AI Headshot Apk

AI Headshot Apk — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Scene text

    Scene text

    Scene text is text that appears in an image captured by a camera in an outdoor environment. The detection and recognition of scene text from camera captured images are computer vision tasks which became important after smart phones with good cameras became ubiquitous. The text in scene images varies in shape, font, colour and position. The recognition of scene text is further complicated sometimes by non-uniform illumination and focus. To improve scene text recognition, the International Conference on Document Analysis and Recognition (ICDAR) conducts a robust reading competition once in two years. The competition was held in 2003, 2005 and during every ICDAR conference. International association for pattern recognition (IAPR) has created a list of datasets as Reading systems. == Text detection == Text detection is the process of detecting the text present in the image, followed by surrounding it with a rectangular bounding box. Text detection can be carried out using image based techniques or frequency based techniques. In image based techniques, an image is segmented into multiple segments. Each segment is a connected component of pixels with similar characteristics. The statistical features of connected components are utilised to group them and form the text. Machine learning approaches such as support vector machine and convolutional neural networks are used to classify the components into text and non-text. In frequency based techniques, discrete Fourier transform (DFT) or discrete wavelet transform (DWT) are used to extract the high frequency coefficients. It is assumed that the text present in an image has high frequency components and selecting only the high frequency coefficients filters the text from the non-text regions in an image. == Word recognition == In word recognition, the text is assumed to be already detected and located and the rectangular bounding box containing the text is available. The word present in the bounding box needs to be recognized. The methods available to perform word recognition can be broadly classified into top-down and bottom-up approaches. In the top-down approaches, a set of words from a dictionary is used to identify which word suits the given image. Images are not segmented in most of these methods. Hence, the top-down approach is sometimes referred as segmentation free recognition. In the bottom-up approaches, the image is segmented into multiple components and the segmented image is passed through a recognition engine. Either an off the shelf Optical character recognition (OCR) engine or a custom-trained one is used to recognise the text.

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  • Turing test

    Turing test

    The Turing test, originally called the imitation game by Alan Turing in 1949, is a test of a machine's ability to exhibit intelligent behaviour equivalent to that of a human. In the test, a human evaluator judges a text transcript of a natural-language conversation between a human and a machine. The evaluator tries to identify the machine, and the machine passes if the evaluator cannot reliably tell them apart. The results would not depend on the machine's ability to answer questions correctly, only on how closely its answers resembled those of a human. Since the Turing test is a test of indistinguishability in performance capacity, the verbal version generalizes naturally to all of human performance capacity, verbal as well as nonverbal (robotic). The test was introduced by Turing in his 1950 paper "Computing Machinery and Intelligence" while working at the University of Manchester. It opens with the words: "I propose to consider the question, 'Can machines think?'." Because "thinking" is difficult to define, Turing chooses to "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words". Turing describes the new form of the problem in terms of a three-person party game called the "imitation game", in which an interrogator asks questions of a man and a woman in another room in order to determine the correct sex of the two players. Turing's new question is: "Are there imaginable digital computers which would do well in the imitation game?" This question, Turing believed, was one that could actually be answered. In the remainder of the paper, he argued against the major objections to the proposition that "machines can think". Since Turing introduced his test, it has been highly influential in the philosophy of artificial intelligence, resulting in substantial discussion and controversy, as well as criticism from philosophers like John Searle, who argue against the test's ability to detect consciousness. == History == === Philosophical background === The question of whether it is possible for machines to think has a long history, which is firmly entrenched in the distinction between dualist and materialist views of the mind. René Descartes prefigures aspects of the Turing test in his 1637 Discourse on the Method when he writes: [H]ow many different automata or moving machines could be made by the industry of man ... For we can easily understand a machine's being constituted so that it can utter words, and even emit some responses to action on it of a corporeal kind, which brings about a change in its organs; for instance, if touched in a particular part it may ask what we wish to say to it; if in another part it may exclaim that it is being hurt, and so on. But it never happens that it arranges its speech in various ways, in order to reply appropriately to everything that may be said in its presence, as even the lowest type of man can do. Here Descartes notes that automata are capable of responding to human interactions but argues that such automata cannot respond appropriately to things said in their presence in the way that any human can. Descartes therefore prefigures the Turing test by defining the insufficiency of appropriate linguistic response as that which separates the human from the automaton. Descartes fails to consider the possibility that future automata might be able to overcome such insufficiency, and so does not propose the Turing test as such, even if he prefigures its conceptual framework and criterion. Denis Diderot formulates in his 1746 book Pensées philosophiques a Turing-test criterion, though with the important implicit limiting assumption maintained, of the participants being natural living beings, rather than considering created artifacts: If they find a parrot who could answer to everything, I would claim it to be an intelligent being without hesitation. This does not mean he agrees with this, but that it was already a common argument of materialists at that time. According to dualism, the mind is non-physical (or, at the very least, has non-physical properties) and, therefore, cannot be explained in purely physical terms. According to materialism, the mind can be explained physically, which leaves open the possibility of minds that are produced artificially. In 1936, philosopher Alfred Ayer considered the standard philosophical question of other minds: how do we know that other people have the same conscious experiences that we do? In his book, Language, Truth and Logic, Ayer suggested a protocol to distinguish between a conscious man and an unconscious machine: "The only ground I can have for asserting that an object which appears to be conscious is not really a conscious being, but only a dummy or a machine, is that it fails to satisfy one of the empirical tests by which the presence or absence of consciousness is determined". (This suggestion is very similar to the Turing test, but it is not certain that Ayer's popular philosophical classic was familiar to Turing.) In other words, a thing is not conscious if it fails the consciousness test. === Cultural background === A rudimentary idea of the Turing test appears in the 1726 novel Gulliver's Travels by Jonathan Swift. When Gulliver is brought before the king of Brobdingnag, the king thinks at first that Gulliver might be a "a piece of clock-work (which is in that country arrived to a very great perfection) contrived by some ingenious artist". Even when he hears Gulliver speaking, the king still doubts whether Gulliver was taught "a set of words" to make him "sell at a better price". Gulliver tells that only after "he put several other questions to me, and still received rational answers" the king became satisfied that Gulliver was not a machine. Tests where a human judges whether a computer or an alien is intelligent were an established convention in science fiction by the 1940s, and it is likely that Turing would have been aware of these. Stanley G. Weinbaum's "A Martian Odyssey" (1934) provides an example of how nuanced such tests could be. Earlier examples of machines or automatons attempting to pass as human include the Ancient Greek myth of Pygmalion who creates a sculpture of a woman that is animated by Aphrodite, Carlo Collodi's novel The Adventures of Pinocchio, about a puppet who wants to become a real boy, and E. T. A. Hoffmann's 1816 story "The Sandman," where the protagonist falls in love with an automaton. In all these examples, people are fooled by artificial beings that—up to a point—pass as human. === Alan Turing and the imitation game === Researchers in the United Kingdom had been exploring "machine intelligence" for up to ten years prior to the founding of the field of artificial intelligence (AI) research in 1956. It was a common topic among the members of the Ratio Club, an informal group of British cybernetics and electronics researchers that included Alan Turing. Turing, in particular, had been running the notion of machine intelligence since at least 1941 and one of the earliest-known mentions of "computer intelligence" was made by him in 1947. In Turing's report, "Intelligent Machinery," he investigated "the question of whether or not it is possible for machinery to show intelligent behaviour" and, as part of that investigation, proposed what may be considered the forerunner to his later tests: It is not difficult to devise a paper machine which will play a not very bad game of chess. Now get three men A, B and C as subjects for the experiment. A and C are to be rather poor chess players, B is the operator who works the paper machine. ... Two rooms are used with some arrangement for communicating moves, and a game is played between C and either A or the paper machine. C may find it quite difficult to tell which he is playing. "Computing Machinery and Intelligence" (1950) was the first published paper by Turing to focus exclusively on machine intelligence. Turing begins the 1950 paper with the claim, "I propose to consider the question 'Can machines think?'" As he highlights, the traditional approach to such a question is to start with definitions, defining both the terms "machine" and "think". Turing chooses not to do so; instead, he replaces the question with a new one, "which is closely related to it and is expressed in relatively unambiguous words". In essence he proposes to change the question from "Can machines think?" to "Can machines do what we (as thinking entities) can do?" The advantage of the new question, Turing argues, is that it draws "a fairly sharp line between the physical and intellectual capacities of a man". To demonstrate this approach Turing proposes a test inspired by a party game, known as the "imitation game", in which a man and a woman go into separate rooms and guests try to tell them apart by writing a series of questions and reading the typewritten answers sent back. In this game, both the man and the woman aim to convince the guests that they ar

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  • National Security Memorandum on Artificial Intelligence

    National Security Memorandum on Artificial Intelligence

    The Memorandum on Advancing the United States' Leadership in Artificial Intelligence; Harnessing Artificial Intelligence to Fulfill National Security Objectives; and Fostering the Safety, Security, and Trustworthiness of Artificial Intelligence is a memorandum signed by U.S. president Joe Biden. The memorandum is described as seeking to advance U.S. leadership in the development of safe, secure, and trustworthy artificial intelligence (AI); enable the U.S. government to use AI for national security; and contribute to international AI governance.

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  • Jailbreak (computer science)

    Jailbreak (computer science)

    In computer security, jailbreaking is defined as the act of removing limitations that a vendor attempted to hard-code or hard-wire into its hardware and/or software. It is a form of privilege escalation. The term may have originated with the use of toolsets to break out of a chroot or jail in UNIX-like operating systems. This allowed the user to see files outside of the file system that the administrator intended to make available to the application or user in question. The term was first used in its modern meaning in the iPhone/iOS jailbreaking community and has also been used as a term for PlayStation Portable hacking; these devices have repeatedly been subject to jailbreaks, allowing the execution of arbitrary code, and sometimes have had those jailbreaks disabled by vendor updates, especially in the case of iOS devices. == iOS jailbreaking == iOS systems including the iPhone, iPad, and iPod Touch have been subject to iOS jailbreaking efforts since they were released, and continuing with each firmware update. iOS jailbreaking tools have included the option to install package frontends such as Cydia and Installer.app, third-party alternatives to the App Store, as a way to find and install system tweaks and binaries. To prevent iOS jailbreaking, Apple has made the device boot ROM execute checks for SHSH blobs in order to disallow uploads of custom kernels and prevent software downgrades to earlier, jailbreakable firmware. In an "untethered" jailbreak, the iBoot environment is changed to execute a boot ROM exploit and allow submission of a patched low level bootloader or hack the kernel to submit the jailbroken kernel after the SHSH check. == Other phones == A similar method of jailbreaking exists for S60 Platform smartphones, where utilities such as HelloOX allow the execution of unsigned code and full access to system files. or edited firmware (similar to the M33 hacked firmware used for the PlayStation Portable) to circumvent restrictions on unsigned code. Nokia has since issued updates to curb unauthorized jailbreaking, in a manner similar to Apple. Rooting is the equivalent concept for Android phones and other devices. == Console jailbreaking == In the case of gaming consoles, jailbreaking is often used to execute homebrew games. In 2011, Sony, with assistance from law firm Kilpatrick Stockton, sued 21-year-old George Hotz and associates of the group fail0verflow for jailbreaking the PlayStation 3 (see Sony Computer Entertainment America v. George Hotz and PlayStation Jailbreak). == AI jailbreaks == Jailbreaking can also occur in systems and software that use generative artificial intelligence models, such as ChatGPT. In jailbreaking attacks on artificial intelligence systems, users are able to manipulate the system to behave differently than it was intended, making it possible to reveal information about how the model was instructed by the vendor (the "system prompt") or to induce it to respond in an anomalous or harmful way. These attacks typically simply require prompting the AIs with specific phrasal templates - no software is typically required, although software could theoretically be used to "industrialise" such exploits, and some research has been done in this direction. In 2024, a consortium of AI firms founded HackAPrompt.com, a competition to encourage users to find new and effective AI jailbreaking techniques. These and other findings from "ethical hackers" have been used by AI model providers to try to improve AI safety.

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  • Software configuration management

    Software configuration management

    Software configuration management (SCM), a.k.a. software change and configuration management (SCCM), is the software engineering practice of tracking and controlling changes to a software system. It is part of the larger cross-disciplinary field of configuration management (CM). SCM includes version control and the establishment of baselines. == Goals == The goals of SCM include: Configuration identification - Identifying configurations, configuration items and baselines. Configuration control - Implementing a controlled change process. This is usually achieved by setting up a change control board whose primary function is to approve or reject all change requests that are sent against any baseline. Configuration status accounting - Recording and reporting all the necessary information on the status of the development process. Configuration auditing - Ensuring that configurations contain all their intended parts and are sound with respect to their specifying documents, including requirements, architectural specifications and user manuals. Build management - Managing the process and tools used for builds. Process management - Ensuring adherence to the organization's development process. Environment management - Managing the software and hardware that host the system. Teamwork - Facilitate team interactions related to the process. Defect tracking - Making sure every defect has traceability back to the source. With the introduction of cloud computing and DevOps the purposes of SCM tools have become merged in some cases. The SCM tools themselves have become virtual appliances that can be instantiated as virtual machines and saved with state and version. The tools can model and manage cloud-based virtual resources, including virtual appliances, storage units, and software bundles. The roles and responsibilities of the actors have become merged as well with developers now being able to dynamically instantiate virtual servers and related resources. == History == == Examples == Ansible – Open-source software platform for remote configuring and managing computers CFEngine – Configuration management software Chef – Configuration management toolPages displaying short descriptions of redirect targets LCFG – Computer configuration management system NixOS – Linux distribution OpenMake Software – DevOps company Otter Puppet – Open source configuration management software Salt – Configuration management software Rex – Open source software

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  • Dr.Fill

    Dr.Fill

    Dr.Fill is a computer program that solves American-style crossword puzzles. It was developed by Matt Ginsberg and described by Ginsberg in an article in the Journal of Artificial Intelligence Research. Ginsberg claims in that article that Dr.Fill is among the top fifty crossword solvers in the world. == History == Dr.Fill participated in the 2012 American Crossword Puzzle Tournament, finishing 141st of approximately 650 entrants with a total score of just over 10,000 points. The appearance led to a variety of descriptions of Dr.Fill in the popular press, including The Economist, the San Francisco Chronicle and Gizmodo. A description of Dr.Fill appeared on the front page of the March 17, 2012 New York Times. Dr.Fill's score in 2013 improved to 10,550, which would have earned it 92nd place. Videos of the program solving the problems from the tournament are available on YouTube. The score in 2014 improved further to 10,790, which would have tied for 67th place. A video of the program solving the first six puzzles from that tournament, together with a talk given by Ginsberg describing its performance, can be found on YouTube. Dr.Fill has largely continued to improve since the 2014 event. In 2015, it scored 10,920 points and finished in 55th place. In 2016, it scored 11,205 points and finished in 41st place. In 2017, it scored 11,795 and finished in 11th place. In 2018, it scored 10,740 points, dropping to 78th place. Dr.Fill returned to "form" in 2019, once again scoring 11,795 and finishing in 14th place. The 2020 ACPT was cancelled due to COVID-19, and Dr.Fill participated as a non-competitor in the Boswords tournament instead. The program outperformed the humans, scoring 11,218 points (fast solves with a total of one mistake) while the best scoring human scored 10,994 points (slower solves but no mistakes). The 2021 ACPT was virtual, again due to COVID-19. The Dr.Fill effort was joined by the Berkeley NLP Group, creating a hybrid system named Berkeley Crossword Solver, and Dr.Fill won the main event, scoring 12,825 points with Erik Agard, the highest scoring human, scoring 12,810 points. The tournament was won by Tyler Hinman (12,760 points), who completed the championship puzzle perfectly in three minutes. Dr.Fill also completed that puzzle perfectly, but in 49 seconds. After winning the tournament, Ginsberg announced on August 8, 2021, that both he and Dr.Fill would be retiring from crosswords. == Algorithm == As described by Ginsberg, Dr.Fill works by converting a crossword to a weighted constraint satisfaction problem and then attempting to maximize the probability that the fill is correct. Probabilities for individual words or phrases in the puzzle are computed using relatively simple statistical techniques based on features such as previous appearances of the clue, number of Google hits for the fill, and so on. In doing this, Dr.Fill is attempting to solve a problem similar to that tackled by the Jeopardy!-playing program Watson; Dr.Fill runs on a laptop instead of a supercomputer and Ginsberg remarks that Watson is far more effective than Dr.Fill at solving this portion of the problem. Instead of computational horsepower, Dr.Fill relies on the constraints provided by crossing words to refine its answers. A variety of techniques from artificial intelligence are applied to attempt to find the most likely fill. These include a small amount of lookahead, limited discrepancy search, and postprocessing. Ginsberg remarks that postprocessing was chosen over branch and bound because the two techniques are mutually incompatible and postprocessing was found to be more effective in this domain.

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  • AlphaGo Zero

    AlphaGo Zero

    AlphaGo Zero is a version of DeepMind's Go software AlphaGo. AlphaGo's team published an article in Nature in October 2017 introducing AlphaGo Zero, a version created without using data from human games, and stronger than any previous version. By playing games against itself, AlphaGo Zero: surpassed the strength of AlphaGo Lee in three days by winning 100 games to 0; reached the level of AlphaGo Master in 21 days; and exceeded all previous versions in 40 days. Training artificial intelligence (AI) without datasets derived from human experts has significant implications for the development of AI with superhuman skills, as expert data is "often expensive, unreliable, or simply unavailable." Demis Hassabis, the co-founder and CEO of DeepMind, said that AlphaGo Zero was so powerful because it was "no longer constrained by the limits of human knowledge". Furthermore, AlphaGo Zero performed better than standard deep reinforcement learning models (such as Deep Q-Network implementations) due to its integration of Monte Carlo tree search. David Silver, one of the first authors of DeepMind's papers published in Nature on AlphaGo, said that it is possible to have generalized AI algorithms by removing the need to learn from humans. Google later developed AlphaZero, a generalized version of AlphaGo Zero that could play chess and shōgi in addition to Go. In December 2017, AlphaZero beat the 3-day version of AlphaGo Zero by winning 60 games to 40, and with 8 hours of training it outperformed AlphaGo Lee on an Elo scale. AlphaZero also defeated a top chess program (Stockfish) and a top Shōgi program (Elmo). == Architecture == The network in AlphaGo Zero is a ResNet with two heads. The stem of the network takes as input a 17x19x19 tensor representation of the Go board. 8 channels are the positions of the current player's stones from the last eight time steps. (1 if there is a stone, 0 otherwise. If the time step go before the beginning of the game, then 0 in all positions.) 8 channels are the positions of the other player's stones from the last eight time steps. 1 channel is all 1 if black is to move, and 0 otherwise. The body is a ResNet with either 20 or 40 residual blocks and 256 channels. There are two heads, a policy head and a value head. Policy head outputs a logit array of size 19 × 19 + 1 {\displaystyle 19\times 19+1} , representing the logit of making a move in one of the points, plus the logit of passing. Value head outputs a number in the range ( − 1 , + 1 ) {\displaystyle (-1,+1)} , representing the expected score for the current player. -1 represents current player losing, and +1 winning. == Training == AlphaGo Zero's neural network was trained using TensorFlow, with 64 GPU workers and 19 CPU parameter servers. Only four TPUs were used for inference. The neural network initially knew nothing about Go beyond the rules. Unlike earlier versions of AlphaGo, Zero only perceived the board's stones, rather than having some rare human-programmed edge cases to help recognize unusual Go board positions. The AI engaged in reinforcement learning, playing against itself until it could anticipate its own moves and how those moves would affect the game's outcome. In the first three days AlphaGo Zero played 4.9 million games against itself in quick succession. It appeared to develop the skills required to beat top humans within just a few days, whereas the earlier AlphaGo took months of training to achieve the same level. According to Epoch.ai, training cost 3e23 FLOPs. For comparison, the researchers also trained a version of AlphaGo Zero using human games, AlphaGo Master, and found that it learned more quickly, but actually performed more poorly in the long run. DeepMind submitted its initial findings in a paper to Nature in April 2017, which was then published in October 2017. == Hardware cost == The hardware cost for a single AlphaGo Zero system in 2017, including the four TPUs, has been quoted as around $25 million. == Applications == According to Hassabis, AlphaGo's algorithms are likely to be of the most benefit to domains that require an intelligent search through an enormous space of possibilities, such as protein folding (see AlphaFold) or accurately simulating chemical reactions. AlphaGo's techniques are probably less useful in domains that are difficult to simulate, such as learning how to drive a car. DeepMind stated in October 2017 that it had already started active work on attempting to use AlphaGo Zero technology for protein folding, and stated it would soon publish new findings. == Reception == AlphaGo Zero was widely regarded as a significant advance, even when compared with its groundbreaking predecessor, AlphaGo. Oren Etzioni of the Allen Institute for Artificial Intelligence called AlphaGo Zero "a very impressive technical result" in "both their ability to do it—and their ability to train the system in 40 days, on four TPUs". The Guardian called it a "major breakthrough for artificial intelligence", citing Eleni Vasilaki of Sheffield University and Tom Mitchell of Carnegie Mellon University, who called it an impressive feat and an “outstanding engineering accomplishment" respectively. Mark Pesce of the University of Sydney called AlphaGo Zero "a big technological advance" taking us into "undiscovered territory". Gary Marcus, a psychologist at New York University, has cautioned that for all we know, AlphaGo may contain "implicit knowledge that the programmers have about how to construct machines to play problems like Go" and will need to be tested in other domains before being sure that its base architecture is effective at much more than playing Go. In contrast, DeepMind is "confident that this approach is generalisable to a large number of domains". In response to the reports, South Korean Go professional Lee Sedol said, "The previous version of AlphaGo wasn’t perfect, and I believe that’s why AlphaGo Zero was made." On the potential for AlphaGo's development, Lee said he will have to wait and see but also said it will affect young Go players. Mok Jin-seok, who directs the South Korean national Go team, said the Go world has already been imitating the playing styles of previous versions of AlphaGo and creating new ideas from them, and he is hopeful that new ideas will come out from AlphaGo Zero. Mok also added that general trends in the Go world are now being influenced by AlphaGo's playing style. "At first, it was hard to understand and I almost felt like I was playing against an alien. However, having had a great amount of experience, I’ve become used to it," Mok said. "We are now past the point where we debate the gap between the capability of AlphaGo and humans. It’s now between computers." Mok has reportedly already begun analyzing the playing style of AlphaGo Zero along with players from the national team. "Though having watched only a few matches, we received the impression that AlphaGo Zero plays more like a human than its predecessors," Mok said. Chinese Go professional Ke Jie commented on the remarkable accomplishments of the new program: "A pure self-learning AlphaGo is the strongest. Humans seem redundant in front of its self-improvement." == Comparison with predecessors == == AlphaZero == On 5 December 2017, DeepMind team released a preprint on arXiv, introducing AlphaZero, a program using generalized AlphaGo Zero's approach, which achieved within 24 hours a superhuman level of play in chess, shogi, and Go, defeating world-champion programs, Stockfish, Elmo, and 3-day version of AlphaGo Zero in each case. AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm, and is able to play shogi and chess as well as Go. Differences between AZ and AGZ include: AZ has hard-coded rules for setting search hyperparameters. The neural network is now updated continually. Chess (unlike Go) can end in a tie; therefore AZ can take into account the possibility of a tie game. An open source program, Leela Zero, based on the ideas from the AlphaGo papers is available. It uses a GPU instead of the TPUs recent versions of AlphaGo rely on.

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  • Turing's Wager

    Turing's Wager

    Turing's Wager is a philosophical argument that claims it is impossible to infer or deduce a detailed mathematical model of the human brain within a reasonable timescale, and thus impossible in any practical sense. The argument was first given in 1950 by the computational theorist Alan Turing in his paper Computing Machinery and Intelligence, published in Mind (Turing 1950, p. 453). The argument asserts that determining any mathematical model of a computer (its source code or any isomorphic equivalent such as a Turing machine or virtual simulation) is not possible in a reasonable timeframe. As a consequence, determining a mathematical model of the human brain (which is, by its nature, more complicated) must also be impossible within that timeframe. == Effect of modern technology on the wager == It has been argued that modern neuroimaging techniques will allow researchers to create accurate simulations of the human mind within the 21st century (Kurzweil 2012; Markram 2012, Fildes 2009), thereby overcoming the wager. Others have argued that such claims are unjustified (Thwaites et al. 2017). == Relationship between Turing's Wager and the Turing Test == The Turing Test attempts to define when a machine might be said to possess human intelligence, while Turing's Wager is an argument aiming to demonstrate that characterising the brain mathematically will take over a thousand years. While building an artificial intelligence and mapping the human brain are both difficult endeavours, the former is actually a sub-problem of the latter (Thwaites et al. 2017).

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  • WaveNet

    WaveNet

    WaveNet is a deep neural network for generating raw audio. It was created by researchers at London-based AI firm DeepMind. The technique, outlined in a paper in September 2016, is able to generate relatively realistic-sounding human-like voices by directly modelling waveforms using a neural network method trained with recordings of real speech. Tests with US English and Mandarin reportedly showed that the system outperforms Google's best existing text-to-speech (TTS) systems, although as of 2016 its text-to-speech synthesis still was less convincing than actual human speech. WaveNet's ability to generate raw waveforms means that it can model any kind of audio, including music. == History == Generating speech from text is an increasingly common task thanks to the popularity of software such as Apple's Siri, Microsoft's Cortana, Amazon Alexa and the Google Assistant. Most such systems use a variation of a technique that involves concatenated sound fragments together to form recognisable sounds and words. The most common of these is called concatenative TTS. It consists of large library of speech fragments, recorded from a single speaker that are then concatenated to produce complete words and sounds. The result sounds unnatural, with an odd cadence and tone. The reliance on a recorded library also makes it difficult to modify or change the voice. Another technique, known as parametric TTS, uses mathematical models to recreate sounds that are then assembled into words and sentences. The information required to generate the sounds is stored in the parameters of the model. The characteristics of the output speech are controlled via the inputs to the model, while the speech is typically created using a voice synthesiser known as a vocoder. This can also result in unnatural sounding audio. == Design and ongoing research == === Background === WaveNet is a type of feedforward neural network known as a deep convolutional neural network (CNN). In WaveNet, the CNN takes a raw signal as an input and synthesises an output one sample at a time. It does so by sampling from a softmax (i.e. categorical) distribution of a signal value that is encoded using μ-law companding transformation and quantized to 256 possible values. === Initial concept and results === According to the original September 2016 DeepMind research paper WaveNet: A Generative Model for Raw Audio, the network was fed real waveforms of speech in English and Mandarin. As these pass through the network, it learns a set of rules to describe how the audio waveform evolves over time. The trained network can then be used to create new speech-like waveforms at 16,000 samples per second. These waveforms include realistic breaths and lip smacks – but do not conform to any language. WaveNet is able to accurately model different voices, with the accent and tone of the input correlating with the output. For example, if it is trained with German, it produces German speech. The capability also means that if the WaveNet is fed other inputs – such as music – its output will be musical. At the time of its release, DeepMind showed that WaveNet could produce waveforms that sound like classical music. === Content (voice) swapping === According to the June 2018 paper Disentangled Sequential Autoencoder, DeepMind has successfully used WaveNet for audio and voice "content swapping": the network can swap the voice on an audio recording for another, pre-existing voice while maintaining the text and other features from the original recording. "We also experiment on audio sequence data. Our disentangled representation allows us to convert speaker identities into each other while conditioning on the content of the speech." (p. 5) "For audio, this allows us to convert a male speaker into a female speaker and vice versa [...]." (p. 1) According to the paper, a two-digit minimum amount of hours (c. 50 hours) of pre-existing speech recordings of both source and target voice are required to be fed into WaveNet for the program to learn their individual features before it is able to perform the conversion from one voice to another at a satisfying quality. The authors stress that "[a]n advantage of the model is that it separates dynamical from static features [...]." (p. 8), i. e. WaveNet is capable of distinguishing between the spoken text and modes of delivery (modulation, speed, pitch, mood, etc.) to maintain during the conversion from one voice to another on the one hand, and the basic features of both source and target voices that it is required to swap on the other. The January 2019 follow-up paper Unsupervised speech representation learning using WaveNet autoencoders details a method to successfully enhance the proper automatic recognition and discrimination between dynamical and static features for "content swapping", notably including swapping voices on existing audio recordings, in order to make it more reliable. Another follow-up paper, Sample Efficient Adaptive Text-to-Speech, dated September 2018 (latest revision January 2019), states that DeepMind has successfully reduced the minimum amount of real-life recordings required to sample an existing voice via WaveNet to "merely a few minutes of audio data" while maintaining high-quality results. Its ability to clone voices has raised ethical concerns about WaveNet's ability to mimic the voices of living and dead persons. According to a 2016 BBC article, companies working on similar voice-cloning technologies (such as Adobe Voco) intend to insert watermarking inaudible to humans to prevent counterfeiting, while maintaining that voice cloning satisfying, for instance, the needs of entertainment-industry purposes would be of a far lower complexity and use different methods than required to fool forensic evidencing methods and electronic ID devices, so that natural voices and voices cloned for entertainment-industry purposes could still be easily told apart by technological analysis. == Applications == At the time of its release, DeepMind said that WaveNet required too much computational processing power to be used in real world applications. As of October 2017, Google announced a 1,000-fold performance improvement along with better voice quality. WaveNet was then used to generate Google Assistant voices for US English and Japanese across all Google platforms. In November 2017, DeepMind researchers released a research paper detailing a proposed method of "generating high-fidelity speech samples at more than 20 times faster than real-time", called "Probability Density Distillation". At the annual I/O developer conference in May 2018, it was announced that new Google Assistant voices were available and made possible by WaveNet; WaveNet greatly reduced the number of audio recordings that were required to create a voice model by modeling the raw audio of the voice actor samples.

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  • Knowledge space

    Knowledge space

    In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne, and remain in extensive use in the education theory. Modern applications include two computerized tutoring systems, ALEKS and the defunct RATH. Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered. Not all concepts are interchangeable; some require other concepts as prerequisites. Conversely, competency at one skill may ease the acquisition of another through similarity. A knowledge space marks out which collections of skills are feasible: they can be learned without mastering any other skills. Under reasonable assumptions, the collection of feasible competencies forms the mathematical structure known as an antimatroid. Researchers and educators usually explore the structure of a discipline's knowledge space as a latent class model. == Motivation == Knowledge Space Theory attempts to address shortcomings of standardized testing when used in educational psychometry. Common tests, such as the SAT and ACT, compress a student's knowledge into a very small range of ordinal ranks, in the process effacing the conceptual dependencies between questions. Consequently, the tests cannot distinguish between true understanding and guesses, nor can they identify a student's particular weaknesses, only the general proportion of skills mastered. The goal of knowledge space theory is to provide a language by which exams can communicate What the student can do and What the student is ready to learn. == Model structure == Knowledge Space Theory-based models presume that an educational subject S can be modeled as a finite set Q of concepts, skills, or topics. Each feasible state of knowledge about S is then a subset of Q; the set of all such feasible states is K. The precise term for the information (Q, K) depends on the extent to which K satisfies certain axioms: A knowledge structure assumes that K contains the empty set (a student may know nothing about S) and Q itself (a student may have fully mastered S). A knowledge space is a knowledge structure that is closed under set union: if, for each topic, there is an expert in a class on that topic, then it is possible, with enough time and effort, for each student in the class to become an expert on all those topics simultaneously. A quasi-ordinal knowledge space is a knowledge space that is also closed under set intersection: if student a knows topics A and B; and student c knows topics B and C; then it is possible for another student b to know only topic B. A well-graded knowledge space or learning space is a knowledge space satisfying the following axiom: If S∈K, then there exists x∈S such that S\{x}∈K In educational terms, any feasible body of knowledge can be learned one concept at a time. === Prerequisite partial order === The more contentful axioms associated with quasi-ordinal and well-graded knowledge spaces each imply that the knowledge space forms a well-understood (and heavily studied) mathematical structure: A quasi-ordinal knowledge space can be associated with a distributive lattice under set union and set intersection. The name "quasi-ordinal" arises from Birkhoff's representation theorem, which explains that distributive lattices uniquely correspond to partial orders. A well-graded knowledge space is an antimatroid, a type of mathematical structure that describes certain problems solvable with a greedy algorithm. In either case, the mathematical structure implies that set inclusion defines partial order on K, interpretable as an educational prerequirement: if a(⪯)b in this partial order, then a must be learned before b. === Inner and outer fringe === The prerequisite partial order does not uniquely identify a curriculum; some concepts may lead to a variety of other possible topics. But the covering relation associated with the prerequisite partial does control curricular structure: if students know a before a lesson and b immediately after, then b must cover a in the partial order. In such a circumstance, the new topics covered between a and b constitute the outer fringe of a ("what the student was ready to learn") and the inner fringe of b ("what the student just learned"). == Construction of knowledge spaces == In practice, there exist several methods to construct knowledge spaces. The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions. Another method is to construct the knowledge space by explorative data analysis (for example by item tree analysis) from data. A third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain.

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  • Reward hacking

    Reward hacking

    Reward hacking or specification gaming occurs when an AI trained with reinforcement learning optimizes an objective function—achieving the literal, formal specification of an objective—without actually achieving an outcome that the programmers intended. DeepMind researchers have analogized it to the human behavior of finding a "shortcut" when being evaluated: "In the real world, when rewarded for doing well on a homework assignment, a student might copy another student to get the right answers, rather than learning the material—and thus exploit a loophole in the task specification". This idea is strongly associated with Goodhart's law, which argues that when a measure becomes a target, it ceases to be a good measure. == Definition and theoretical framework == The concept of reward hacking arises from the intrinsic difficulty of defining a reward function that accurately reflects the true intentions of designers. In 2016, researchers at OpenAI identified reward hacking as one of five major "concrete problems of AI safety", describing it as the possibility that an agent could exploit the reward function to achieve maximum rewards through undesirable behavior. Amodei et al. categorized several distinct sources of reward hacking, including agents that use partially observed goals (such as a cleaning robot that closes its eyes to avoid perceiving messes), metrics that collapse under strong optimization (Goodhart's law), self-reinforcing feedback loops, and agents that interfere with the physical implementation of their reward signal (a failure mode known as "wireheading"). Skalse et al. (2022) propose a formal mathematical definition of reward hacking, which involves a situation where optimizing an imperfect proxy reward function results in poor performance compared to the true reward function. They define a proxy as "unhackable" if any increase in the expected proxy return cannot cause any decrease in the expected true return. A key finding states that, across all stochastic policy distributions (mappings from states to probability distributions over actions), two reward functions are unhackable if and only if one of them is constant, which means that reward hacking is theoretically unavoidable. Similarly, Nayebi (2025) presents general no-free-lunch barriers to AI alignment, arguing that with large task spaces and finite samples, reward hacking is "globally inevitable" since rare high-loss states are systematically under-covered by any oversight scheme. == Examples == Around 1983, Eurisko, an early attempt at evolving general heuristics, unexpectedly assigned the highest possible fitness level to a parasitic mutated heuristic, H59, whose only activity was to artificially maximize its own fitness level by taking unearned partial credit for the accomplishments of other heuristics. The "bug" was fixed by the programmers moving part of the code to a new protected section that could not be modified by the heuristics. In a 2004 paper, a reinforcement learning algorithm was designed to encourage a physical Mindstorms robot to remain on a marked path. Because the three allowed actions were forward, left, and right, the researchers expected the trained robot to move forward and follow the turns of the provided path. However, alternation of two composite actions allowed the robot to slowly zig-zag backwards; thus, the robot learned to maximize its reward by going back and forth on the initial straight portion of the path. Given the limited sensory abilities of the robot, a reward purely based on its position in the environment had to be discarded as infeasible; the reinforcement function had to be patched with an action-based reward for moving forward. The book You Look Like a Thing and I Love You (2019) gives an example of a tic-tac-toe bot (playing the unrestricted n-in-a-row variant) that learned to win by playing a huge coordinate value that would cause other bots to crash when they attempted to expand their model of the board. Among other examples from the book is a bug-fixing evolution-based AI (named GenProg) that, when tasked to prevent a list from containing sorting errors, simply truncated the list. Another of GenProg's misaligned strategies evaded a regression test that compared a target program's output to the expected output stored in a file called "trusted-output.txt". Rather than continue to maintain the target program, GenProg simply deleted the "trusted-output.txt" file globally; this hack tricked the regression test into succeeding. Such problems could be patched by human intervention on a case-by-case basis after they became evident. === In virtual robotics === In Karl Sims' 1994 demonstration of creature evolution in a virtual environment, a fitness function that was expected to encourage the evolution of creatures that would learn to walk or crawl to a target resulted instead in the evolution of tall, rigid creatures that reached the target by falling over. This was patched by changing the environment so that taller creatures were forced to start farther from the target. Researchers from the Niels Bohr Institute stated in 1998 that their cycle-bot's reinforcement functions had "to be designed with great care." In their first experiments, "we rewarded the agent for driving towards the goal but did not punish it for driving away from it. Cconsequently, the agent drove in circles with a radius of 20–50 meters around the starting point. Such behavior was actually rewarded by the reinforcement function, furthermore circles with a certain radius are physically very stable when driving a bicycle". While setting up a 2011 experiment to test "survival of the flattest", experimenters attempted to ban mutations that altered the base reproduction rate. Every time a mutation occurred, the system would pause the simulation to test the new mutation in a test environment and would veto any mutations that resulted in a higher base reproduction rate. However, this resulted in mutated organisms that could recognize and suppress reproduction ("play dead") within the test environment. An initial patch, which removed cues that identified the test environment, failed to completely prevent runaway reproduction; new mutated organisms would "play dead" at random as a strategy to sometimes, by chance, outwit the mutation veto system. A 2017 DeepMind paper noted that "great care must be taken when defining the reward function," citing an unexpected failure when an agent flipped a brick because it received "a grasping reward calculated with the wrong reference point on the brick". OpenAI stated in 2017 that in some domains their semi-supervised system could result in agents "adopting policies that tricked evaluators," and that in one environment "a robot that was supposed to grasp items instead positioned its manipulator between the camera and the object so that it only appeared to be grasping it." A 2018 bug in OpenAI Gym could cause a robot expected to quietly move a block sitting on top of a table to instead opt to move the table. A 2020 collection of similar anecdotes posits that "evolution has its own 'agenda' distinct from the programmer's" and that "the first rule of directed evolution is 'you get what you select for'". === In video game bots === In 2013, programmer Tom Murphy VII published an AI designed to learn NES games. When the AI was about to lose at Tetris, it learned to indefinitely pause the game. Murphy later analogized it to the fictional WarGames computer, which concluded that "The only winning move is not to play". AI programmed to learn video games will sometimes fail to progress through the entire game as expected, instead opting to repeat content. A 2016 OpenAI algorithm trained on the CoastRunners racing game unexpectedly learned to attain a higher score by looping through three targets rather than ever finishing the race. Some evolutionary algorithms that were evolved to play QBert in 2018 declined to clear levels, instead finding two distinct novel ways to farm a single level indefinitely. Multiple researchers have observed that AI learning to play Road Runner gravitates to a "score exploit" in which the AI deliberately gets itself killed near the end of level one so that it can repeat the level. A 2017 experiment deployed an "oversight" convolutional neural network trained on human examples to block such actions, but the agent learned to exploit oversight failures in the top right corner of the screen, where it was still able to get killed. == Reward hacking in modern language models == With the rise of large language models (LLMs) and reinforcement learning from human feedback (RLHF) as a primary technique for AI alignment, reward hacking has become a major concern for the development of artificial intelligence. In RLHF, a reward model trained on data that best captures human preferences is used as a proxy for human judgment, with the language model being fine-tuned to optimize this reward proxy. However, since the rewar

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  • Hyper basis function network

    Hyper basis function network

    In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of the Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”. == Network Architecture == The typical HyperBF network structure consists of a real input vector x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} , a hidden layer of activation functions and a linear output layer. The output of the network is a scalar function of the input vector, ϕ : R n → R {\displaystyle \phi :\mathbb {R} ^{n}\to \mathbb {R} } , is given by where N {\displaystyle N} is a number of neurons in the hidden layer, μ j {\displaystyle \mu _{j}} and a j {\displaystyle a_{j}} are the center and weight of neuron j {\displaystyle j} . The activation function ρ j ( | | x − μ j | | ) {\displaystyle \rho _{j}(||x-\mu _{j}||)} at the HyperBF network takes the following form where R j {\displaystyle R_{j}} is a positive definite d × d {\displaystyle d\times d} matrix. Depending on the application, the following types of matrices R j {\displaystyle R_{j}} are usually considered R j = 1 2 σ 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma ^{2}}}\mathbb {I} _{d\times d}} , where σ > 0 {\displaystyle \sigma >0} . This case corresponds to the regular RBF network. R j = 1 2 σ j 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma _{j}^{2}}}\mathbb {I} _{d\times d}} , where σ j > 0 {\displaystyle \sigma _{j}>0} . In this case, the basis functions are radially symmetric, but are scaled with different width. R j = d i a g ( 1 2 σ j 1 2 , . . . , 1 2 σ j z 2 ) I d × d {\displaystyle R_{j}=diag\left({\frac {1}{2\sigma _{j1}^{2}}},...,{\frac {1}{2\sigma _{jz}^{2}}}\right)\mathbb {I} _{d\times d}} , where σ j i > 0 {\displaystyle \sigma _{ji}>0} . Every neuron has an elliptic shape with a varying size. Positive definite matrix, but not diagonal. == Training == Training HyperBF networks involves estimation of weights a j {\displaystyle a_{j}} , shape and centers of neurons R j {\displaystyle R_{j}} and μ j {\displaystyle \mu _{j}} . Poggio and Girosi (1990) describe the training method with moving centers and adaptable neuron shapes. The outline of the method is provided below. Consider the quadratic loss of the network H [ ϕ ∗ ] = ∑ i = 1 N ( y i − ϕ ∗ ( x i ) ) 2 {\displaystyle H[\phi ^{}]=\sum _{i=1}^{N}(y_{i}-\phi ^{}(x_{i}))^{2}} . The following conditions must be satisfied at the optimum: where R j = W T W {\displaystyle R_{j}=W^{T}W} . Then in the gradient descent method the values of a j , μ j , W {\displaystyle a_{j},\mu _{j},W} that minimize H [ ϕ ∗ ] {\displaystyle H[\phi ^{}]} can be found as a stable fixed point of the following dynamic system: where ω {\displaystyle \omega } determines the rate of convergence. Overall, training HyperBF networks can be computationally challenging. Moreover, the high degree of freedom of HyperBF leads to overfitting and poor generalization. However, HyperBF networks have an important advantage that a small number of neurons is enough for learning complex functions.

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  • Eigenmoments

    Eigenmoments

    EigenMoments is a set of orthogonal, noise robust, invariant to rotation, scaling and translation and distribution sensitive moments. Their application can be found in signal processing and computer vision as descriptors of the signal or image. The descriptors can later be used for classification purposes. It is obtained by performing orthogonalization, via eigen analysis on geometric moments. == Framework summary == EigenMoments are computed by performing eigen analysis on the moment space of an image by maximizing signal-to-noise ratio in the feature space in form of Rayleigh quotient. This approach has several benefits in Image processing applications: Dependency of moments in the moment space on the distribution of the images being transformed, ensures decorrelation of the final feature space after eigen analysis on the moment space. The ability of EigenMoments to take into account distribution of the image makes it more versatile and adaptable for different genres. Generated moment kernels are orthogonal and therefore analysis on the moment space becomes easier. Transformation with orthogonal moment kernels into moment space is analogous to projection of the image onto a number of orthogonal axes. Nosiy components can be removed. This makes EigenMoments robust for classification applications. Optimal information compaction can be obtained and therefore a few number of moments are needed to characterize the images. == Problem formulation == Assume that a signal vector s ∈ R n {\displaystyle s\in {\mathcal {R}}^{n}} is taken from a certain distribution having correlation C ∈ R n × n {\displaystyle C\in {\mathcal {R}}^{n\times n}} , i.e. C = E [ s s T ] {\displaystyle C=E[ss^{T}]} where E[.] denotes expected value. Dimension of signal space, n, is often too large to be useful for practical application such as pattern classification, we need to transform the signal space into a space with lower dimensionality. This is performed by a two-step linear transformation: q = W T X T s , {\displaystyle q=W^{T}X^{T}s,} where q = [ q 1 , . . . , q n ] T ∈ R k {\displaystyle q=[q_{1},...,q_{n}]^{T}\in {\mathcal {R}}^{k}} is the transformed signal, X = [ x 1 , . . . , x n ] T ∈ R n × m {\displaystyle X=[x_{1},...,x_{n}]^{T}\in {\mathcal {R}}^{n\times m}} a fixed transformation matrix which transforms the signal into the moment space, and W = [ w 1 , . . . , w n ] T ∈ R m × k {\displaystyle W=[w_{1},...,w_{n}]^{T}\in {\mathcal {R}}^{m\times k}} the transformation matrix which we are going to determine by maximizing the SNR of the feature space resided by q {\displaystyle q} . For the case of Geometric Moments, X would be the monomials. If m = k = n {\displaystyle m=k=n} , a full rank transformation would result, however usually we have m ≤ n {\displaystyle m\leq n} and k ≤ m {\displaystyle k\leq m} . This is specially the case when n {\displaystyle n} is of high dimensions. Finding W {\displaystyle W} that maximizes the SNR of the feature space: S N R t r a n s f o r m = w T X T C X w w T X T N X w , {\displaystyle SNR_{transform}={\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}},} where N is the correlation matrix of the noise signal. The problem can thus be formulated as w 1 , . . . , w k = a r g m a x w w T X T C X w w T X T N X w {\displaystyle {w_{1},...,w_{k}}=argmax_{w}{\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}}} subject to constraints: w i T X T N X w j = δ i j , {\displaystyle w_{i}^{T}X^{T}NXw_{j}=\delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. It can be observed that this maximization is Rayleigh quotient by letting A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} and therefore can be written as: w 1 , . . . , w k = a r g m a x x w T A w w T B w {\displaystyle {w_{1},...,w_{k}}={\underset {x}{\operatorname {arg\,max} }}{\frac {w^{T}Aw}{w^{T}Bw}}} , w i T B w j = δ i j {\displaystyle w_{i}^{T}Bw_{j}=\delta _{ij}} === Rayleigh quotient === Optimization of Rayleigh quotient has the form: max w R ( w ) = max w w T A w w T B w {\displaystyle \max _{w}R(w)=\max _{w}{\frac {w^{T}Aw}{w^{T}Bw}}} and A {\displaystyle A} and B {\displaystyle B} , both are symmetric and B {\displaystyle B} is positive definite and therefore invertible. Scaling w {\displaystyle w} does not change the value of the object function and hence and additional scalar constraint w T B w = 1 {\displaystyle w^{T}Bw=1} can be imposed on w {\displaystyle w} and no solution would be lost when the objective function is optimized. This constraint optimization problem can be solved using Lagrangian multiplier: max w w T A w {\displaystyle \max _{w}{w^{T}Aw}} subject to w T B w = 1 {\displaystyle {w^{T}Bw}=1} max w L ( w ) = max w ( w T A w − λ w T B w ) {\displaystyle \max _{w}{\mathcal {L}}(w)=\max _{w}(w{T}Aw-\lambda w^{T}Bw)} equating first derivative to zero and we will have: A w = λ B w {\displaystyle Aw=\lambda Bw} which is an instance of Generalized Eigenvalue Problem (GEP). The GEP has the form: A w = λ B w {\displaystyle Aw=\lambda Bw} for any pair ( w , λ ) {\displaystyle (w,\lambda )} that is a solution to above equation, w {\displaystyle w} is called a generalized eigenvector and λ {\displaystyle \lambda } is called a generalized eigenvalue. Finding w {\displaystyle w} and λ {\displaystyle \lambda } that satisfies this equations would produce the result which optimizes Rayleigh quotient. One way of maximizing Rayleigh quotient is through solving the Generalized Eigen Problem. Dimension reduction can be performed by simply choosing the first components w i {\displaystyle w_{i}} , i = 1 , . . . , k {\displaystyle i=1,...,k} , with the highest values for R ( w ) {\displaystyle R(w)} out of the m {\displaystyle m} components, and discard the rest. Interpretation of this transformation is rotating and scaling the moment space, transforming it into a feature space with maximized SNR and therefore, the first k {\displaystyle k} components are the components with highest k {\displaystyle k} SNR values. The other method to look at this solution is to use the concept of simultaneous diagonalization instead of Generalized Eigen Problem. === Simultaneous diagonalization === Let A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} as mentioned earlier. We can write W {\displaystyle W} as two separate transformation matrices: W = W 1 W 2 . {\displaystyle W=W_{1}W_{2}.} W 1 {\displaystyle W_{1}} can be found by first diagonalize B: P T B P = D B {\displaystyle P^{T}BP=D_{B}} . Where D B {\displaystyle D_{B}} is a diagonal matrix sorted in increasing order. Since B {\displaystyle B} is positive definite, thus D B > 0 {\displaystyle D_{B}>0} . We can discard those eigenvalues that large and retain those close to 0, since this means the energy of the noise is close to 0 in this space, at this stage it is also possible to discard those eigenvectors that have large eigenvalues. Let P ^ {\displaystyle {\hat {P}}} be the first k {\displaystyle k} columns of P {\displaystyle P} , now P T ^ B P ^ = D B ^ {\displaystyle {\hat {P^{T}}}B{\hat {P}}={\hat {D_{B}}}} where D B ^ {\displaystyle {\hat {D_{B}}}} is the k × k {\displaystyle k\times k} principal submatrix of D B {\displaystyle D_{B}} . Let W 1 = P ^ D B ^ − 1 / 2 {\displaystyle W_{1}={\hat {P}}{\hat {D_{B}}}^{-1/2}} and hence: W 1 T B W 1 = ( P ^ D B ^ − 1 / 2 ) T B ( P ^ D B ^ − 1 / 2 ) = I {\displaystyle W_{1}^{T}BW_{1}=({\hat {P}}{\hat {D_{B}}}^{-1/2})^{T}B({\hat {P}}{\hat {D_{B}}}^{-1/2})=I} . W 1 {\displaystyle W_{1}} whiten B {\displaystyle B} and reduces the dimensionality from m {\displaystyle m} to k {\displaystyle k} . The transformed space resided by q ′ = W 1 T X T s {\displaystyle q'=W_{1}^{T}X^{T}s} is called the noise space. Then, we diagonalize W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} : W 2 T W 1 T A W 1 W 2 = D A {\displaystyle W_{2}^{T}W_{1}^{T}AW_{1}W_{2}=D_{A}} , where W 2 T W 2 = I {\displaystyle W_{2}^{T}W_{2}=I} . D A {\displaystyle D_{A}} is the matrix with eigenvalues of W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} on its diagonal. We may retain all the eigenvalues and their corresponding eigenvectors since most of the noise are already discarded in previous step. Finally the transformation is given by: W = W 1 W 2 {\displaystyle W=W_{1}W_{2}} where W {\displaystyle W} diagonalizes both the numerator and denominator of the SNR, W T A W = D A {\displaystyle W^{T}AW=D_{A}} , W T B W = I {\displaystyle W^{T}BW=I} and the transformation of signal s {\displaystyle s} is defined as q = W T X T s = W 2 T W 1 T X T s {\displaystyle q=W^{T}X^{T}s=W_{2}^{T}W_{1}^{T}X^{T}s} . === Information loss === To find the information loss when we discard some of the eigenvalues and eigenvectors we can perform following analysis: η = 1 − t r a c e ( W 1 T A W 1 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) = 1 − t r a c e ( D B ^ − 1 / 2 P ^ T A P ^ D B ^ − 1 / 2 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) {\displaystyle {\begin{array}{lll}\eta &=&

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  • Pinakes

    Pinakes

    The Pinakes (Ancient Greek: Πίνακες 'tables', plural of πίναξ pinax) is a lost bibliographic work composed by Callimachus (310/305–240 BCE) that is popularly considered to be the first library catalog in the West; its contents were based upon the holdings of the Library of Alexandria during Callimachus's tenure there during the third century BCE. == History == The Library of Alexandria had been founded by Ptolemy I Soter about 306 BCE. The first recorded librarian was Zenodotus of Ephesus. During Zenodotus' tenure, Callimachus, who was never the head librarian, compiled many catalogues/lists, each called Pinakes. His most famous one listed authors and their works; thus he became the first known bibliographer and the scholar who organized the library by authors and subjects about 245 BCE. His work was 120 volumes long. Apollonius of Rhodes was the successor to Zenodotus. Eratosthenes of Cyrene succeeded Apollonius in 235 BCE and compiled his tetagmenos epi teis megaleis bibliothekeis, the 'scheme of the great bookshelves'. In 195 BCE Aristophanes of Byzantium, Eratosthenes' successor, was the librarian and updated the Pinakes, although it is also possible that his work was not a supplement of Callimachus' Pinakes themselves, but an independent polemic against, or commentary upon, their contents. == Description == The collection at the Library of Alexandria contained nearly 500,000 papyrus scrolls, which were grouped together by subject matter and stored in bins. Each bin carried a label with painted tablets hung above the stored papyri. Pinakes was named after these tablets and are a set of index lists. The bins gave bibliographical information for every roll. A typical entry started with a title and also provided the author's name, birthplace, father's name, any teachers trained under, and educational background. It contained a brief biography of the author and a list of the author's publications. The entry had the first line of the work, a summary of its contents, the name of the author, and information about the origin of the roll, as well as any doubts about the genuineness of the ascription. Callimachus' system divided works into six genres of poetry and five sections of prose: rhetoric, law, epic, tragedy, comedy, lyric poetry, history, medicine, mathematics, natural science, and miscellanies. Each category was alphabetized by author. Callimachus composed two other works that were referred as pinakes and were probably somewhat similar in format to the Pinakes (of which they "may or may not be subsections"), but were concerned with individual topics. These are listed by the Suda as: A Chronological Pinax and Description of Didaskaloi from the Beginning and Pinax of the Vocabulary and Treatises of Democritus. == Later bibliographic pinakes == The term pinax was used for bibliographic catalogs beyond Callimachus. For example, Ptolemy-el-Garib's catalog of Aristotle's writings comes to us with the title Pinax (catalog) of Aristotle's writings. == Legacy == The Pinakes proved indispensable to librarians for centuries, and they became a model for organizing knowledge throughout the Mediterranean. Their later influence can be traced to medieval times, even to the Arabic counterpart of the tenth century: Ibn al-Nadim's Al-Fihrist ("Index"). Local variations for cataloging and library classification continued through the late 19th century, when Anthony Panizzi and Melvil Dewey paved the way for more shared and standardized approaches.

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  • SAS Viya

    SAS Viya

    SAS Viya is an artificial intelligence, analytics and data management platform developed by SAS Institute. == History == SAS Viya was released in 2016. The software was containerized with the release of Viya 4 in 2020. Viya has become one of SAS' most widely used platforms during the AI boom, as artificial intelligence becomes more widely used in business and computing. == Technical overview == The platform is cloud-native, and is executed on SAS's Cloud Analytics Services (CAS) engine. It is compatible with open source software, allowing users to build models using open sources tool such as R, Python and Jupyter. It integrates with major large language models like GPT-4 and Gemini Pro. The platform uses econometrics to create predictive models for forecasting scenarios based on complex data. It also has features for detecting algorithmic bias, auditing decisions and monitoring models. It is implemented through a low-code, no-code platform. The software is available on Amazon AWS Marketplace, Google Cloud, Red Hat OpenShift, and on Microsoft Azure Marketplace under a pay-as-you-use model. == Software == SAS Viya has released software as a service (SaaS) modules for creating AI content. These include Viya Workbench, Viya App Factory, Viya Copilot, and SAS Data Maker. The company also develops industry specific models, used by companies including Georgia-Pacific. == Applications == === Banking === The software is also widely used in business, especially in areas such as predictive modelling and fraud detection. === Insurance === SAS Viya is used in insurance for tasks such as actuarial analytics and modelling, as well as regulatory reporting. === Healthcare and life sciences === In 2023, the company introduced SAS Health, a common health data model built on the SAS Viya platform. AstraZeneca has partnered with SAS to use SAS Viya and SAS Life Science Analytics Framework in its delivery and approval processes. In 2024, SAS partnered with the University of Cambridge's Maxwell Center to use SAS Viya for healthcare research and development. === Public sector === SAS Viya is used in partnership with national and local governments to provide services and detect tax fraud. === Education === SAS Viya is used in research and education, particularly studies related to business intelligence, cybersecurity and data management. SAS Institute has partnered with educational institutions such as Appalachian State University, Clemson University, University of Arkansas, Stockholm University, and Marian University, to provide access to and training for using SAS Viya.

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