COREU (French: Correspondance Européenne – Telex network of European correspondents, also EUKOR-Netzwerk in Austria) is a communication network of the European Union for the communication of the Council of the European Union, the European correspondents of the foreign ministries of the EU member states, permanent representatives of member states in Brussels, the European Commission, and the General Secretariat of the Council of the European Union. The European Parliament is not among the participants. COREU is the European equivalent of the American Secret Internet Protocol Router Network (SIPRNet, also known as Intelink-S). COREU's official aim is fast communication in case of crisis. The network enables a closer cooperation in matters regarding foreign affairs. In actuality the system's function exceeds that of mere communication, it also enables decision-making. COREU's first goal is to enable the exchange of information before and after decisions. Relaying upfront negotiations in preparation of meetings is the second goal. In addition, the system also allows the editing of documents and the decision-making, especially if there is little time. While the first two goals are preparatory measures for a shared foreign policy, the third is a methodical variant marked by practise that is defining for the image of the Common Foreign and Security Policy. == Members == (The following information dates from 2013): There is one representative in each of the capital cities in the EU.(since 1973) In Germany for example, this is the European correspondent (EU-KOR) from the Foreign Office. In Austria it is the European correspondent from the Referat II.1.a in the Federal Ministry for Europe, Integration and Foreign Affairs They are the correspondents (since 1982) for the European Commission They comprise the secretariat for the European Council They also make up the European External Action Service (EEAS) (responsible for foreign policy issues, since 1987) == Data volume and technical details == COREU functions as a spoke-hub distribution paradigm system with the hub in Brussels. The network is operated by the European Union Intelligence and Situation Centre (formerly Joint Situation Center, JSC). The technical infrastructure is located in a building of the European Council. COREU may be described as an advanced telex system with encrypted messages via dedicated terminals. Once a message has reached the destination, it is then redistributed via the local media. In contrast, messages of governments are transmitted via local media to the correspondents and from there delivered point-to-point to Brussels via COREU. In 2010, approximately 8500 communications had been distributed over this network. == History == A telex-based communication system under the name COREU was established in 1973. Originally, only the ministries of Foreign Affairs in the European capitals were connected to it. This telex system was replaced in 1997 by the mail system CORTESY (COREU Terminal Equipment System). The name was retained despite the technical innovation. COREU was reportedly compromised by hackers working for the People's Liberation Army Strategic Support Force, allowing for the theft of thousands of low-classified documents and diplomatic cables.
NHS COVID-19
NHS COVID-19 was a voluntary contact tracing app for monitoring the spread of the COVID-19 pandemic in England and Wales, in use from 24 September 2020 until 27 April 2023. It was available for Android and iOS smartphones, and could be used by anyone aged 16 or over. Two versions of the app were created. The first was commissioned by NHSX and developed by the Pivotal division of American software company VMware. A pilot deployment began in May 2020, but on 18 June development of the app was abandoned in favour of a second design using the Apple/Google Exposure Notification system. Scotland and Northern Ireland had separate contact tracing apps. A 2023 study estimated that in its first year of use, the app's contact tracing function prevented an estimated 1 million cases, and 9,600 deaths. == Description == The app allowed users to: See the alert level of their local authority area (in Wales) or information about restrictions (in England); to enable this, the user must enter the first half of their postcode "Check in" at places displaying an NHS QR code poster (no longer required by legislation after 26 January 2022, removed from the app the next month) Be notified when they have been in close contact with someone who has tested positive for the virus Be notified when local health protection teams determine that people with the virus had attended a business or other venue around the same time as the user Check their symptoms, and book a coronavirus test if necessary If asked to self-isolate, receive information and a daily "countdown". At first, "close contact" was defined as being within 2 metres for 15 minutes, or within 4 metres for a longer time. These time durations were reduced from 29 October 2020, to as little as three minutes when the other person is at their most infectious, i.e. soon after they begin showing symptoms. === Implementation === The Android app was coded in Kotlin, and the iOS app in Swift. The backend used Java and is deployed to Amazon Web Services using Terraform. The code of the app and back-end is open-source and available on GitHub. == Context == The app was part of the UK's test and trace programme which was chaired by Dido Harding; from 12 May 2020 Tom Riordan, chief executive of Leeds City Council, led the tracing effort. == First phase and cancellation == === Description === In March 2020, NHSX commissioned a contact tracing app to monitor the spread in the United Kingdom of the coronavirus disease 2019 (COVID-19) in the 2020 pandemic, developed by the Pivotal division of American software company VMware. The app used a centralised approach, in contrast to the Google / Apple contact tracing project. NHSX consulted ethicists and GCHQ's National Cyber Security Centre (NCSC) about the privacy aspects. The app recorded the make and model of the phone and asked the user for their postcode area. It generated a unique installation identification number and also a daily identification number. It then used Bluetooth Low Energy (BLE) to record the daily identification number of other users nearby. If a user was unwell, they could tell the app about symptoms which are characteristic of COVID-19, such as a fever and cough. These details were then passed to a central NHS server. This would assess the information and notify other users that have been in contact, giving them appropriate advice such as physical distancing. The NHS would also arrange for a swab test of the unwell user and the outcome would determine further notifications to contacts: if the test confirmed infection with COVID-19, the contacts would be asked to isolate. By June 2020, £11.8 million had been spent on the app; in 2020–21, £35 million was spent on the app. === Deployment === The first public trial of the app began on the Isle of Wight on 5 May 2020 and by 11 May it had been downloaded 55,000 times. When the first national contact tracing schemes were launched – Test, Trace, Protect in Wales on 13 May, then on 28 May NHS Test and Trace in England, and Test and Protect in Scotland – the app was not ready to be included. Replying to a question at the government's daily briefing on 8 June, Hancock was unable to give a date for rollout of the app in England, saying it would be brought in "when it's right to do so". On 17 June, Lord Bethell, junior minister for Innovation at the Department of Health and Social Care, said "we're seeking to get something going before the winter ... it isn't a priority for us at the moment". On 18 June, Health Secretary Matt Hancock announced development would switch to the Apple/Google system after admitting that Apple's restrictions on usage of Bluetooth prevented the app from working effectively. At the same press briefing Dido Harding, leader of the UK's test and trace programme, said "What we've done in really rigorously testing both our own Covid-19 app and the Google-Apple version is demonstrate that none of them are working sufficiently well enough to be actually reliable to determine whether any of us should self-isolate for two weeks [and] that's true across the world". === Concerns === The first, ultimately rejected, version of the app was subject to privacy concerns, the government backtracking on initial statements that the data collected from the app would not be shared outside the NHS. Matthew Gould, CEO of NHSX, the government department responsible for the app, said the data would be accessible to other organisations, but did not disclose which. Data collected would not necessarily be anonymised and would be held in a centralised repository. Over 150 of the UK's security and privacy experts warned the app's data could be used by 'a bad actor (state, private sector, or hacker)' to spy on citizens. Fears were discussed by the House of Commons' Human Rights Select Committee about plans for the app to record user location data. Parliament's Joint Committee on Human Rights said this version of the app should not be released without proper privacy protections. The second version of the app, released nationwide, addressed these concerns by employing a decentralised framework, the Apple/Google Exposure Notification system. Under this system, users remain pseudonymous: a person diagnosed with COVID-19 does not know which people are informed about an encounter, and contacted persons do not receive any information about the person diagnosed with COVID-19. The functionality of the app was also questioned in late April and early May 2020, as the software's use of Bluetooth required the app to be constantly running, meaning users could not use other apps or lock their device if the app was to function properly. The developers of the app were said to have found a way of working around this restriction. === Related contracts === Faculty – a company linked to Cambridge Analytica – provided research and modelling to NHSX in support of the response to the pandemic. Palantir, also linked to Cambridge Analytica, provided their data management platform. These contracts began in February and March respectively. == Second phase == As outlined on cancellation of the first app on 18 June 2020, the Department of Health and Social Care published on 30 July a brief description of the "next phase" app. Users would be able to scan a QR code at venues they visit, and later be notified if they had visited a place which was the source of a number of infections; the app would also assist with identifying symptoms and ordering a test. By using the Exposure Notification system from Apple and Google, personal data would be decentralised. Zuhlke Engineering Ltd, the UK branch of Swiss-based Zühlke Group, used 70 staff to complete the development of the app in 12 weeks. Zuhlke Engineering was awarded "Development Team of the Year" title at UK IT Industry awards in November 2021 for development of NHS COVID-19 application. === Timeline === Testing of the app by NHS volunteer responders, and selected residents of the Isle of Wight and the London Borough of Newham, began around 13 August. The app was made available to the public (aged 16 or over) in England and Wales on 24 September. An updated app released on 29 October, in part from collaboration with the Alan Turing Institute, improved the accuracy of measurements of the distance between the user's phone and other phones. At the same time, the duration threshold for determining exposure was reduced; this was expected to lead to an increase in the number of users told to self-isolate. An update to the app in April 2021, timed to coincide with easing of restrictions on hospitality businesses, was blocked by Apple and Google. It was intended that users who tested positive would be asked to share their history of visited venues, to assist in warning others, but this would have contravened assurances by Apple and Google that location data from devices would not be shared. === Statistics and effectiveness === The app was downloaded six million times on the first day it was generally availa
Self-management (computer science)
Self-management is the process by which computer systems manage their own operation without human intervention. Self-management technologies are expected to pervade the next generation of network management systems. The growing complexity of modern networked computer systems is a limiting factor in their expansion. The increasing heterogeneity of corporate computer systems, the inclusion of mobile computing devices, and the combination of different networking technologies like WLAN, cellular phone networks, and mobile ad hoc networks make the conventional, manual management difficult, time-consuming, and error-prone. More recently, self-management has been suggested as a solution to increasing complexity in cloud computing. An industrial initiative towards realizing self-management is the Autonomic Computing Initiative (ACI) started by IBM in 2001. The ACI defines the following four functional areas: Self-configuration Auto-configuration of components Self-healing Automatic discovery, and correction of faults; automatically applying all necessary actions to bring system back to normal operation Self-optimization Automatic monitoring and control of resources to ensure the optimal functioning with respect to the defined requirements Self-protection Proactive identification and protection from arbitrary attacks
Time series
In mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries. Common examples include heights of ocean tides, counts of sunspots, daily temperature readings, and the closing values of stock market indices such as the Dow Jones Industrial Average. A time series is often visualized using a run chart (a type of temporal line chart), which helps identify patterns such as trends, seasonal effects, and irregular fluctuations. Time series are widely used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and many other areas of applied science and engineering that involve temporal measurements. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modeled as a stochastic process. While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series. Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility). Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language). == Methods for analysis == Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation, thereby mitigating the need to operate in the frequency domain. Additionally, time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving-average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear, and univariate and multivariate. == Panel data == A time series is one type of panel data. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate. == Analysis == There are several types of motivation and data analysis available for time series which are appropriate for different purposes. === Motivation === In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting. In the context of signal processing, control engineering and communication engineering it is used for signal detection. Other applications are in data mining, pattern recognition and machine learning, where time series analysis can be used for clustering, classification, query by content, anomaly detection as well as forecasting. === Exploratory analysis === A simple way to examine a regular time series is manually with a line chart. The datagraphic shows tuberculosis deaths in the United States, along with the yearly change and the percentage change from year to year. The total number of deaths declined in every year until the mid-1980s, after which there were occasional increases, often proportionately - but not absolutely - quite large. A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns. Visual tools that represent time series data as heat map matrices can help overcome these challenges. === Estimation, filtering, and smoothing === This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation. Its development was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. An equivalent effect may be achieved in the time domain, as in a Kalman filter; see filtering and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral analysis to examine cyclic behavior which need not be related to seasonality. For example, sunspot activity varies over 11 year cycles. Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity. Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see trend estimation and decomposition of time series === Curve fitting === Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For processes that are expected to generally grow in magnitude one of the curves in the graphic (and many others) can be fitted by estimating their parameters. The construction of economic time series involves the estimation of some components for some dates by interpolation between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines"). Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a relat
Artificial intelligence arms race
A military artificial intelligence arms race is a technological, economic, and military competition between two or more states to develop and deploy advanced AI technologies and lethal autonomous weapons systems (LAWS). The goal is to gain a strategic or tactical advantage over rivals, similar to previous arms races involving nuclear or conventional military technologies. Since the mid-2010s, many analysts have noted the emergence of such an arms race between superpowers for better AI technology and military AI, driven by increasing geopolitical and military tensions. An AI arms race is sometimes placed in the context of an AI Cold War between the United States and China. Several influential figures and publications have emphasized that whoever develops artificial general intelligence (AGI) first could dominate global affairs in the 21st century. Russian President Vladimir Putin stated that the leader in AI will "rule the world." Researchers and experts, such as Leopold Aschenbrenner and Adrian Pecotic respectively, warn that the AGI race between major powers like the U.S. and China could reshape geopolitical power. This includes AI for surveillance, autonomous weapons, decision-making systems, cyber operations, and more. == Terminology == Lethal autonomous weapons systems use artificial intelligence to identify and kill human targets without human intervention. LAWS have colloquially been called "slaughterbots" or "killer robots". Broadly, any competition for superior AI is sometimes framed as an "arms race". Advantages in military AI overlap with advantages in other sectors, as countries pursue both economic and military advantages, as per previous arms races throughout history. == History == In 2014, AI specialist Steve Omohundro warned that "An autonomous weapons arms race is already taking place". According to Siemens, worldwide military spending on robotics was US$5.1 billion in 2010 and US$7.5 billion in 2015. China became a top player in artificial intelligence research in the 2010s. According to the Financial Times, in 2016, for the first time, China published more AI research papers than the entire European Union. When restricted to number of AI papers in the top 5% of cited papers, China overtook the United States in 2016 but lagged behind the European Union. 23% of the researchers presenting at the 2017 American Association for the Advancement of Artificial Intelligence (AAAI) conference were Chinese. Eric Schmidt, the former chairman and chief executive officer of Alphabet, has predicted China will be the leading country in AI by 2025. == Risks == One risk concerns the AI race itself, whether or not the race is won by any one group. There are strong incentives for development teams to cut corners with regard to the safety of the system, increasing the risk of critical failures and unintended consequences. This is in part due to the perceived advantage of being the first to develop advanced AI technology. One team appearing to be on the brink of a breakthrough can encourage other teams to take shortcuts, ignore precautions and deploy a system that is less ready. Some argue that using "race" terminology at all in this context can exacerbate this effect. Another potential danger of an AI arms race is the possibility of losing control of the AI systems; the risk is compounded in the case of a race to artificial general intelligence, which may present an existential risk. In 2023, a United States Air Force official reportedly said that during a computer test, a simulated AI drone killed the human character operating it. The USAF later said the official had misspoken and that it never conducted such simulations. A third risk of an AI arms race is whether or not the race is actually won by one group. The concern is regarding the consolidation of power and technological advantage in the hands of one group. A US government report argued that "AI-enabled capabilities could be used to threaten critical infrastructure, amplify disinformation campaigns, and wage war":1, and that "global stability and nuclear deterrence could be undermined".:11 == By nation == === United States === In 2014, former Secretary of Defense Chuck Hagel posited the "Third Offset Strategy" that rapid advances in artificial intelligence will define the next generation of warfare. According to data science and analytics firm Govini, the U.S. Department of Defense (DoD) increased investment in artificial intelligence, big data and cloud computing from $5.6 billion in 2011 to $7.4 billion in 2016. However, the civilian NSF budget for AI saw no increase in 2017. Japan Times reported in 2018 that the United States private investment is around $70 billion per year. The November 2019 'Interim Report' of the United States' National Security Commission on Artificial Intelligence confirmed that AI is critical to US technological military superiority. The U.S. has many military AI combat programs, such as the Sea Hunter autonomous warship, which is designed to operate for extended periods at sea without a single crew member, and to even guide itself in and out of port. From 2017, a temporary US Department of Defense directive requires a human operator to be kept in the loop when it comes to the taking of human life by autonomous weapons systems. On October 31, 2019, the United States Department of Defense's Defense Innovation Board published the draft of a report recommending principles for the ethical use of artificial intelligence by the Department of Defense that would ensure a human operator would always be able to look into the 'black box' and understand the kill-chain process. However, a major concern is how the report will be implemented. The Joint Artificial Intelligence Center (JAIC) (pronounced "jake") is an American organization on exploring the usage of AI (particularly edge computing), Network of Networks, and AI-enhanced communication, for use in actual combat. It is a subdivision of the United States Armed Forces and was created in June 2018. The organization's stated objective is to "transform the US Department of Defense by accelerating the delivery and adoption of AI to achieve mission impact at scale. The goal is to use AI to solve large and complex problem sets that span multiple combat systems; then, ensure the combat Systems and Components have real-time access to ever-improving libraries of data sets and tools." In 2023, Microsoft pitched the DoD to use DALL-E models to train its battlefield management system. OpenAI, the developer of DALL-E, removed the blanket ban on military and warfare use from its usage policies in January 2024. The Biden administration imposed restrictions on the export of advanced NVIDIA chips and GPUs to China in an effort to limit China's progress in artificial intelligence and high-performance computing. The policy aimed to prevent the use of cutting-edge U.S. technology in military or surveillance applications and to maintain a strategic advantage in the global AI race. In 2025, under the second Trump administration, the United States began a broad deregulation campaign aimed at accelerating growth in sectors critical to artificial intelligence, including nuclear energy, infrastructure, and high-performance computing. The goal was to remove regulatory barriers and attract private investment to boost domestic AI capabilities. This included easing restrictions on data usage, speeding up approvals for AI-related infrastructure projects, and incentivizing innovation in cloud computing and semiconductors. Companies like NVIDIA, Oracle, and Cisco played a central role in these efforts, expanding their AI research, data center capacity, and partnerships to help position the U.S. as a global leader in AI development. ==== Project Maven ==== Project Maven is a Pentagon project involving using machine learning and engineering talent to distinguish people and objects in drone videos, apparently giving the government real-time battlefield command and control, and the ability to track, tag and spy on targets without human involvement. Initially the effort was led by Robert O. Work who was concerned about China's military use of the emerging technology. Reportedly, Pentagon development stops short of acting as an AI weapons system capable of firing on self-designated targets. The project was established in a memo by the U.S. Deputy Secretary of Defense on 26 April 2017. Also known as the Algorithmic Warfare Cross Functional Team, it is, according to Lt. Gen. of the United States Air Force Jack Shanahan in November 2017, a project "designed to be that pilot project, that pathfinder, that spark that kindles the flame front of artificial intelligence across the rest of the [Defense] Department". Its chief, U.S. Marine Corps Col. Drew Cukor, said: "People and computers will work symbiotically to increase the ability of weapon systems to detect objects." Project Maven has been noted by allies, such as Australia's Ian Langford, for the
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics is a peer-reviewed scientific journal published by the IEEE Computer Society. It covers subjects related to computer graphics and visualization techniques, systems, software, hardware, and user interface issues. TVCG has been considered the top journal in the field of visualization. Since 2011, TVCG has allowed authors to present recently accepted papers at partner conferences. These include: IEEE Visualization (VIS), including VAST, InfoVis, and SciVis. IEEE Virtual Reality Conference (IEEE VR) IEEE International Symposium on Mixed and Augmented Reality (ISMAR) ACM Symposium on Interactive 3D Graphics and Games (I3D) IEEE Pacific Visualization Conference (IEEE PacificVis) ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) Eurographics Symposium on Geometry Processing (SGP) Pacific Graphics Conference (PG) Eurovis - The EG and VGTC Conference on Visualization Graphics Interfaces (GI)
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.