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
Example-based machine translation
Example-based machine translation (EBMT) is a method of machine translation often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base at run-time. It is essentially a translation by analogy and can be viewed as an implementation of a case-based reasoning approach to machine learning. == Translation by analogy == At the foundation of example-based machine translation is the idea of translation by analogy. When applied to the process of human translation, the idea that translation takes place by analogy is a rejection of the idea that people translate sentences by doing deep linguistic analysis. Instead, it is founded on the belief that people translate by first decomposing a sentence into certain phrases, then by translating these phrases, and finally by properly composing these fragments into one long sentence. Phrasal translations are translated by analogy to previous translations. The principle of translation by analogy is encoded to example-based machine translation through the example translations that are used to train such a system. Other approaches to machine translation, including statistical machine translation, also use bilingual corpora to learn the process of translation. == History == Example-based machine translation was first suggested by Makoto Nagao in 1984. He pointed out that it is especially adapted to translation between two totally different languages, such as English and Japanese. In this case, one sentence can be translated into several well-structured sentences in another language, therefore, it is no use to do the deep linguistic analysis characteristic of rule-based machine translation. == Example == Example-based machine translation systems are trained from bilingual parallel corpora containing sentence pairs like the example shown in the table above. Sentence pairs contain sentences in one language with their translations into another. The particular example shows an example of a minimal pair, meaning that the sentences vary by just one element. These sentences make it simple to learn translations of portions of a sentence. For example, an example-based machine translation system would learn three units of translation from the above example: How much is that X ? corresponds to Ano X wa ikura desu ka. red umbrella corresponds to akai kasa small camera corresponds to chiisai kamera Composing these units can be used to produce novel translations in the future. For example, if we have been trained using some text containing the sentences: President Kennedy was shot dead during the parade. and The convict escaped on July 15th., then we could translate the sentence The convict was shot dead during the parade. by substituting the appropriate parts of the sentences. == Phrasal verbs == Example-based machine translation is best suited for sub-language phenomena like phrasal verbs. Phrasal verbs have highly context-dependent meanings. They are common in English, where they comprise a verb followed by an adverb and/or a preposition, which are called the particle to the verb. Phrasal verbs produce specialized context-specific meanings that may not be derived from the meaning of the constituents. There is almost always an ambiguity during word-to-word translation from source to the target language. As an example, consider the phrasal verb "put on" and its Hindustani translation. It may be used in any of the following ways: Ram put on the lights. (Switched on) (Hindustani translation: Jalana) Ram put on a cap. (Wear) (Hindustani translation: Pahenna)
Xaitment
xaitment is a German-based company that develops and sells artificial intelligence (AI) software to video game developers and simulation developers. The company was founded in 2004 by Dr. Andreas Gerber, and is a spin-off of the German Research Centre for Artificial Intelligence, or DFKI. xaitment has its main office in Quierschied, Germany, and field offices in San Francisco and China. == Products == xaitment currently sells two AI software modules: xaitMap and xaitControl. xaitMap provides runtime libraries and graphical tools for navigation mesh generation (also called NavMesh generation), pathfinding, dynamic collision avoidance, and individual and crowd movement. xaitControl is a finite-state machine for game logic and character behavior modeling that also includes a real-time debugger. On January 11, 2012, xaitment announced that it making its source code for these modules available to "all current and future US and European licensees". On February 22, 2012 xaitment released two new plug-ins, xaitMap and xaitControl for the Unity Game Engine. The full versions are available for PC (Windows and Linux), PlayStation 3, Xbox 360 and Wii. The pathfinding plug-in is available with a Windows dev environment, but can deployed on iOS, Mac, Android and the Unity Web Player. == Partners == xaitment's AI software is currently integrated into the Unity game engine, Havok's Vision Engine, Bohemia Interactive's VBS2 Simulation Engine, GameBase's Gamebryo game engine. == Customers == xaitment sells its AI software products to video game developers and military and civil simulation developers. Current customers include Tencent, gamania, TML Studios, Emobi Games, IP Keys and others. A full list of customers can be found on xaitment's website.
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.
International Olympiad in Artificial Intelligence
The International Olympiad in Artificial Intelligence (IOAI) is an annual International Science Olympiad in the field of artificial intelligence (AI) for secondary education students under the age of 20. The first IOAI was held in Burgas, Bulgaria, in 2024. Each country or territory may send up to two teams, each consisting of up to four students supported by one leader. Participants are selected through a multi-stage National Olympiad in Artificial Intelligence (NOAI) and/or a Regional Olympiad such as the NAOAI or APOAI. Participants at the IOAI compete on an individual basis. As of 2025, there were 61 countries and territories participating in the IOAI. Three hundred students participated in IOAI 2025. As of 2026, 130 countries and territories are accredited for participation in the IOAI. == Competition Structure == The IOAI consists of three contests: the Individual Contest, the Team Challenge, and the GAITE contest. Medals are awarded based solely on the Individual Contest. === Individual Contest === The Individual Contest is the main competition of the IOAI in which contestants compete individually on separate computers and are not permitted to communicate during the contest. Medals are awarded solely on the basis of the total score from the two-day Individual Contest. The Individual Contest consists of two on-site contest days (six hours per day), preceded by an at-home practice round and an on-site practice session. In IOAI 2025, three at-home problems were released for preparation approximately one month before the on-site contest. Results from this at-home round do not affect final results. The first on-site contest day (Individual Contest 1) comprises three tasks as extensions and continuations of the at-home tasks, while the second day (Individual Contest 2) comprises two or three tasks which are novel and different from the at-home tasks. The Individual Contest tasks span various AI domains such as machine learning, natural language processing, and computer vision. The IOAI 2025 contest rules describe tasks as requiring typical machine-learning workflows, including writing code, fitting models on training data, and running inference on test data, using identical local machines and GPU resources (minimum 24 GB RAM). Tasks, datasets, and submissions are handled through a contest platform (Bohrium), including a web-based Jupyter notebook environment for GPU access. Internet access is restricted to a whitelist of documentation sites and an integrated compact large language model accessible within the platform. The use of external APIs are prohibited unless a task explicitly allows them. In IOAI 2025, each contest task was scored up to 100 points and could include multiple subtasks. Scores are normalized using a baseline solution and a maximum score derived from either a Scientific Committee solution or the best contestant submission. Contestants can view only their own scores during the contest; a live scoreboard may be available publicly outside the contest hall but is not permitted to be viewed by contestants during the contest. For non-English-speaking teams, the IOAI hold a translation session beginning three hours before each contest day in which team leaders review and may amend machine-translated task statements; translations must match the English original and are published after the contest. The IOAI committee also enforces quarantine restrictions during these translation sessions, where neither contestants or team leaders may not use cell phones, laptops, and other communication devices. === Team Challenge === The Team Challenge is a team-based component of the IOAI. The results of this part do not affect the distribution of medals. The IOAI 2025 rules describe it as a “creative and AI-oriented challenge” in which a team's contestants sit together and cooperate, with the format varying by year. In IOAI 2024, teams worked with existing AI image and video generation tools to produce a visual result. In IOAI 2025, teams were assigned to program a robot to complete various tasks. === GAITE Contest === The GAITE (Global AI Talent Empowerment) contest is a simplified version of the individual contest with a separate scoreboard, where participants may ask for hints. It is designed for countries and territories with limited International Science Olympiads history, and it awards alternative prizes instead of medals. == Awards Distribution == The top 50% of the participants in the individual contest receive gold, silver and bronze medals in ratio of 1:2:3, respectively. The top three individuals receive honorary trophies. As in other International Science Olympiads, if an individual is in the top 50% on one of the days, but does not receive a medal, they receive an honorary mention during the awards ceremony. The GAITE contest has similar cutoff logic, but receives a reward instead of a medal. The top three teams in the Team Challenge receive trophies. == National selection and regional competitions == National delegations are selected through country-level qualification processes referred to as National Olympiads in Artificial Intelligence (NOAI) or equivalent, which are widely known for their low success rates. Although the total number of participants worldwide is not published, available data indicate exceptionally competitive national pools; for example, Brazil reports over 716,000 competitors, while Russia reports more than 72,000. In addition, Regional Olympiads (for example, APOAI or NAOAI) provide continent-level competition and preparation platforms in most regions. === National Selection (National Olympiads in Artificial Intelligence) === Participating countries and territories select their students for the IOAI through a National Olympiad in Artificial Intelligence (NOAI) or an equivalent process. The names of these selection processes differ by country, but almost all of them (excluding newer countries participating in the GAITE contest) have in common that the process comprises multiple and/or extremely rigorous selection stages. United States / Canada – The USA–North America AI Olympiad (USAAIO) is a three-round process including an invitational in-person round and a subsequent selection camp, after which a national delegation is selected for IOAI. Russia – The Russian Olympiad in Artificial Intelligence is organized as a multi-stage process (training, qualification, main round, final). Organizers reported 72,316 registrations for the training round and 52,260 registrations for the qualifying round in one season, with tasks spanning mathematics, algorithms/programming, and machine learning; 977 students were disqualified following plagiarism checks. Japan – Japan's national selection consists of multiple stages, beginning with the Japan Olympiad in Artificial Intelligence (JOAI), a large-scale Kaggle-style competition. High-performing participants advance through additional assessment stages, including written solution reports and technical interviews. From this process, eight students are selected for the APOAI team, with four ultimately chosen to represent Japan at the IOAI. Brazil – Brazil's National Olympiad in Artificial Intelligence (ONIA) is conducted as a large competition which consists of progressive rounds of evaluation. It identifies 28 top students from over 716,000 competitors, four of which are selected for the IOAI. The competition is held in four phases across two cycles, including a two-step third phase and a final training-and-evaluation phase that selects a four-student national team. Singapore – Singapore's national Olympiad consists of two rounds: an online preliminary round (300 MCQs in 3 hours) selects the top 150 performers to advance to the final assessment, which includes both theory questions and Python programming tasks. Additional training and selection may follow the finals for top performers. Poland – The Polish AI Olympiad adopts a two-stage structure: an open online first stage (at-home tasks) and a second-stage competitive camp with 30 selected participants competing for a four-person IOAI team. France – The Olympiades Françaises d'Intelligence Artificielle (OFIA), organized by France-IOI, follow a three-stage structure consisting of an open online qualification round, a second selection round, and a multi-day national training camp and final in Paris. Bangladesh – The Bangladesh AI Olympiad (BdAIO) selects competitors in three rounds: the online preliminary round, the national finals, and the team selection camp. In 2025, 406 participants competed in the national finals. Norway – The Norwrgian AI Olympiad (NOKI) is a three-stage selection system; however, unlike other countries, its first two rounds are shared with the Norwegian Informatics Olympiad. The national Olympiad reports 1,180 participants in the first round. Hong Kong – The national Olympiad reported more than 800 preliminary-round entrants, narrowing through multiple rounds to 25 finalists, with a subsequent
Read Along
Read Along, formerly known as Bolo, is an Android language-learning app for children developed by Google for the Android operating system. The application was released on the Play Store on March 7, 2019. It features a character named Diya helping children learn to read through illustrated stories. It has the facility to learn English and Indian major languages i.e. Hindi, Bengali, Tamil, Telugu, Marathi and Urdu, as well as Spanish, Portuguese and Arabic. == Technology == The app uses text-to-speech technology, through which the character named Dia reads the story, as well as speech-to-text technology, which mechanically identifies the matches between the text and the reading of the user. The story of Chhota Bheem and Katha Kids was added in September 2019. In April 2020, a new version of the application was released. In September 2020, it added Arabic language to its language option. A web version was launched in August 2022.
Really Simple Licensing
Really Simple Licensing (RSL) is an open content licensing standard that allows web publishers to set terms for web crawlers gathering training data for generative AI use. It was launched on September 10, 2025 and is managed by the nonprofit RSL Collective, co-founded by RSS co-creator Eckart Walther and former Ask.com CEO Doug Leeds. Participating companies at launch include Reddit, Yahoo, and Medium. Publishers can implement the RSL standard by adding licensing terms to their robots.txt files.