season than during the summer, for example. Concept drift generally occurs when the covariates that comprise the data set begin to explain the variation of your target set less accurately — there may be some confounding variables that have emerged, and that one simply cannot account for, which renders the model accuracy to progressively decrease with time. Generally, it is advised to perform health checks as part of the post-production analysis and to re-train the model with new assumptions upon signs of concept drift. == Possible remedies == To prevent deterioration in prediction accuracy because of concept drift, reactive and tracking solutions can be adopted. Reactive solutions retrain the model in reaction to a triggering mechanism, such as a change-detection test or control charts from statistical process control, to explicitly detect concept drift as a change in the statistics of the data-generating process. When concept drift is detected, the current model is no longer up-to-date and must be replaced by a new one to restore prediction accuracy. A shortcoming of reactive approaches is that performance may decay until the change is detected. Tracking solutions seek to track the changes in the concept by continually updating the model. Methods for achieving this include online machine learning, frequent retraining on the most recently observed samples, and maintaining an ensemble of classifiers where one new classifier is trained on the most recent batch of examples and replaces the oldest classifier in the ensemble. Contextual information, when available, can be used to better explain the causes of the concept drift: for instance, in the sales prediction application, concept drift might be compensated by adding information about the season to the model. By providing information about the time of the year, the rate of deterioration of your model is likely to decrease, but concept drift is unlikely to be eliminated altogether. This is because actual shopping behavior does not follow any static, finite model. New factors may arise at any time that influence shopping behavior, the influence of the known factors or their interactions may change. Concept drift cannot be avoided for complex phenomena that are not governed by fixed laws of nature. All processes that arise from human activity, such as socioeconomic processes, and biological processes are likely to experience concept drift. Therefore, periodic retraining, also known as refreshing, of any model is necessary. === Remedy methods === DDM (Drift Detection Method): detects drift by monitoring the model's error rate over time. When the error rate passes a set threshold, it enters a warning phase, and if it passes another threshold, it enters a drift phase. EDDM (Early Drift Detection Method): improves DDM's detection rate by tracking the average distance between two errors instead of only the error rate. ADWIN (Adaptive Windowing): dynamically stores a window of recent data and warns the user if it detects a significant change between the statistics of the window's earlier data compared to more recent data. KSWIN (Kolmogorov–Smirnov Windowing): detects drift based on the Kolmogorov-Smirnov statistical test. DDM and EDDM: Concept Drift Detection online supervised methods that rely on sequential error monitoring to estimate the evolving error rate. ADWIN and KSWIN: Windowing maintain a "window", a subset of the most recent data, of the data stream, which it checks for statistical differences across the window. == Applications in security == Concept drift is a recurring issue in security analytics, especially in malware and intrusion detection. In these systems, models are often trained on past logs, binaries or network traces, but the behaviour of attackers changes over time as new malware families, obfuscation techniques and campaigns appear. When the data no longer resemble the training set, the decision boundaries learned by classifiers or anomaly detectors can become misaligned with the current threat landscape and detection performance can drop unless the models are updated or replaced. Several studies on Windows malware model detection as an evolving data stream and track how performance changes as time passes. They show that classifiers trained on a fixed time window can perform well on nearby data but deteriorate quickly when evaluated on samples collected months or years later, even when large amounts of training data are available. In order to keep up with this, security systems often use sliding or adaptive windows, which restrict training to the most recent portion of the data so that older, less relevant examples are gradually discarded. They also employ drift detectors such as ADWIN and KSWIN that monitor error rates or changes in the distribution of recent observations and signal when the statistics of the incoming stream differ significantly from the past, prompting retraining or model replacement. Related problems appear in spam filtering, fraud detection and intrusion detection, where adversaries change content, patterns of activity or network behavior to evade models trained on historical data. In these settings drift can be gradual, as new types of spam or fraud emerge, or abrupt, after a sudden shift in attack techniques. Common strategies to remain eff
Read more →
Lexical choice

Lexical choice is the subtask of Natural language generation that involves choosing the content words (nouns, non-auxiliary verbs, adjectives, and adverbs) in a generated text. Function words (determiners, for example) are usually chosen during realisation. == Examples == The simplest type of lexical choice involves mapping a domain concept (perhaps represented in an ontology) to a word. For example, the concept Finger might be mapped to the word finger. A more complex situation is when a domain concept is expressed using different words in different situations. For example, the domain concept Value-Change can be expressed in many ways: The temperature rose: the verb rose is used for a Value-Change in temperature which increases the value. The temperature fell: the verb fell is used for a Value-Change in temperature which decreases the value. The rain got heavier: the phrase got heavier is used for a Value-Change in precipitation amount when the precipitation is rain. Sometimes words can communicate additional contextual information, for example: The temperature plummeted: the verb plummeted is used for a Value-Change in temperature which decreases the value, when the change is rapid and large. Contextual information is especially significant for vague terms such as tall. For example, a 2m tall man is tall, but a 2m tall horse is small. == Linguistic perspective == Lexical choice modules must be informed by linguistic knowledge of how the system's input data maps onto words. This is a question of semantics, but it is also influenced by syntactic factors (such as collocation effects) and pragmatic factors (such as context). Hence NLG systems need linguistic models of how meaning is mapped to words in the target domain (genre) of the NLG system. Genre tends to be very important; for example the verb veer has a very specific meaning in weather forecasts (wind direction is changing in a clockwise direction) which it does not have in general English, and a weather-forecast generator must be aware of this genre-specific meaning. In some cases there are major differences in how different people use the same word; for example, some people use by evening to mean 6PM and others use it to mean midnight. Psycholinguists have shown that when people speak to each other, they agree on a common interpretation via lexical alignment; this is not something which NLG systems can yet do. Ultimately, lexical choice must deal with the fundamental issue of how language relates to the non-linguistic world. For example, a system which chose colour terms such as red to describe objects in a digital image would need to know which RGB pixel values could generally be described as red; how this was influenced by visual (lighting, other objects in the scene) and linguistic (other objects being discussed) context; what pragmatic connotations were associated with red (for example, when an apple is called red, it is assumed to be ripe as well as have the colour red); and so forth. == Algorithms and models == A number of algorithms and models have been developed for lexical choice in the research community, for example Edmonds developed a model for choosing between near-synonyms (words with similar core meanings but different connotations). However such algorithms and models have not been widely used in applied NLG systems; such systems have instead often used quite simple computational models, and invested development effort in linguistic analysis instead of algorithm development.
Read more →
SmarterChild

SmarterChild was a chatbot available on AOL Instant Messenger and Windows Live Messenger (previously MSN Messenger) networks. == History == SmarterChild was an apparently intelligent agent or "bot" developed by ActiveBuddy, Inc., with offices in New York and Sunnyvale. It was widely distributed across global instant messaging networks. SmarterChild became very popular, attracting over 30 million Instant Messenger "buddies" on AIM (AOL), MSN and Yahoo Messenger over the course of its lifetime. Founded in 2000, ActiveBuddy was the brainchild of Robert Hoffer and Timothy Kay, who later brought seasoned advertising executive Peter Levitan on board as CEO. The concept for conversational instant messaging bots came from the founder's vision to add natural language comprehension functionality to the increasingly popular AIM instant messaging application. The original implementation took shape as a demo that Kay programmed in Perl in his Los Altos garage to connect a single buddy name, "ActiveBuddy", to look up stock symbols, and later allow AIM users to play Colossal Cave Adventure, a word-based adventure game, and MIT's Boris Katz Start Question Answering System but quickly grew to include a wide range of database applications the company called 'knowledge domains' including instant access to news, weather, stock information, movie times, yellow pages listings, and detailed sports data, as well as a variety of tools (personal assistant, calculators, translator, etc.). None of the individual domains which the company had named “stocksBuddy”, “sportsBuddy”, etc. ever launched publicly. When Stephen Klein came on board as COO — and eventually CEO — he insisted that all of the disparate test “buddies” be launched together with the company’s highly-developed colloquial chat domain. He suggested using “SmarterChild”, a username coined by Tim Kay which Tim was using to test various things. The bundled domains were launched publicly as SmarterChild (on AIM initially) in June 2001. SmarterChild provided information wrapped in fun and quirky conversation. The company generated no revenue from SmarterChild, but used it as a demonstration of the power of what Klein called “conversational computing”. The company subsequently marketed Automated Service Agents—delivering immediate answers to customer service inquiries—-to large corporations, like Comcast, Cingular, TimeWarner Cable, etc. SmarterChild's popularity spawned targeted marketing-oriented bots for Radiohead, Austin Powers, Intel, Keebler, The Sporting News and others. ActiveBuddy co-founders, Kay and Hoffer, as co-inventors, were issued two controversial U.S. patents in 2002. ActiveBuddy changed its name to Colloquis (briefly Conversagent) and targeted development of consumer-facing enterprise customer service agents, which the company marketed as Automated Service Agents. Microsoft acquired Colloquis in October 2006 and proceeded to de-commission SmarterChild and kill off the Automated Service Agent business as well. Robert Hoffer, ActiveBuddy co-founder, licensed the technology from Microsoft after Microsoft abandoned the Colloquis technology.
Read more →
Quantexa

Quantexa is a UK-based software company that develops artificial intelligence-based applications for data analytics and decision-making. The company was founded in 2016 and is headquartered in London, with operations in North America, Europe, and the Asia-Pacific region. As of 2025, Quantexa reported a valuation of $2.6 billion and provides services to organizations in over 70 countries. Investors include Warburg Pincus, HSBC, and the Ontario Teachers’ Pension Plan. == History == Quantexa was founded in London in 2016 by several co-founders, including Jamie Hutton, Richard Seewald, Imam Hoque, Felix Hoddinott, and Vishal Marria, who also serves as the company's chief executive officer. The company was established to develop tools intended to address limitations in traditional data analysis methods, particularly those related to identifying hidden connections across large datasets. The name "Quantexa" is derived from the company's focus on quantitative methods and data analysis. In 2023, Quantexa acquired Dublin-based AI firm Aylien. In April 2023, the company completed a Series E funding round, raising $129 million at a valuation of approximately $1.8 billion, marking its entry into "unicorn" status. In October 2024, the company reported annual recurring revenue (ARR) exceeding $100 million. In early 2025, Quantexa participated in the World Economic Forum's Unicorn Program, which supports high-growth technology companies. In March 2025, Quantexa completed a Series F funding round of $175 million, led by Teachers' Venture Growth, the venture arm of the Ontario Teachers' Pension Plan. That August, the company was reported to be considering a 2026 IPO. The company formed a partnership with Zurich in October 2025, the first insurer to add its AI-based Decision Intelligence platform to enhance fraud detection.
Read more →
AI data center

An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w
Read more →
Neural network Gaussian process

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
Read more →
KidDesk

KidDesk is an alternative desktop software application. The early childhood learning company Hatch Early Childhood created KidDesk; it subsequently went to Edmark, which was bought by IBM then sold to Riverdeep (now Houghton Mifflin Harcourt Learning Technology). KidDesk is compatible with Microsoft Windows 95 and newer, as well as Apple System 7 and newer. KidDesk can be set to start when the computer starts up, and can only be exited through password entry. Adults choose what programs are included for the child to use, what icon represented the desk, and customize the software programs available for use. == History == Edmark first started shipping KidDesk in 1992. In 1993, Edmark updated KidDesk with KidDesk Family Edition for Macintosh and DOS, adding more desk accessories and desk styles (Sometimes included as a free exclusive offer with the Early Learning House and Thinkin' Things Series). In 1995, KidDesk Family Edition was enhanced for Windows 95, and released one month after the new operating system shipped. In 1998, Edmark developed KidDesk Internet Safe. The Internet Safe edition was written for Windows 95, Windows 98, and Macintosh (including OS8). In 2008, HMH ported KidDesk Family Edition was to run on Windows Vista and in 2011 version 3.07 of KidDesk Family Edition was released as part of the 'Young Explorer' suite which is fully supported on Windows XP, Windows Vista and Windows 7. == Features == A picture editor incorporated into the desk. Used both in the Adult settings menu and in the desk itself. KidDesk users can edit their user logo with a pixel grid paint program. A calendar incorporated into the desk. This allows the user to set dates that the user finds important, and allows the date to be marked with a picture or text. A password exit feature. For security reasons, the adult can set a password so that KidDesk can only be exited if it is entered. As an extra security measure, the password exit function could only be accessed if the user pressed the ctrl + alt + A keyboard buttons simultaneously. A skin changer with several themes - farm, princess, sports, ocean, etc. These themes can be changed. The e-mail and voicemail features are customizable depending on the KidDesk installation. The ability to add websites that can be accessed on KidDesk, and the ability to block hyperlinks, JavaScript, data entry, etc., on said sites was an added for the 'Internet Safe' edition released in 1998. KidDesk Internet Safe edition is available in Spanish and Brazilian-Portuguese versions. == Reception == KidDesk was given a platinum award at the 1994 Oppenheim Toy Portfolio Awards. The judges praised the program's security features allowing "configur[ation] so that kids never have access to the possibly destructive DOS prompt", and concluded that "[i]f you and your kids share a computer, you need to install Kiddesk immediately!" === Awards === Since 1992, KidDesk has won 15 major awards.
Read more →