In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same squareness parameter ϵ 2 {\displaystyle \epsilon _{2}} , and whose vertical sections through the center are superellipses with the squareness parameter ϵ 1 {\displaystyle \epsilon _{1}} . It is a generalization of an ellipsoid, which is a special case when ϵ 1 = ϵ 2 = 1 {\displaystyle \epsilon _{1}=\epsilon _{2}=1} . Superellipsoids as computer graphics primitives were popularized by Alan H. Barr (who used the name "superquadrics" to refer to both superellipsoids and supertoroids). In modern computer vision and robotics literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Superellipsoids have a rich shape vocabulary, including cuboids, cylinders, ellipsoids, octahedra and their intermediates. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. The main advantage of describing objects and environment with superellipsoids is its conciseness and expressiveness in shape. Furthermore, a closed-form expression of the Minkowski sum between two superellipsoids is available. This makes it a desirable geometric primitive for robot grasping, collision detection, and motion planning. == Special cases == A handful of notable mathematical figures can arise as special cases of superellipsoids given the correct set of values, which are depicted in the above graphic: Cylinder Sphere Steinmetz solid Bicone Regular octahedron Cube, as a limiting case where the exponents tend to infinity Piet Hein's supereggs are also special cases of superellipsoids. == Formulas == === Basic (normalized) superellipsoid === The basic superellipsoid is defined by the implicit function f ( x , y , z ) = ( x 2 ϵ 2 + y 2 ϵ 2 ) ϵ 2 / ϵ 1 + z 2 ϵ 1 {\displaystyle f(x,y,z)=\left(x^{\frac {2}{\epsilon _{2}}}+y^{\frac {2}{\epsilon _{2}}}\right)^{\epsilon _{2}/\epsilon _{1}}+z^{\frac {2}{\epsilon _{1}}}} The parameters ϵ 1 {\displaystyle \epsilon _{1}} and ϵ 2 {\displaystyle \epsilon _{2}} are positive real numbers that control the squareness of the shape. The surface of the superellipsoid is defined by the equation: f ( x , y , z ) = 1 {\displaystyle f(x,y,z)=1} For any given point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} , the point lies inside the superellipsoid if f ( x , y , z ) < 1 {\displaystyle f(x,y,z)<1} , and outside if f ( x , y , z ) > 1 {\displaystyle f(x,y,z)>1} . Any "parallel of latitude" of the superellipsoid (a horizontal section at any constant z between -1 and +1) is a Lamé curve with exponent 2 / ϵ 2 {\displaystyle 2/\epsilon _{2}} , scaled by a = ( 1 − z 2 ϵ 1 ) ϵ 1 2 {\displaystyle a=(1-z^{\frac {2}{\epsilon _{1}}})^{\frac {\epsilon _{1}}{2}}} , which is ( x a ) 2 ϵ 2 + ( y a ) 2 ϵ 2 = 1. {\displaystyle \left({\frac {x}{a}}\right)^{\frac {2}{\epsilon _{2}}}+\left({\frac {y}{a}}\right)^{\frac {2}{\epsilon _{2}}}=1.} Any "meridian of longitude" (a section by any vertical plane through the origin) is a Lamé curve with exponent 2 / ϵ 1 {\displaystyle 2/\epsilon _{1}} , stretched horizontally by a factor w that depends on the sectioning plane. Namely, if x = u cos θ {\displaystyle x=u\cos \theta } and y = u sin θ {\displaystyle y=u\sin \theta } , for a given θ {\displaystyle \theta } , then the section is ( u w ) 2 ϵ 1 + z 2 ϵ 1 = 1 , {\displaystyle \left({\frac {u}{w}}\right)^{\frac {2}{\epsilon _{1}}}+z^{\frac {2}{\epsilon _{1}}}=1,} where w = ( cos 2 ϵ 2 θ + sin 2 ϵ 2 θ ) − ϵ 2 2 . {\displaystyle w=(\cos ^{\frac {2}{\epsilon _{2}}}\theta +\sin ^{\frac {2}{\epsilon _{2}}}\theta )^{-{\frac {\epsilon _{2}}{2}}}.} In particular, if ϵ 2 {\displaystyle \epsilon _{2}} is 1, the horizontal cross-sections are circles, and the horizontal stretching w {\displaystyle w} of the vertical sections is 1 for all planes. In that case, the superellipsoid is a solid of revolution, obtained by rotating the Lamé curve with exponent 2 / ϵ 1 {\displaystyle 2/\epsilon _{1}} around the vertical axis. === Superellipsoid === The basic shape above extends from −1 to +1 along each coordinate axis. The general superellipsoid is obtained by scaling the basic shape along each axis by factors a x {\displaystyle a_{x}} , a y {\displaystyle a_{y}} , a z {\displaystyle a_{z}} , the semi-diameters of the resulting solid. The implicit function is F ( x , y , z ) = ( ( x a x ) 2 ϵ 2 + ( y a y ) 2 ϵ 2 ) ϵ 2 ϵ 1 + ( z a z ) 2 ϵ 1 {\displaystyle F(x,y,z)=\left(\left({\frac {x}{a_{x}}}\right)^{\frac {2}{\epsilon _{2}}}+\left({\frac {y}{a_{y}}}\right)^{\frac {2}{\epsilon _{2}}}\right)^{\frac {\epsilon _{2}}{\epsilon _{1}}}+\left({\frac {z}{a_{z}}}\right)^{\frac {2}{\epsilon _{1}}}} . Similarly, the surface of the superellipsoid is defined by the equation F ( x , y , z ) = 1 {\displaystyle F(x,y,z)=1} For any given point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} , the point lies inside the superellipsoid if f ( x , y , z ) < 1 {\displaystyle f(x,y,z)<1} , and outside if f ( x , y , z ) > 1 {\displaystyle f(x,y,z)>1} . Therefore, the implicit function is also called the inside-outside function of the superellipsoid. The superellipsoid has a parametric representation in terms of surface parameters η ∈ [ − π / 2 , π / 2 ) {\displaystyle \eta \in [-\pi /2,\pi /2)} , ω ∈ [ − π , π ) {\displaystyle \omega \in [-\pi ,\pi )} . x ( η , ω ) = a x cos ϵ 1 η cos ϵ 2 ω {\displaystyle x(\eta ,\omega )=a_{x}\cos ^{\epsilon _{1}}\eta \cos ^{\epsilon _{2}}\omega } y ( η , ω ) = a y cos ϵ 1 η sin ϵ 2 ω {\displaystyle y(\eta ,\omega )=a_{y}\cos ^{\epsilon _{1}}\eta \sin ^{\epsilon _{2}}\omega } z ( η , ω ) = a z sin ϵ 1 η {\displaystyle z(\eta ,\omega )=a_{z}\sin ^{\epsilon _{1}}\eta } === General posed superellipsoid === In computer vision and robotic applications, a superellipsoid with a general pose in the 3D Euclidean space is usually of more interest. For a given Euclidean transformation of the superellipsoid frame g = [ R ∈ S O ( 3 ) , t ∈ R 3 ] ∈ S E ( 3 ) {\displaystyle g=[\mathbf {R} \in SO(3),\mathbf {t} \in \mathbb {R} ^{3}]\in SE(3)} relative to the world frame, the implicit function of a general posed superellipsoid surface defined the world frame is F ( g − 1 ∘ ( x , y , z ) ) = 1 {\displaystyle F\left(g^{-1}\circ (x,y,z)\right)=1} where ∘ {\displaystyle \circ } is the transformation operation that maps the point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} in the world frame into the canonical superellipsoid frame. === Volume of superellipsoid === The volume encompassed by the superelllipsoid surface can be expressed in terms of the beta functions β ( ⋅ , ⋅ ) {\displaystyle \beta (\cdot ,\cdot )} , V ( ϵ 1 , ϵ 2 , a x , a y , a z ) = 2 a x a y a z ϵ 1 ϵ 2 β ( ϵ 1 2 , ϵ 1 + 1 ) β ( ϵ 2 2 , ϵ 2 + 2 2 ) {\displaystyle V(\epsilon _{1},\epsilon _{2},a_{x},a_{y},a_{z})=2a_{x}a_{y}a_{z}\epsilon _{1}\epsilon _{2}\beta ({\frac {\epsilon _{1}}{2}},\epsilon _{1}+1)\beta ({\frac {\epsilon _{2}}{2}},{\frac {\epsilon _{2}+2}{2}})} or equivalently with the Gamma function Γ ( ⋅ ) {\displaystyle \Gamma (\cdot )} , since β ( m , n ) = Γ ( m ) Γ ( n ) Γ ( m + n ) {\displaystyle \beta (m,n)={\frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}}} == Recovery from data == Recoverying the superellipsoid (or superquadrics) representation from raw data (e.g., point cloud, mesh, images, and voxels) is an important task in computer vision, robotics, and physical simulation. Traditional computational methods model the problem as a least-square problem. The goal is to find out the optimal set of superellipsoid parameters θ ≐ [ ϵ 1 , ϵ 2 , a x , a y , a z , g ] {\displaystyle \theta \doteq [\epsilon _{1},\epsilon _{2},a_{x},a_{y},a_{z},g]} that minimize an objective function. Other than the shape parameters, g ∈ {\displaystyle g\in } SE(3) is the pose of the superellipsoid frame with respect to the world coordinate. There are two commonly used objective functions. The first one is constructed directly based on the implicit function G 1 ( θ ) = a x a y a z ∑ i = 1 N ( F ϵ 1 ( g − 1 ∘ ( x i , y i , z i ) ) − 1 ) 2 {\displaystyle G_{1}(\theta )=a_{x}a_{y}a_{z}\sum _{i=1}^{N}\left(F^{\epsilon _{1}}\left(g^{-1}\circ (x_{i},y_{i},z_{i})\right)-1\right)^{2}} The minimization of the objective function provides a recovered superellipsoid as close as possible to all the input points { ( x i , y i , z i ) ∈ R 3 , i = 1 , 2 , . . . , N } {\displaystyle \{(x_{i},y_{i},z_{i})\in \mathbb {R} ^{3},i=1,2,...,N\}} . At the mean time, the scalar value a x , a y , a z {\displaystyle a_{x},a_{y},a_{z}} is positively proportional to the volume of the superellipsoid, and thus have the effect of minimizing the volume as well. The other objective function tries to minimized the radial distance between the points and the superellipsoid. That is G 2 ( θ ) = ∑ i = 1 N ( | r
Meta AI
Meta AI is a research division of Meta (formerly Facebook) that develops artificial intelligence and augmented reality technologies. == History == Meta AI was founded in 2013 as Facebook Artificial Intelligence Research (FAIR). It has workspaces in Menlo Park, London, New York City, Paris, Seattle, Pittsburgh, Tel Aviv, and Montreal as of 2025. In 2016, FAIR partnered with Google, Amazon, IBM, and Microsoft in creating the Partnership on Artificial Intelligence to Benefit People and Society. Meta AI was directed by Yann LeCun until 2018, when Jérôme Pesenti succeeded the role. Pesenti is formerly the CTO of IBM's big data group. FAIR's research includes self-supervised learning, generative adversarial networks, document classification and translation, and computer vision. FAIR released Torch deep-learning modules as well as PyTorch in 2017, an open-source machine learning framework, which was subsequently used in several deep learning technologies, such as Tesla's autopilot and Uber's Pyro. That same year, a pair of chatbots were falsely rumored to be discontinued for developing a language that was unintelligible to humans. FAIR clarified that the research had been shut down because they had accomplished their initial goal to understand how languages are generated by their models, rather than out of fear. FAIR was renamed Meta AI following the rebranding that changed Facebook, Inc. to Meta Platforms Inc. On October 1, 2025, Facebook announced "We will soon use your interactions with AI at Meta to personalize the content and ads you see". == Virtual assistant == Meta AI is also the name of the virtual assistant developed by the team, now integrated as a chatbot into Meta's social networking products. It is also available as a subscription-based stand-alone app. The virtual assistant was pre-installed on the second generation of Ray-Ban Meta smartglasses, and can incorporate inputs from the glasses' cameras after an update. It is also available on Quest 2 and newer HMDs. Since May 2024, the chatbot has summarized news from various outlets without linking directly to original articles, including in Canada, where news links are banned on its platforms. This use of news content without compensation and attribution has raised ethical and legal concerns, especially as Meta continues to reduce news visibility on its platforms. == Current research == === Natural language processing and chatbot === Natural language processing is the ability for machines to understand and generate natural language. The team is also researching unsupervised machine translation and multilingual chatbots. ==== Galactica ==== Galactica is a large language model (LLM) designed for generating scientific text. It was available for three days from 15 November 2022, before being withdrawn for generating racist and inaccurate content. ==== Llama ==== Llama is an LLM released in February 2023. As of January 2026, the most recent release is the Llama 4. === Hardware === Meta used CPUs and in-house custom chips before 2022; they switched to Nvidia GPUs since then. MTIA v1, one of their early chips, is designed for the company's content recommendation algorithms. It was fabricated on TSMC's 7 nm process technology and consumed 25W, capable of 51.2 TFlops FP16. == Controversy == The French media outlet Mediapart reports that in 2022, Facebook's parent company illegally used works accumulated by the pirate site LibGen to train its artificial intelligence.
Confusion matrix
In machine learning, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one. In unsupervised learning it is usually called a matching matrix. The term is used specifically in the problem of statistical classification. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The diagonal of the matrix therefore represents all instances that are correctly predicted. The name stems from the fact that it makes it easy to identify whether the system is confusing two classes (i.e., commonly mislabeling one class as another). The confusion matrix has its origins in human perceptual studies of auditory stimuli. It was adapted for machine learning studies and used by Frank Rosenblatt, among other early researchers, to compare human and machine classifications of visual (and later auditory) stimuli. It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table). == Example == Given a sample of 12 individuals, 8 that have been diagnosed with cancer and 4 that are cancer-free, where individuals with cancer belong to class 1 (positive) and non-cancer individuals belong to class 0 (negative), we can display that data as follows: Assume that we have a classifier that distinguishes between individuals with and without cancer in some way, we can take the 12 individuals and run them through the classifier. The classifier then makes 9 accurate predictions and misses 3: 2 individuals with cancer wrongly predicted as being cancer-free (sample 1 and 2), and 1 person without cancer that is wrongly predicted to have cancer (sample 9). Notice, that if we compare the actual classification set to the predicted classification set, there are 4 different outcomes that could result in any particular column: The actual classification is positive and the predicted classification is positive (1,1). This is called a true positive result because the positive sample was correctly identified by the classifier. The actual classification is positive and the predicted classification is negative (1,0). This is called a false negative result because the positive sample is incorrectly identified by the classifier as being negative. The actual classification is negative and the predicted classification is positive (0,1). This is called a false positive result because the negative sample is incorrectly identified by the classifier as being positive. The actual classification is negative and the predicted classification is negative (0,0). This is called a true negative result because the negative sample gets correctly identified by the classifier. We can then perform the comparison between actual and predicted classifications and add this information to the table, making correct results appear in green so they are more easily identifiable. The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications. The four outcomes can be formulated in a 2×2 confusion matrix, as follows: The color convention of the three data tables above were picked to match this confusion matrix, in order to easily differentiate the data. Now, we can simply total up each type of result, substitute into the template, and create a confusion matrix that will concisely summarize the results of testing the classifier: In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will represent them. By summing up the 2 rows of the confusion matrix, one can also deduce the total number of positive (P) and negative (N) samples in the original dataset, i.e. P = T P + F N {\displaystyle P=TP+FN} and N = F P + T N {\displaystyle N=FP+TN} . == Table of confusion == In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer). According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their significance and use. Some researchers have argued that the confusion matrix, and the metrics derived from it, do not truly reflect a model's knowledge. In particular, the confusion matrix cannot show whether correct predictions were reached through sound reasoning or merely by chance (a problem known in philosophy as epistemic luck). It also does not capture situations where the facts used to make a prediction later change or turn out to be wrong (defeasibility). This means that while the confusion matrix is a useful tool for measuring classification performance, it may give an incomplete picture of a model’s true reliability. == Confusion matrices with more than two categories == Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, with zero values omitted for clarity. == Confusion matrices in multi-label and soft-label classification == Confusion matrices are not limited to single-label classification (where only one class is present) or hard-label settings (where classes are either fully present, 1, or absent, 0). They can also be extended to Multi-label classification (where multiple classes can be predicted at once) and soft-label classification (where classes can be partially present). One such extension is the Transport-based Confusion Matrix (TCM), which builds on the theory of optimal transport and the principle of maximum entropy. TCM applies to single-label, multi-label, and soft-label settings. It retains the familiar structure of the standard confusion matrix: a square matrix sized by the number of classes, with diagonal entries indicating correct predictions and off-diagonal entries indicating confusion. In the single-label case, TCM is identical to the standard confusion matrix. TCM follows the same reasoning as the standard confusion matrix: if class A is overestimated (its predicted value is greater than its label value) and class B is underestimated (its predicted value is less than its label value), A is considered confused with B, and the entry (B, A) is increased. If a class is both predicted and present, it is correctly identified, and the diagonal entry (A, A) increases. Optimal transport and maximum entropy are used to determine the extent to which these entries are updated. TCM enables clearer comparison between predictions and labels in complex classification tasks, while maintaining a consistent matrix format across settings.
Hierarchical control system
A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. == Overview == A human-built system with complex behavior is often organized as a hierarchy. For example, a command hierarchy has among its notable features the organizational chart of superiors, subordinates, and lines of organizational communication. Hierarchical control systems are organized similarly to divide the decision making responsibility. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas sensations and command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a hierarchical control system are related to its layers. Each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer. The lower layers have local tasks, goals, and sensations, and their activities are planned and coordinated by higher layers which do not generally override their decisions. The layers form a hybrid intelligent system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning. A hierarchical task network is a good fit for planning in a hierarchical control system. Besides artificial systems, an animal's control systems are proposed to be organized as a hierarchy. In perceptual control theory, which postulates that an organism's behavior is a means of controlling its perceptions, the organism's control systems are suggested to be organized in a hierarchical pattern as their perceptions are constructed so. == Control system structure == The accompanying diagram is a general hierarchical model which shows functional manufacturing levels using computerised control of an industrial control system. Referring to the diagram; Level 0 contains the field devices such as flow and temperature sensors, and final control elements, such as control valves Level 1 contains the industrialised Input/Output (I/O) modules, and their associated distributed electronic processors. Level 2 contains the supervisory computers, which collate information from processor nodes on the system, and provide the operator control screens. Level 3 is the production control level, which does not directly control the process, but is concerned with monitoring production and monitoring targets Level 4 is the production scheduling level. == Applications == === Manufacturing, robotics and vehicles === Among the robotic paradigms is the hierarchical paradigm in which a robot operates in a top-down fashion, heavy on planning, especially motion planning. Computer-aided production engineering has been a research focus at NIST since the 1980s. Its Automated Manufacturing Research Facility was used to develop a five layer production control model. In the early 1990s DARPA sponsored research to develop distributed (i.e. networked) intelligent control systems for applications such as military command and control systems. NIST built on earlier research to develop its Real-Time Control System (RCS) and Real-time Control System Software which is a generic hierarchical control system that has been used to operate a manufacturing cell, a robot crane, and an automated vehicle. In November 2007, DARPA held the Urban Challenge. The winning entry, Tartan Racing employed a hierarchical control system, with layered mission planning, motion planning, behavior generation, perception, world modelling, and mechatronics. === Artificial intelligence === Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a particular goal of the software agent (i.e. system as a whole), and higher layers are increasingly more abstract. Each layer's goal subsumes that of the underlying layers, e.g. the decision to move forward by the eat-food layer takes into account the decision of the lowest obstacle-avoidance layer. Behavior need not be planned by a superior layer, rather behaviors may be triggered by sensory inputs and so are only active under circumstances where they might be appropriate. Reinforcement learning has been used to acquire behavior in a hierarchical control system in which each node can learn to improve its behavior with experience. James Albus, while at NIST, developed a theory for intelligent system design named the Reference Model Architecture (RMA), which is a hierarchical control system inspired by RCS. Albus defines each node to contain these components. Behavior generation is responsible for executing tasks received from the superior, parent node. It also plans for, and issues tasks to, the subordinate nodes. Sensory perception is responsible for receiving sensations from the subordinate nodes, then grouping, filtering, and otherwise processing them into higher level abstractions that update the local state and which form sensations that are sent to the superior node. Value judgment is responsible for evaluating the updated situation and evaluating alternative plans. World Model is the local state that provides a model for the controlled system, controlled process, or environment at the abstraction level of the subordinate nodes. At its lowest levels, the RMA can be implemented as a subsumption architecture, in which the world model is mapped directly to the controlled process or real world, avoiding the need for a mathematical abstraction, and in which time-constrained reactive planning can be implemented as a finite-state machine. Higher levels of the RMA however, may have sophisticated mathematical world models and behavior implemented by automated planning and scheduling. Planning is required when certain behaviors cannot be triggered by current sensations, but rather by predicted or anticipated sensations, especially those that come about as result of the node's actions.
Learning to rank
Learning to rank (LTR) or machine-learned ranking (MLR) is the application of machine learning, often supervised, semi-supervised or reinforcement learning, in the construction of ranking models for information retrieval and recommender systems. Training data may, for example, consist of lists of items with some partial order specified between items in each list. This order is typically induced by giving a numerical or ordinal score or a binary judgment (e.g. "relevant" or "not relevant") for each item. The goal of constructing the ranking model is to rank new, unseen lists in a similar way to rankings in the training data. == Applications == === In information retrieval === Ranking is a central part of many information retrieval problems, such as document retrieval, collaborative filtering, sentiment analysis, and online advertising. A possible architecture of a machine-learned search engine is shown in the accompanying figure. Training data consists of queries and documents matching them together with the relevance degree of each match. It may be prepared manually by human assessors (or raters, as Google calls them), who check results for some queries and determine relevance of each result. It is not feasible to check the relevance of all documents, and so typically a technique called pooling is used — only the top few documents, retrieved by some existing ranking models are checked. This technique may introduce selection bias. Alternatively, training data may be derived automatically by analyzing clickthrough logs (i.e. search results which got clicks from users), query chains, or such search engines' features as Google's (since-replaced) SearchWiki. Clickthrough logs can be biased by the tendency of users to click on the top search results on the assumption that they are already well-ranked. Training data is used by a learning algorithm to produce a ranking model which computes the relevance of documents for actual queries. Typically, users expect a search query to complete in a short time (such as a few hundred milliseconds for web search), which makes it impossible to evaluate a complex ranking model on each document in the corpus, and so a two-phase scheme is used. First, a small number of potentially relevant documents are identified using simpler retrieval models which permit fast query evaluation, such as the vector space model, Boolean model, weighted AND, or BM25. This phase is called top- k {\displaystyle k} document retrieval and many heuristics were proposed in the literature to accelerate it, such as using a document's static quality score and tiered indexes. In the second phase, a more accurate but computationally expensive machine-learned model is used to re-rank these documents. === In other areas === Learning to rank algorithms have been applied in areas other than information retrieval: In machine translation for ranking a set of hypothesized translations; In computational biology for ranking candidate 3-D structures in protein structure prediction problems; In recommender systems for identifying a ranked list of related news articles to recommend to a user after he or she has read a current news article. == Feature vectors == For the convenience of MLR algorithms, query-document pairs are usually represented by numerical vectors, which are called feature vectors. Such an approach is sometimes called bag of features and is analogous to the bag of words model and vector space model used in information retrieval for representation of documents. Components of such vectors are called features, factors or ranking signals. They may be divided into three groups (features from document retrieval are shown as examples): Query-independent or static features — those features, which depend only on the document, but not on the query. For example, PageRank or document's length. Such features can be precomputed in off-line mode during indexing. They may be used to compute document's static quality score (or static rank), which is often used to speed up search query evaluation. Query-dependent or dynamic features — those features, which depend both on the contents of the document and the query, such as TF-IDF score or other non-machine-learned ranking functions. Query-level features or query features, which depend only on the query. For example, the number of words in a query. Some examples of features, which were used in the well-known LETOR dataset: TF, TF-IDF, BM25, and language modeling scores of document's zones (title, body, anchors text, URL) for a given query; Lengths and IDF sums of document's zones; Document's PageRank, HITS ranks and their variants. Selecting and designing good features is an important area in machine learning, which is called feature engineering. == Evaluation measures == There are several measures (metrics) which are commonly used to judge how well an algorithm is doing on training data and to compare the performance of different MLR algorithms. Often a learning-to-rank problem is reformulated as an optimization problem with respect to one of these metrics. Examples of ranking quality measures: Mean average precision (MAP); DCG and NDCG; Precision@n, NDCG@n, where "@n" denotes that the metrics are evaluated only on top n documents; Mean reciprocal rank; Kendall's tau; Spearman's rho. DCG and its normalized variant NDCG are usually preferred in academic research when multiple levels of relevance are used. Other metrics such as MAP, MRR and precision, are defined only for binary judgments. Recently, there have been proposed several new evaluation metrics which claim to model user's satisfaction with search results better than the DCG metric: Expected reciprocal rank (ERR); Yandex's pfound. Both of these metrics are based on the assumption that the user is more likely to stop looking at search results after examining a more relevant document, than after a less relevant document. == Approaches == Learning to Rank approaches are often categorized using one of three approaches: pointwise (where individual documents are ranked), pairwise (where pairs of documents are ranked into a relative order), and listwise (where an entire list of documents are ordered). Tie-Yan Liu of Microsoft Research Asia has analyzed existing algorithms for learning to rank problems in his book Learning to Rank for Information Retrieval. He categorized them into three groups by their input spaces, output spaces, hypothesis spaces (the core function of the model) and loss functions: the pointwise, pairwise, and listwise approach. In practice, listwise approaches often outperform pairwise approaches and pointwise approaches. This statement was further supported by a large scale experiment on the performance of different learning-to-rank methods on a large collection of benchmark data sets. In this section, without further notice, x {\displaystyle x} denotes an object to be evaluated, for example, a document or an image, f ( x ) {\displaystyle f(x)} denotes a single-value hypothesis, h ( ⋅ ) {\displaystyle h(\cdot )} denotes a bi-variate or multi-variate function and L ( ⋅ ) {\displaystyle L(\cdot )} denotes the loss function. === Pointwise approach === In this case, it is assumed that each query-document pair in the training data has a numerical or ordinal score. Then the learning-to-rank problem can be approximated by a regression problem — given a single query-document pair, predict its score. Formally speaking, the pointwise approach aims at learning a function f ( x ) {\displaystyle f(x)} predicting the real-value or ordinal score of a document x {\displaystyle x} using the loss function L ( f ; x j , y j ) {\displaystyle L(f;x_{j},y_{j})} . A number of existing supervised machine learning algorithms can be readily used for this purpose. Ordinal regression and classification algorithms can also be used in pointwise approach when they are used to predict the score of a single query-document pair, and it takes a small, finite number of values. === Pairwise approach === In this case, the learning-to-rank problem is approximated by a classification problem — learning a binary classifier h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} that can tell which document is better in a given pair of documents. The classifier shall take two documents as its input and the goal is to minimize a loss function L ( h ; x u , x v , y u , v ) {\displaystyle L(h;x_{u},x_{v},y_{u,v})} . The loss function typically reflects the number and magnitude of inversions in the induced ranking. In many cases, the binary classifier h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} is implemented with a scoring function f ( x ) {\displaystyle f(x)} . As an example, RankNet adapts a probability model and defines h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} as the estimated probability of the document x u {\displaystyle x_{u}} has higher quality than x v {\displaystyle x_{v}} : P u , v ( f ) = CDF ( f ( x u ) − f ( x v ) ) , {\displaystyle P_{u,v}(f)={\text{CDF}
Smart object
A smart object is an object that enhances the interaction with not only people but also with other smart objects. Also known as smart connected products or smart connected things (SCoT), they are products, assets and other things embedded with processors, sensors, software and connectivity that allow data to be exchanged between the product and its environment, manufacturer, operator/user, and other products and systems. Connectivity also enables some capabilities of the product to exist outside the physical device, in what is known as the product cloud. The data collected from these products can be then analysed to inform decision-making, enable operational efficiencies and continuously improve the performance of the product. It can not only refer to interaction with physical world objects but also to interaction with virtual (computing environment) objects. A smart physical object may be created either as an artifact or manufactured product or by embedding electronic tags such as RFID tags or sensors into non-smart physical objects. Smart virtual objects are created as software objects that are intrinsic when creating and operating a virtual or cyber world simulation or game. The concept of a smart object has several origins and uses, see History. There are also several overlapping terms, see also smart device, tangible object or tangible user interface and Thing as in the Internet of things. == History == In the early 1990s, Mark Weiser, from whom the term ubiquitous computing originated, referred to a vision "When almost every object either contains a computer or can have a tab attached to it, obtaining information will be trivial", Although Weiser did not specifically refer to an object as being smart, his early work did imply that smart physical objects are smart in the sense that they act as digital information sources. Hiroshi Ishii and Brygg Ullmer refer to tangible objects in terms of tangibles bits or tangible user interfaces that enable users to "grasp & manipulate" bits in the center of users' attention by coupling the bits with everyday physical objects and architectural surfaces. The smart object concept was introduced by Marcelo Kallman and Daniel Thalmann as an object that can describe its own possible interactions. The main focus here is to model interactions of smart virtual objects with virtual humans, agents, in virtual worlds. The opposite approach to smart objects is 'plain' objects that do not provide this information. The additional information provided by this concept enables far more general interaction schemes, and can greatly simplify the planner of an artificial intelligence agent. In contrast to smart virtual objects used in virtual worlds, Lev Manovich focuses on physical space filled with electronic and visual information. Here, "smart objects" are described as "objects connected to the Net; objects that can sense their users and display smart behaviour". More recently in the early 2010s, smart objects are being proposed as a key enabler for the vision of the Internet of things. The combination of the Internet and emerging technologies such as near field communications, real-time localization, and embedded sensors enables everyday objects to be transformed into smart objects that can understand and react to their environment. Such objects are building blocks for the Internet of things and enable novel computing applications. In 2018, one of the world's first smart houses was built in Klaukkala, Finland in the form of a five-floor apartment block, using the Kone Residential Flow solution created by KONE, allowing even a smartphone to act as a home key. == Characteristics == Although we can view interaction with physical smart object in the physical world as distinct from interaction with virtual smart objects in a virtual simulated world, these can be related. Poslad considers the progression of: how humans use models of smart objects situated in the physical world to enhance human to physical world interaction; versus how smart physical objects situated in the physical world can model human interaction in order to lessen the need for human to physical world interaction; versus how virtual smart objects by modelling both physical world objects and modelling humans as objects and their subsequent interactions can form a predominantly smart virtual object environment. === Smart physical objects === The concept smart for a smart physical object simply means that it is active, digital, networked, can operate to some extent autonomously, is reconfigurable and has local control of the resources it needs such as energy, data storage, etc. Note, a smart object does not necessarily need to be intelligent as in exhibiting a strong essence of artificial intelligence—although it can be designed to also be intelligent. Physical world smart objects can be described in terms of three properties: Awareness: is a smart object's ability to understand (that is, sense, interpret, and react to) events and human activities occurring in the physical world. Representation: refers to a smart object's application and programming model—in particular, programming abstractions. Interaction: denotes the object's ability to converse with the user in terms of input, output, control, and feedback. Based upon these properties, these have been classified into three types: Activity-Aware Smart Objects: Are objects that can record information about work activities and its own use. Policy-Aware Smart Objects: Are objects that are activity-aware Objects can interpret events and activities with respect to predefined organizational policies. Process-Aware Smart Objects: Processes play a fundamental role in industrial work management and operation. A process is a collection of related activities or tasks that are ordered according to their position in time and space. === Smart virtual objects === For the virtual object in a virtual world case, an object is called smart when it has the ability to describe its possible interactions. This focuses on constructing a virtual world using only virtual objects that contain their own interaction information. There are four basic elements to constructing such a smart virtual object framework. Object properties: physical properties and a text description Interaction information: position of handles, buttons, grips, and the like Object behavior: different behaviors based on state variables Agent behaviors: description of the behavior an agent should follow when using the object Some versions of smart objects also include animation information in the object information, but this is not considered to be an efficient approach, since this can make objects inappropriately oversized. === Categorization === The terms smart, connected product or smart product can be confusing as it is used to cover a broad range of different products, ranging from smart home appliances (e.g., smart bathroom scales or smart light bulbs) to smart cars (e.g., Tesla). While these products share certain similarities, they often differ substantially in their capabilities. Raff et al. developed a conceptual framework that distinguishes different smart products based on their capabilities, which features 4 types of smart product archetypes (in ascending order of "smartness"). Digital Connected Responsive Intelligent == Advantages == Smart, connected products have three primary components: Physical – made up of the product's mechanical and electrical parts. Smart – made up of sensors, microprocessors, data storage, controls, software, and an embedded operating system with enhanced user interface. Connectivity – made up of ports, antennae, and protocols enabling wired/wireless connections that serve two purposes, it allows data to be exchanged with the product and enables some functions of the product to exist outside the physical device. Each component expands the capabilities of one another resulting in "a virtuous cycle of value improvement". First, the smart components of a product amplify the value and capabilities of the physical components. Then, connectivity amplifies the value and capabilities of the smart components. These improvements include: Monitoring of the product's conditions, its external environment, and its operations and usage. Control of various product functions to better respond to changes in its environment, as well as to personalize the user experience. Optimization of the product's overall operations based on actual performance data, and reduction of downtimes through predictive maintenance and remote service. Autonomous product operation, including learning from their environment, adapting to users' preferences and self-diagnosing and service. === The Internet of things (IoT) === The Internet of things is the network of physical objects that contain embedded technology to communicate and sense or interact with their internal states or the external environment. The phrase "Internet of things" reflects the gro
AI nationalism
AI nationalism is the idea that nations should develop and control their own artificial intelligence technologies to advance their own interests and ensure technological sovereignty. This concept is gaining traction globally, leading countries to implement new laws, form strategic alliances, and invest significantly in domestic AI capabilities. == Global trends and national strategies == In 2018, British technology investor Ian Hogarth published an influential essay titled AI Nationalism. He argued that as AI gains more power and its economic and military significance expands, governments will take measures to bolster their own domestic AI industries, and predicted that the advancement of machine learning systems would lead to what he termed "AI nationalism." He anticipated that this rise in AI would accelerate a global arms race, resulting in more closed economies, restrictions on foreign acquisitions, and limitations on the movement of talent. Hogarth predicted that AI policy would become a central focus of government agendas. He also criticized Britain’s approach to AI strategy, citing the sale of London-based DeepMind—one of the leading AI laboratories, acquired by Google for a relatively modest £400 million in 2014—as a significant misstep. AI nationalism is chiefly reflected in the escalating rhetoric of an artificial intelligence arms race, portraying AI development as a zero-sum game where the winner gains significant economic, political, and military advantages. This mindset, as highlighted in a 2017 Pentagon report, warns that sharing AI technology could erode technological supremacy and enhance rivals' capabilities. The winner-takes-all mentality of AI nationalism poses risks including unsafe AI development, increased geopolitical tension, and potential military aggression (such as cyberattacks or targeting AI professionals). Several countries, including Canada, France, and India, have formulated national strategies to advance their positions in AI. In the United States, a leading player in the global AI arena, trade policies have been enacted to restrict China's access to critical microchips, reflecting a strategic effort to maintain a technological edge. The United States’ National Security Commission on Artificial Intelligence (NSCAI) frames AI development as a critical aspect of a broader technology competition crucial for national success. It emphasizes the need to outpace China in AI to maintain strategic advantage, reflecting AI nationalism by linking geopolitical power directly to advancements in AI. France has seen notable governmental support for local AI startups, particularly those specializing in language technologies that cater to French and other non-English languages. In Saudi Arabia, Crown Prince Mohammed bin Salman is investing billions in AI research and development. The country has actively collaborated with major technology firms such as Amazon, IBM, and Microsoft to establish itself as a prominent AI hub. == Historical and cultural context == AI nationalism is seen as deeply connected to historical racism and imperialism. It is viewed not merely as a technological competition but as a contest over racial and civilizational superiority. Historically, technological achievements were often used to justify colonialism and racial hierarchies, with Western societies perceiving their advancements as evidence of superiority. In the context of AI, this historical context continues to shape views on intelligence and development. Some argue that AI nationalism reinforces the idea of fundamental civilizational divides, especially between the Western world and China. This perspective often frames China's progress in AI as a direct challenge to Western values, presenting the AI competition as a struggle over values. AI nationalism is said to draw from long-standing anti-Asian stereotypes, such as the "Yellow Peril," which portray Asian nations as threats to Western civilization. This viewpoint links Asian technological advances with dehumanization and artificiality, reflecting persistent anxieties about China's growing role in the global tech landscape. == Implications == AI nationalism is seen as a component of a broader trend towards the fragmentation of the internet, where digital services are increasingly influenced by local regulations and national interests. This shift is creating a new technological landscape in which the impact of artificial intelligence on individuals' lives can vary significantly depending on their geographic location. J. Paul Goode argues that AI nationalism may exacerbate existing societal divisions by promoting the development of systems that embed cultural biases, thereby privileging certain groups while disadvantaging others.