AI Art Name Generator Free

AI Art Name Generator Free — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Description logic

  Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that

  Read more →
• 

  Surrogate model

  A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. == Goals == The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively: Sample selection (also known as sequential design, optimal experimental design (OED) or active learning) Construction of the surrogate model and optimizing the model parameters (i.e., bias-variance tradeoff) Appraisal of the accuracy of the surrogate. The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. A systematic data representation during training can improve model scalability, thereby reducing the need for expensive simulations. Various design of experiments (DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model. == Types of surrogate models == Popular surrogate modeling approaches are: polynomial response surfaces; kriging; more generalized Bayesian approaches; gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks and Bayesian networks. Other methods recently explored include Fourier surrogate modeling , random forests, convolutional neural networks, and generative adversarial networks. For some problems, the nature of the true function is not known a priori, and therefore it is not clear which surrogate model will be the most accurate one. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. In these cases, physics-based surrogates such as space-mapping based models are commonly used. == Invariance properties == Recently proposed comparison-based surrogate models (e.g., ranking support vector machines) for evolutionary algorithms, such as CMA-ES, allow preservation of some invariance properties of surrogate-assisted optimizers: Invariance with respect to monotonic transformations of the function (scaling) Invariance with respect to orthogonal transformations of the search space (rotation) == Applications == An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation). In surrogate model-based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually takes the form of the following search/update procedure. Initial sample selection (the experiments and/or simulations to be run) Construct surrogate model Search surrogate model (the model can be searched extensively, e.g., using a genetic algorithm, as it is cheap to evaluate) Run and update experiment/simulation at new location(s) found by search and add to sample Iterate steps 2 to 4 until out of time or design is "good enough" Depending on the type of surrogate used and the complexity of the problem, the process may converge on a local or global optimum, or perhaps none at all. In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated. == Surrogate modeling software == Surrogate Modeling Toolbox (SMT: https://github.com/SMTorg/smt) is a Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing spline interpolation. Python library SAMBO Optimization supports sequential optimization with arbitrary models, with tree-based models and Gaussian process models built in. Surrogates.jl is a Julia packages which offers tools like random forests, radial basis methods and kriging. == Surrogate-Assisted Evolutionary Algorithms (SAEAs) == SAEAs are an advanced class of optimization techniques that integrate evolutionary algorithms (EAs) with surrogate models. In traditional EAs, evaluating the fitness of candidate solutions often requires computationally expensive simulations or experiments. SAEAs address this challenge by building a surrogate model, which is a computationally inexpensive approximation of the objective function or constraint functions. The surrogate model serves as a substitute for the actual evaluation process during the evolutionary search. It allows the algorithm to quickly estimate the fitness of new candidate solutions, thereby reducing the number of expensive evaluations needed. This significantly speeds up the optimization process, especially in cases where the objective function evaluations are time-consuming or resource-intensive. SAEAs typically involve three main steps: (1) building the surrogate model using a set of initial sampled data points, (2) performing the evolutionary search using the surrogate model to guide the selection, crossover, and mutation operations, and (3) periodically updating the surrogate model with new data points generated during the evolutionary process to improve its accuracy. By balancing exploration (searching new areas in the solution space) and exploitation (refining known promising areas), SAEAs can efficiently find high-quality solutions to complex optimization problems. They have been successfully applied in various fields, including engineering design, machine learning, and computational finance, where traditional optimization methods may struggle due to the high computational cost of fitness evaluations.

  Read more →
• 

  AI Overviews

  AI Overviews is an artificial intelligence (AI) feature integrated into Google Search that produces AI-generated summaries of search results. The feature has been criticized for its inaccuracy and for reducing website traffic. == History and development == AI Overviews were first introduced as part of Google's Search Generative Experience (SGE), which was unveiled at the Google I/O conference in May 2023. In May 2024 at Google I/O 2024, the feature was rebranded as AI Overviews and launched in the United States. The introduction of AI Overviews was seen as a strategic move to compete with other generative AI advancements, including OpenAI's ChatGPT. By August 2024, AI Overviews was rolled out to several other countries, including the United Kingdom, India, Japan, Brazil, Mexico, and Indonesia, with support for multiple languages. In October 2024, Google expanded the feature globally, making it available in over 100 countries. In December 2024, Botify x Demandsphere released findings stating that when AI Overviews and featured snippets appear together on the search engine results page, they take up approximately 67.1% of the screen on desktop and 75.7% on mobile. Even if content is ranking in the #1 position, it may not be visible to consumers if other visual elements on the results page are more prominent. In March 2025, Google started testing an "AI Mode", where the search results page is AI-generated. The company was also considering adding advertisements to the AI Mode, as they already exist in AI Overviews. As of May 2025, AI Overviews are available in over 200 countries and territories and in more than 40 languages. As of March 2026, Google AI Overviews appear on more than 48% of total Google Search queries, compared to just 6.49% in the previous year (58% year-over-year growth). == Functionality == The AI Overviews feature uses large language models to generate summaries from web content. The overviews are designed to be concise, providing a snapshot of relevant information about the queried topic. Google allows users to adjust the language complexity in summaries, offering both simplified and detailed options. The overviews also include links to sources. According to a June 2025 study by Semrush, the most cited source is Quora, followed by Reddit. == Reception == The feature has faced criticism for inaccuracies, including instances where erroneous or nonsensical content was generated. Depending on what is searched for, the overview may also consist of hallucinated content, such as when searching for idioms that do not exist. In May 2024, Google temporarily restricted the AI tool after it provided suggestions that were seen as nonsensical and harmful, such as telling users to eat rocks or apply glue on pizza. Concerns were also raised by content publishers, who feared a decline in web traffic as users relied on the summaries instead of visiting source websites. A Google patent from 2026 raised the concern of webmasters that Google could entirely replace the landing page of websites by an AI optimized copy of the website in its results. There is also apprehension about the ethical implications of AI-driven content aggregation, including its impact on intellectual property rights and the visibility of smaller content providers. The European Commission announced in December 2025 that they were investigating whether AI Overviews breached European competition law. In response, Google has stated its commitment to improve content validation and refine the algorithms used to filter unreliable information. Google implemented measures to prioritize link placement within AI Overviews, aiming to balance user convenience with the needs of content creators. In January 2026, Google restricted AI Overviews on certain health-related searches following an investigation by The Guardian. == Lawsuits == On February 24, 2025, Chegg sued Alphabet over the AI Overviews feature, claiming that it was leading to students preferring "low-quality, unverified AI summaries", thus violating antitrust law. Chegg also said it was considering either a sale or a take-private transaction. In September 2025, Penske Media Corporation, the publisher of Rolling Stone and The Hollywood Reporter, sued Google, claiming that AI Overviews illegally regurgitate content from their websites and drive off potential site visitors by always appearing on top of the search results while leaving little incentive to see the linked sources. The company stated that "the future of digital media and [...] its integrity [...] is threatened by Google's current actions", alleging that 20% of searches that link to Penske-owned websites show AI Overviews and that the figure is expected to rise. Google spokesperson José Castañeda called the claims "meritless" and stated that "AI Overviews send traffic to a greater diversity of sites." In 2026, Canadian musician Ashley MacIsaac filed a lawsuit against Google claiming that the AI Overview feature had wrongly stated that MacIsaac had been convicted of numerous criminal offences and was on the sex offender registry. He claims this incorrect information led to the cancellation of a December 2025 gig organized by the Sipekne'katik First Nation.

  Read more →
• 

  Hierarchical Risk Parity

  Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners and Cornell University. HRP is a probabilistic graph-based alternative to the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample. HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets. Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions. == Key features == HRP portfolios have been proposed as a robust alternative to traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated with quadratic optimizers: numerical instability, excessive concentration in a small number of assets, and poor out-of-sample performance. HRP leverages techniques from graph theory and machine learning to construct diversified portfolios using only the information embedded in the covariance matrix. Unlike quadratic programming methods, HRP does not require the covariance matrix to be invertible. Consequently, HRP remains applicable even in cases where the covariance matrix is ill-conditioned or singular—conditions under which standard optimizers fail. Monte Carlo simulations indicate that HRP achieves lower out-of-sample variance than CLA, despite the fact that minimizing variance is the explicit optimization objective of CLA. Furthermore, HRP portfolios exhibit lower realized risk compared to those generated by traditional risk parity methodologies. Empirical backtests have demonstrated that HRP would have historically outperformed conventional portfolio construction techniques. Algorithms within the HRP framework are characterized by the following features: Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations. This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network. Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio. This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates. Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix. This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high. == The problem: Markowitz's Curse == Portfolio construction is perhaps the most recurrent financial problem. On a daily basis, investment managers must build portfolios that incorporate their views and forecasts on risks and returns. Despite the theoretical elegance of Markowitz's mean-variance framework, its practical implementation is hindered by several limitations that undermine the reliability of solutions derived from the Critical Line Algorithm (CLA). A principal concern is the high sensitivity of optimal portfolios to small perturbations in expected returns: even minor forecasting errors can result in significantly different allocations (Michaud, 1998). Given the inherent difficulty of producing accurate return forecasts, numerous researchers have advocated for approaches that forgo expected returns entirely and instead rely solely on the covariance structure of asset returns. This has given rise to risk-based allocation methods, among which risk parity is a widely cited example (Jurczenko, 2015). While eliminating return forecasts mitigates some instability, it does not eliminate it. Quadratic programming techniques employed in portfolio optimization require the inversion of a positive-definite covariance matrix, meaning all eigenvalues must be strictly positive. When the matrix is numerically ill-conditioned—that is, when the ratio of its largest to smallest eigenvalue (its condition number) is large—matrix inversion becomes unreliable and prone to significant numerical errors (Bailey and López de Prado, 2012). The condition number of a covariance, correlation, or any symmetric (and thus diagonalizable) matrix is defined as the absolute value of the ratio between its largest and smallest eigenvalues in modulus. The figure on the right presents the sorted eigenvalues of several correlation matrices; the condition number is represented by the ratio of the first to last eigenvalues in each sequence. A diagonal correlation matrix, which is equal to its own inverse, exhibits the minimum possible condition number. As the number of correlated (or multicollinear) assets in a portfolio increases, the condition number rises. At high levels, this leads to severe numerical instability, whereby slight modifications in any matrix entry may result in drastically different inverses. This phenomenon, often referred to as Markowitz’s curse, encapsulates the paradox wherein increased correlation among assets heightens the theoretical need for diversification, yet simultaneously increases the likelihood of unstable optimization outcomes. Consequently, the potential benefits of diversification are frequently overshadowed by estimation errors. These problems are exacerbated as the dimensionality of the covariance matrix increases. The estimation of each covariance term consumes degrees of freedom, and in general, a minimum of 1 2 N ( N + 1 ) {\displaystyle {\frac {1}{2}}N(N+1)} independent and identically distributed (IID) observations is required to estimate a non-singular covariance matrix of dimension N {\displaystyle N} . For example, constructing an invertible covariance matrix of dimension 50 necessitates at least five years of daily IID observations. However, empirical evidence suggests that the correlation structure of financial assets is highly unstable over such extended periods. These difficulties are highlighted by the observation that even naïve allocation strategies—such as equally weighted portfolios—have frequently outperformed both mean-variance and risk-based optimizations in out-of-sample tests (De Miguel et al., 2009). == The solution: Hierarchical Risk Parity == The HRP algorithm addresses Markowitz's curse in three steps: Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure. Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure. Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance. === Step 1: Hierarchical clustering === Given a T × N {\displaystyle T\times N} matrix of asset returns X {\displaystyle X} , where each column represents a time series of returns for one of N {\displaystyle N} assets over T {\displaystyle T} time periods, a hierarchical clustering process can be used to construct a tree-based representation of asset relationships. First, we compute the N × N {\displaystyle N\times N} correlation matrix ρ = ρ i , j i , j = 1 . . . N {\displaystyle \rho ={\rho _{i,j}}\;{i,j=1\;...\;N}} , where ρ i , j = c o r r ( X i , X j ) {\displaystyle \rho _{i,j}=\mathrm {corr} (X_{i},X_{j})} . From this, a pairwise distance matrix D = d i , j {\displaystyle D={d_{i,j}}} is defined using the transformation: d i , j = 1 2 ( 1 − ρ i , j ) {\displaystyle d_{i,j}={\sqrt {{\frac {1}{2}}(1-\rho _{i,j})}}} This distance function defines a proper metric space, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Next, a secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between the distance profiles of two assets: d ~ i , j = ∑ n = 1 N ( d n , i − d n , j ) 2 {\displaystyle {\tilde {d}}_{i,j}={\sqrt {\sum _{n=1}^{N}(d_{n,i}-d_{n,j})^{2}}}} While d i , j {\displaystyle d_{i,j}} reflects correlation-based proximity between two assets, d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} quantifies dissimilarity across the entire system, as it depends on all pairwise distances. Hierarchical clustering proceeds by identifying the pair ( i , j ) {\displaystyle (i,j)} with the smallest value of d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} (for i ≠ j {\displaystyle i\neq j} ), and forming a new cluster u [ 1 ] = ( i , j ) {\displaystyle u[1]=(i,j)} .

  Read more →
• 

  Princh

  Princh is a Danish software company, which is headquartered in Aarhus, Denmark. Founded in 2015, Princh develops cloud printing and electronic payment products. The company is headquartered in the city of Aarhus. While utilizing a smartphone or web app, users can locate a nearby printer to their current location, get directions to access said printer, and/or authorize a print and pay for the print job in question. The product is available as a native mobile apps for Android and iOS, as well as on web and desktop products for businesses and libraries. The app connects a network of printer owners and users around the world. Princh supports an array of printable files. == History == The company was founded in 2015. The company is currently based in the southern part of Aarhus. The Princh printing service was officially launched on June 23, 2015. Currently, Princh is available as a service in a multitude of locations such as print shops, libraries, hotels, or universities. Princh is a popular printing and payment product among libraries and can among other places be found in Denmark, Sweden, Norway, Germany, United Kingdom, United States, and Canada. == How it works == With the Princh app, users will be able to locate their nearest printer. Once the user is at the printer, the user chooses the document to be printed out and shares it with the Princh app. The user then selects the desired nearby printer entering the printer ID number or scanning the QR-code located on top of the printer, pays electronically and the print job is processed by the printer. Printer owners get access to a personal control panel where they can set printing prices and monitor all Princh activity for their business. == Notes and references ==

  Read more →
• 

  EM algorithm and GMM model

  In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model. == Background == In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the control group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia. x {\displaystyle x} is a random vector such as x := ( red blood cell volume , red blood cell hemoglobin concentration ) {\displaystyle x:={\big (}{\text{red blood cell volume}},{\text{red blood cell hemoglobin concentration}}{\big )}} , and from medical studies it is known that x {\displaystyle x} are normally distributed in each group, i.e. x ∼ N ( μ , Σ ) {\displaystyle x\sim {\mathcal {N}}(\mu ,\Sigma )} . z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to the Anemia group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to the control group. Also z ∼ Categorical ⁡ ( k , ϕ ) {\displaystyle z\sim \operatorname {Categorical} (k,\phi )} where k = 2 {\displaystyle k=2} , ϕ j ≥ 0 , {\displaystyle \phi _{j}\geq 0,} and ∑ j = 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ⁡ ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i)}=1}^{k}p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)p(z^{(i)};\phi )} As the z i {\displaystyle z_{i}} for each x i {\displaystyle x_{i}} are known, the log likelihood function can be simplified as below: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ p ( x ( i ) ∣ z ( i ) ; μ , Σ ) + log ⁡ p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j } x ( i ) ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \mu _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}x^{(i)}}{\sum _{i=1}^{m}1\left\{z^{(i)}=j\right\}}}} Σ j = ∑ i = 1 m 1 { z ( i ) = j } ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \Sigma _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}(x^{(i)}-\mu _{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. not observed), with unlabeled scenario, the expectation maximization algorithm is needed to estimate z {\displaystyle z} as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed. In machine learning, the latent variable z {\displaystyle z} is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x i {\displaystyle x_{i}} is the known data, while ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } are the parameter of the model. With the EM algorithm, some underlying pattern z {\displaystyle z} in the data x i {\displaystyle x_{i}} can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important. == EM algorithm in GMM == The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of z ( i ) {\displaystyle z^{(i)}} of the E-step. These two steps are repeated until convergence is reached. The algorithm in GMM is: Repeat until convergence: 1. (E-step) For each i , j {\displaystyle i,j} , set w j ( i ) := p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) {\displaystyle w_{j}^{(i)}:=p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)} 2. (M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m w j ( i ) {\displaystyle \Sigma _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}\left(x^{(i)}-\mu _{j}\right)\left(x^{(i)}-\mu _{j}\right)^{T}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} With Bayes' rule, the following result is obtained by the E-step: p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{k}p\left(x^{(i)}|z^{(i)}=l;\mu ,\Sigma \right)p\left(z^{(i)}=l;\phi \right)}}} According to GMM setting, these following formulas are obtained: p ( x ( i ) | z ( i ) = j ; μ , Σ ) = 1 ( 2 π ) n / 2 | Σ j | 1 / 2 exp ⁡ ( − 1 2 ( x ( i ) − μ j ) T Σ j − 1 ( x ( i ) − μ j ) ) {\displaystyle p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.

  Read more →
• 

  AI data center

  An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w

  Read more →
• 

  Lynda Soderholm

  Lynda Soderholm is a physical chemist at the U.S. Department of Energy's (DOE) Argonne National Laboratory with a specialty in f-block elements. She is a senior scientist and the lead of the Actinide, Geochemistry & Separation Sciences Theme within Argonne's Chemical Sciences and Engineering Division. Her specific role is the Separation Science group leader within Heavy Element Chemistry and Separation Science (HESS), directing basic research focused on low-energy methods for isolating lanthanide and actinide elements from complex mixtures. She has made fundamental contributions to understanding f-block chemistry and characterizing f-block elements. Soderholm became a Fellow of the American Association for the Advancement of Science (AAAS) in 2013, and is also an Argonne Distinguished Fellow. == Early life and education == Soderholm was awarded her PhD in 1982 by McMaster University under the direction of Prof John Greedan. Her dissertation focused on characterizing the structural and magnetic properties of a series of ternary f-ion oxides. After graduating, she was awarded a NATO postdoctoral fellow at the Centre national de la recherche scientifique in France from 1982 until 1985. After a short postdoctoral appointment as an Argonne postdoctoral fellow she was promoted to staff scientist the same year. Over several years, she moved up the ranks, becoming a senior chemist in 2001. She was also an adjunct professor at the University of Notre Dame from 2003 until 2007. In 2021, Soderholm was appointed interim Division Director for the Chemical Sciences and Engineering Division. == Career and research == === Uncovering structure of Yttrium-123 Superconductor === Early in her career, Soderholm focused on the characterizing the magnetic and electronic behavior of compounds containing f-ions (lanthanides and actinides) with a focus on high-Tc materials, compounds that are superconducting under usually high temperatures. She was part of the research group that first determined the structure of YBa2Cu3O7. Their discovery formed the foundation for the further developments in the broad field of superconductivity. === Understanding f-ion speciation in solution === Continuing her interest in the f-elements, Soderholm shifted her focus from solid-state materials to nanoparticles and solutions, taking advantage of advances in X-ray structural probes made available by synchrotron facilities. Building on her earlier work using neutron scattering, her team became the first to discover that plutonium exists in solution as tiny, well-defined nanoparticles. This work solved a longstanding problem in understanding transport of plutonium in the environment and resulted in the development of a new, patented approach to separating plutonium during nuclear reprocessing. === Using machine learning to evaluate molecular structures === Soderholm's more recent projects use machine learning to understand the influence of complex molecular structuring in solutions, in connection with low-energy processes for separation of f-block elements from complex mixtures. == Awards and honors == University of Chicago Board of Governors' Distinguished Performance Award, 2009. Fellow of the American Association for the Advancement of Science, 2013. Argonne Distinguished Fellow, 2016 DOE materials sciences research competition for Outstanding Scientific Accomplishments in Solid State Physics, 1987. == Select publications == Beno, M. A.; Soderholm, L.; Capone, D. W., II; Hinks, D. G.; Jorgensen, J. D.; Grace, J. D.; Schuller, I. K.; Segre, C. U.; Zhang, K., Structure of the single-phase high-temperature superconductor yttrium barium copper oxide (YBa2Cu3O7−δ). Appl. Phys. Lett. 1987, 51 (1), 57–9. Soderholm, L.; Zhang, K.; Hinks, D. G.; Beno, M. A.; Jorgensen, J. D.; Segre, C. U.; Schuller, I. K., Incorporation of praseodymium in YBa2Cu3O7−δ: electronic effects on superconductivity. Nature (London) 1987, 328 (6131), 604–5. Antonio, M. R.; Williams, C. W.; Soderholm, L., Berkelium redox speciation. Radiochim. Acta 2002, 90 (12), 851–856. Soderholm, L.; Skanthakumar, S.; Neuefeind, J., Determination of actinide speciation in solution using high-energy X-ray scattering. Anal. Bioanal. Chem. 2005, 383 (1), 48–55. Forbes, T. Z.; Burns, P. C.; Skanthakumar, S.; Soderholm, L., Synthesis, structure, and magnetism of Np2O5. J. Am. Chem. Soc. 2007, 129 (10), 2760–2761. Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C., The structure of the plutonium oxide nanocluster [Pu38O56Cl54(H2O)8]14-. Angew. Chem., Int. Ed. 2008, 47 (2), 298–302. Jensen, M. P.; Gorman-Lewis, D.; Aryal, B.; Paunesku, T.; Vogt, S.; Rickert, P. G.; Seifert, S.; Lai, B.; Woloschak, G. E.; Soderholm, L., An iron-dependent and transferrin-mediated cellular uptake pathway for plutonium. Nat. Chem. Biol. 2011, 7 (8), 560–565. Wilson, R. E.; Skanthakumar, S.; Soderholm, L., Separation of Plutonium Oxide Nanoparticles and Colloids. Angew. Chem., Int. Ed. 2011, 50 (47), 11234–11237. Knope, K. E.; Soderholm, L., Solution and solid-state structural chemistry of actinide hydrates and their hydrolysis and condensation products. Chem. Rev. 2013, 113 (2), 944–994. Luo, G.; Bu, W.; Mihaylov, M.; Kuzmenko, I.; Schlossman, M. L.; Soderholm, L., X-ray reflectivity reveals a nonmonotonic ion-density profile perpendicular to the surface of ErCl3 aqueous solutions. J. Phys. Chem. C 2013, 117 (37), 19082–19090. Jin, G. B.; Lin, J.; Estes, S. L.; Skanthakumar, S.; Soderholm, L., Influence of countercation hydration enthalpies on the formation of molecular complexes: A thorium-nitrate example. J. Am. Chem. Soc. 2017, 139 (49), 18003–18008. == Patents == Solvent extraction system for plutonium colloids and other oxide nano-particles, (2016).

  Read more →
• 

  Stairstep interpolation

  In the field of image processing, stairstep interpolation is a widely employed method technique for interpolating pixels after enlarging an image. The fundamental concept is to interpolate multiple times, in small increments, using any interpolation algorithm that is better than nearest-neighbor interpolation such as; bilinear interpolation, and bicubic interpolation. A common scenario is to interpolate an image by using a bicubic interpolation which increases the image size by no more than 10% (110% of the original size) at a time until the desired size is reached. Fred Miranda, a developer, popularized this method by creating and developing several Photoshop plug-ins that incorporate this technique. == Example ==

  Read more →
• 

  Learning curve (machine learning)

  In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. Typically, the number of training epochs or training set size is plotted on the x-axis, and the value of the loss function (and possibly some other metric such as the cross-validation score) on the y-axis. Synonyms include error curve, experience curve, improvement curve and generalization curve. More abstractly, learning curves plot the difference between learning effort and predictive performance, where "learning effort" usually means the number of training samples, and "predictive performance" means accuracy on testing samples. Learning curves have many useful purposes in ML, including: choosing model parameters during design, adjusting optimization to improve convergence, and diagnosing problems such as overfitting (or underfitting). Learning curves can also be tools for determining how much a model benefits from adding more training data, and whether the model suffers more from a variance error or a bias error. If both the validation score and the training score converge to a certain value, then the model will no longer significantly benefit from more training data. == Formal definition == When creating a function to approximate the distribution of some data, it is necessary to define a loss function L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} to measure how good the model output is (e.g., accuracy for classification tasks or mean squared error for regression). We then define an optimization process which finds model parameters θ {\displaystyle \theta } such that L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} is minimized, referred to as θ ∗ {\displaystyle \theta ^{}} . === Training curve for amount of data === If the training data is { x 1 , x 2 , … , x n } , { y 1 , y 2 , … y n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\},\{y_{1},y_{2},\dots y_{n}\}} and the validation data is { x 1 ′ , x 2 ′ , … x m ′ } , { y 1 ′ , y 2 ′ , … y m ′ } {\displaystyle \{x_{1}',x_{2}',\dots x_{m}'\},\{y_{1}',y_{2}',\dots y_{m}'\}} , a learning curve is the plot of the two curves i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ) , Y i ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}),Y_{i})} i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ′ ) , Y i ′ ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}'),Y_{i}')} where X i = { x 1 , x 2 , … x i } {\displaystyle X_{i}=\{x_{1},x_{2},\dots x_{i}\}} === Training curve for number of iterations === Many optimization algorithms are iterative, repeating the same step (such as backpropagation) until the process converges to an optimal value. Gradient descent is one such algorithm. If θ i ∗ {\displaystyle \theta _{i}^{}} is the approximation of the optimal θ {\displaystyle \theta } after i {\displaystyle i} steps, a learning curve is the plot of i ↦ L ( f θ i ∗ ( X , Y ) ( X ) , Y ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X),Y)} i ↦ L ( f θ i ∗ ( X , Y ) ( X ′ ) , Y ′ ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X'),Y')}

  Read more →
• 

  Relational data mining

  Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.

  Read more →
• 

  Halite AI Programming Competition

  Halite is an open-source computer programming contest developed by the hedge fund/tech firm Two Sigma in partnership with a team at Cornell Tech. Programmers can see the game environment and learn everything they need to know about the game. Participants are asked to build bots in whichever language they choose to compete on a two-dimensional virtual battle field. == History == Benjamin Spector and Michael Truell created the first Halite competition in 2016, before partnering with Two Sigma later that year. === Halite I === Halite I asked participants to conquer territory on a grid. It launched in November 2016 and ended in February 2017. Halite I attracted about 1,500 players. === Halite II === Halite II was similar to Halite I, but with a space-war theme. It ran from October 2017 until January 2018. The second installment of the competition attracted about 6,000 individual players from more than 100 countries. Among the participants were professors, physicists and NASA engineers, as well as high school and university students. === Halite III === Halite III launched in mid-October 2018. It ran from October 2018 to January 2019, with an ocean themed playing field. Players were asked to collect and manage Halite, an energy resource. By the end of the competition, Halite III included more than 4000 players and 460 organizations. === Halite IV === Halite IV was hosted by Kaggle, and launched in mid-June 2020.

  Read more →
• 

  Active learning (machine learning)

  Active learning is a special case of machine learning in which a learning algorithm can interactively query a human user (or some other information source) to label new data points with the desired outputs. The human user must possess expertise in the problem domain, including the ability to consult authoritative sources when necessary. In statistics literature, it is sometimes also called optimal experimental design. The information source is also called teacher or oracle. There are situations in which unlabeled data is abundant but manual labeling is expensive. In such a scenario, learning algorithms can actively query the teacher for labels. Since the learner chooses the examples, the number of examples to learn a concept can often be much lower than the number required in normal supervised learning. However, there is a risk that the algorithm is overwhelmed by uninformative examples. Recent developments are dedicated to multi-label active learning, hybrid active learning and active learning in a single-pass (on-line) context, combining concepts from the field of machine learning (e.g. conflict and ignorance) with adaptive, incremental learning policies in the field of online machine learning. Using active learning allows for faster development of a machine learning algorithm, when comparative updates would require a quantum or super computer. Large-scale active learning projects may benefit from crowdsourcing frameworks such as Amazon Mechanical Turk that include many humans in the active learning loop. == Definitions == Let T be the total set of all data under consideration. For example, in a protein engineering problem, T would include all proteins that are known to have a certain interesting activity and all additional proteins that one might want to test for that activity. During each iteration, i, T is broken up into three subsets T K , i {\displaystyle \mathbf {T} _{K,i}} : Data points where the label is known. T U , i {\displaystyle \mathbf {T} _{U,i}} : Data points where the label is unknown. T C , i {\displaystyle \mathbf {T} _{C,i}} : A subset of TU,i that is chosen to be labeled. Most of the current research in active learning involves the best method to choose the data points for TC,i. == Scenarios == Pool-based sampling: In this approach, which is the most well known scenario, the learning algorithm attempts to evaluate the entire dataset before selecting data points (instances) for labeling. It is often initially trained on a fully labeled subset of the data using a machine-learning method such as logistic regression or SVM that yields class-membership probabilities for individual data instances. The candidate instances are those for which the prediction is most ambiguous. Instances are drawn from the entire data pool and assigned a confidence score, a measurement of how well the learner "understands" the data. The system then selects the instances for which it is the least confident and queries the teacher for the labels. The theoretical drawback of pool-based sampling is that it is memory-intensive and is therefore limited in its capacity to handle enormous datasets, but in practice, the rate-limiting factor is that the teacher is typically a (fatiguable) human expert who must be paid for their effort, rather than computer memory. Stream-based selective sampling: Here, each consecutive unlabeled instance is examined one at a time with the machine evaluating the informativeness of each item against its query parameters. The learner decides for itself whether to assign a label or query the teacher for each datapoint. As contrasted with Pool-based sampling, the obvious drawback of stream-based methods is that the learning algorithm does not have sufficient information, early in the process, to make a sound assign-label-vs ask-teacher decision, and it does not capitalize as efficiently on the presence of already labeled data. Therefore, the teacher is likely to spend more effort in supplying labels than with the pool-based approach. Membership query synthesis: This is where the learner generates synthetic data from an underlying natural distribution. For example, if the dataset are pictures of humans and animals, the learner could send a clipped image of a leg to the teacher and query if this appendage belongs to an animal or human. This is particularly useful if the dataset is small. The challenge here, as with all synthetic-data-generation efforts, is in ensuring that the synthetic data is consistent in terms of meeting the constraints on real data. As the number of variables/features in the input data increase, and strong dependencies between variables exist, it becomes increasingly difficult to generate synthetic data with sufficient fidelity. For example, to create a synthetic data set for human laboratory-test values, the sum of the various white blood cell (WBC) components in a white blood cell differential must equal 100, since the component numbers are really percentages. Similarly, the enzymes alanine transaminase (ALT) and aspartate transaminase (AST) measure liver function (though AST is also produced by other tissues, e.g., lung, pancreas) A synthetic data point with AST at the lower limit of normal range (8–33 units/L) with an ALT several times above normal range (4–35 units/L) in a simulated chronically ill patient would be physiologically impossible. == Query strategies == Algorithms for determining which data points should be labeled can be organized into a number of different categories, based upon their purpose: Balance exploration and exploitation: the choice of examples to label is seen as a dilemma between the exploration and the exploitation over the data space representation. This strategy manages this compromise by modelling the active learning problem as a contextual bandit problem. For example, Bouneffouf et al. propose a sequential algorithm named Active Thompson Sampling (ATS), which, in each round, assigns a sampling distribution on the pool, samples one point from this distribution, and queries the oracle for this sample point label. Expected model change: label those points that would most change the current model. Expected error reduction: label those points that would most reduce the model's generalization error. Exponentiated Gradient Exploration for Active Learning: In this paper, the author proposes a sequential algorithm named exponentiated gradient (EG)-active that can improve any active learning algorithm by an optimal random exploration. Uncertainty sampling: label those points for which the current model is least certain as to what the correct output should be. Query by committee: a variety of models are trained on the current labeled data, and vote on the output for unlabeled data; label those points for which the "committee" disagrees the most Querying from diverse subspaces or partitions: When the underlying model is a forest of trees, the leaf nodes might represent (overlapping) partitions of the original feature space. This offers the possibility of selecting instances from non-overlapping or minimally overlapping partitions for labeling. Variance reduction: label those points that would minimize output variance, which is one of the components of error. Conformal prediction: predicts that a new data point will have a label similar to old data points in some specified way and degree of the similarity within the old examples is used to estimate the confidence in the prediction. Mismatch-first farthest-traversal: The primary selection criterion is the prediction mismatch between the current model and nearest-neighbour prediction. It targets on wrongly predicted data points. The second selection criterion is the distance to previously selected data, the farthest first. It aims at optimizing the diversity of selected data. User-centered labeling strategies: Learning is accomplished by applying dimensionality reduction to graphs and figures like scatter plots. Then the user is asked to label the compiled data (categorical, numerical, relevance scores, relation between two instances). A wide variety of algorithms have been studied that fall into these categories. While the traditional AL strategies can achieve remarkable performance, it is often challenging to predict in advance which strategy is the most suitable in a particular situation. In recent years, meta-learning algorithms have been gaining in popularity. Some of them have been proposed to tackle the problem of learning AL strategies instead of relying on manually designed strategies. A benchmark which compares 'meta-learning approaches to active learning' to 'traditional heuristic-based Active Learning' may give intuitions if 'Learning active learning' is at the crossroads == Minimum marginal hyperplane == Some active learning algorithms are built upon support-vector machines (SVMs) and exploit the structure of the SVM to determine which data points to label. Such methods usually calculate the margin, W, of each u

  Read more →
• 

  Artificial intelligence controversies

  The controversies surrounding artificial intelligence encompass a broad range of public, academic, and political debates regarding the societal effects of artificial intelligence (AI). These debates intensified particularly in the late 2010s and 2020s, coinciding with an accelerated period of development known as the AI boom. While advocates emphasize the technology's potential to solve complex problems and enhance human quality of life, detractors highlight a wide array of dangers and challenges. These include concerns over ethics, plagiarism and theft, fraud, safety and alignment, environmental impacts, technological unemployment, and the spread of misinformation. It also covers severe future or theoretical challenges, such as the emergence of artificial superintelligence and existential risks. == 2016 == === Microsoft Tay chatbot (2016) === On March 23, 2016, Microsoft released Tay, a chatbot designed to mimic the language patterns of a 19-year-old American girl and learn from interactions with Twitter users. Soon after its launch, Tay began posting racist, sexist, and otherwise inflammatory tweets after Twitter users deliberately taught it offensive phrases and exploited its "repeat after me" capability. Examples of controversial outputs included Holocaust denial and calls for genocide using racial slurs. Within 16 hours of its release, Microsoft suspended the Twitter account, deleted the offensive tweets, and stated that Tay had suffered from a "coordinated attack by a subset of people" that "exploited a vulnerability." Tay was briefly and accidentally re-released on March 30 during testing, after which it was permanently shut down. Microsoft CEO Satya Nadella later stated that Tay "has had a great influence on how Microsoft is approaching AI" and taught the company the importance of taking accountability. == 2022 == === Voiceverse NFT plagiarism scandal (2022) === On January 14, 2022, voice actor Troy Baker announced a partnership with Voiceverse, a blockchain-based company that marketed proprietary AI voice cloning technology as non-fungible tokens (NFT), triggering immediate backlash over environmental concerns, fears that AI could displace human voice actors, and concerns about fraud. Later that same day, the pseudonymous creator of 15.ai—a free, non-commercial AI voice synthesis research project—revealed through server logs that Voiceverse had used 15.ai to generate voice samples, pitch-shifted them to make them unrecognizable, and falsely marketed them as their own proprietary technology before selling them as NFTs; the developer of 15.ai had previously stated that they had no interest in incorporating NFTs into their work. Voiceverse confessed within an hour and stated that their marketing team had used 15.ai without attribution while rushing to create a demo. News publications and AI watchdog groups universally characterized the incident as theft stemming from generative artificial intelligence. === Théâtre D'opéra Spatial (2022) === On August 29, 2022, Jason Michael Allen won first place in the "emerging artist" (non-professional) division of the "Digital Arts/Digitally-Manipulated Photography" category of the Colorado State Fair's fine arts competition with Théâtre D'opéra Spatial, a digital artwork created using the AI image generator Midjourney, Adobe Photoshop, and AI upscaling tools, becoming one of the first images made using generative AI to win such a prize. Allen disclosed his use of Midjourney when submitting, though the judges did not know it was an AI tool but stated they would have awarded him first place regardless. While there was little contention about the image at the fair, reactions to the win on social media were negative. On September 5, 2023, the United States Copyright Office ruled that the work was not eligible for copyright protection as the human creative input was de minimis and that copyright rules "exclude works produced by non-humans." == 2023 == === Statements on AI risk (2023) === On March 22, 2023, the Future of Life Institute published an open letter calling on "all AI labs to immediately pause for at least 6 months the training of AI systems more powerful than GPT-4", citing risks such as AI-generated propaganda, extreme automation of jobs, human obsolescence, and a society-wide loss of control. The letter, published a week after the release of OpenAI's GPT-4, asserted that current large language models were "becoming human-competitive at general tasks". It received more than 30,000 signatures, including academic AI researchers and industry CEOs such as Yoshua Bengio, Stuart Russell, Elon Musk, Steve Wozniak and Yuval Noah Harari. The letter was criticized for diverting attention from more immediate societal risks such as algorithmic biases, with Timnit Gebru and others arguing that it amplified "some futuristic, dystopian sci-fi scenario" instead of current problems with AI. On May 30, 2023, the Center for AI Safety released a one-sentence statement signed by hundreds of artificial intelligence experts and other notable figures: "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war." Signatories included Turing laureates Geoffrey Hinton and Yoshua Bengio, as well as the scientific and executive leaders of several major AI companies, including Sam Altman, Demis Hassabis, and Bill Gates. The statement prompted responses from political leaders, including UK Prime Minister Rishi Sunak, who retweeted it with a statement that the UK government would look carefully into it, and White House Press Secretary Karine Jean-Pierre, who commented that AI "is one of the most powerful technologies that we see currently in our time." Skeptics, including from Human Rights Watch, argued that scientists should focus on known risks of AI instead of speculative future risks. === Removal of Sam Altman from OpenAI (2023) === On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman, stating that "the board no longer has confidence in his ability to continue leading OpenAI." The removal was precipitated by employee concerns about his handling of artificial intelligence safety and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors, including a letter signed by 745 of OpenAI's 770 employees threatening mass resignations if the board did not resign. The removal and subsequent reinstatement caused widespread reactions, including Microsoft's stock falling nearly three percent following the initial announcement and then rising over two percent to an all-time high after Altman was hired to lead a Microsoft AI research team before his reinstatement. The incident also prompted investigations from the Competition and Markets Authority and the Federal Trade Commission into Microsoft's relationship with OpenAI. == 2024 == === Taylor Swift deepfake pornography controversy (2024) === In late January 2024, sexually explicit AI-generated deepfake images of Taylor Swift were proliferated on X, with one post reported to have been seen over 47 million times before its removal. Disinformation research firm Graphika traced the images back to 4chan, while members of a Telegram group had discussed ways to circumvent censorship safeguards of AI image generators to create pornographic images of celebrities. The images prompted responses from anti-sexual assault advocacy groups, US politicians, and Swifties. Microsoft CEO Satya Nadella called the incident "alarming and terrible." X briefly blocked searches of Swift's name on January 27, 2024, and Microsoft enhanced its text-to-image model safeguards to prevent future abuse. On January 30, US senators Dick Durbin, Lindsey Graham, Amy Klobuchar, and Josh Hawley introduced a bipartisan bill that would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made without consent. === Google Gemini image generation controversy (2024) === In February 2024, social media users reported that Google's Gemini chatbot was generating images that featured people of color and women in historically inaccurate contexts—such as Vikings, Nazi soldiers, and the Founding Fathers—and refusing prompts to generate images of white people. The images were derided on social media, including by conservatives who cited them as evidence of Google's "wokeness", and criticized by Elon Musk, who denounced Google's products as biased and racist. In response, Google paused Gemini's ability to generate images of people. Google executive Prabhakar Raghavan released a statement explaining that Gemini had "overcompensate[d]" in its efforts to strive for diversity and acknowledging that the images were "embarrassing and wrong". Google CEO Sundar Pichai called the incident offensive and unacceptable in an internal memo, promising struc

  Read more →
• 

  ELMo

  ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.

  Read more →