AI Email Generator

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  AI warfare

  AI warfare refers to the use of artificial intelligence technologies to automate military operation and enhance or bypass human decision-making in armed conflicts. AI is used to rapidly analyze large volumes of military intelligence data, including making recommendations or decisions on who and what to target. Abdul-Rahman al-Rawi, a 20-year-old student, was the first acknowledged civilian killed by AI-assisted airstrike in a U.S. strike in Iraq in 2024. In 2026, the U.S. declared it would become an 'AI-first' warfighting force. Husain et al (2018) coined the term hyperwar to refer to warfare which is algorithmic or controlled by artificial intelligence, with little to no human decision-making. == 2026 Iran war == The 2026 Iran war has been described as the "first AI war", although the Untied States and Israel have previously used AI to identify targets during the Gaza war. The U.S. has used AI tools to attack Iran. These tools have been used for military intelligence, targeting, and damage assessment in the war in Iran. Using the Maven smart system, the U.S. attacked 1,000 targets in the first 24 hours of the war and 5,000 targets over the course of 10 days. While the U.S. had used Maven in 2022 to share targeting information with Ukraine and strike against Iraq, Syria, and against the Houthis in 2024, Iran's attacks are its biggest. Authorities are looking into whether artificial intelligence was involved in the airstrike on an Iranian girls' school that killed 170 civilians, the majority of whom were female students. The United States Central Command emphasized that humans were making final targeting decisions. Per a White House tally released on April 8, the U.S. military hit over 13,000 targets in Iran during the war's first 38 days, including more than 2,000 command-and-control sites, 1,500 air defense targets, and 1,450 industrial infrastructure targets. == Gaza war == As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. IDF's Unit 8200 developed AI systems, dubbed the Gospel and Lavender, to find targets for the Israeli Air Force to bomb. The Gospel automatically provides targeting recommendations to human analysts, who decide whether to approve strikes. Lavender identified 37,000 Hamas-linked individuals early in the war, and was used alongside the Gospel, which chooses buildings or structures as targets. According to a report by +972 Magazine and Local Call, strikes assisted by Lavender were routinely permitted to kill 5–20 civilians for each suspected Hamas militant, who were often bombed at home with their families. The IDF denies these claims, maintaining that every strike is assessed to minimize collateral damage, and that there is no policy "to kill tens of thousands of people in their homes." Israel deployed AI technologies during the Gaza war for audio analysis, facial recognition, and airstrike targeting. One such system was used to help identify the location of Hamas commander Ibrahim Biari through phone call analysis, leading to strikes that killed him as well as more than 125 civilians. == 2022 Russian Ukraine war == Kyiv launched a project with Palantir called Brave1 Dataroom to build AI systems using the extensive combat data Ukraine has gathered since Russia’s full-scale invasion in 2022. The country has also created tools for in-depth airstrike analysis, introduced AI to process large volumes of intelligence, and incorporated these technologies into the planning of long-range strike operations. == Involved companies == Maven Smart System is developed by Palantir. It integrates Anthropic's Claude as its large language model, and uses Amazon's AWS servers as its cloud infrastructure. Since Anthropic's refusal to support autonomous weapons development and domestic surveillance efforts. In its place, other AI firms, including OpenAI, have been brought in to take over that role. == Involved state actors == In 2024, the United States Department of Defense had 800-plus active AI-related projects and requested $1.8 billion in AI funding, with Project Maven and Project Artemis (AI-resistant drones developed together with Ukraine) being the main ones. The technology has been used in Iran, Iraq, Syria and Yemen to identify targets. China is pursuing intelligentized warfare, integrating AI across all combat domains—land, sea, air, space, and cyber—with military AI spending exceeding $1.6 billion annually. == International regulation == Since 2014, states meeting within the framework of the Convention on Certain Conventional Weapons have discussed lethal autonomous weapon systems. In 2016, the treaty's states parties established an open-ended Group of Governmental Experts on Lethal Autonomous Weapons Systems to continue those discussions. The discussions have addressed international humanitarian law, accountability, possible prohibitions and regulations, and the extent of human control required over AI-enabled weapons.

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  Instance (computer science)

  In computer science, an instance or token (from metalogic and metamathematics) is a specific occurrence of a software element that is based on a type definition. When created, an occurrence is said to have been instantiated, and both the creation process and the result of creation are called instantiation. == Examples == Chat AI instance In chat-based AI systems, an assistant can be invoked across many independent conversation sessions (often called a thread), each with its own message history. A specific execution of the assistant over that session may be represented as a run (an execution on a thread). Class instance In object-oriented programming, an object created from a class type. Each instance of a class shares the class-defined structure and behavior but has its own identity and state. Procedural instance In some contexts (including Simula), each procedure call can be viewed as an instance of that procedure—an activation with its own parameters and local variables. Computer instance In cloud computing and virtualization, an instance commonly refers to a provisioned virtual machine or virtual server with an allocated combination of compute, memory, network, and storage resources. Polygonal model In computer graphics, a model may be instanced so it can be drawn multiple times with different transforms and parameters, improving performance by reusing shared geometry data. Program instance In a POSIX-oriented operating system, a running process is an instance of a program. It can be instantiated via system calls such as fork() and exec(). Each executing process is an instance of a program it has been instantiated from.

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  Non-human

  Non-human (also spelled nonhuman) is any entity displaying some, but not enough, human characteristics to be considered a human. The term has been used in a variety of contexts and may refer to objects that have been developed with human intelligence, such as robots or vehicles. == Organisms == === Animal rights and personhood === In the animal rights movement, it is common to distinguish between "human animals" and "non-human animals". Participants in the animal rights movement generally recognize that non-human animals have some similar characteristics to those of human persons. For example, various non-human animals have been shown to register pain, compassion, memory, and some cognitive function. Some animal rights activists argue that the similarities between human and non-human animals justify giving non-human animals rights that human society has afforded to humans, such as the right to self-preservation, and some even wish for all non-human animals or at least those that bear a fully thinking and conscious mind, such as vertebrates and some invertebrates such as cephalopods, to be given a full right of personhood. === The non-human in philosophy === Contemporary philosophers have drawn on the work of Henri Bergson, Gilles Deleuze, Félix Guattari, and Claude Lévi-Strauss (among others) to suggest that the non-human poses epistemological and ontological problems for humanist and post-humanist ethics, and have linked the study of non-humans to materialist and ethological approaches to the study of society and culture. == Software and robots == The term non-human has been used to describe computer programs and robot-like devices that display some human-like characteristics. In both science fiction and in the real world, computer programs and robots have been built to perform tasks that require human-computer interactions in a manner that suggests sentience and compassion. There is increasing interest in the use of robots in nursing homes and to provide elder care. Computer programs have been used for years in schools to provide one-on-one education with children. The Tamagotchi toy required children to provide care, attention, and nourishment to keep it "alive".

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  Kolmogorov–Arnold Networks

  Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.

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  BigDog

  BigDog is a dynamically stable quadruped military robot platform that was created in 2005 by Boston Dynamics with the Harvard University Concord Field Station. It was funded by the U.S. Defense Advanced Research Projects Agency (DARPA), but the project was shelved after the BigDog's gas engine was deemed too loud for combat. == History == BigDog was funded by the Defense Advanced Research Projects Agency (DARPA) in the hopes that it would be able to serve as a mechanic pack mule to accompany soldiers in terrain too rough for conventional vehicles. Instead of wheels or treads, BigDog uses four legs for movement, allowing it to move across surfaces that would be difficult for wheels. The legs contain a variety of sensors, including joint position and ground contact. BigDog also features a laser gyroscope and a stereo vision system. BigDog is 3 feet (0.91 m) long, stands 2.5 feet (0.76 m) tall, and weighs 240 pounds (110 kg), making it about the size of a small mule. It is capable of traversing difficult terrain, running at four miles per hour (6.4 km/h), carrying 340 pounds (150 kg), and climbing a 35 degree incline. Locomotion is controlled by an onboard computer that receives input from the robot's various sensors. Navigation and balance are also managed by the control system. BigDog's walking pattern is controlled through four legs, each equipped with four low-friction hydraulic cylinder actuators that power the joints. BigDog's locomotion behaviors can vary greatly. It can stand up, sit down, walk with a crawling gait that lifts one leg at a time, walk with a trotting gait lifting diagonal legs, or trot with a running gait. The travel speed of BigDog varies from a 0.62 mph (1 km/h) crawl to a 3.3 mph (5.3 km/h) trot. The BigDog project was headed by Dr. Martin Buehler, who received the Joseph Engelberger Award from the Robotics Industries Association in 2012 for the work. Dr. Buehler while previously a professor at McGill University, headed the robotics lab there, developing four-legged walking and running robots. Built onto the actuators are sensors for joint position and force, and movement is ultimately controlled through an onboard computer which manages the sensors. Approximately 50 sensors are located on BigDog. These measure the attitude and acceleration of the body, motion, and force of joint actuators as well as engine speed, temperature and hydraulic pressure inside the robot's internal engine. Low-level control, such as position and force of the joints, and high-level control such as velocity and altitude during locomotion, are both controlled through the onboard computer. BigDog was featured in episodes of Web Junk 20 and Hungry Beast, and in articles in New Scientist, Popular Science, Popular Mechanics, and The Wall Street Journal. In September 2011 Boston Dynamics released video footage of a new generation of BigDog known as AlphaDog. The footage shows AlphaDog's ability to walk on rough terrain and recover its balance when kicked from the side. The refined equivalent has been designed by Boston Dynamics to exceed the BigDog in terms of capabilities and use to dismounted soldiers. In February 2012, with further DARPA support, the militarized Legged Squad Support System (LS3) variant of BigDog demonstrated its capabilities during a hike over a rough terrain. Starting in the summer of 2012, DARPA planned to complete the overall development of the system and refine its key capabilities in 18 months, ensuring its worth to dismounted warfighters before it is rolled out to squads operating in-theatre. BigDog must be able to demonstrate its ability to complete a 20-mile (32 km) trail in 24 hours, without refuelling, while carrying a 325-pound (150 kg) load. A refinement of its vision sensors will also be conducted. At the end of February 2013, Boston Dynamics released video footage of a modified BigDog with an arm. The arm could pick up objects and throw them. The robot is relying on its legs and torso to help power the motions of the arm. It is believed that it can lift weights around 55 pounds (25 kg). This work was funded by the United States Army Research Laboratory and paved the way for integrating manipulators with quadrupeds as found on Spot, the spiritual successor of BigDog. === Discontinuation === At the end of December 2013, the BigDog project was discontinued. Despite hopes that it would one day work like a pack mule for US soldiers in the field, the gasoline-powered engine was deemed too noisy for use in combat, and it could be heard from hundreds of meters away. A similar project for an all-electric robot named Spot in 2016 was much quieter, but could only carry 45 pounds (20 kg). Both projects are no longer in progress, but the Spot was only released in 2020. == Hardware == BigDog is powered by a small two-stroke, one-cylinder, 15-brake-horsepower (11 kW) engine operating at 9,000 RPM. The engine drives a hydraulic pump, which in turn drives the hydraulic leg actuators. Each leg has four actuators (two for the hip joint, and two each for the knee and ankle joints), for a total of 16. Each actuator unit consists of a hydraulic cylinder, servo valve, position sensor, and force sensor. Onboard computing power is a ruggedized PC/104 board stack with two computers, one running a Pentium M processor running QNX (used for sensor data processing) and another running a Core Duo processor (used for visual data processing). == Gallery ==

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  Connectionist expert system

  Connectionist expert systems are artificial neural network (ANN) based expert systems where the ANN generates inferencing rules e.g., fuzzy-multi layer perceptron where linguistic and natural form of inputs are used. Apart from that, rough set theory may be used for encoding knowledge in the weights better and also genetic algorithms may be used to optimize the search solutions better. Symbolic reasoning methods may also be incorporated (see hybrid intelligent system). (Also see expert system, neural network, clinical decision support system.)

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  Leakage (machine learning)

  In statistics and machine learning, leakage (also known as data leakage or target leakage) refers to the use of information during model training that would not be available at prediction time. This results in overly optimistic performance estimates, as the model appears to perform better during evaluation than it actually would in a production environment. Leakage is often subtle and indirect, making it difficult to detect and eliminate. It can lead a statistician or modeler to select a suboptimal model, which may be outperformed by a leakage-free alternative. == Leakage modes == Leakage can occur at multiple stages of the machine learning workflow. Broadly, its sources can be divided into two categories: those arising from features and those arising from training examples. === Feature leakage === Feature or column-wise leakage is caused by the inclusion of columns which are one of the following: a duplicate label, a proxy for the label, or the label itself. These features, known as anachronisms, will not be available when the model is used for predictions, and result in leakage if included when the model is trained. For example, including a "MonthlySalary" column when predicting "YearlySalary"; or "MinutesLate" when predicting "IsLate". === Training example leakage === Row-wise leakage is caused by improper sharing of information between rows of data. Types of row-wise leakage include: Premature featurization; leaking from premature featurization before Cross-validation/Train/Test split (must fit MinMax/ngrams/etc on only the train split, then transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different rotations/augmentations of a single image; bootstrap sampling before splitting; or duplicating rows to up sample the minority class) Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test set using a train/test split or rolling-origin cross-validation) Group leakage—not including a grouping split column (for example, Andrew Ng's group had 100k x-rays of 30k patients, meaning ~3 images per patient. The paper used random splitting instead of ensuring that all images of a patient were in the same split. Hence the model partially memorized the patients instead of learning to recognize pneumonia in chest x-rays.) A 2023 review found data leakage to be "a widespread failure mode in machine-learning (ML)-based science", having affected at least 294 academic publications across 17 disciplines, and causing a potential reproducibility crisis. == Detection == Data leakage in machine learning can be detected through various methods, focusing on performance analysis, feature examination, data auditing, and model behavior analysis. Performance-wise, unusually high accuracy or significant discrepancies between training and test results often indicate leakage. Inconsistent cross-validation outcomes may also signal issues. Feature examination involves scrutinizing feature importance rankings and ensuring temporal integrity in time series data. A thorough audit of the data pipeline is crucial, reviewing pre-processing steps, feature engineering, and data splitting processes. Detecting duplicate entries across dataset splits is also important. For language models, the Min-K% method can detect the presence of data in a pretraining dataset. It presents a sentence suspected to be present in the pretraining dataset, and computes the log-likelihood of each token, then compute the average of the lowest K of these. If this exceeds a threshold, then the sentence is likely present. This method is improved by comparing against a baseline of the mean and variance. Analyzing model behavior can reveal leakage. Models relying heavily on counter-intuitive features or showing unexpected prediction patterns warrant investigation. Performance degradation over time when tested on new data may suggest earlier inflated metrics due to leakage. Advanced techniques include backward feature elimination, where suspicious features are temporarily removed to observe performance changes. Using a separate hold-out dataset for final validation before deployment is advisable.

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  ELMo

  ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.

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  Automated Mathematician

  The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.

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  Graphics processing unit

  A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a component on a discrete graphics card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs are increasingly being used for artificial intelligence (AI) processing due to linear algebra acceleration, which is also used extensively in graphics processing. Although there is no single definition of the term, and it may be used to describe any video display system, in modern use a GPU includes the ability to internally perform the calculations needed for various graphics tasks, like rotating and scaling 3D images, and often the additional ability to run custom programs known as shaders. This contrasts with earlier graphics controllers known as video display controllers which had no internal calculation capabilities, or blitters, which performed only basic memory movement operations. The modern GPU emerged during the 1990s, adding the ability to perform operations like drawing lines and text without CPU help, and later adding 3D functionality. Graphics functions are generally independent and this lends these tasks to being implemented on separate calculation engines. Modern GPUs include hundreds, or thousands, of calculation units. This made them useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. == History == === 1960s === Dedicated 3D graphics hardware dates back to graphic terminals such as the Adage AGT-30 from 1967 with analog matrix processors. In 1969 Evans & Sutherland (E&S) introduced the Line Drawing System-1 (LDS-1), which was the first all-digital system to provide matrix multiplication. Also in 1969, the low-cost graphics terminal IMLAC PDS-1 was introduced. It later saw use as an early 3D gaming machine with the likes of Maze War. === 1970s === In professional hardware, in 1972 PLATO IV system becomes operational at the University of Illinois Urbana-Champaign. Between around 1973 and 1978, several networked multiplayer wireframe 3D games are implemented and popularized by users of the system. Also in 1972, the E&S Continuous Tone 1 (CT1) "Watkins box" system (consisting of an E&S LDS-2 and Shaded Picture System) is delivered to Case Western Reserve University. It offered the first real-time Gouraud shading. In 1975, a joint effort between Evans & Sutherland Computer Corporation and the University of Utah's computer graphics department results in the first ever MOSFET video framebuffer, capable of color and smooth shading. E&S Continuous Tone 3 (CT3) system was delivered in 1977 to Lufthansa for pilot training using computer simulation. It was the first graphics system capable of real-time texture mapping. Ikonas made graphics systems with 8- and 24-bit graphics and 3D acceleration in the late 70s. Arcade system boards have used specialized 2D graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor. A specialized barrel shifter circuit helped the CPU animate the framebuffer graphics for various 1970s arcade video games from Midway and Taito, such as Gun Fight (1975), Sea Wolf (1976), and Space Invaders (1978). The Namco Galaxian arcade system in 1979 used specialized graphics hardware that supported RGB color, multi-colored sprites, and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega, and Taito. The Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. Atari 8-bit computers (1979) had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored (so there did not need to be a contiguous frame buffer). 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU. === 1980s === In the 1980s significant advancements were made in professional 3D graphics hardware. Perhaps most impactful was the 1981 development of the Geometry Engine, a VLSI vector processor ASIC designed by Jim Clark and Marc Hannah at Stanford University. This processor is the forerunner of modern tensor cores and other similar processors marketed for graphics and AI. The Geometry Engine went on to be used in Silicon Graphics workstations for many years. Silicon Graphics's first product, shipped in November 1983, was the IRIS 1000, a terminal with hardware-accelerated 3D graphics based on the Geometry Engine. The Geometry Engine was capable of approximately 6 million operations per second. The 1981 NEC μPD7220 was the first implementation of a personal computer graphics display processor as a single large-scale integration (LSI) integrated circuit chip. This enabled the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU until the mid-1980s. It was the first fully integrated VLSI (very large-scale integration) metal–oxide–semiconductor (NMOS) graphics display processor for PCs, supported up to 1024×1024 resolution, and laid the foundations for the PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games Robotron: 2084, Joust, Sinistar, and Bubbles, all released in 1982, contain custom blitter chips for operating on 16-color bitmaps. In 1984, Hitachi released the ARTC HD63484, the first major CMOS graphics processor for personal computers. The ARTC could display up to 4K resolution when in monochrome mode. It was used in a number of graphics cards and terminals during the late 1980s. In 1985, the Amiga was released with a custom graphics chip called Agnus including a blitter for bitmap manipulation, line drawing, and area fill. It also included a coprocessor with its own simple instruction set, that was capable of manipulating graphics hardware registers in sync with the video beam (e.g. for per-scanline palette switches, sprite multiplexing, and hardware windowing), or driving the blitter. Also in 1985, IBM released the Professional Graphics Controller, designed by later to be Nvidia co-founder Curtis Priem, which was a rudimentary 3D card with 640 × 480 256-color graphics which used a dedicated CPU to draw graphics independently of the main system. It was used as the basis of cards by a number of makers (including Matrox) and its analog RGB signaling led directly to the VGA video standard. Priem later in the 80s worked on the influential Sun Microsystems GX (also known as cgsix) accelerated 2D graphics card. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code but also had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture ("TIGA") Windows accelerator cards. Following in 1987, the IBM 8514 graphics system was released. It was one of the first video cards for IBM PC compatibles that implemented fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields. It served as a development machine for Capcom's CP System arcade board. Fujitsu's FM Towns computer, released in 1989, had support for a 16,777,216 color palette. For context, IBM also introduced its Video Graphics Array (VGA) display system in 1987, with a maximum resolution of 640 × 480 pixels. Unlike 8514/A, VGA had no hardware acceleration features. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association (VESA) to develop and promote a Super VGA (SVGA) computer display standard as a successor to VGA. Super VGA enabled graphics display resolutions up to 800 × 600 pixels, a 56% increase. In 1988 SGI sold IRIS workstation graphics with 10-12 Geometry Engines and introduced the IrisVision add-in board for IBM MicroChannel bus (RS/6000) based on the Geometry Engine as well. In 1988 as well, the first dedicated polygonal 3D graphics boards in arcade machines were introduced wit

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  Belief–desire–intention model

  For popular psychology, the belief–desire–intention (BDI) model of human practical reasoning was developed by Michael Bratman as a way of explaining future-directed intention. BDI is fundamentally reliant on folk psychology (the 'theory theory'), which is the notion that our mental models of the world are theories. It was used as a basis for developing the belief–desire–intention software model. == Applications == BDI was part of the inspiration behind the BDI software architecture, which Bratman was also involved in developing. Here, the notion of intention was seen as a way of limiting time spent on deliberating about what to do, by eliminating choices inconsistent with current intentions. BDI has also aroused some interest in psychology. BDI formed the basis for a computational model of childlike reasoning CRIBB.

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  Autognostics

  Autognostics is a new paradigm that describes the capacity for computer networks to be self-aware. It is considered one of the major components of Autonomic Networking. == Introduction == One of the most important characteristics of today's Internet that has contributed to its success is its basic design principle: a simple and transparent core with intelligence at the edges (the so-called "end-to-end principle"). Based on this principle, the network carries data without knowing the characteristics of that data (e.g., voice, video, etc.) - only the end-points have application-specific knowledge. If something goes wrong with the data, only the edge may be able to recognize that since it knows about the application and what the expected behavior is. The core has no information about what should happen with that data - it only forwards packets. Although an effective and beneficial attribute, this design principle has also led to many of today's problems, limitations, and frustrations. Currently, it is almost impossible for most end-users to know why certain network-based applications do not work well and what they need to do to make it better. Also, network operators who interact with the core in low-level terms such as router configuration have problems expressing their high-level goals into low-level actions. In high-level terms, this may be summarized as a weak coupling between the network and application layers of the overall system. As a consequence of the Internet end-to-end principle, the network performance experienced by a particular application is difficult to attribute based on the behavior of the individual elements. At any given moment, the measure of performance between any two points is typically unknown and applications must operate blindly. As a further consequence, changes to the configuration of given element, or changes in the end-to-end path, cannot easily be validated. Optimization and provisioning cannot then be automated except against only the simplest design specifications. There is an increasing interest in Autonomic Networking research, and a strong conviction that an evolution from the current networking status quo is necessary. Although to date there have not been any practical implementations demonstrating the benefits of an effective autonomic networking paradigm, there seems to be a consensus as to the characteristics which such implementations would need to demonstrate. These specifically include continuous monitoring, identifying, diagnosing and fixing problems based on high-level policies and objectives. Autognostics, as a major part of the autonomic networking concept, intends to bring networks to a new level of awareness and eliminate the lack of visibility which currently exists in today's networks. == Definition == Autognostics is a new paradigm that describes the capacity for computer networks to be self-aware, in part and as a whole, and dynamically adapt to the applications running on them by autonomously monitoring, identifying, diagnosing, resolving issues, subsequently verifying that any remediation was successful, and reporting the impact with respect to the application's use (i.e., providing visibility into the changes to networks and their effects). Although similar to the concept of network awareness, i.e., the capability of network devices and applications to be aware of network characteristics (see References section below), it is noteworthy that autognostics takes that concept one step further. The main difference is the auto part of autognostics, which entails that network devices are self-aware of network characteristics, and have the capability to adapt themselves as a result of continuous monitoring and diagnostics. == Path to autognostics == Autognostics, or in other words deep self-knowledge, can be best described as the ability of a network to know itself and the applications that run on it. This knowledge is used to autonomously adapt to dynamic network and application conditions such as utilization, capacity, quality of service/application/user experience, etc. In order to achieve autognosis, networks need a means to: Continuously monitor/test the network for application-specific performance Analyze the monitoring/test data to detect problems (e.g., performance degradation) Diagnose, identify and localize sources of degradation Automatically take actions to resolve problems via remediation/provisioning Verify the problems have been resolved (potentially rolling back changes if ineffective) Subsequently, continue to monitor/test for performance

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  MeituPic

  Meitu Xiu Xiu ("Meitu") (Chinese: 美图秀秀) is an image editing software that is mostly used in Mainland China but is also popular in Hong Kong and Taiwan. It is only available on Google Play and App Store in certain countries. It provides tools for editing photos: filters, retouching, collage, scenes, frames, and photo decorations, as well as generative AI features such as text-to-images, AI removal and AI repainting etc. Meitu is one of the apps developed by Meitu, Inc.; it also produced BeautyCam, Wink and X-Design. == History == Meitu's PC version was created in 2008 by Wu Xinhong, the CEO of Meitu. In 2013, its mobile version became one of the first must-have mobile apps in China. Meitu, Inc. is a photo and video-centered app developer, which was founded in 2008 in Xiamen. Currently, the major revenue source of Meitu is premium subscription. Meitu, Inc. was initially funded by Cai Wensheng, a well-known angel investor. The company has an approximately 250 million monthly active users globally. == Function == === Edit === MeituPic provides a number of photo-editing tools. The major functions are auto enhance, edit, enhance, filters, frames, magic brush, mosaic, text, and blur. Auto enhance focuses on the nature of photos taken, while Edit includes functions of cropping, rotation, sharpening, and adjustment of ratio. For Enhance, users can apply slight adjustment on the photo by controlling the levels of brightness, contrast, colour temperature, saturation, highlight, shadow and smart light. Major types of filters are LOMO, beauty, style as well as art. Different frames can be chosen from poster, simple, and fantasy. Magic brush provides a great variety of brushes with different colours and patterns for users to decorate the photos. Mosaic brush enables users to cover certain parts of the photo. Texts can be added to the photo. Choices of different bubbles, font as well as style of words are available. Blurring effect is also available to make the photo less distinct and clear. === Beauty Retouch === There are seven major functions for retouching a photo: automatic retouch, smooth and whiten skin, remove blemish, make slimmer, remove dark circles and bags under the eyes, make taller, and enhance the eyes. Automatic retouch enhances portraits by lightening the skin tone, brightening the eyes, and simulating a face-lift by tapping on just one button. This helps to remove wrinkles and optimizes the skin tone. Acne, blemishes, and other skin imperfections can also be removed. The face-lift and weight-loss functions in the slimming option can be used to reshape the body. The option to make the subject taller can be used to change the perceived height of the subject and give the impression of slimmer, longer legs. The option to enhance the eyes can enlarge and brighten the eyes. === Collage === Collage has four types: template, freestyle, poster, PicStrip, which all maximize to insert nine photos. Template integrates photos in a vertical rectangle tightly. MeituPic has 15 frames or free download function for users. MeituPic also provides different templates according to number of photos inserted. Freestyle separates photos on a background freely. There are two parts of background: custom and more. For custom, users choose from album. For more, there are plain and picture with 18 choices. Poster makes a poster with photos. Users choose a poster among 8 choices or tap ‘more’ to download a new one. PicStrip combines photos vertically making an elongated file. Users choose a frame from 15 choices. Pinching thumb and forefinger together or apart zooms photos in/out. Putting two fingers and turning hand rotates photos. Pressing moves photos to ideal location. After designing, users tap ‘save/share’ on the upper right corner and the photo made is saved into album automatically. == Awards ==

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  Inductive programming

  Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses learning of typically declarative (logic or functional) and often recursive programs from incomplete specifications, such as input/output examples or constraints. Depending on the programming language used, there are several kinds of inductive programming. Inductive functional programming, which uses functional programming languages such as Lisp or Haskell, and most especially inductive logic programming, which uses logic programming languages such as Prolog and other logical representations such as description logics, have been more prominent, but other (programming) language paradigms have also been used, such as constraint programming or probabilistic programming. == Definition == Inductive programming incorporates all approaches which are concerned with learning programs or algorithms from incomplete (formal) specifications. Possible inputs in an IP system are a set of training inputs and corresponding outputs or an output evaluation function, describing the desired behavior of the intended program, traces or action sequences which describe the process of calculating specific outputs, constraints for the program to be induced concerning its time efficiency or its complexity, various kinds of background knowledge such as standard data types, predefined functions to be used, program schemes or templates describing the data flow of the intended program, heuristics for guiding the search for a solution or other biases. Output of an IP system is a program in some arbitrary programming language containing conditionals and loop or recursive control structures, or any other kind of Turing-complete representation language. In many applications the output program must be correct with respect to the examples and partial specification, and this leads to the consideration of inductive programming as a special area inside automatic programming or program synthesis, usually opposed to 'deductive' program synthesis, where the specification is usually complete. In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intelligence. A distinctive feature is the number of examples or partial specification needed. Typically, inductive programming techniques can learn from just a few examples. The diversity of inductive programming usually comes from the applications and the languages that are used: apart from logic programming and functional programming, other programming paradigms and representation languages have been used or suggested in inductive programming, such as functional logic programming, constraint programming, probabilistic programming, abductive logic programming, modal logic, action languages, agent languages and many types of imperative languages. == History == The early works of Plotkin, and his "relative least general generalization (rlgg)", had an enormous impact in inductive logic programming. There were some encouraging results on learning recursive Prolog programs such as quicksort from examples together with suitable background knowledge, for example with GOLEM. However, after initial success, the community got disappointed by limited progress about the induction of recursive programs with ILP less and less focusing on recursive programs and leaning more and more towards a machine learning setting with applications in relational data mining and knowledge discovery. In parallel to work in ILP, Koza proposed genetic programming in the early 1990s as a generate-and-test based approach to learning programs. The idea of genetic programming was further developed into the inductive programming system ADATE and the systematic-search-based system MagicHaskeller. Here again, functional programs are learned from sets of positive examples together with an output evaluation (fitness) function which specifies the desired input/output behavior of the program to be learned. The early work in grammar induction (also known as grammatical inference) is related to inductive programming, as rewriting systems or logic programs can be used to represent production rules. In fact, early works in inductive inference considered grammar induction and Lisp program inference as basically the same problem. The results in terms of learnability were related to classical concepts, such as identification-in-the-limit, as introduced in the seminal work of Gold. More recently, the language learning problem was addressed by the inductive programming community. In the recent years, the classical approaches have been resumed and advanced with great success. Therefore, the synthesis problem has been reformulated on the background of constructor-based term rewriting systems taking into account modern techniques of functional programming, as well as moderate use of search-based strategies and usage of background knowledge as well as automatic invention of subprograms. Many new and successful applications have recently appeared beyond program synthesis, most especially in the area of data manipulation, programming by example and cognitive modelling (see below). Other ideas have also been explored with the common characteristic of using declarative languages for the representation of hypotheses. For instance, the use of higher-order features, schemes or structured distances have been advocated for a better handling of recursive data types and structures; abstraction has also been explored as a more powerful approach to cumulative learning and function invention. One powerful paradigm that has been recently used for the representation of hypotheses in inductive programming (generally in the form of generative models) is probabilistic programming (and related paradigms, such as stochastic logic programs and Bayesian logic programming). == Application areas == The first workshop on Approaches and Applications of Inductive Programming (AAIP) Archived 2016-03-03 at the Wayback Machine held in conjunction with ICML 2005 identified all applications where "learning of programs or recursive rules are called for, [...] first in the domain of software engineering where structural learning, software assistants and software agents can help to relieve programmers from routine tasks, give programming support for end users, or support of novice programmers and programming tutor systems. Further areas of application are language learning, learning recursive control rules for AI-planning, learning recursive concepts in web-mining or for data-format transformations". Since then, these and many other areas have shown to be successful application niches for inductive programming, such as end-user programming, the related areas of programming by example and programming by demonstration, and intelligent tutoring systems. Other areas where inductive inference has been recently applied are knowledge acquisition, artificial general intelligence, reinforcement learning and theory evaluation, and cognitive science in general. There may also be prospective applications in intelligent agents, games, robotics, personalisation, ambient intelligence and human interfaces.

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  Inception score

  The Inception Score (IS) is an algorithm used to assess the quality of images created by a generative image model such as a generative adversarial network (GAN). The score is calculated based on the output of a separate, pretrained Inception v3 image classification model applied to a sample of (typically around 30,000) images generated by the generative model. The Inception Score is maximized when the following conditions are true: The entropy of the distribution of labels predicted by the Inceptionv3 model for the generated images is minimized. In other words, the classification model confidently predicts a single label for each image. Intuitively, this corresponds to the desideratum of generated images being "sharp" or "distinct". The predictions of the classification model are evenly distributed across all possible labels. This corresponds to the desideratum that the output of the generative model is "diverse". It has been somewhat superseded by the related Fréchet inception distance. While the Inception Score only evaluates the distribution of generated images, the FID compares the distribution of generated images with the distribution of a set of real images ("ground truth"). == Definition == Let there be two spaces, the space of images Ω X {\displaystyle \Omega _{X}} and the space of labels Ω Y {\displaystyle \Omega _{Y}} . The space of labels is finite. Let p g e n {\displaystyle p_{gen}} be a probability distribution over Ω X {\displaystyle \Omega _{X}} that we wish to judge. Let a discriminator be a function of type p d i s : Ω X → M ( Ω Y ) {\displaystyle p_{dis}:\Omega _{X}\to M(\Omega _{Y})} where M ( Ω Y ) {\displaystyle M(\Omega _{Y})} is the set of all probability distributions on Ω Y {\displaystyle \Omega _{Y}} . For any image x {\displaystyle x} , and any label y {\displaystyle y} , let p d i s ( y | x ) {\displaystyle p_{dis}(y|x)} be the probability that image x {\displaystyle x} has label y {\displaystyle y} , according to the discriminator. It is usually implemented as an Inception-v3 network trained on ImageNet. The Inception Score of p g e n {\displaystyle p_{gen}} relative to p d i s {\displaystyle p_{dis}} is I S ( p g e n , p d i s ) := exp ⁡ ( E x ∼ p g e n [ D K L ( p d i s ( ⋅ | x ) ‖ ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x ) ] ) {\displaystyle IS(p_{gen},p_{dis}):=\exp \left(\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\int p_{dis}(\cdot |x)p_{gen}(x)dx\right)\right]\right)} Equivalent rewrites include ln ⁡ I S ( p g e n , p d i s ) := E x ∼ p g e n [ D K L ( p d i s ( ⋅ | x ) ‖ E x ∼ p g e n [ p d i s ( ⋅ | x ) ] ) ] {\displaystyle \ln IS(p_{gen},p_{dis}):=\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]\right)\right]} ln ⁡ I S ( p g e n , p d i s ) := H [ E x ∼ p g e n [ p d i s ( ⋅ | x ) ] ] − E x ∼ p g e n [ H [ p d i s ( ⋅ | x ) ] ] {\displaystyle \ln IS(p_{gen},p_{dis}):=H[\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]]-\mathbb {E} _{x\sim p_{gen}}[H[p_{dis}(\cdot |x)]]} ln ⁡ I S {\displaystyle \ln IS} is nonnegative by Jensen's inequality. Pseudocode:INPUT discriminator p d i s {\displaystyle p_{dis}} . INPUT generator g {\displaystyle g} . Sample images x i {\displaystyle x_{i}} from generator. Compute p d i s ( ⋅ | x i ) {\displaystyle p_{dis}(\cdot |x_{i})} , the probability distribution over labels conditional on image x i {\displaystyle x_{i}} . Sum up the results to obtain p ^ {\displaystyle {\hat {p}}} , an empirical estimate of ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x {\displaystyle \int p_{dis}(\cdot |x)p_{gen}(x)dx} . Sample more images x i {\displaystyle x_{i}} from generator, and for each, compute D K L ( p d i s ( ⋅ | x i ) ‖ p ^ ) {\displaystyle D_{KL}\left(p_{dis}(\cdot |x_{i})\|{\hat {p}}\right)} . Average the results, and take its exponential. RETURN the result. === Interpretation === A higher inception score is interpreted as "better", as it means that p g e n {\displaystyle p_{gen}} is a "sharp and distinct" collection of pictures. ln ⁡ I S ( p g e n , p d i s ) ∈ [ 0 , ln ⁡ N ] {\displaystyle \ln IS(p_{gen},p_{dis})\in [0,\ln N]} , where N {\displaystyle N} is the total number of possible labels. ln ⁡ I S ( p g e n , p d i s ) = 0 {\displaystyle \ln IS(p_{gen},p_{dis})=0} iff for almost all x ∼ p g e n {\displaystyle x\sim p_{gen}} p d i s ( ⋅ | x ) = ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x {\displaystyle p_{dis}(\cdot |x)=\int p_{dis}(\cdot |x)p_{gen}(x)dx} That means p g e n {\displaystyle p_{gen}} is completely "indistinct". That is, for any image x {\displaystyle x} sampled from p g e n {\displaystyle p_{gen}} , discriminator returns exactly the same label predictions p d i s ( ⋅ | x ) {\displaystyle p_{dis}(\cdot |x)} . The highest inception score N {\displaystyle N} is achieved if and only if the two conditions are both true: For almost all x ∼ p g e n {\displaystyle x\sim p_{gen}} , the distribution p d i s ( y | x ) {\displaystyle p_{dis}(y|x)} is concentrated on one label. That is, H y [ p d i s ( y | x ) ] = 0 {\displaystyle H_{y}[p_{dis}(y|x)]=0} . That is, every image sampled from p g e n {\displaystyle p_{gen}} is exactly classified by the discriminator. For every label y {\displaystyle y} , the proportion of generated images labelled as y {\displaystyle y} is exactly E x ∼ p g e n [ p d i s ( y | x ) ] = 1 N {\displaystyle \mathbb {E} _{x\sim p_{gen}}[p_{dis}(y|x)]={\frac {1}{N}}} . That is, the generated images are equally distributed over all labels.

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