Erkki Oja (born 22 March 1948) is a Finnish computer scientist and Aalto Distinguished Professor in the Department of Information and Computer Science at Aalto University School of Science. He is recognized for developing Oja's rule, which is a model of how neurons in the brain or in artificial neural networks learn over time. == Early life and education == Oja was born in Helsinki and studied at Helsinki University of Technology, where he received his diploma engineer in 1972, licentiate in technology in 1975 and Doctor of Technology in 1977. == Career == Oja was a research associate at the Center for Cognitive Science at Brown University between 1977 and 1978 and a research fellow at the Academy of Finland from 1976 to 1981. Since 1981, he took up a professorship in applied mathematics at Kuopio University (now University of Eastern Finland). He was a visiting research scholar at Tokyo Institute of Technology from 1983 to 1984. From 1987 to 1993, he was a professor in computer science at the Lappeenranta University of Technology. He moved back to the Helsinki University of Technology (now Aalto University) from 1993 as a professor in computer science. He retired in 2015. == Honors and awards == Oja is a Fellow of the International Association for Pattern Recognition and the IEEE, and a member of the Finnish Academy of Sciences. He served as chairman of the European Neural Network Society between 2000 and 2005, and as the chairman of the Academy of Finland’s Research Council for Natural Sciences and Engineering between 2007 and 2012. He was awarded the Frank Rosenblatt Award for his contributions to artificial intelligence research in 2019. Oja was a member of the Board of Governors for the International Neural Network Society (INNIS) in 2003. He received honorary doctorates from Uppsala University and Lappeenranta University of Technology in 2008.
Windows Live OneCare Safety Scanner
Windows Live OneCare Safety Scanner (formerly Windows Live Safety Center and codenamed Vegas) was an online scanning, PC cleanup, and diagnosis service to help remove of viruses, spyware/adware, and other malware. It was a free web service that was part of Windows Live. On November 18, 2008, Microsoft announced the discontinuation of Windows Live OneCare, offering users a new free anti-malware suite Microsoft Security Essentials, which had been available since the second half of 2009. However, Windows Live OneCare Safety Scanner, under the same branding as Windows Live OneCare, was not discontinued during that time. The service was officially discontinued on April 15, 2011 and replaced with Microsoft Safety Scanner. == Overview == Windows Live OneCare Safety Scanner offered a free online scanning and protection from threats. The Windows Live OneCare Safety Scanner must be downloaded and installed to your computer to scan your computer. The "Full Service Scan" looks for common PC health issues such as viruses, temporary files, and open network ports. It searches and removes viruses, improves a computer's performance, and removes unnecessary clutter on the PC's hard disk. The user can choose between a "Full Scan" (which can be customized) or a "Quick Scan". The "Full Scan" scans for viruses (comprehensive scan or quick scan), hard disk performance (Disk fragmentation scan and/or Desk cleanup scan) and network safety (open port scan). The "Quick Scan" only scans for viruses, only on specific areas on the computer. The quick scan is faster than the full scan, hence that appellation. The service also provides a virus database, information about online threats, and general computer security documentation and tools. == Limits == The virus scanner on the Windows Live OneCare Safety Scanner site runs a scan of the user's computer only when the site is visited. It does not run periodic scans of the system, and does not provide features to prevent viruses from infecting the computer at the time, or thereafter. It simply resolves detected infections. Many users who have posted on the Product Feedback forum report script errors relating to Internet Explorer 7 (besides IE being the only browser supported by this service). The OneCare safety scanner team have been actively solving these problems, many of them registry-related.
Fuzzy classification
Fuzzy classification is the process of grouping elements into fuzzy sets whose membership functions are defined by the truth value of a fuzzy propositional function. A fuzzy propositional function is analogous to an expression containing one or more variables, such that when values are assigned to these variables, the expression becomes a fuzzy proposition. Accordingly, fuzzy classification is the process of grouping individuals having the same characteristics into a fuzzy set. A fuzzy classification corresponds to a membership function μ C ~ : P F ~ × U → T ~ {\textstyle \mu _{\tilde {C}}:{\tilde {PF}}\times U\to {\tilde {T}}} that indicates the degree to which an individual i ∈ U {\textstyle i\in U} is a member of the fuzzy class C ~ {\textstyle {\tilde {C}}} , given its fuzzy classification predicate Π ~ C ~ ∈ P F ~ {\textstyle {\tilde {\Pi }}_{\tilde {C}}\in {\tilde {PF}}} . Here, T ~ {\textstyle {\tilde {T}}} is the set of fuzzy truth values, i.e., the unit interval [ 0 , 1 ] {\textstyle [0,1]} . The fuzzy classification predicate Π ~ C ~ ( i ) {\textstyle {\tilde {\Pi }}_{\tilde {C}}(i)} corresponds to the fuzzy restriction " i {\textstyle i} is a member of C ~ {\textstyle {\tilde {C}}} ". == Classification == Intuitively, a class is a set that is defined by a certain property, and all objects having that property are elements of that class. The process of classification evaluates for a given set of objects whether they fulfill the classification property, and consequentially are a member of the corresponding class. However, this intuitive concept has some logical subtleties that need clarification. A class logic is a logical system which supports set construction using logical predicates with the class operator { ⋅ | ⋅ } {\textstyle \{\cdot |\cdot \}} . A class C = { i | Π ( i ) } {\displaystyle C=\{i|\Pi (i)\}} is defined as a set C of individuals i satisfying a classification predicate Π which is a propositional function. The domain of the class operator { .| .} is the set of variables V and the set of propositional functions PF, and the range is the powerset of this universe P(U) that is, the set of possible subsets: { ⋅ | ⋅ } : V × P F → P ( U ) {\displaystyle \{\cdot |\cdot \}:V\times PF\rightarrow P(U)} Here is an explanation of the logical elements that constitute this definition: An individual is a real object of reference. A universe of discourse is the set of all possible individuals considered. A variable V :→ R {\textstyle V:\rightarrow R} is a function which maps into a predefined range R without any given function arguments: a zero-place function. A propositional function is "an expression containing one or more undetermined constituents, such that, when values are assigned to these constituents, the expression becomes a proposition". In contrast, classification is the process of grouping individuals having the same characteristics into a set. A classification corresponds to a membership function μ that indicates whether an individual is a member of a class, given its classification predicate Π. μ : P F × U → T {\displaystyle \mu :PF\times U\rightarrow T} The membership function maps from the set of propositional functions PF and the universe of discourse U into the set of truth values T. The membership μ of individual i in Class C is defined by the truth value τ of the classification predicate Π. μ C ( i ) := τ ( Π ( i ) ) {\displaystyle \mu C(i):=\tau (\Pi (i))} In classical logic the truth values are certain. Therefore a classification is crisp, since the truth values are either exactly true or exactly false.
Smartglasses
Smartglasses or smart glasses are eye or head-worn wearable computers. Many smartglasses include displays that add information alongside or to what the wearer sees. Alternatively, smartglasses are sometimes defined as glasses that are able to change their optical properties, such as smart sunglasses that are programmed to change tint by electronic means. Alternatively, smartglasses are sometimes defined as glasses that include headphone functionality. A pair of smartglasses can be considered an augmented reality device if it performs pose tracking. Superimposing information onto a field of view is achieved through an optical head-mounted display (OHMD) or embedded wireless glasses with transparent heads-up display (HUD) or augmented reality (AR) overlay. These systems have the capability to reflect projected digital images as well as allowing the user to see through it or see better with it. While early models can perform basic tasks, such as serving as a front end display for a remote system, as in the case of smartglasses utilizing cellular technology or Wi-Fi, modern smart glasses are effectively wearable computers which can run self-contained mobile apps. Some are handsfree and can communicate with the Internet via natural language voice commands, while others use touch buttons. Like other computers, smartglasses may collect information from internal or external sensors. It may control or retrieve data from other instruments or computers. In most cases, it supports wireless technologies like Bluetooth, Wi-Fi, and GPS. A small number of models run a mobile operating system and function as portable media players to send audio and video files to the user via a Bluetooth or WiFi headset. Some smartglasses models also feature full lifelogging and activity tracker capability. Smartglasses devices may also have features found on a smartphone. Some have activity tracker functionality features (also known as "fitness tracker") as seen in some GPS watches. == Features and applications == As with other lifelogging and activity tracking devices, the GPS tracking unit and digital camera of some smartglasses can be used to record historical data. For example, after the completion of a workout, data can be uploaded into a computer or online to create a log of exercise activities for analysis. Some smart watches can serve as full GPS navigation devices, displaying maps and current coordinates. Users can "mark" their current location and then edit the entry's name and coordinates, which enables navigation to those new coordinates. Although some smartglasses models manufactured in the 21st century are completely functional as standalone products, most manufacturers recommend or even require that consumers purchase mobile phone handsets that run the same operating system so that the two devices can be synchronized for additional and enhanced functionality. The smartglasses can work as an extension, for head-up display (HUD) or remote control of the phone and alert the user to communication data such as calls, SMS messages, emails, and calendar invites. === Security applications === Smart glasses could be used as a body camera. In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas. === Sport applications === Smart glasses are used in sports like cycling, running, skiing, golf, tennis, or sailing, giving athletes real-time, heads-up data without looking down at the screen of a watch or smartphone. In 2025, Meta has announced a new partnership with sports eyewear brand Oakley. === Healthcare applications === Several proofs of concept for Google Glasses have been proposed in healthcare. In July 2013, Lucien Engelen started research on the usability and impact of Google Glass in health care. Engelen, who is based at Singularity University and in Europe at Radboud University Medical Center, is participating in the Glass Explorer program. Key findings of Engelen's research included: The quality of pictures and video are usable for healthcare education, reference, and remote consultation. The camera needs to be tilted to different angle for most of the operative procedures Tele-consultation is possible—depending on the available bandwidth—during operative procedures. A stabilizer should be added to the video function to prevent choppy transmission when a surgeon looks to screens or colleagues. Battery life can be easily extended with the use of an external battery. Controlling the device and/or programs from another device is needed for some features because of a sterile environment. Text-to-speech ("Take a Note" to Evernote) exhibited a correction rate of 60 percent, without the addition of a medical thesaurus. A protocol or checklist displayed on the screen of Google Glass can be helpful during procedures. Dr. Phil Haslam and Dr. Sebastian Mafeld demonstrated the first concept for Google Glass in the field of interventional radiology. They demonstrated the manner in which the concept of Google Glass could assist a liver biopsy and fistulaplasty, and the pair stated that Google Glass has the potential to improve patient safety, operator comfort, and procedure efficiency in the field of interventional radiology. In June 2013, surgeon Dr. Rafael Grossmann was the first person to integrate Google Glass into the operating theater, when he wore the device during a PEG (percutaneous endoscopic gastrostomy) procedure. In August 2013, Google Glass was also used at Wexner Medical Center at Ohio State University. Surgeon Dr. Christopher Kaeding used Google Glass to consult with a colleague in a distant part of Columbus, Ohio. A group of students at The Ohio State University College of Medicine also observed the operation on their laptop computers. Following the procedure, Kaeding stated, "To be honest, once we got into the surgery, I often forgot the device was there. It just seemed very intuitive and fit seamlessly." 16 November 2013, in Santiago de Chile, the maxillofacial team led by Dr.gn Antonio Marino conducted the first orthognathic surgery assisted with Google Glass in Latin America, interacting with them and working with simultaneous three-dimensional navigation. The surgical team was interviewed by ADN radio. In January 2014, Indian Orthopedic Surgeon Selene G. Parekh conducted the foot and ankle surgery using Google Glass in Jaipur, which was broadcast live on Google website via the internet. The surgery was held during a three-day annual Indo-US conference attended by a team of experts from the US and co-organized by Ashish Sharma. Sharma said Google Glass allows looking at an X-Ray or MRI without taking the eye off of the patient and allows a doctor to communicate with a patient's family or friends during a procedure. In Australia, during January 2014, Melbourne tech startup Small World Social collaborated with the Australian Breastfeeding Association to create the first hands-free breastfeeding Google Glass application for new mothers. The application, named Google Glass Breastfeeding app trial, allows mothers to nurse their baby while viewing instructions about common breastfeeding issues (latching on, posture etc.) or call a lactation consultant via a secure Google Hangout, who can view the issue through the mother's Google Glass camera. The trial was successfully concluded in Melbourne in April 2014, and 100% of participants were breastfeeding confidently. == Display types == Various techniques have existed for see-through HMDs. Most of these techniques can be summarized into two main families: "Curved Mirror" (or Curved Combiner) based and "Waveguide" or "Light-guide" based. The mirror technique has been used in EyeTaps, by Meta in their Meta 1, by Vuzix in their Star 1200 product, by Olympus, and by Laster Technologies. Various waveguide techniques have existed for some time. These techniques include diffraction optics, holographic optics, polarized optics, reflective optics, and projection: Diffractive waveguide – slanted diffraction grating elements (nanometric 10E-9). Nokia technique now licensed to Vuzix. Holographic waveguide – 3 holographic optical elements (HOE) sandwiched together (RGB). Used by Sony and Konica Minolta. Reflective waveguide – A thick light guide with single semi-reflective mirror is used by Epson in their Moverio product. A curved light guide with partial-reflective segmented mirror array to out-couple the light is used by tooz technologies GmbH. Virtual retinal display (VRD) – Also known as a retinal scan display (RSD) or retinal projector (RP), is a display technology that draws a raster display (like a television) directly onto the retina of the eye - developed by MicroVision, Inc. OLED microdisplays for near-eye applications (outdoor optical equipment, night vision glasses, ocular equipment for medical devices, augme
The 100 (TV series)
The 100 (pronounced "The Hundred" ) is an American post-apocalyptic science fiction drama television series that premiered on March 19, 2014, on the CW network, and ended on September 30, 2020. Developed by Jason Rothenberg, the series is based on the young adult novel series The 100 by Kass Morgan. The 100 follows descendants of post-apocalyptic survivors from a space habitat, the Ark, who return to Earth nearly a century after a devastating nuclear apocalypse; the first people sent to Earth are a group of juvenile delinquents who encounter another group of survivors on the ground. The juvenile delinquents include Clarke Griffin (Eliza Taylor), Finn Collins (Thomas McDonell), Bellamy Blake (Bob Morley), Octavia Blake (Marie Avgeropoulos), Jasper Jordan (Devon Bostick), Monty Green (Christopher Larkin), and John Murphy (Richard Harmon). Other lead characters include Clarke's mother Dr. Abby Griffin (Paige Turco), Marcus Kane (Henry Ian Cusick), and Chancellor Thelonious Jaha (Isaiah Washington), all of whom are council members on the Ark, and Raven Reyes (Lindsey Morgan), a mechanic aboard the Ark. == Plot == Ninety-seven years after a devastating nuclear apocalypse wipes out most human life on Earth, thousands of people now live in a space station orbiting Earth, which they call the Ark. Three generations have been born in space, but when life-support systems on the Ark begin to fail, one hundred juvenile detainees are sent to Earth in a last attempt to determine whether it is habitable, or at least save resources for the remaining residents of the Ark. They discover that some humans survived the apocalypse: the Grounders, who live in clans locked in a power struggle; the Reapers, another group of grounders who have been turned into cannibals by the Mountain Men; and the Mountain Men, who live in Mount Weather, descended from those who locked themselves away before the apocalypse. Under the leadership of Clarke and Bellamy, the juveniles attempt to survive the harsh surface conditions, battle hostile grounders and establish communication with the Ark. In the second season, the survivors face a new threat from the Mountain Men, who harvest their bone marrow to survive the radiation. Clarke and the others form a fragile alliance with the grounders to rescue their people. The season ends with Clarke making a devastating choice to save them all. In season three, power struggles erupt between the Arkadians and the grounders after a controversial new leader takes charge. Meanwhile, an AI named A.L.I.E., responsible for the original apocalypse, begins taking control of people’s minds. Clarke destroys A.L.I.E. but learns another disaster is imminent. In the fourth season, nuclear reactors are melting down, threatening to wipe out life again. Clarke and her friends search for ways to survive, including experimenting with radiation-resistant blood and finding an underground bunker. As time runs out, only a select few are able to take shelter. The fifth season picks up six years later, when Earth is left largely uninhabitable except for one green valley, where new enemies arrive. Clarke protects her adopted daughter Madi while former survivors return from space and underground, triggering another war. The battle ends with the valley destroyed and the group entering cryosleep to find a new home. In season six, the group awakens 125 years later on a new planet called Sanctum, ruled by powerful families known as the Primes. Clarke fights to stop body-snatching rituals and protect her people from new threats, including a rebel group and a dangerous AI influence. The season ends with major losses and the destruction of the Primes' rule. In the seventh and final season, the survivors face unrest on Sanctum and clash with a mysterious group called the Disciples, who believe Clarke is key to saving humanity. A wormhole network reveals multiple planets and a final "test" that determines the fate of the species. Most transcend into a higher consciousness, but Clarke and a few others choose to live out their lives on a reborn Earth. == Cast and characters == Eliza Taylor as Clarke Griffin Paige Turco as Abigail "Abby" Griffin (seasons 1–6; guest season 7) Thomas McDonell as Finn Collins (seasons 1–2) Eli Goree as Wells Jaha (season 1; guest season 2) Marie Avgeropoulos as Octavia Blake Bob Morley as Bellamy Blake Kelly Hu as Callie "Cece" Cartwig (season 1) Christopher Larkin as Monty Green (seasons 1–5; guest season 6) Devon Bostick as Jasper Jordan (seasons 1–4) Isaiah Washington as Thelonious Jaha (seasons 1–5) Henry Ian Cusick as Marcus Kane (seasons 1–6) Lindsey Morgan as Raven Reyes (seasons 2–7; recurring season 1) Ricky Whittle as Lincoln (seasons 2–3; recurring season 1) Richard Harmon as John Murphy (seasons 3–7; recurring seasons 1–2) Zach McGowan as Roan (season 4; recurring season 3; guest season 7) Tasya Teles as Echo / Ash (seasons 5–7; guest seasons 2–3; recurring season 4) Shannon Kook as Jordan Green (seasons 6–7; guest season 5) JR Bourne as Russell Lightbourne / Malachi / Sheidheda (season 7; recurring season 6) Chuku Modu as Gabriel Santiago (season 7; recurring season 6) Shelby Flannery as Hope Diyoza (season 7; guest season 6) =
Alerts.in.ua
alerts.in.ua is an online service that visualizes information about air alerts and other threats on the map of Ukraine. == History == The idea of the site appeared in the first weeks of the 2022 Russian invasion of Ukraine, during the development of other projects related to alerting the population about alarms. So, on March 2, 2022, the "Lviv Siren" bot was created, which reported on air alarms in Lviv on Twitter. Later, the idea arose to monitor alarms all over Ukraine and display them on a map. However, the lack of a single official source reporting alarms made this task much more difficult. On March 15, 2022, the Ajax Systems company announced the creation of the official Telegram channel "Air Alarm". This channel receives signals from the "Air Alarm" application and instantly publishes messages about the start and end of alarms in different regions of Ukraine. This immediately solved the problem with the source of information and gave impetus to the further implementation of the project. On March 22, 2022, the first version of the "Air Alarm Map" website was published, located on the war.ukrzen.in.ua domain. The map quickly gained popularity in social networks. It, like several other similar projects, began to be widely distributed by the mass media: Suspilne, Novyi Kanal, UNIAN, DW, Fakty ICTV, Vikna TV, Ukrainian Radio, STB, Espresso, dev.ua, itc.ua and state bodies: Center for Countering Disinformation at the National Security and Defense Council of Ukraine, Verkhovna Rada of Ukraine, Khmelnytska OVA, etc. On April 8, 2022, the site moved to the alerts.in.ua domain, where it is still available today. On August 25, 2022, the service began monitoring local official channels in addition to the main "Air Alarm". On September 11, 2022, the English version of the site was published. On March 22, 2023, its own Android application was published. The project is actively developing and has its own community. == Description == The main part of the site is a map of Ukraine, on which the regions where an air alert or other threats have been declared are highlighted in real time. As of October 16, 2022, 5 types of threats are supported: Air alarm. The threat of artillery fire. The threat of street fighting. Chemical threat. Nuclear threat. Additionally, based on media reports, information is published about other dangerous events, such as explosions, demining, etc. On the site, you can view the history of announced alarms with links to sources. Alarm statistics for different time periods are also available. For developers, there is an API that allows you to develop your own services based on information about declared alarms. The site is available in Ukrainian, English, Polish and Japanese. == Use == The map is used by: To monitor the situation in the country and the region. To illustrate the alarms announced in the mass media: TSN, Ukrainian truth, Channel 24, Suspilne, RBC Ukraine, Gromadske, Glavkom. As a map of alarms in mobile applications, there is Alarm and AirAlert. As an API for its services, including alternative alarm maps, Telegram, Viber channels, Discord bots, IoT projects, etc. == Statistics == 89.5% of users use the map from a mobile phone, 10% from a PC and 1% from a tablet. Top 6 countries by visit: Ukraine, United States, Poland, Germany, Great Britain and Japan . == Alternative projects == eMap was created by the developer Vadym Klymenko. AlarmMap is an online from the Ukrainian office of Agroprep. The official map of air alarms was developed by Ajax Systems together with the developer Artem Lemeshev, Stfalcon with the support of the Ministry of Statistics.
Generative adversarial network
A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative artificial intelligence. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss. Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, fully supervised learning, and reinforcement learning. The core idea of a GAN is based on the "indirect" training through the discriminator, another neural network that can tell how "realistic" the input seems, which itself is also being updated dynamically. This means that the generator is not trained to minimize the distance to a specific image, but rather to fool the discriminator. This enables the model to learn in an unsupervised manner. GANs are similar to mimicry in evolutionary biology, with an evolutionary arms race between both networks. == Definition == === Mathematical === The original GAN is defined as the following game: Each probability space ( Ω , μ ref ) {\displaystyle (\Omega ,\mu _{\text{ref}})} defines a GAN game. There are 2 players: generator and discriminator. The generator's strategy set is P ( Ω ) {\displaystyle {\mathcal {P}}(\Omega )} , the set of all probability measures μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , where P [ 0 , 1 ] {\displaystyle {\mathcal {P}}[0,1]} is the set of probability measures on [ 0 , 1 ] {\displaystyle [0,1]} . The GAN game is a zero-sum game, with objective function L ( μ G , μ D ) := E x ∼ μ ref , y ∼ μ D ( x ) [ ln y ] + E x ∼ μ G , y ∼ μ D ( x ) [ ln ( 1 − y ) ] . {\displaystyle L(\mu _{G},\mu _{D}):=\operatorname {E} _{x\sim \mu _{\text{ref}},y\sim \mu _{D}(x)}[\ln y]+\operatorname {E} _{x\sim \mu _{G},y\sim \mu _{D}(x)}[\ln(1-y)].} The generator aims to minimize the objective, and the discriminator aims to maximize the objective. The generator's task is to approach μ G ≈ μ ref {\displaystyle \mu _{G}\approx \mu _{\text{ref}}} , that is, to match its own output distribution as closely as possible to the reference distribution. The discriminator's task is to output a value close to 1 when the input appears to be from the reference distribution, and to output a value close to 0 when the input looks like it came from the generator distribution. === In practice === The generative network generates candidates while the discriminative network evaluates them. This creates a contest based on data distributions, where the generator learns to map from a latent space to the true data distribution, aiming to produce candidates that the discriminator cannot distinguish from real data. The discriminator's goal is to correctly identify these candidates, but as the generator improves, its task becomes more challenging, increasing the discriminator's error rate. A known dataset serves as the initial training data for the discriminator. Training involves presenting it with samples from the training dataset until it achieves acceptable accuracy. The generator is trained based on whether it succeeds in fooling the discriminator. Typically, the generator is seeded with randomized input that is sampled from a predefined latent space (e.g. a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the generator produces better samples, while the discriminator becomes more skilled at flagging synthetic samples. When used for image generation, the generator is typically a deconvolutional neural network, and the discriminator is a convolutional neural network. === Relation to other statistical machine learning methods === GANs are implicit generative models, which means that they do not explicitly model the likelihood function nor provide a means for finding the latent variable corresponding to a given sample, unlike alternatives such as flow-based generative model. Compared to fully visible belief networks such as WaveNet and PixelRNN and autoregressive models in general, GANs can generate one complete sample in one pass, rather than multiple passes through the network. Compared to Boltzmann machines and linear ICA, there is no restriction on the type of function used by the network. Since neural networks are universal approximators, GANs are asymptotically consistent. Variational autoencoders might be universal approximators, but it is not proven as of 2017. == Mathematical properties == === Measure-theoretic considerations === This section provides some of the mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra. As a result, a more rigorous definition of the GAN game would make the following changes:Each probability space ( Ω , B , μ ref ) {\displaystyle (\Omega ,{\mathcal {B}},\mu _{\text{ref}})} defines a GAN game. The generator's strategy set is P ( Ω , B ) {\displaystyle {\mathcal {P}}(\Omega ,{\mathcal {B}})} , the set of all probability measures μ G {\displaystyle \mu _{G}} on the measure-space ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's strategy set is the set of Markov kernels μ D : ( Ω , B ) → P ( [ 0 , 1 ] , B ( [ 0 , 1 ] ) ) {\displaystyle \mu _{D}:(\Omega ,{\mathcal {B}})\to {\mathcal {P}}([0,1],{\mathcal {B}}([0,1]))} , where B ( [ 0 , 1 ] ) {\displaystyle {\mathcal {B}}([0,1])} is the Borel σ-algebra on [ 0 , 1 ] {\displaystyle [0,1]} .Since issues of measurability never arise in practice, these will not concern us further. === Choice of the strategy set === In the most generic version of the GAN game described above, the strategy set for the discriminator contains all Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , and the strategy set for the generator contains arbitrary probability distributions μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . However, as shown below, the optimal discriminator strategy against any μ G {\displaystyle \mu _{G}} is deterministic, so there is no loss of generality in restricting the discriminator's strategies to deterministic functions D : Ω → [ 0 , 1 ] {\displaystyle D:\Omega \to [0,1]} . In most applications, D {\displaystyle D} is a deep neural network function. As for the generator, while μ G {\displaystyle \mu _{G}} could theoretically be any computable probability distribution, in practice, it is usually implemented as a pushforward: μ G = μ Z ∘ G − 1 {\displaystyle \mu _{G}=\mu _{Z}\circ G^{-1}} . That is, start with a random variable z ∼ μ Z {\displaystyle z\sim \mu _{Z}} , where μ Z {\displaystyle \mu _{Z}} is a probability distribution that is easy to compute (such as the uniform distribution, or the Gaussian distribution), then define a function G : Ω Z → Ω {\displaystyle G:\Omega _{Z}\to \Omega } . Then the distribution μ G {\displaystyle \mu _{G}} is the distribution of G ( z ) {\displaystyle G(z)} . Consequently, the generator's strategy is usually defined as just G {\displaystyle G} , leaving z ∼ μ Z {\displaystyle z\sim \mu _{Z}} implicit. In this formalism, the GAN game objective is L ( G , D ) := E x ∼ μ ref [ ln D ( x ) ] + E z ∼ μ Z [ ln ( 1 − D ( G ( z ) ) ) ] . {\displaystyle L(G,D):=\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln D(x)]+\operatorname {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z)))].} === Generative reparametrization === The GAN architecture has two main components. One is casting optimization into a game, of form min G max D L ( G , D ) {\displaystyle \min _{G}\max _{D}L(G,D)} , which is different from the usual kind of optimization, of form min θ L ( θ ) {\displaystyle \min _{\theta }L(\theta )} . The other is the decomposition of μ G {\displaystyle \mu _{G}} into μ Z ∘ G − 1 {\displaystyle \mu _{Z}\circ G^{-1}} , which can be understood as a reparametrization trick. To see its significance, one must compare GAN with previous methods for learning generative models, which were plagued with "intractable probabilistic computations that arise in maximum likelihood estimation and related strategies". At the same time, Kingma and Welling and Rezende et al. developed the same idea of reparametrization into a general stochastic backpropagation method. Among its first applications was the variational autoencoder. === Move order and st