Asynchronous module definition (AMD) is a specification for the programming language JavaScript. It defines an application programming interface (API) that defines code modules and their dependencies, and loads them asynchronously if desired. Implementations of AMD provide the following benefits: Website performance improvements. AMD implementations load smaller JavaScript files, and then only when they are needed. Fewer page errors. AMD implementations allow developers to define dependencies that must load before a module is executed, so the module does not try to use outside code that is not available yet.... In addition to loading multiple JavaScript files at runtime, AMD implementations allow developers to encapsulate code in smaller, more logically-organized files, in a way similar to other programming languages such as Java. For production and deployment, developers can concatenate and minify JavaScript modules based on an AMD API into one file, the same as traditional JavaScript. AMD provides some CommonJS interoperability. It allows for using a similar exports and require() interface in the code, although its own define() interface is more basal and preferred. The AMD specification is implemented by Dojo Toolkit, RequireJS, and other libraries.
Cepstral mean and variance normalization
Cepstral mean and variance normalization (CMVN) is a computationally efficient normalization technique for robust speech recognition. The performance of CMVN is known to degrade for short utterances. This is due to insufficient data for parameter estimation and loss of discriminable information as all utterances are forced to have zero mean and unit variance. CMVN minimizes distortion by noise contamination for robust feature extraction by linearly transforming the cepstral coefficients to have the same segmental statistics. Cepstral Normalization has been effective in the CMU Sphinx for maintaining a high level of recognition accuracy over a wide variety of acoustical environments. == Cepstral Normalization Techniques == There are multiple algorithms that achieve Cepstral Normalization in different ways. === Fixed codeword-dependent cepstral normalization (FCDCN) === FCDCN was developed to provide a form of compensation that provides greater recognition accuracy than SDCN but in a more computationally-efficient manner than the CDCN algorithm. The FCDCN algorithm applies an additive correction that depends on the instantaneous SNR of the input (like SDCN), but that can also vary from codeword to codeword (like CDCN). === Multiple Fixed Codeword-dependent Cepstral Normalization (MFCDCN) === MFCDCN is a simple extension of FCDCN algorithm that does not need environment specific training. In MFCDCN, compensation vectors are pre-computed in parallel for a set of target environments, using the FCDCN algorithm. === Incremental Multiple Fixed Codeword-dependent Cepstral Normalization (IMFCDCN) === While environment selection for the compensation vectors of MFCDCN is generally performed on an utterance-by-utterance basis, IMFCFCN improves on it by allowing the classification process to make use of cepstral vectors from previous utterances in a given session. == Cepstral Noise Subtraction == Automatic speech recognition (ASR) describes the steps of transcribing speech utterances represented as acoustic wave forms to written words. As is, CMVN has been used in different applications as this technique has proven to provide better speech recognitions results in different environments. CMVN has the capabilities to reduce differences between test and training data produced by channel distortions and colorizations . CMVN has also been found to be able to reduce differences in feature representation between speakers can also partly reduce the influence of background noise.
Privacy Lost
Privacy Lost is a 2023 short science fiction film directed by Peter Stoel and Robert Berger. It follows a family using augmented reality (AR) and artificial intelligence (AI) devices capable of reading emotional states, raising questions about privacy and manipulation. == Premise == Privacy Lost follows a family using AR glasses that capture and interpret emotions in real time. As the parents argue in a restaurant, their emotional states and even hidden feelings become visible through these glasses. An AI-driven waiter adapts its appearance for each family member, employing emotional data to influence their decisions. == Cast == Brian Kant as Waiter Michael Krass as Husband Estelle Levinson as Waitress Thor van der Linden as Scotty Carlijn van Ramshorst as Wife == Production == Filming took place at HeadQ Productions, a virtual studio located in Amsterdam. The creators sought to depict a near-future scenario in which real-time emotion analysis becomes part of daily interactions. The film was screened at the Augmented World Expo (AWE), where it was noted for its thematic focus on AI-driven manipulation and emotional tracking. The depiction of AR glasses and AI characters integrates modern visual effects to show how devices might analyze emotional responses in real time. It also depicts how AI-driven interactions could influence consumer decisions, pointing to concerns over potential misuse. == Themes == Privacy Lost focuses on the intersection of advanced AI capabilities and AR environments, showing how real-time emotional analysis can be leveraged for targeted persuasion. The film aims to highlight the social and ethical implications of emerging AR and AI technologies, underlining how establishing clear regulatory frameworks for them is necessary to protect individual privacy, govern the storage of emotion-based data, and prevent manipulative practices. Critics describe the film’s theme as dystopian and note that such a reality is unlikely to occur in the near future. However, despite the exaggerated scenario, the film emphasizes the importance of a responsible approach by developers toward emerging technologies.
Computing Machinery and Intelligence
"Computing Machinery and Intelligence" is a paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in Mind, was the first to introduce his concept of what is now known as the Turing test to the general public. Turing's paper considers the question "Can machines think?" Turing says that since the words "think" and "machine" cannot clearly be defined, we should "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words." To achieve this objective, Turing proposes a three-step approach. First, he identifies a simple and unambiguous concept to substitute for the term "think." Second, he delineates the specific "machines" under consideration. Third, armed with these tools, he poses a new question related to the first, which he believes he can answer in the affirmative. == Turing's test == Rather than trying to determine if a machine is thinking, Turing suggests we should ask if the machine can win a game, called the "Imitation Game". The original Imitation game, that Turing described, is a simple party game involving three players. Player A is a man, player B is a woman and player C (who plays the role of the interrogator) can be of either sex. In the Imitation Game, player C is unable to see either player A or player B (and knows them only as X and Y), and can communicate with them only through written notes or any other form that does not give away any details about their gender. By asking questions of player A and player B, player C tries to determine which of the two is the man and which is the woman. Player A's role is to trick the interrogator into making the wrong decision, while player B attempts to assist the interrogator in making the right one. Turing proposes a variation of this game that involves the computer: We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?" So the modified game becomes one that involves three participants in isolated rooms: a computer (which is being tested), a human, and a (human) judge. The human judge can converse with both the human and the computer by typing into a terminal. Both the computer and the human try to convince the judge that they are the human. If the judge cannot consistently tell which is which, then the computer wins the 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. As Stevan Harnad notes, the question has become "Can machines do what we (as thinking entities) can do?" In other words, Turing is no longer asking whether a machine can "think"; he is asking whether a machine can act indistinguishably from the way a thinker acts. This question avoids the difficult philosophical problem of pre-defining the verb "to think" and focuses instead on the performance capacities that being able to think makes possible, and how a causal system can generate them. Since Turing introduced his test, it has been both highly influential and widely criticised, and has become an important concept in the philosophy of artificial intelligence. Some of its criticisms, such as John Searle's Chinese room, are themselves controversial. Some have taken Turing's question to have been "Can a computer, communicating over a teleprinter, fool a person into believing it is human?" but it seems clear that Turing was not talking about fooling people but about generating human cognitive capacity. == Digital machines == Turing also notes that we need to determine which "machines" we wish to consider. He points out that a human clone, while man-made, would not provide a very interesting example. Turing suggested that we should focus on the capabilities of digital machinery—machines which manipulate the binary digits of 1 and 0, rewriting them into memory using simple rules. He gave two reasons. First, there is no reason to speculate whether or not they can exist. They already did in 1950. Second, digital machinery is "universal". Turing's research into the foundations of computation had proved that a digital computer can, in theory, simulate the behaviour of any other digital machine, given enough memory and time. (This is the essential insight of the Church–Turing thesis and the universal Turing machine.) Therefore, if any digital machine can "act like it is thinking", then every sufficiently powerful digital machine can. Turing writes, "all digital computers are in a sense equivalent." This allows the original question to be made even more specific. Turing now restates the original question as "Let us fix our attention on one particular digital computer C. Is it true that by modifying this computer to have an adequate storage, suitably increasing its speed of action, and providing it with an appropriate programme, C can be made to play satisfactorily the part of A in the imitation game, the part of B being taken by a man?" Hence, Turing states that the focus is not on "whether all digital computers would do well in the game nor whether the computers that are presently available would do well, but whether there are imaginable computers which would do well". What is more important is to consider the advancements possible in the state of our machines today regardless of whether we have the available resource to create one or not. == Nine common objections == Having clarified the question, Turing turned to answering it: he considered the following nine common objections, which include all the major arguments against artificial intelligence raised in the years since his paper was first published. Religious Objection: This states that thinking is a function of man's immortal soul; therefore, a machine cannot think. "In attempting to construct such machines," wrote Turing, "we should not be irreverently usurping His power of creating souls, any more than we are in the procreation of children: rather we are, in either case, instruments of His will providing mansions for the souls that He creates." 'Heads in the Sand' Objection: "The consequences of machines thinking would be too dreadful. Let us hope and believe that they cannot do so." This thinking is popular among intellectual people, as they believe superiority derives from higher intelligence and the possibility of being overtaken is a threat (as machines have efficient memory capacities and processing speed, machines exceeding the learning and knowledge capabilities are highly probable). This objection is a fallacious appeal to consequences, confusing what should not be with what can or cannot be (Wardrip-Fruin, 56). The Mathematical Objection: This objection uses mathematical theorems, such as Gödel's incompleteness theorem, to show that there are limits to what questions a computer system based on logic can answer. Turing suggests that humans are too often wrong themselves and pleased at the fallibility of a machine. (This argument would be made again by philosopher John Lucas in 1961 and physicist Roger Penrose in 1989, and later would be called Penrose–Lucas argument.) Argument From Consciousness: This argument, suggested by Professor Geoffrey Jefferson in his 1949 Lister Oration (acceptance speech for his 1948 award of Lister Medal) states that "not until a machine can write a sonnet or compose a concerto because of thoughts and emotions felt, and not by the chance fall of symbols, could we agree that machine equals brain." Turing replies by saying that we have no way of knowing that any individual other than ourselves experiences emotions, and that therefore we should accept the test. He adds, "I do not wish to give the impression that I think there is no mystery about consciousness ... [b]ut I do not think these mysteries necessarily need to be solved before we can answer the question [of whether machines can think]." (This argument, that a computer can't have conscious experiences or understanding, would be made in 1980 by philosopher John Searle in his Chinese room argument. Turing's reply is now known as the "other minds reply". See also Can a machine have a mind? in the philosophy of AI.) Arguments from various disabilities. These arguments all have the form "a computer will never do X". Turing offers a selection:Be kind, resourceful, beautiful, friendly, have initiative, have a sense of humour, tell right from wrong, make mistakes, fall in love, enjo
Midjourney
Midjourney is a generative artificial intelligence program and service created and hosted by the San Francisco–based "independent research lab" Midjourney, Inc. Midjourney generates images from natural language descriptions, called prompts, similar to OpenAI's DALL-E and Stability AI's Stable Diffusion. It is one of the technologies of the AI boom. The tool was launched into open beta on July 12, 2022. The Midjourney team is led by David Holz, who co-founded Leap Motion. Holz told The Register in August 2022 that the company was already profitable. Users generate images with Midjourney using Discord bot commands or the official website. == History == Midjourney, Inc. was founded in San Francisco, California, by David Holz, previously a co-founder of Leap Motion. The Midjourney image generation platform entered open beta on July 12, 2022. On March 14, 2022, the Midjourney Discord server launched with a request to post high-quality photographs to Twitter and Reddit for systems training. === Model versions === The company has been working on improving its algorithms, releasing new model versions every few months. Version 2 of their algorithm was launched in April 2022, and version 3 on July 25. On November 5, 2022, the alpha iteration of version 4 was released to users. Starting from the 4th version, MJ models were trained on Google TPUs. On March 15, 2023, the alpha iteration of version 5 was released. The 5.1 model is more opinionated than version 5, applying more of its own stylization to images, while the 5.1 RAW model adds improvements while working better with more literal prompts. The version 5.2 included a new "aesthetics system", and the ability to "zoom out" by generating surroundings to an existing image. On December 21, 2023, the alpha iteration of version 6 was released. The model was trained from scratch over a nine month period. Support was added for better text rendition and a more literal interpretation of prompts. == Functionality == Midjourney is accessible through a Discord bot or by accessing their website. Users can use Midjourney through Discord either through their official Discord server, by directly messaging the bot, or by inviting the bot to a third-party server. To generate images, users use the /imagine command and type in a prompt; the bot then returns a set of four images, which users are given the option to upscale. To generate images on the website, users initially needed to have generated at least 1,000 images through the bot; this limitation has since been removed. === Vary (Region) + remix feature === Midjourney released a Vary (Region) feature on September 5, 2023, as part of MidJourney V5.2. This feature allows users to select a specific area of an image and apply variations only to that region while keeping the rest of the image unchanged. === Midjourney web interface === Midjourney introduced its web interface to make its tools more accessible, moving beyond its initial reliance on Discord. This web-based platform was launched in August 2024 alongside the release of Midjourney version 6.1. The web editor consolidates tools such as image editing, panning, zooming, region variation, and inpainting into a single interface. The introduction of the web interface also syncs conversations between Midjourney's Discord channels and web rooms, further enhancing collaboration across both platforms. This shift was in response to growing competition from other AI image generation platforms like Adobe Firefly and Google’s Imagen, which had already launched as native web apps with integration into popular design tools. === Image Weight === This feature lets users control how much influence an uploaded image has on the final output. By adjusting the "image weight" parameter, users can prioritize either the content of the prompt or the characteristics of the image. For instance, setting a higher weight will ensure that the generated result closely follows the image's structure and details, while a lower weight allows the text prompt to have more influence over the final output. === Style Reference === With Style Reference, users can upload an image to use as a stylistic guide for their creation. This tool enables MidJourney to extract the style—whether it is the color palette, texture, or overall atmosphere—from the reference image and apply it to a newly generated image. The feature allows users to fine-tune the aesthetics of their creations by integrating specific artistic styles or moods. === Character Reference === The Character Reference feature allows for a more targeted approach in defining characters. Users can upload an image of a character, and the system uses that image as a reference to generate similar characters in the output. This feature is particularly useful in maintaining consistency in appearance for characters across different images. == Uses == Midjourney's founder, David Holz, told The Register that artists use Midjourney for rapid prototyping of artistic concepts to show to clients before starting work themselves. The advertising industry quickly adopted AI tools such as Midjourney, DALL-E, and Stable Diffusion to create original content and brainstorm ideas. Architects have described using the software to generate mood boards for the early stages of projects, as an alternative to searching Google Images. === Notable usage and controversy === The program was used by the British magazine The Economist to create the front cover for an issue in June 2022. In Italy, the leading newspaper Corriere della Sera published a comic created with Midjourney by writer Vanni Santoni in August 2022. Charlie Warzel used Midjourney to generate two images of Alex Jones for Warzel's newsletter in The Atlantic. The use of an AI-generated cover was criticised by people who felt it was taking jobs from artists. Warzel called his action a mistake in an article about his decision to use generated images. Last Week Tonight with John Oliver included a 10-minute segment on Midjourney in an episode broadcast in August 2022. A Midjourney image called Théâtre D'opéra Spatial won first place in the digital art competition at the 2022 Colorado State Fair. Jason Allen, who wrote the prompt that led Midjourney to generate the image, printed the image onto a canvas and entered it into the competition using the name Jason M. Allen via Midjourney. Other digital artists were upset by the news. Allen was unapologetic, insisting that he followed the competition's rules. The two category judges were unaware that Midjourney used AI to generate images, although they later said that had they known this, they would have awarded Allen the top prize anyway. In December 2022, Midjourney was used to generate the images for an AI-generated children's book that was created over a weekend. Titled Alice and Sparkle, the book features a young girl who builds a robot that becomes self-aware. The creator, Ammaar Reeshi, used Midjourney to generate a large number of images, from which he chose 13 for the book. Both the product and process drew criticism. One artist wrote that "the main problem... is that it was trained off of artists' work. It's our creations, our distinct styles that we created, that we did not consent to being used." In 2023, the realism of AI-based text-to-image generators, such as Midjourney, DALL-E, or Stable Diffusion, reached such a high level that it led to a significant wave of viral AI-generated photos. Widespread attention was gained by a Midjourney-generated photo of Pope Francis wearing a white puffer coat, the fictional arrest of Donald Trump, and a hoax of an attack on the Pentagon, as well as the usage in professional creative arts. Research has suggested that the images Midjourney generates can be biased. For example, even neutral prompts in one study returned unequal results on the aspects of gender, skin color, and location. A study by researchers at the nonprofit group Center for Countering Digital Hate found the tool to be easy to use to generate racist and conspiratorial images. In October 2023, Rest of World reported that Midjourney tends to generate images based on national stereotypes. In 2024, a Frontiers journal published a paper which contained gibberish figures generated with Midjourney, one of which was a diagram of a rat with large testicles and a large penis towering over himself. The paper was retracted a day after the images went viral on Twitter. ==== Content moderation and censorship in Midjourney ==== Prior to May 2023, Midjourney implemented a moderation mechanism predicated on a banned word system. This method prohibited the use of language associated with explicit content, such as sexual or pornographic themes, as well as extreme violence. Moreover, the system also banned certain individual words, including those of religious and political figures, such as Allah or General Secretary of the Chinese Communist Party Xi Jinping. This practice occasionally stirred controversy due to perceiv
Kernel embedding of distributions
In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space Ω {\displaystyle \Omega } on which a sensible kernel function (measuring similarity between elements of Ω {\displaystyle \Omega } ) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in R d {\displaystyle \mathbb {R} ^{d}} , discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song, Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in. The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings. Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages: Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables Intermediate density estimation is not needed Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel) If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms. == Definitions == Let X {\displaystyle X} denote a random variable with domain Ω {\displaystyle \Omega } and distribution P {\displaystyle P} . Given a symmetric, positive-definite kernel k : Ω × Ω → R {\displaystyle k:\Omega \times \Omega \rightarrow \mathbb {R} } the Moore–Aronszajn theorem asserts the existence of a unique RKHS H {\displaystyle {\mathcal {H}}} on Ω {\displaystyle \Omega } (a Hilbert space of functions f : Ω → R {\displaystyle f:\Omega \to \mathbb {R} } equipped with an inner product ⟨ ⋅ , ⋅ ⟩ H {\displaystyle \langle \cdot ,\cdot \rangle _{\mathcal {H}}} and a norm ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} ) for which k {\displaystyle k} is a reproducing kernel, i.e., in which the element k ( x , ⋅ ) {\displaystyle k(x,\cdot )} satisfies the reproducing property ⟨ f , k ( x , ⋅ ) ⟩ H = f ( x ) ∀ f ∈ H , ∀ x ∈ Ω . {\displaystyle \langle f,k(x,\cdot )\rangle _{\mathcal {H}}=f(x)\qquad \forall f\in {\mathcal {H}},\quad \forall x\in \Omega .} One may alternatively consider x ↦ k ( x , ⋅ ) {\displaystyle x\mapsto k(x,\cdot )} as an implicit feature mapping φ : Ω → H {\displaystyle \varphi :\Omega \rightarrow {\mathcal {H}}} (which is therefore also called the feature space), so that k ( x , x ′ ) = ⟨ φ ( x ) , φ ( x ′ ) ⟩ H {\displaystyle k(x,x')=\langle \varphi (x),\varphi (x')\rangle _{\mathcal {H}}} can be viewed as a measure of similarity between points x , x ′ ∈ Ω . {\displaystyle x,x'\in \Omega .} While the similarity measure is linear in the feature space, it may be highly nonlinear in the original space depending on the choice of kernel. === Kernel embedding === The kernel embedding of the distribution P {\displaystyle P} in H {\displaystyle {\mathcal {H}}} (also called the kernel mean or mean map) is given by: μ X := E [ k ( X , ⋅ ) ] = E [ φ ( X ) ] = ∫ Ω φ ( x ) d P ( x ) {\displaystyle \mu _{X}:=\mathbb {E} [k(X,\cdot )]=\mathbb {E} [\varphi (X)]=\int _{\Omega }\varphi (x)\ \mathrm {d} P(x)} If P {\displaystyle P} allows a square integrable density p {\displaystyle p} , then μ X = E k p {\displaystyle \mu _{X}={\mathcal {E}}_{k}p} , where E k {\displaystyle {\mathcal {E}}_{k}} is the Hilbert–Schmidt integral operator. A kernel is characteristic if the mean embedding μ : { family of distributions over Ω } → H {\displaystyle \mu :\{{\text{family of distributions over }}\Omega \}\to {\mathcal {H}}} is injective. Each distribution can thus be uniquely represented in the RKHS and all statistical features of distributions are preserved by the kernel embedding if a characteristic kernel is used. === Empirical kernel embedding === Given n {\displaystyle n} training examples { x 1 , … , x n } {\displaystyle \{x_{1},\ldots ,x_{n}\}} drawn independently and identically distributed (i.i.d.) from P , {\displaystyle P,} the kernel embedding of P {\displaystyle P} can be empirically estimated as μ ^ X = 1 n ∑ i = 1 n φ ( x i ) {\displaystyle {\widehat {\mu }}_{X}={\frac {1}{n}}\sum _{i=1}^{n}\varphi (x_{i})} === Joint distribution embedding === If Y {\displaystyle Y} denotes another random variable (for simplicity, assume the co-domain of Y {\displaystyle Y} is also Ω {\displaystyle \Omega } with the same kernel k {\displaystyle k} which satisfies ⟨ φ ( x ) ⊗ φ ( y ) , φ ( x ′ ) ⊗ φ ( y ′ ) ⟩ = k ( x , x ′ ) k ( y , y ′ ) {\displaystyle \langle \varphi (x)\otimes \varphi (y),\varphi (x')\otimes \varphi (y')\rangle =k(x,x')k(y,y')} ), then the joint distribution P ( x , y ) ) {\displaystyle P(x,y))} can be mapped into a tensor product feature space H ⊗ H {\displaystyle {\mathcal {H}}\otimes {\mathcal {H}}} via C X Y = E [ φ ( X ) ⊗ φ ( Y ) ] = ∫ Ω × Ω φ ( x ) ⊗ φ ( y ) d P ( x , y ) {\displaystyle {\mathcal {C}}_{XY}=\mathbb {E} [\varphi (X)\otimes \varphi (Y)]=\int _{\Omega \times \Omega }\varphi (x)\otimes \varphi (y)\ \mathrm {d} P(x,y)} By the equivalence between a tensor and a linear map, this joint embedding may be interpreted as an uncentered cross-covariance operator C X Y : H → H {\displaystyle {\mathcal {C}}_{XY}:{\mathcal {H}}\to {\mathcal {H}}} from which the cross-covariance of functions f , g ∈ H {\displaystyle f,g\in {\mathcal {H}}} can be computed as Cov ( f ( X ) , g ( Y ) ) := E [ f ( X ) g ( Y ) ] − E [ f ( X ) ] E [ g ( Y ) ] = ⟨ f , C X Y g ⟩ H = ⟨ f ⊗ g , C X Y ⟩ H ⊗ H {\displaystyle \operatorname {Cov} (f(X),g(Y)):=\mathbb {E} [f(X)g(Y)]-\mathbb {E} [f(X)]\mathbb {E} [g(Y)]=\langle f,{\mathcal {C}}_{XY}g\rangle _{\mathcal {H}}=\langle f\otimes g,{\mathcal {C}}_{XY}\rangle _{{\mathcal {H}}\otimes {\mathcal {H}}}} Given n {\displaystyle n} pairs of training examples { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}} drawn i.i.d. from P {\displaystyle P} , we can also empirically estimate the joint distribution kernel embedding via C ^ X Y = 1 n ∑ i = 1 n φ ( x i ) ⊗ φ ( y i ) {\displaystyle {\widehat {\mathcal {C}}}_{XY}={\frac {1}{n}}\sum _{i=1}^{n}\varphi (x_{i})\otimes \varphi (y_{i})} === Conditional distribution embedding === Given a conditional distribution P ( y ∣ x ) , {\displaystyle P(y\mid x),} one can define the corresponding RKHS embedding as μ Y ∣ x = E [ φ ( Y ) ∣ X ] = ∫ Ω φ ( y ) d P ( y ∣ x ) {\displaystyle \mu _{Y\mid x}=\mathbb {E} [\varphi (Y)\mid X]=\int _{\Omega
Question (short story)
"Question" is a science fiction short story by American writer Isaac Asimov. The story first appeared in the March 1955 issue of Computers and Automation (thought to be the first computer magazine), and was reprinted in the April 30, 1957, issue of Science World. It is the first of a loosely connected series of stories concerning a fictional supercomputer called Multivac. The story concerns two technicians who are servicing Multivac, and their argument over whether or not the machine is truly intelligent and able to think. Multivac, however, supplies the answer on its own. After the reprint, another author, Robert Sherman Townes, noticed the climax in the last sentence was very similar to one of his own stories, "Problem for Emmy" (Startling Stories, June 1952), and wrote to Asimov about it. After searching in his library, Asimov did find the original story and, although he did not recall having read it, admitted that the endings were pretty similar. He then replied to Townes, apologizing and promising the story would never again be published, and it never was. Asimov mentioned "Question" in an editorial called "Plagiarism" which appeared in the August 1985 issue of Asimov's Science Fiction (although he did not mention Townes' name or the title of either story). "Plagiarism" was reprinted in Asimov's collection Gold (1995).