Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering, chemical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance. Systems designed to perform without requiring human input are called automatic control systems (such as cruise control for regulating the speed of a car). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems. == Overview == Modern day control engineering is a relatively new field of study that gained significant attention during the 20th century with the advancement of technology. It can be broadly defined or classified as practical application of control theory. Control engineering plays an essential role in a wide range of control systems, from simple household washing machines to high-performance fighter aircraft. It seeks to understand physical systems, using mathematical modelling, in terms of inputs, outputs and various components with different behaviors; to use control system design tools to develop controllers for those systems; and to implement controllers in physical systems employing available technology. A system can be mechanical, electrical, fluid, chemical, financial or biological, and its mathematical modelling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem. Control engineering is the engineering discipline that focuses on the modeling of a diverse range of dynamic systems (e.g. mechanical systems) and the design of controllers that will cause these systems to behave in the desired manner. Although such controllers need not be electrical, many are and hence control engineering is often viewed as a subfield of electrical engineering. Electrical circuits, digital signal processors and microcontrollers can all be used to implement control systems. Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles. In most cases, control engineers utilize feedback when designing control systems. This is often accomplished using a proportional–integral–derivative controller (PID controller) system. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system, which adjusts the motor's torque accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. In practically all such systems stability is important and control theory can help ensure stability is achieved. Although feedback is an important aspect of control engineering, control engineers may also work on the control of systems without feedback. This is known as open loop control. A classic example of open loop control is a washing machine that runs through a pre-determined cycle without the use of sensors. == History == Automatic control systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient Ktesibios's water clock in Alexandria, Egypt, around the third century BCE. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. This certainly was a successful device as water clocks of similar design were still being made in Baghdad when the Mongols captured the city in 1258 CE. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply just to entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or "closed-loop" automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt in 1788. In his 1868 paper "On Governors", James Clerk Maxwell was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding complex phenomena, and it signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell's analysis. Control theory made significant strides over the next century. New mathematical techniques, as well as advances in electronic and computer technologies, made it possible to control significantly more complex dynamical systems than the original flyball governor could stabilize. New mathematical techniques included developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and 1980s. Applications of control methodology have helped to make possible space travel and communication satellites, safer and more efficient aircraft, cleaner automobile engines, and cleaner and more efficient chemical processes. Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering since electrical circuits can often be easily described using control theory techniques. In the first control relationships, a current output was represented by a voltage control input. However, not having adequate technology to implement electrical control systems, designers were left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today. === Mathematical modelling === David Quinn Mayne, (1930–2024) was among the early developers of a rigorous mathematical method for analysing Model predictive control algorithms (MPC). It is currently used in tens of thousands of applications and is a core part of the advanced control technology by hundreds of process control producers. MPC's major strength is its capacity to deal with nonlinearities and hard constraints in a simple and intuitive fashion. His work underpins a class of algorithms that are probably correct, heuristically explainable, and yield control system designs which meet practically important objectives. == Control systems == == Control theory == == Education == At many universities around the world, control engineering courses are taught primarily in electrical engineering and mechanical engineering, but some courses can be instructed in mechatronics engineering, and aerospace engineering. In others, control engineering is connected to computer science, as most control techniques today are implemented through computers, often as embedded systems (as in the automotive field). The field of control within chemical engineering is often known as process control. It deals primarily with the control of variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical engineering program and employs many of the same principles in control engineering. Other engineering disciplines also overlap with control engineering as it can be applied to any system for which a suitable model can be derived. However, specialised control engineering departments do exist, for example, in Italy there are several master in Automation & Robotics that are fully specialised in Control engineering or the Department of Automatic Control and Systems Engineering at the University of Sheffield or the Department of Robotics and Control Engineering at the United States Naval Academy and the Department of Control and Automation Engineering at the Istanbul Technical University. Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which req
CloudPassage
CloudPassage is a company that provides an automation platform, delivered via software as a service, that improves security for private, public, and hybrid cloud computing environments. CloudPassage is headquartered in San Francisco. == History == CloudPassage was founded by Carson Sweet, Talli Somekh, and Vitaliy Geraymovych in 2010. The company used cloud computing and big data analytics to implement security monitoring and control in a platform called Halo. CloudPassage spent a year in stealth developing the Halo technology, coming out of stealth mode to a closed beta in January 2011. In June 2012, the company launched the commercial product that included configuration security monitoring, network microsegmentation, and two-factor authentication for privileged access management. By 2013, CloudPassage expanded Halo to support large enterprises with advanced security and compliance requirements with a product called Halo Enterprise. The first round of venture funding for the company raised $6.5 million. In April 2012, CloudPassage raised $14 million. The financing round was led by Tenaya Capital. In February 2014, CloudPassage announced that it had raised $25.5 million in funding led by Shasta Ventures. In total, the company has invested over $30 million in its technology and raised approximately $88 million in capital. == Product == The CloudPassage platform provides cloud workload security and compliance for systems hosted in public or private cloud infrastructure environments, including hybrid cloud and multi-cloud workload hosting models. The flagship product the company offers is called Halo. Halo secures virtual servers in public, private, and hybrid cloud infrastructures and provides file integrity monitoring (FIM) while also administering firewall automation, vulnerability monitoring, network access control, security event alerting, and assessment. The Halo platform also provides security applications such as privileged access management, software vulnerability scanning, multifactor authentication, and log-based IDS. In December 2013, CloudPassage set up six servers with Microsoft Windows and Linux operating systems and combinations of popular programs and invited hackers to attempt to hack into the servers. The top prize was $5,000 and the winning hacker was a novice that completed the task in four hours. CloudPassage programmed the servers to use basic default security settings to show how vulnerable cloud computing programs can be to security threats. == Awards and recognition == In May 2011, Gigaom named CloudPassage in its list of the Top 50 Cloud Innovators. That same month, eWeek recognized CloudPassage as one of 16 Hot Startup Companies Flying Under the Radar. SC Magazine named CloudPassage an Industry Innovator in the Virtualization and Cloud Security category in 2012. Also in 2012, The Wall Street Journal named CloudPassage a runner-up in the Information Security category of its Technology Innovation Awards. The CloudPassage large-scale security program, Halo, won Best Security Solution in 2014 at the SIIA Codie awards.
AI washing
AI washing is a deceptive marketing tactic that consists of promoting a product or a service by overstating the role of artificial intelligence (AI) and the integration of it. Companies often involve in the practice to mislead customers to boost their offerings, and to secure funding from investors. The practice raises concerns regarding transparency, and legal issues. == Definition == AI washing is a deceptive marketing practice. It involves promoting a product or a service by overstating the role of artificial intelligence (AI) and its integration in the design and manufacture of the same. The practice raises concerns regarding transparency, compliance with security regulations, and consumer trust in the AI industry potentially hampering legitimate advancements in AI. The term was first defined by the AI Now Institute, a research institute based at New York University in 2019. The term is derived from greenwashing, another deceptive marketing technique that misrepresents a product's environmental impact in a similar manner. AI washing might involve a company claiming to have used AI in the development or enhancement of its products or services without its actual involvement, or using buzzwords such as "smart" or "AI-powered" without the product actually offering it or making use of it. A company may overstate the usage of AI or misuse the term, which is also construed as AI washing. In 2026, The Washington Post defined AI washing as "a trend for bosses to blame layoffs on the productive capabilities of AI and its ability to replace workers, even when job cuts may have little to do with the technology". == Usage and effects == AI washing can lead to deception of customers and misleading of investors. It is also an illegal and unethical practice that lacks transparency regarding disclosing the details of a product or a service. Companies get involved in such a practice often in response to competition who might have used AI in their offerings. It might also be used as a ploy to secure funding and investment, assuming that it will attract them towards it. AI washing has been compared to dot-com bubble, when businesses appended "dot-com" to the end of the business name to boost their valuation. In September 2023, Coca-Cola released a new product called Coca-Cola Y3000, and the company stated that the Y3000 flavor had been "co-created with human and artificial intelligence". The company was accused of AI washing due to no proof of AI involvement in the creation of the product, and critics believed that AI was used as a way to grab consumer attention more than it was used in the actual product creation. In 2026, mass tech layoffs were attributed to AI washing from AI innovation instead of balance sheet restructuring. == Mitigation == Companies are expected to be transparent and clearer in communicating the usage of AI in their products or services. Consumers can mitigate the same by requesting for hard evidence from the companies regarding the usage of AI tools. Customers should evaluate the product or service as a whole rather than being swayed by the usage of AI. Informed decision making and purchasing can keep them from falling for such marketing gimmicks. The United States Securities and Exchange Commission (SEC) imposes penalties for companies indulging in such practices. In March 2024, the SEC imposed the first civil penalties on two companies for misleading statements about their use of AI, and in July 2024, it charged a corporate executive from a supposed AI hiring startup with fraud for the usage of buzzwords related to AI.
Embodied agent
In artificial intelligence, an embodied agent, also sometimes referred to as an interface agent, is an intelligent agent that interacts with the environment through a physical body within that environment. Agents that are represented graphically with a body, for example a human or a cartoon animal, are also called embodied agents, although they have only virtual, not physical, embodiment. A branch of artificial intelligence focuses on empowering such agents to interact autonomously with human beings and the environment. Mobile robots are one example of physically embodied agents; Ananova and Microsoft Agent are examples of graphically embodied agents. Embodied conversational agents are embodied agents (usually with a graphical front-end as opposed to a robotic body) that are capable of engaging in conversation with one another and with humans employing the same verbal and nonverbal means that humans do (such as gesture, facial expression, and so forth). == Embodied conversational agents == Embodied conversational agents are a form of intelligent user interface. Graphically embodied agents aim to unite gesture, facial expression and speech to enable face-to-face communication with users, providing a powerful means of human-computer interaction. == Advantages == Face-to-face communication allows communication protocols that give a much richer communication channel than other means of communicating. It enables pragmatic communication acts such as conversational turn-taking, facial expression of emotions, information structure and emphasis, visualization and iconic gestures, and orientation in a three-dimensional environment. This communication takes place through both verbal and non-verbal channels such as gaze, gesture, spoken intonation and body posture. Research has found that users prefer a non-verbal visual indication of an embodied system's internal state to a verbal indication, demonstrating the value of additional non-verbal communication channels. As well as this, the face-to-face communication involved in interacting with an embodied agent can be conducted alongside another task without distracting the human participants, instead improving the enjoyment of such an interaction. Furthermore, the use of an embodied presentation agent results in improved recall of the presented information. Embodied agents also provide a social dimension to the interaction. Humans willingly ascribe social awareness to computers, and thus interaction with embodied agents follows social conventions, similar to human to human interactions. This social interaction both raises the believably and perceived trustworthiness of agents, and increases the user's engagement with the system. Rickenberg and Reeves found that the presence of an embodied agent on a website increased the level of user trust in that website, but also increased users' anxiety and affected their performance, as if they were being watched by a real human. Another effect of the social aspect of agents is that presentations given by an embodied agent are perceived as being more entertaining and less difficult than similar presentations given without an agent. Research shows that perceived enjoyment, followed by perceived usefulness and ease of use, is the major factor influencing user adoption of embodied agents. A study in January 2004 by Byron Reeves at Stanford demonstrated how digital characters could "enhance online experiences" through explaining how virtual characters essentially add a sense of familiarity to the user experience and make it more approachable. This increase in likability in turn helps make the products better, which benefits both the end users and those creating the product. === Applications === The rich style of communication that characterizes human conversation makes conversational interaction with embodied conversational agents ideal for many non-traditional interaction tasks. A familiar application of graphically embodied agents is computer games; embodied agents are ideal for this setting because the richer communication style makes interacting with the agent enjoyable. Embodied conversational agents have also been used in virtual training environments, portable personal navigation guides, interactive fiction and storytelling systems, interactive online characters and automated presenters and commentators. Major virtual assistants like Siri, Amazon Alexa and Google Assistant do not come with any visual embodied representation, which is believed to limit the sense of human presence by users. The U.S. Department of Defense utilizes a software agent called SGT STAR on U.S. Army-run Web sites and Web applications for site navigation, recruitment and propaganda purposes. Sgt. Star is run by the Army Marketing and Research Group, a division operated directly from The Pentagon. Sgt. Star is based upon the ActiveSentry technology developed by Next IT, a Washington-based information technology services company. Other such bots in the Sgt. Star "family" are utilized by the Federal Bureau of Investigation and the Central Intelligence Agency for intelligence gathering purposes.
Decision tree pruning
Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as the horizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information. Pruning should reduce the size of a learning tree without reducing predictive accuracy as measured by a cross-validation set. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance. == Techniques == Pruning processes can be divided into two types (pre- and post-pruning). Pre-pruning procedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered to be more efficient because they do not induce an entire set, but rather trees remain small from the start. Prepruning methods share a common problem, the horizon effect. This is to be understood as the undesired premature termination of the induction by the stop () criterion. Post-pruning (or just pruning) is the most common way of simplifying trees. Here, nodes and subtrees are replaced with leaves to reduce complexity. Pruning can not only significantly reduce the size but also improve the classification accuracy of unseen objects. It may be the case that the accuracy of the assignment on the train set deteriorates, but the accuracy of the classification properties of the tree increases overall. The procedures are differentiated on the basis of their approach in the tree (top-down or bottom-up). === Bottom-up pruning === These procedures start at the last node in the tree (the lowest point). Following recursively upwards, they determine the relevance of each individual node. If the relevance for the classification is not given, the node is dropped or replaced by a leaf. The advantage is that no relevant sub-trees can be lost with this method. These methods include Reduced Error Pruning (REP), Minimum Cost Complexity Pruning (MCCP), or Minimum Error Pruning (MEP). === Top-down pruning === In contrast to the bottom-up method, this method starts at the root of the tree. Following the structure below, a relevance check is carried out which decides whether a node is relevant for the classification of all n items or not. By pruning the tree at an inner node, it can happen that an entire sub-tree (regardless of its relevance) is dropped. One of these representatives is pessimistic error pruning (PEP), which brings quite good results with unseen items. == Pruning algorithms == === Reduced error pruning === One of the simplest forms of pruning is reduced error pruning. Starting at the leaves, each node is replaced with its most popular class. If the prediction accuracy is not affected then the change is kept. While somewhat naive, reduced error pruning has the advantage of simplicity and speed. === Cost complexity pruning === Cost complexity pruning generates a series of trees T 0 … T m {\displaystyle T_{0}\dots T_{m}} where T 0 {\displaystyle T_{0}} is the initial tree and T m {\displaystyle T_{m}} is the root alone. At step i {\displaystyle i} , the tree is created by removing a subtree from tree i − 1 {\displaystyle i-1} and replacing it with a leaf node with value chosen as in the tree building algorithm. The subtree that is removed is chosen as follows: Define the error rate of tree T {\displaystyle T} over data set S {\displaystyle S} as err ( T , S ) {\displaystyle \operatorname {err} (T,S)} . The subtree t {\displaystyle t} that minimizes err ( prune ( T , t ) , S ) − err ( T , S ) | leaves ( T ) | − | leaves ( prune ( T , t ) ) | {\displaystyle {\frac {\operatorname {err} (\operatorname {prune} (T,t),S)-\operatorname {err} (T,S)}{\left\vert \operatorname {leaves} (T)\right\vert -\left\vert \operatorname {leaves} (\operatorname {prune} (T,t))\right\vert }}} is chosen for removal. The function prune ( T , t ) {\displaystyle \operatorname {prune} (T,t)} defines the tree obtained by pruning the subtrees t {\displaystyle t} from the tree T {\displaystyle T} . Once the series of trees has been created, the best tree is chosen by generalized accuracy as measured by a training set or cross-validation. == Examples == Pruning could be applied in a compression scheme of a learning algorithm to remove the redundant details without compromising the model's performances. In neural networks, pruning removes entire neurons or layers of neurons.
JustWatch
JustWatch is a website that provides information on the availability of films and TV shows on various streaming platforms such as Netflix, HBO Max, Disney+, Hulu, Peacock, Fandango at Home, Apple TV, and Amazon Prime Video, among others. It is also available as a mobile application and smart TV application. JustWatch provides a search engine that allows users to discover which digital platforms host a particular movie or TV series. As of November 2023, JustWatch is available to users in 139 countries. == Features == JustWatch functions as a search engine by aggregating information about the online availability of films and TV series from video-on-demand streaming services. It aggregates information from more than 100 video content libraries, as well providing information about video resolution quality, pricing, and purchase or rental options. The website includes various filters for searching, including genre, price, release date, rating, and popularity. Users are also able to create lists of shows and movies and to share these lists with other users. == History == JustWatch GmbH is an international database company that is privately held and headquartered in Berlin, Germany. The company specializes in the online availability of movies and TV series. In addition to its user-facing website, the company also has an advertising-focused arm, JustWatch Media, that works with corporate clients, using data about what people watch that it gleans from user behavior to help entertainment companies tailor their marketing strategies. Its clients include Universal Pictures, Paramount Pictures, and Sony Pictures, among others. Development of the website began in 2014, and it was launched in the U.S. and Germany in February 2015. In 2018, the company received funding to improve databases within the European Union. In December 2019, the company acquired a rival streaming aggregation service, GoWatchIt, from Plexus Entertainment. JustWatch also used the acquisition to open its first New York office. In 2019, JustWatch had over 30 million users across 38 countries. By 2020, the company's streaming aggregation service was available in over 45 countries. By November 2023, it was available in 139 countries, and had over 40 million monthly users. === Founding === JustWatch was co-founded in 2013 by David Croyé, Cristoph Hoyer, Kevin Hiller, Dominik Raute, Ingke Weimert, and Michael Wilken. In a company blog post from February 2017, Croyé described the group of co-founders as all having previously "worked in leading roles at successful international tech-startups in Berlin." Croyé, who currently holds the title of CEO at JustWatch GmbH, had previously worked as the chief marketing officer at kaufDA, a European location-based mobile coupon and promotion service, and the background of other co-founders included time at the adtech company Trademob and the streaming site MyVideo. Startup capital for the website initially came from the founders themselves. Croyé in particular was able to reinvest funds he had obtained from the sale of kaufDA to Axel Springer, a European media company, in March 2011. Since 2015, the company has had at least one additional round of seed funding, with investors including venture capital groups CG Partners and STS Ventures.
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.