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  Artificial intelligence in education

  Artificial intelligence in education (often abbreviated as AIEd) is a subfield of educational technology that studies how to use artificial intelligence to create learning environments. Considerations in the field include data-driven decision-making, AI ethics, data privacy and AI literacy. Concerns include the potential for cheating, over-reliance, equity of access, reduced critical thinking, and the perpetuation of misinformation and bias. == History == Efforts to integrate AI into educational contexts have often followed technological advancement in the history of artificial intelligence. In the 1960s, educators and researchers began developing computer-based instruction systems, such as PLATO, developed by the University of Illinois. In the 1970s and 1980s, intelligent tutoring systems (ITS) were being adapted for classroom instruction. The International Artificial Intelligence in Education Society was founded in 1993. Coinciding with the AI boom of the 2020s, the use of large language models in the global north has been promoted and funded by venture capital and big tech. Companies creating AI services have targeted students and educational institutions as customers. Similarly, pre-AI boom educational companies have expanded their use of AI technologies. These commercial incentives for AIEd use may be related to a potential AI bubble. In the U.S., bipartisan support of AI development in K-12 education has been expressed, but specific implementations and best practices remain contentious. == Theory == AIEd applies theory from education studies, machine learning, and related fields. A 2019 review of the previous decade of studies found that most research prioritized technological design over pedagogical integration. Ouyang and Jiao (2021) propose three paradigms for AI in education, which follow roughly from least to most learner-centered and from requiring least to most technical complexity from the AI systems: AI-directed, learner-as-recipient: AIEd systems present a pre-set curriculum based on statistical patterns that do not adjust to learner's feedback. AI-supported, learner-as-collaborator: Systems that incorporate responsiveness to learner's feedback through, for example, natural language processing, wherein AI can support knowledge construction. AI-empowered, learner-as-leader: This model seeks to position AI as a supplement to human intelligence wherein learners take agency and AI provides consistent and actionable feedback. Some scholars place AI in education within a socio-technical framework. This positions AI alongside other emerging educational technologies, such as computing, the internet, and social media. The framework of Tsao, Heinrichs and Camit (2025) draws on new materialism and posthumanism, specifically Donna Haraway's concept of sympoiesis (making-with). This perspective views learning as an entanglement of human and non-human actors (students, teachers, and AI algorithms), where knowledge is co-composed in contact zones between human context and algorithmic prediction. AI agents have been trained on biased datasets, and thus continue to perpetuate societal biases. Since LLMs were created to produce human-like text, algorithmic bias can be introduced and reproduced. AI's data processing and monitoring reinforce neoliberal approaches to education rather than addressing inequalities. == Applications == Uses of generative AI chatbots in education have included assessment and feedback, machine translations, proof-reading exam question generation and copy editing, or as virtual assistants. Emotional AI in education is the study and development of systems that can detect learners' emotions or provide emotional support in learning. == Usage == === Schools and educators === Following the release of ChatGPT in November 2022, some schools and large school districts blocked access to the site and issued warnings that the use of such tools would be seen as cheating. Governmental and non-governmental organizations such as UNESCO, Article 4 of the European Union's AI Act, and the U.S. Department of Education have published reports advocating for specific AIEd approaches. National higher-education bodies have also published guidance on generative AI, including Ireland's Higher Education Authority, which issued a policy framework for higher education teaching and learning in December 2025. In 2024, UNESCO released updated global guidance for generative AI in education, emphasizing ethical use, teacher training, and data protection to ensure responsible integration of AI tools in learning environments. According to Taso (2025), policy implementation in higher education is interpreted and enacted differently by various organizations. These decentralized policies can lead to inconsistent enforcement and confusion among students regarding what constitutes acceptable use, with the burden of ethical navigation falling on individual teachers and students. AI integration in classrooms has created new forms of invisible labour for educators, who must navigate ambiguous policies, redesign assessments to be AI-resilient, and adjudicate potential academic integrity violations. The use of AI detection tools has also been criticised for creating an adversarial relationship between students and institutions, where students may be falsely accused of misconduct based on probabilistic software. AIEd advocates say that efforts should be made towards increasing global accessibility and training educators to serve underprivileged areas. === Students === Reliance on generative AI has been linked with reduced academic self-esteem and performance, and heightened learned helplessness. Algorithm errors and hallucinations are common flaws in AI agents, making them less trustworthy and reliable. According to a 2025 survey from Inside Higher Ed, 85% of higher education students use generative AI technology in some way, with 25% using AI to complete assignments for them. The most common reason cited for using AI to cheat was pressure to get high grades. 97% of students wanted some form of action from schools on the threat to academic integrity caused by AI, with the most popular options being clearer policies and more education about ethical uses of AI. In September 2025, The Atlantic published an op-ed from a high school senior arguing that the normalization of AI cheating was eroding critical thinking, academic integrity, creativity, and the shared student experience.

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  Word2vec

  Word2vec is a technique in natural language processing for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov, Kai Chen, Greg Corrado, Ilya Sutskever and Jeff Dean at Google, and published in 2013. Word2vec represents a word as a high-dimension vector of numbers which capture relationships between words. In particular, words which appear in similar contexts are mapped to vectors which are nearby as measured by cosine similarity. This indicates the level of semantic similarity between the words, so for example the vectors for walk and ran are nearby, as are those for "but" and "however", and "Berlin" and "Germany". == Approach == Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a mapping of the set of words to a vector space, typically of several hundred dimensions, with each unique word in the corpus being assigned a vector in the space. Word2vec can use either of two model architectures to produce these distributed representations of words: continuous bag of words (CBOW) or continuously sliding skip-gram. In both architectures, word2vec considers both individual words and a sliding context window as it iterates over the corpus. The CBOW can be viewed as a 'fill in the blank' task, where the word embedding represents the way the word influences the relative probabilities of other words in the context window. Words which are semantically similar should influence these probabilities in similar ways, because semantically similar words should be used in similar contexts. The order of context words does not influence prediction (bag of words assumption). In the continuous skip-gram architecture, the model uses the current word to predict the surrounding window of context words. The skip-gram architecture weighs nearby context words more heavily than more distant context words. According to the authors' note, CBOW is faster while skip-gram does a better job for infrequent words. After the model is trained, the learned word embeddings are positioned in the vector space such that words that share common contexts in the corpus — that is, words that are semantically and syntactically similar — are located close to one another in the space. More dissimilar words are located farther from one another in the space. == Mathematical details == This section is based on expositions. A corpus is a sequence of words. Both CBOW and skip-gram are methods to learn one vector per word appearing in the corpus. Let V {\displaystyle V} ("vocabulary") be the set of all words appearing in the corpus C {\displaystyle C} . Our goal is to learn one vector v w ∈ R d {\displaystyle v_{w}\in \mathbb {R} ^{d}} for each word w ∈ V {\displaystyle w\in V} . The idea of skip-gram is that the vector of a word should be close to the vector of each of its neighbors. The idea of CBOW is that the vector-sum of a word's neighbors should be close to the vector of the word. === Continuous bag-of-words (CBOW) === The idea of CBOW is to represent each word with a vector, such that it is possible to predict a word using the sum of the vectors of its neighbors. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i + j : j ∈ N ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i+j}\colon j\in N)} where N {\displaystyle N} is a set of (non-zero) indices representing the relative locations of nearby words considered to be in w i {\displaystyle w_{i}} 's neighborhood. For example, if we want each word in the corpus to be predicted by every other word in a small span of 4 words. The set of relative indexes of neighbor words will be: N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} , and the objective is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i − 2 , w i − 1 , w i + 1 , w i + 2 ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i-2},w_{i-1},w_{i+1},w_{i+2})} . In standard bag-of-words, a word's context is represented by a word-count (aka a word histogram) of its neighboring words. For example, the "sat" in "the cat sat on the mat" is represented as {"the": 2, "cat": 1, "on": 1}. Note that the last word "mat" is not used to represent "sat", because it is outside the neighborhood N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} . In continuous bag-of-words, the histogram is multiplied by a matrix V {\displaystyle V} to obtain a continuous representation of the word's context. The matrix V {\displaystyle V} is also called a dictionary. Its columns are the word vectors. It has D {\displaystyle D} columns, where D {\displaystyle D} is the size of the dictionary. Let d {\displaystyle d} be the length of each word vector. We have V ∈ R d × D {\displaystyle V\in \mathbb {R} ^{d\times D}} . For example, multiplying the word histogram {"the": 2, "cat": 1, "on": 1} with V {\displaystyle V} , we obtain 2 v the + v cat + v on {\displaystyle 2v_{\text{the}}+v_{\text{cat}}+v_{\text{on}}} . This is then multiplied with another matrix V ′ {\displaystyle V'} of shape R D × d {\displaystyle \mathbb {R} ^{D\times d}} . Each row of it is a word vector v ′ {\displaystyle v'} . This results in a vector of length D {\displaystyle D} , one entry per dictionary entry. Then, apply the softmax to obtain a probability distribution over the dictionary. This system can be visualized as a neural network, similar in spirit to an autoencoder, of architecture linear-linear-softmax, as depicted in the diagram. The system is trained by gradient descent to minimize the cross-entropy loss. In full formula, the cross-entropy loss is: − ∑ i ln ⁡ e v w i ′ ⋅ ( ∑ j ∈ N v w j + i ) ∑ w ′ e v w ′ ′ ⋅ ( ∑ j ∈ N v w j + i ) {\displaystyle -\sum _{i}\ln {\frac {e^{v_{w_{i}}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}{\sum _{w'}e^{v_{w'}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}}} where the outer summation ∑ i {\displaystyle \sum _{i}} is over the words in a corpus, the quantity ∑ j ∈ N v w j + i {\displaystyle \sum _{j\in N}v_{w_{j+i}}} is the sum of a word's neighbors' vectors, etc. Once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. For example, the word "sat" can be represented as either the "sat"-th column of V {\displaystyle V} or the "sat"-th row of V ′ {\displaystyle V'} . It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. === Skip-gram === The idea of skip-gram is to represent each word with a vector, such that it is possible to predict the vectors of its neighbors using the vector of a word. The architecture is still linear-linear-softmax, the same as CBOW, but the input and the output are switched. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ∑ j ∈ N ln ⁡ Pr ( w j + i ∣ w i ) {\displaystyle \sum _{i}\sum _{j\in N}\ln \Pr(w_{j+i}\mid w_{i})} . In full formula, the loss function is − ∑ i ∑ j ∈ N ln ⁡ e v w j + i ′ ⋅ v w i ∑ w ′ e v w ′ ′ ⋅ v w i {\displaystyle -\sum _{i}\sum _{j\in N}\ln {\frac {e^{v_{w_{j+i}}'\cdot v_{w_{i}}}}{\sum _{w'}e^{v_{w'}'\cdot v_{w_{i}}}}}} Same as CBOW, once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. Essentially, skip-gram and CBOW are exactly the same in architecture. They only differ in the objective function during training. == History == During the 1980s, there were some early attempts at using neural networks to represent words and concepts as vectors. In 2010, Tomáš Mikolov (then at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden

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  Statistical classification

  When classification is performed by a computer, statistical methods are normally used to develop the algorithm. Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. "A", "B", "AB" or "O", for blood type), ordinal (e.g. "large", "medium" or "small"), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure). Other classifiers work by comparing observations to previous observations by means of a similarity or distance function. An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category. Terminology across fields is quite varied. In statistics, where classification is often done with logistic regression or a similar procedure, the properties of observations are termed explanatory variables (or independent variables, regressors, etc.), and the categories to be predicted are known as outcomes, which are considered to be possible values of the dependent variable. In machine learning, the observations are often known as instances, the explanatory variables are termed features (grouped into a feature vector), and the possible categories to be predicted are classes. Other fields may use different terminology: e.g. in community ecology, the term "classification" normally refers to cluster analysis. == Relation to other problems == Classification and clustering are examples of the more general problem of pattern recognition, which is the assignment of some sort of output value to a given input value. Other examples are regression, which assigns a real-valued output to each input; sequence labeling, which assigns a class to each member of a sequence of values (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); parsing, which assigns a parse tree to an input sentence, describing the syntactic structure of the sentence; etc. A common subclass of classification is probabilistic classification. Algorithms of this nature use statistical inference to find the best class for a given instance. Unlike other algorithms, which simply output a "best" class, probabilistic algorithms output a probability of the instance being a member of each of the possible classes. The best class is normally then selected as the one with the highest probability. However, such an algorithm has numerous advantages over non-probabilistic classifiers: It can output a confidence value associated with its choice (in general, a classifier that can do this is known as a confidence-weighted classifier). Correspondingly, it can abstain when its confidence of choosing any particular output is too low. Because of the probabilities which are generated, probabilistic classifiers can be more effectively incorporated into larger machine-learning tasks, in a way that partially or completely avoids the problem of error propagation. == Frequentist procedures == Early work on statistical classification was undertaken by Fisher, in the context of two-group problems, leading to Fisher's linear discriminant function as the rule for assigning a group to a new observation. This early work assumed that data-values within each of the two groups had a multivariate normal distribution. The extension of this same context to more than two groups has also been considered with a restriction imposed that the classification rule should be linear. Later work for the multivariate normal distribution allowed the classifier to be nonlinear: several classification rules can be derived based on different adjustments of the Mahalanobis distance, with a new observation being assigned to the group whose centre has the lowest adjusted distance from the observation. == Bayesian procedures == Unlike frequentist procedures, Bayesian classification procedures provide a natural way of taking into account any available information about the relative sizes of the different groups within the overall population. Bayesian procedures tend to be computationally expensive and, in the days before Markov chain Monte Carlo computations were developed, approximations for Bayesian clustering rules were devised. Some Bayesian procedures involve the calculation of group-membership probabilities: these provide a more informative outcome than a simple attribution of a single group-label to each new observation. == Binary and multiclass classification == Classification can be thought of as two separate problems – binary classification and multiclass classification. In binary classification, a better understood task, only two classes are involved, whereas multiclass classification involves assigning an object to one of several classes. Since many classification methods have been developed specifically for binary classification, multiclass classification often requires the combined use of multiple binary classifiers. == Feature vectors == Most algorithms describe an individual instance whose category is to be predicted using a feature vector of individual, measurable properties of the instance. Each property is termed a feature, also known in statistics as an explanatory variable (or independent variable, although features may or may not be statistically independent). Features may variously be binary (e.g. "on" or "off"); categorical (e.g. "A", "B", "AB" or "O", for blood type); ordinal (e.g. "large", "medium" or "small"); integer-valued (e.g. the number of occurrences of a particular word in an email); or real-valued (e.g. a measurement of blood pressure). If the instance is an image, the feature values might correspond to the pixels of an image; if the instance is a piece of text, the feature values might be occurrence frequencies of different words. Some algorithms work only in terms of discrete data and require that real-valued or integer-valued data be discretized into groups (e.g. less than 5, between 5 and 10, or greater than 10). == Linear classifiers == A large number of algorithms for classification can be phrased in terms of a linear function that assigns a score to each possible category k by combining the feature vector of an instance with a vector of weights, using a dot product. The predicted category is the one with the highest score. This type of score function is known as a linear predictor function and has the following general form: score ⁡ ( X i , k ) = β k ⋅ X i , {\displaystyle \operatorname {score} (\mathbf {X} _{i},k)={\boldsymbol {\beta }}_{k}\cdot \mathbf {X} _{i},} where Xi is the feature vector for instance i, βk is the vector of weights corresponding to category k, and score(Xi, k) is the score associated with assigning instance i to category k. In discrete choice theory, where instances represent people and categories represent choices, the score is considered the utility associated with person i choosing category k. Algorithms with this basic setup are known as linear classifiers. What distinguishes them is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted. Examples of such algorithms include Logistic regression – Statistical model for a binary dependent variable Multinomial logistic regression – Regression for more than two discrete outcomes Probit regression – Statistical regression where the dependent variable can take only two valuesPages displaying short descriptions of redirect targets The perceptron algorithm Support vector machine – Set of methods for supervised statistical learning Linear discriminant analysis – Method used in statistics, pattern recognition, and other fields == Algorithms == Since no single form of classification is appropriate for all data sets, a large toolkit of classification algorithms has been developed. The most commonly used include: Artificial neural networks – Computational model used in machine learningPages displaying short descriptions of redirect targets Boosting (machine learning) – Ensemble learning method Random forest – Tree-based ensemble machine learning methods Genetic programming – Evolving computer programs with techniques analogous to natural genetic processes Gene expression programming – Evolutionary algorithm Multi expression programming Linear genetic programming Kernel estimation – Concept in statisticsPages displaying short descriptions of redirect targets k-nearest neighbor – Non-parametric classification methodPages displaying short descriptions of redirect targets Learning vector quantization Linear classifier – Statistical classification in machine learning Fisher's linear discriminant – Method used in statistics, pattern recognition, and other fieldsPages displaying short descriptions of redirect targets Logistic r

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  Crossover (evolutionary algorithm)

  Crossover in evolutionary algorithms and evolutionary computation, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. New solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions may be mutated before being added to the population. The aim of recombination is to transfer good characteristics from two different parents to one child. Different algorithms in evolutionary computation may use different data structures to store genetic information, and each genetic representation can be recombined with different crossover operators. Typical data structures that can be recombined with crossover are bit arrays, vectors of real numbers, or trees. The list of operators presented below is by no means complete and serves mainly as an exemplary illustration of this dyadic genetic operator type. More operators and more details can be found in the literature. == Crossover for binary arrays == Traditional genetic algorithms store genetic information in a chromosome represented by a bit array. Crossover methods for bit arrays are popular and an illustrative example of genetic recombination. === One-point crossover === A point on both parents' chromosomes is picked randomly, and designated a 'crossover point'. Bits to the right of that point are swapped between the two parent chromosomes. This results in two offspring, each carrying some genetic information from both parents. === Two-point and k-point crossover === In two-point crossover, two crossover points are picked randomly from the parent chromosomes. The bits in between the two points are swapped between the parent organisms. Two-point crossover is equivalent to performing two single-point crossovers with different crossover points. This strategy can be generalized to k-point crossover for any positive integer k, picking k crossover points. === Uniform crossover === In uniform crossover, typically, each bit is chosen from either parent with equal probability. Other mixing ratios are sometimes used, resulting in offspring which inherit more genetic information from one parent than the other. In a uniform crossover, we don’t divide the chromosome into segments, rather we treat each gene separately. In this, we essentially flip a coin for each chromosome to decide whether or not it will be included in the off-spring. == Crossover for integer or real-valued genomes == For the crossover operators presented above and for most other crossover operators for bit strings, it holds that they can also be applied accordingly to integer or real-valued genomes whose genes each consist of an integer or real-valued number. Instead of individual bits, integer or real-valued numbers are then simply copied into the child genome. The offspring lie on the remaining corners of the hyperbody spanned by the two parents P 1 = ( 1.5 , 6 , 8 ) {\displaystyle P_{1}=(1.5,6,8)} and P 2 = ( 7 , 2 , 1 ) {\displaystyle P_{2}=(7,2,1)} , as exemplified in the accompanying image for the three-dimensional case. === Discrete recombination === If the rules of the uniform crossover for bit strings are applied during the generation of the offspring, this is also called discrete recombination. === Intermediate recombination === In this recombination operator, the allele values of the child genome a i {\displaystyle a_{i}} are generated by mixing the alleles of the two parent genomes a i , P 1 {\displaystyle a_{i,P_{1}}} and a i , P 2 {\displaystyle a_{i,P_{2}}} : α i = α i , P 1 ⋅ β i + α i , P 2 ⋅ ( 1 − β i ) w i t h β i ∈ [ − d , 1 + d ] {\displaystyle \alpha _{i}=\alpha _{i,P_{1}}\cdot \beta _{i}+\alpha _{i,P_{2}}\cdot \left(1-\beta _{i}\right)\quad {\mathsf {with}}\quad \beta _{i}\in \left[-d,1+d\right]} randomly equally distributed per gene i {\displaystyle i} The choice of the interval [ − d , 1 + d ] {\displaystyle [-d,1+d]} causes that besides the interior of the hyperbody spanned by the allele values of the parent genes additionally a certain environment for the range of values of the offspring is in question. A value of 0.25 {\displaystyle 0.25} is recommended for d {\displaystyle d} to counteract the tendency to reduce the allele values that otherwise exists at d = 0 {\displaystyle d=0} . The adjacent figure shows for the two-dimensional case the range of possible new alleles of the two exemplary parents P 1 = ( 3 , 6 ) {\displaystyle P_{1}=(3,6)} and P 2 = ( 9 , 2 ) {\displaystyle P_{2}=(9,2)} in intermediate recombination. The offspring of discrete recombination C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} are also plotted. Intermediate recombination satisfies the arithmetic calculation of the allele values of the child genome required by virtual alphabet theory. Discrete and intermediate recombination are used as a standard in the evolution strategy. == Crossover for permutations == For combinatorial tasks, permutations are usually used that are specifically designed for genomes that are themselves permutations of a set. The underlying set is usually a subset of N {\displaystyle \mathbb {N} } or N 0 {\displaystyle \mathbb {N} _{0}} . If 1- or n-point or uniform crossover for integer genomes is used for such genomes, a child genome may contain some values twice and others may be missing. This can be remedied by genetic repair, e.g. by replacing the redundant genes in positional fidelity for missing ones from the other child genome. In order to avoid the generation of invalid offspring, special crossover operators for permutations have been developed which fulfill the basic requirements of such operators for permutations, namely that all elements of the initial permutation are also present in the new one and only the order is changed. It can be distinguished between combinatorial tasks, where all sequences are admissible, and those where there are constraints in the form of inadmissible partial sequences. A well-known representative of the first task type is the traveling salesman problem (TSP), where the goal is to visit a set of cities exactly once on the shortest tour. An example of the constrained task type is the scheduling of multiple workflows. Workflows involve sequence constraints on some of the individual work steps. For example, a thread cannot be cut until the corresponding hole has been drilled in a workpiece. Such problems are also called order-based permutations. In the following, two crossover operators are presented as examples, the partially mapped crossover (PMX) motivated by the TSP and the order crossover (OX1) designed for order-based permutations. A second offspring can be produced in each case by exchanging the parent chromosomes. === Partially mapped crossover (PMX) === The PMX operator was designed as a recombination operator for TSP like Problems. The explanation of the procedure is illustrated by an example: === Order crossover (OX1) === The order crossover goes back to Davis in its original form and is presented here in a slightly generalized version with more than two crossover points. It transfers information about the relative order from the second parent to the offspring. First, the number and position of the crossover points are determined randomly. The resulting gene sequences are then processed as described below: Among other things, order crossover is well suited for scheduling multiple workflows, when used in conjunction with 1- and n-point crossover. === Further crossover operators for permutations === Over time, a large number of crossover operators for permutations have been proposed, so the following list is only a small selection. For more information, the reader is referred to the literature. cycle crossover (CX) order-based crossover (OX2) position-based crossover (POS) edge recombination voting recombination (VR) alternating-positions crossover (AP) maximal preservative crossover (MPX) merge crossover (MX) sequential constructive crossover operator (SCX) The usual approach to solving TSP-like problems by genetic or, more generally, evolutionary algorithms, presented earlier, is either to repair illegal descendants or to adjust the operators appropriately so that illegal offspring do not arise in the first place. Alternatively, Riazi suggests the use of a double chromosome representation, which avoids illegal offspring.

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  GeoNetwork opensource

  The GeoNetwork opensource (GNOS) project is a free and open source (FOSS) cataloging application for spatially referenced resources. It is a catalog of location-oriented information. == Outline == It is a standardized and decentralized spatial information management environment designed to enable access to geo-referenced databases, cartographic products and related metadata from a variety of sources, enhancing the spatial information exchange and sharing between organizations and their audience, using the capacities of the internet. Using the Z39.50 protocol it both accesses remote catalogs and makes its data available to other catalog services. As of 2007, OGC Web Catalog Service are being implemented. Maps, including those derived from satellite imagery, are effective communicational tools and play an important role in the work of decision makers (e.g., sustainable development planners and humanitarian and emergency managers) in need of quick, reliable and up-to-date user-friendly cartographic products as a basis for action and to better plan and monitor their activities; GIS experts in need of exchanging consistent and updated geographical data; and spatial analysts in need of multidisciplinary data to perform preliminary geographical analysis and make reliable forecasts. == Deployment == The software has been deployed to various organizations, the first being FAO GeoNetwork and WFP VAM-SIE-GeoNetwork, both at their headquarters in Rome, Italy. Furthermore, the WHO, CGIAR, BRGM, ESA, FGDC and the Global Change Information and Research Centre (GCIRC) of China are working on GeoNetwork opensource implementations as their spatial information management capacity. It is used for several risk information systems, in particular in the Gambia. Several related tools are packaged with GeoNetwork, including GeoServer. GeoServer stores geographical data, while GeoNetwork catalogs collections of such data.

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  Spiking neural network

  Spiking neural networks (SNNs) are artificial neural networks (ANN) that mimic natural neural networks. These models leverage timing of discrete spikes as the main information carrier. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neurons in the SNN do not transmit information at each propagation cycle (as it happens with typical multi-layer perceptron networks), but rather transmit information only when a membrane potential—an intrinsic quality of the neuron related to its membrane electrical charge—reaches a specific value, called the threshold. When the membrane potential reaches the threshold, the neuron fires, and generates a signal that travels to other neurons which, in turn, increase or decrease their potentials in response to this signal. A neuron model that fires at the moment of threshold crossing is also called a spiking neuron model. While spike rates can be considered the analogue of the variable output of a traditional ANN, neurobiology research indicated that high speed processing cannot be performed solely through a rate-based scheme. For example humans can perform an image recognition task requiring no more than 10ms of processing time per neuron through the successive layers (going from the retina to the temporal lobe). This time window is too short for rate-based encoding. The precise spike timings in a small set of spiking neurons also has a higher information coding capacity compared with a rate-based approach. The most prominent spiking neuron model is the leaky integrate-and-fire model. In that model, the momentary activation level (modeled as a differential equation) is normally considered to be the neuron's state, with incoming spikes pushing this value higher or lower, until the state eventually either decays or—if the firing threshold is reached—the neuron fires. After firing, the state variable is reset to a lower value. Various decoding methods exist for interpreting the outgoing spike train as a real-value number, relying on either the frequency of spikes (rate-code), the time-to-first-spike after stimulation, or the interval between spikes. == History == Many multi-layer artificial neural networks are fully connected, receiving input from every neuron in the previous layer and signalling every neuron in the subsequent layer. Although these networks have achieved breakthroughs, they do not match biological networks and do not mimic neurons. The biology-inspired Hodgkin–Huxley model of a spiking neuron was proposed in 1952. This model described how action potentials are initiated and propagated. Communication between neurons, which requires the exchange of chemical neurotransmitters in the synaptic gap, is described in models such as the integrate-and-fire model, FitzHugh–Nagumo model (1961–1962), and Hindmarsh–Rose model (1984). The leaky integrate-and-fire model (or a derivative) is commonly used as it is easier to compute than Hodgkin–Huxley. While the notion of an artificial spiking neural network became popular only in the twenty-first century, studies between 1980 and 1995 supported the concept. The first models of this type of ANN appeared to simulate non-algorithmic intelligent information processing systems. However, the notion of the spiking neural network as a mathematical model was first worked on in the early 1970s. As of 2019 SNNs lagged behind ANNs in accuracy, but the gap is decreasing, and has vanished on some tasks. == Underpinnings == Information in the brain is represented as action potentials (neuron spikes), which may group into spike trains or coordinated waves. A fundamental question of neuroscience is to determine whether neurons communicate by a rate or temporal code. Temporal coding implies that a single spiking neuron can replace hundreds of hidden units on a conventional neural net. SNNs define a neuron's current state as its potential (possibly modeled as a differential equation). An input pulse causes the potential to rise and then gradually decline. Encoding schemes can interpret these pulse sequences as a number, considering pulse frequency and pulse interval. Using the precise time of pulse occurrence, a neural network can consider more information and offer better computing properties. SNNs compute in the continuous domain. Such neurons test for activation only when their potentials reach a certain value. When a neuron is activated, it produces a signal that is passed to connected neurons, accordingly raising or lowering their potentials. The SNN approach produces a continuous output instead of the binary output of traditional ANNs. Pulse trains are not easily interpretable, hence the need for encoding schemes. However, a pulse train representation may be more suited for processing spatiotemporal data (or real-world sensory data classification). SNNs connect neurons only to nearby neurons so that they process input blocks separately (similar to CNN using filters). They consider time by encoding information as pulse trains so as not to lose information. This avoids the complexity of a recurrent neural network (RNN). Impulse neurons are more powerful computational units than traditional artificial neurons. SNNs are theoretically more powerful than so called "second-generation networks" defined as ANNs "based on computational units that apply activation function with a continuous set of possible output values to a weighted sum (or polynomial) of the inputs"; however, SNN training issues and hardware requirements limit their use. Although unsupervised biologically inspired learning methods are available such as Hebbian learning and STDP, no effective supervised training method is suitable for SNNs that can provide better performance than second-generation networks. Spike-based activation of SNNs is not differentiable, thus gradient descent-based backpropagation (BP) is not available. SNNs have much larger computational costs for simulating realistic neural models than traditional ANNs. Pulse-coupled neural networks (PCNN) are often confused with SNNs. A PCNN can be seen as a kind of SNN. Researchers are actively working on various topics. The first concerns differentiability. The expressions for both the forward- and backward-learning methods contain the derivative of the neural activation function which is not differentiable because a neuron's output is either 1 when it spikes, and 0 otherwise. This all-or-nothing behavior disrupts gradients and makes these neurons unsuitable for gradient-based optimization. Approaches to resolving it include: resorting to entirely biologically inspired local learning rules for the hidden units translating conventionally trained "rate-based" NNs to SNNs smoothing the network model to be continuously differentiable defining an SG (Surrogate Gradient) as a continuous relaxation of the real gradients The second concerns the optimization algorithm. Standard BP can be expensive in terms of computation, memory, and communication and may be poorly suited to the hardware that implements it (e.g., a computer, brain, or neuromorphic device). Incorporating additional neuron dynamics such as Spike Frequency Adaptation (SFA) is a notable advance, enhancing efficiency and computational power. These neurons sit between biological complexity and computational complexity. Originating from biological insights, SFA offers significant computational benefits by reducing power usage, especially in cases of repetitive or intense stimuli. This adaptation improves signal/noise clarity and introduces an elementary short-term memory at the neuron level, which in turn, improves accuracy and efficiency. This was mostly achieved using compartmental neuron models. The simpler versions are of neuron models with adaptive thresholds, are an indirect way of achieving SFA. It equips SNNs with improved learning capabilities, even with constrained synaptic plasticity, and elevates computational efficiency. This feature lessens the demand on network layers by decreasing the need for spike processing, thus lowering computational load and memory access time—essential aspects of neural computation. Moreover, SNNs utilizing neurons capable of SFA achieve levels of accuracy that rival those of conventional ANNs, while also requiring fewer neurons for comparable tasks. This efficiency streamlines the computational workflow and conserves space and energy, while maintaining technical integrity. High-performance deep spiking neural networks can operate with 0.3 spikes per neuron. == Applications == SNNs can in principle be applied to the same applications as traditional ANNs. In addition, SNNs can model the central nervous system of biological organisms, such as an insect seeking food without prior knowledge of the environment. Due to their relative realism, they can be used to study biological neural circuits. Starting with a hypothesis about the topology of a biological neuronal circuit and its functi

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  U-matrix

  The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of neighboring neurons is depicted in a grayscale image. This image is used to visualize the data in a high-dimensional space using a 2D image. == Construction procedure == Once the SOM is trained using the input data, the final map is not expected to have any twists. If the map is twist-free, the distance between the codebook vectors of neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a grayscale image, light colors depict closely spaced node codebook vectors and darker colors indicate more widely separated node codebook vectors. Thus, groups of light colors can be considered as clusters, and the dark parts as the boundaries between the clusters. This representation can help to visualize the clusters in the high-dimensional spaces, or to automatically recognize them using relatively simple image processing techniques.

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  Natarajan dimension

  In the theory of Probably Approximately Correct Machine Learning, the Natarajan dimension characterizes the complexity of learning a set of functions, generalizing from the Vapnik–Chervonenkis dimension for boolean functions to multi-class functions. Originally introduced as the Generalized Dimension by Natarajan, it was subsequently renamed the Natarajan Dimension by Haussler and Long. == Definition == Let H {\displaystyle H} be a set of functions from a set X {\displaystyle X} to a set Y {\displaystyle Y} . H {\displaystyle H} shatters a set C ⊂ X {\displaystyle C\subset X} if there exist two functions f 0 , f 1 ∈ H {\displaystyle f_{0},f_{1}\in H} such that For every x ∈ C , f 0 ( x ) ≠ f 1 ( x ) {\displaystyle x\in C,f_{0}(x)\neq f_{1}(x)} . For every B ⊂ C {\displaystyle B\subset C} , there exists a function h ∈ H {\displaystyle h\in H} such that for all x ∈ B , h ( x ) = f 0 ( x ) {\displaystyle x\in B,h(x)=f_{0}(x)} and for all x ∈ C − B , h ( x ) = f 1 ( x ) {\displaystyle x\in C-B,h(x)=f_{1}(x)} . The Natarajan dimension of H is the maximal cardinality of a set shattered by H {\displaystyle H} . It is easy to see that if | Y | = 2 {\displaystyle |Y|=2} , the Natarajan dimension collapses to the Vapnik–Chervonenkis dimension. Shalev-Shwartz and Ben-David present comprehensive material on multi-class learning and the Natarajan dimension, including uniform convergence and learnability. Recently, Cohen et al showed that the Natarajan dimension is the dominant term governing agnostic multi-class PAC learnability.

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  Bottlenose (company)

  Bottlenose.com, also known as Bottlenose, is an enterprise trend intelligence company that analyzes big data and business data to detect trends for brands. It helps Fortune 500 enterprises discover, and track emerging trends that affect their brands. The company uses natural language processing, sentiment analysis, statistical algorithms, data mining, and machine learning heuristics to determine trends, and has a search engine that gathers information from social networks. KPMG Capital has invested a "substantial amount" in the company. Bottlenose processed 72 billion messages per day, in real-time, from across social and broadcast media, as of December 2014. == History == The company is based in Los Angeles, CA. Bottlenose is a real-time trend intelligence tool that measures social media campaigns and trends. The company also provides a free version of its Sonar tool that shows real-time trends across social media. In October 2012, the company received $1 million of funding from ff Venture Capital and Prosper Capital. By 2014, the company raised about $7 million in funding. In December 2014, KPMG Capital announced further investment in the company. In February 2015, the company confirmed it had raised $13.4 million in Series B funding led by KPMG Capital. Bottlenose partnered with the nonprofit No Labels during the 2014 State of the Union Address to analyze Twitter conversations for bipartisanship. The company also partnered with media monitoring company Critical Mention to analyze broadcast analytics. The Bottlenose Nerve Center integrated with the Critical Mention API to analyze real-time trends in television and radio broadcasts. In June 2014, Bottlenose updated its trend detection product to Nerve Center 2.0. It creates a newsfeed to show changes in trends and sends alerts when trends occur. It also has "emotion detection," which will display the emotions associated with specific comments on trending topics. In 2016, Bottlenose released its Nerve Center 3.0 platform, which was designed to automate the work of data scientists and lower the cost of artificial intelligence for businesses.

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  FastICA

  FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify. FastICA can also be alternatively derived as an approximative Newton iteration. == Algorithm == === Prewhitening the data === Let the X := ( x i j ) ∈ R N × M {\displaystyle \mathbf {X} :=(x_{ij})\in \mathbb {R} ^{N\times M}} denote the input data matrix, M {\displaystyle M} the number of columns corresponding with the number of samples of mixed signals and N {\displaystyle N} the number of rows corresponding with the number of independent source signals. The input data matrix X {\displaystyle \mathbf {X} } must be prewhitened, or centered and whitened, before applying the FastICA algorithm to it. Centering the data entails demeaning each component of the input data X {\displaystyle \mathbf {X} } , that is, for each i = 1 , … , N {\displaystyle i=1,\ldots ,N} and j = 1 , … , M {\displaystyle j=1,\ldots ,M} . After centering, each row of X {\displaystyle \mathbf {X} } has an expected value of 0 {\displaystyle 0} . Whitening the data requires a linear transformation L : R N × M → R N × M {\displaystyle \mathbf {L} :\mathbb {R} ^{N\times M}\to \mathbb {R} ^{N\times M}} of the centered data so that the components of L ( X ) {\displaystyle \mathbf {L} (\mathbf {X} )} are uncorrelated and have variance one. More precisely, if X {\displaystyle \mathbf {X} } is a centered data matrix, the covariance of L x := L ( X ) {\displaystyle \mathbf {L} _{\mathbf {x} }:=\mathbf {L} (\mathbf {X} )} is the ( N × N ) {\displaystyle (N\times N)} -dimensional identity matrix, that is, A common method for whitening is by performing an eigenvalue decomposition on the covariance matrix of the centered data X {\displaystyle \mathbf {X} } , E { X X T } = E D E T {\displaystyle E\left\{\mathbf {X} \mathbf {X} ^{T}\right\}=\mathbf {E} \mathbf {D} \mathbf {E} ^{T}} , where E {\displaystyle \mathbf {E} } is the matrix of eigenvectors and D {\displaystyle \mathbf {D} } is the diagonal matrix of eigenvalues. The whitened data matrix is defined thus by === Single component extraction === The iterative algorithm finds the direction for the weight vector w ∈ R N {\displaystyle \mathbf {w} \in \mathbb {R} ^{N}} that maximizes a measure of non-Gaussianity of the projection w T X {\displaystyle \mathbf {w} ^{T}\mathbf {X} } , with X ∈ R N × M {\displaystyle \mathbf {X} \in \mathbb {R} ^{N\times M}} denoting a prewhitened data matrix as described above. Note that w {\displaystyle \mathbf {w} } is a column vector. To measure non-Gaussianity, FastICA relies on a nonquadratic nonlinear function f ( u ) {\displaystyle f(u)} , its first derivative g ( u ) {\displaystyle g(u)} , and its second derivative g ′ ( u ) {\displaystyle g^{\prime }(u)} . Hyvärinen states that the functions are useful for general purposes, while may be highly robust. The steps for extracting the weight vector w {\displaystyle \mathbf {w} } for single component in FastICA are the following: Randomize the initial weight vector w {\displaystyle \mathbf {w} } Let w + ← E { X g ( w T X ) T } − E { g ′ ( w T X ) } w {\displaystyle \mathbf {w} ^{+}\leftarrow E\left\{\mathbf {X} g(\mathbf {w} ^{T}\mathbf {X} )^{T}\right\}-E\left\{g'(\mathbf {w} ^{T}\mathbf {X} )\right\}\mathbf {w} } , where E { . . . } {\displaystyle E\left\{...\right\}} means averaging over all column-vectors of matrix X {\displaystyle \mathbf {X} } Let w ← w + / ‖ w + ‖ {\displaystyle \mathbf {w} \leftarrow \mathbf {w} ^{+}/\|\mathbf {w} ^{+}\|} If not converged, go back to 2 === Multiple component extraction === The single unit iterative algorithm estimates only one weight vector which extracts a single component. Estimating additional components that are mutually "independent" requires repeating the algorithm to obtain linearly independent projection vectors - note that the notion of independence here refers to maximizing non-Gaussianity in the estimated components. Hyvärinen provides several ways of extracting multiple components with the simplest being the following. Here, 1 M {\displaystyle \mathbf {1_{M}} } is a column vector of 1's of dimension M {\displaystyle M} . Algorithm FastICA Input: C {\displaystyle C} Number of desired components Input: X ∈ R N × M {\displaystyle \mathbf {X} \in \mathbb {R} ^{N\times M}} Prewhitened matrix, where each column represents an N {\displaystyle N} -dimensional sample, where C <= N {\displaystyle C<=N} Output: W ∈ R N × C {\displaystyle \mathbf {W} \in \mathbb {R} ^{N\times C}} Un-mixing matrix where each column projects X {\displaystyle \mathbf {X} } onto independent component. Output: S ∈ R C × M {\displaystyle \mathbf {S} \in \mathbb {R} ^{C\times M}} Independent components matrix, with M {\displaystyle M} columns representing a sample with C {\displaystyle C} dimensions. for p in 1 to C: w p ← {\displaystyle \mathbf {w_{p}} \leftarrow } Random vector of length N while w p {\displaystyle \mathbf {w_{p}} } changes w p ← 1 M X g ( w p T X ) T − 1 M g ′ ( w p T X ) 1 M w p {\displaystyle \mathbf {w_{p}} \leftarrow {\frac {1}{M}}\mathbf {X} g(\mathbf {w_{p}} ^{T}\mathbf {X} )^{T}-{\frac {1}{M}}g'(\mathbf {w_{p}} ^{T}\mathbf {X} )\mathbf {1_{M}} \mathbf {w_{p}} } w p ← w p − ∑ j = 1 p − 1 ( w p T w j ) w j {\displaystyle \mathbf {w_{p}} \leftarrow \mathbf {w_{p}} -\sum _{j=1}^{p-1}(\mathbf {w_{p}} ^{T}\mathbf {w_{j}} )\mathbf {w_{j}} } w p ← w p ‖ w p ‖ {\displaystyle \mathbf {w_{p}} \leftarrow {\frac {\mathbf {w_{p}} }{\|\mathbf {w_{p}} \|}}} output W ← [ w 1 , … , w C ] {\displaystyle \mathbf {W} \leftarrow {\begin{bmatrix}\mathbf {w_{1}} ,\dots ,\mathbf {w_{C}} \end{bmatrix}}} output S ← W T X {\displaystyle \mathbf {S} \leftarrow \mathbf {W^{T}} \mathbf {X} }

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  Genetic representation

  In computer programming, genetic representation is a way of presenting solutions/individuals in evolutionary computation methods. The term encompasses both the concrete data structures and data types used to realize the genetic material of the candidate solutions in the form of a genome, and the relationships between search space and problem space. In the simplest case, the search space corresponds to the problem space (direct representation). The choice of problem representation is tied to the choice of genetic operators, both of which have a decisive effect on the efficiency of the optimization. Genetic representation can encode appearance, behavior, physical qualities of individuals. Difference in genetic representations is one of the major criteria drawing a line between known classes of evolutionary computation. Terminology is often analogous with natural genetics. The block of computer memory that represents one candidate solution is called an individual. The data in that block is called a chromosome. Each chromosome consists of genes. The possible values of a particular gene are called alleles. A programmer may represent all the individuals of a population using binary encoding, permutational encoding, encoding by tree, or any one of several other representations. == Representations in some popular evolutionary algorithms == Genetic algorithms (GAs) are typically linear representations; these are often, but not always, binary. Holland's original description of GA used arrays of bits. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size. This facilitates simple crossover operation. Depending on the application, variable-length representations have also been successfully used and tested in evolutionary algorithms (EA) in general and genetic algorithms in particular, although the implementation of crossover is more complex in this case. Evolution strategy uses linear real-valued representations, e.g., an array of real values. It uses mostly gaussian mutation and blending/averaging crossover. Genetic programming (GP) pioneered tree-like representations and developed genetic operators suitable for such representations. Tree-like representations are used in GP to represent and evolve functional programs with desired properties. Human-based genetic algorithm (HBGA) offers a way to avoid solving hard representation problems by outsourcing all genetic operators to outside agents, in this case, humans. The algorithm has no need for knowledge of a particular fixed genetic representation as long as there are enough external agents capable of handling those representations, allowing for free-form and evolving genetic representations. === Common genetic representations === binary array integer or real-valued array binary tree natural language parse tree directed graph == Distinction between search space and problem space == Analogous to biology, EAs distinguish between problem space (corresponds to phenotype) and search space (corresponds to genotype). The problem space contains concrete solutions to the problem being addressed, while the search space contains the encoded solutions. The mapping from search space to problem space is called genotype-phenotype mapping. The genetic operators are applied to elements of the search space, and for evaluation, elements of the search space are mapped to elements of the problem space via genotype-phenotype mapping. == Relationships between search space and problem space == The importance of an appropriate choice of search space for the success of an EA application was recognized early on. The following requirements can be placed on a suitable search space and thus on a suitable genotype-phenotype mapping: === Completeness === All possible admissible solutions must be contained in the search space. === Redundancy === When more possible genotypes exist than phenotypes, the genetic representation of the EA is called redundant. In nature, this is termed a degenerate genetic code. In the case of a redundant representation, neutral mutations are possible. These are mutations that change the genotype but do not affect the phenotype. Thus, depending on the use of the genetic operators, there may be phenotypically unchanged offspring, which can lead to unnecessary fitness determinations, among other things. Since the evaluation in real-world applications usually accounts for the lion's share of the computation time, it can slow down the optimization process. In addition, this can cause the population to have higher genotypic diversity than phenotypic diversity, which can also hinder evolutionary progress. In biology, the Neutral Theory of Molecular Evolution states that this effect plays a dominant role in natural evolution. This has motivated researchers in the EA community to examine whether neutral mutations can improve EA functioning by giving populations that have converged to a local optimum a way to escape that local optimum through genetic drift. This is discussed controversially and there are no conclusive results on neutrality in EAs. On the other hand, there are other proven measures to handle premature convergence. === Locality === The locality of a genetic representation corresponds to the degree to which distances in the search space are preserved in the problem space after genotype-phenotype mapping. That is, a representation has a high locality exactly when neighbors in the search space are also neighbors in the problem space. In order for successful schemata not to be destroyed by genotype-phenotype mapping after a minor mutation, the locality of a representation must be high. === Scaling === In genotype-phenotype mapping, the elements of the genotype can be scaled (weighted) differently. The simplest case is uniform scaling: all elements of the genotype are equally weighted in the phenotype. A common scaling is exponential. If integers are binary coded, the individual digits of the resulting binary number have exponentially different weights in representing the phenotype. Example: The number 90 is written in binary (i.e., in base two) as 1011010. If now one of the front digits is changed in the binary notation, this has a significantly greater effect on the coded number than any changes at the rear digits (the selection pressure has an exponentially greater effect on the front digits). For this reason, exponential scaling has the effect of randomly fixing the "posterior" locations in the genotype before the population gets close enough to the optimum to adjust for these subtleties. == Hybridization and repair in genotype-phenotype mapping == When mapping the genotype to the phenotype being evaluated, domain-specific knowledge can be used to improve the phenotype and/or ensure that constraints are met. This is a commonly used method to improve EA performance in terms of runtime and solution quality. It is illustrated below by two of the three examples. == Examples == === Example of a direct representation === An obvious and commonly used encoding for the traveling salesman problem and related tasks is to number the cities to be visited consecutively and store them as integers in the chromosome. The genetic operators must be suitably adapted so that they only change the order of the cities (genes) and do not cause deletions or duplications. Thus, the gene order corresponds to the city order and there is a simple one-to-one mapping. === Example of a complex genotype-phenotype mapping === In a scheduling task with heterogeneous and partially alternative resources to be assigned to a set of subtasks, the genome must contain all necessary information for the individual scheduling operations or it must be possible to derive them from it. In addition to the order of the subtasks to be executed, this includes information about the resource selection. A phenotype then consists of a list of subtasks with their start times and assigned resources. In order to be able to create this, as many allocation matrices must be created as resources can be allocated to one subtask at most. In the simplest case this is one resource, e.g., one machine, which can perform the subtask. An allocation matrix is a two-dimensional matrix, with one dimension being the available time units and the other being the resources to be allocated. Empty matrix cells indicate availability, while an entry indicates the number of the assigned subtask. The creation of allocation matrices ensures firstly that there are no inadmissible multiple allocations. Secondly, the start times of the subtasks can be read from it as well as the assigned resources. A common constraint when scheduling resources to subtasks is that a resource can only be allocated once per time unit and that the reservation must be for a contiguous period of time. To achieve this in a timely manner, which is a c

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  Error-driven learning

  In reinforcement learning, error-driven learning is a method for adjusting a model's (intelligent agent's) parameters based on the difference between its output results and the ground truth. These models stand out as they depend on environmental feedback, rather than explicit labels or categories. They are based on the idea that language acquisition involves the minimization of the prediction error (MPSE). By leveraging these prediction errors, the models consistently refine expectations and decrease computational complexity. Typically, these algorithms are operated by the GeneRec algorithm. Error-driven learning has widespread applications in cognitive sciences and computer vision. These methods have also found successful application in natural language processing (NLP), including areas like part-of-speech tagging, parsing, named entity recognition (NER), machine translation (MT), speech recognition (SR), and dialogue systems. == Formal Definition == Error-driven learning models are ones that rely on the feedback of prediction errors to adjust the expectations or parameters of a model. The key components of error-driven learning include the following: A set S {\displaystyle S} of states representing the different situations that the learner can encounter. A set A {\displaystyle A} of actions that the learner can take in each state. A prediction function P ( s , a ) {\displaystyle P(s,a)} that gives the learner's current prediction of the outcome of taking action a {\displaystyle a} in state s {\displaystyle s} . An error function E ( o , p ) {\displaystyle E(o,p)} that compares the actual outcome o {\displaystyle o} with the prediction p {\displaystyle p} and produces an error value. An update rule U ( p , e ) {\displaystyle U(p,e)} that adjusts the prediction p {\displaystyle p} in light of the error e {\displaystyle e} . == Algorithms == Error-driven learning algorithms refer to a category of reinforcement learning algorithms that leverage the disparity between the real output and the expected output of a system to regulate the system's parameters. Typically applied in supervised learning, these algorithms are provided with a collection of input-output pairs to facilitate the process of generalization. The widely utilized error backpropagation learning algorithm is known as GeneRec, a generalized recirculation algorithm primarily employed for gene prediction in DNA sequences. Many other error-driven learning algorithms are derived from alternative versions of GeneRec. == Applications == === Cognitive science === Simpler error-driven learning models effectively capture complex human cognitive phenomena and anticipate elusive behaviors. They provide a flexible mechanism for modeling the brain's learning process, encompassing perception, attention, memory, and decision-making. By using errors as guiding signals, these algorithms adeptly adapt to changing environmental demands and objectives, capturing statistical regularities and structure. Furthermore, cognitive science has led to the creation of new error-driven learning algorithms that are both biologically acceptable and computationally efficient. These algorithms, including deep belief networks, spiking neural networks, and reservoir computing, follow the principles and constraints of the brain and nervous system. Their primary aim is to capture the emergent properties and dynamics of neural circuits and systems. === Computer vision === Computer vision is a complex task that involves understanding and interpreting visual data, such as images or videos. In the context of error-driven learning, the computer vision model learns from the mistakes it makes during the interpretation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This repeated process of learning from errors helps improve the model's performance over time. For NLP to do well at computer vision, it employs deep learning techniques. This form of computer vision is sometimes called neural computer vision (NCV), since it makes use of neural networks. NCV therefore interprets visual data based on a statistical, trial and error approach and can deal with context and other subtleties of visual data. === Natural Language Processing === ==== Part-of-speech tagging ==== Part-of-speech (POS) tagging is a crucial component in Natural Language Processing (NLP). It helps resolve human language ambiguity at different analysis levels. In addition, its output (tagged data) can be used in various applications of NLP such as information extraction, information retrieval, question Answering, speech eecognition, text-to-speech conversion, partial parsing, and grammar correction. ==== Parsing ==== Parsing in NLP involves breaking down a text into smaller pieces (phrases) based on grammar rules. If a sentence cannot be parsed, it may contain grammatical errors. In the context of error-driven learning, the parser learns from the mistakes it makes during the parsing process. When an error is encountered, the parser updates its internal model to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the parser's performance over time. In conclusion, error-driven learning plays a crucial role in improving the accuracy and efficiency of NLP parsers by allowing them to learn from their mistakes and adapt their internal models accordingly. ==== Named entity recognition (NER) ==== NER is the task of identifying and classifying entities (such as persons, locations, organizations, etc.) in a text. Error-driven learning can help the model learn from its false positives and false negatives and improve its recall and precision on (NER). In the context of error-driven learning, the significance of NER is quite profound. Traditional sequence labeling methods identify nested entities layer by layer. If an error occurs in the recognition of an inner entity, it can lead to incorrect identification of the outer entity, leading to a problem known as error propagation of nested entities. This is where the role of NER becomes crucial in error-driven learning. By accurately recognizing and classifying entities, it can help minimize these errors and improve the overall accuracy of the learning process. Furthermore, deep learning-based NER methods have shown to be more accurate as they are capable of assembling words, enabling them to understand the semantic and syntactic relationship between various words better. ==== Machine translation ==== Machine translation is a complex task that involves converting text from one language to another. In the context of error-driven learning, the machine translation model learns from the mistakes it makes during the translation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Speech recognition ==== Speech recognition is a complex task that involves converting spoken language into written text. In the context of error-driven learning, the speech recognition model learns from the mistakes it makes during the recognition process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Dialogue systems ==== Dialogue systems are a popular NLP task as they have promising real-life applications. They are also complicated tasks since many NLP tasks deserving study are involved. In the context of error-driven learning, the dialogue system learns from the mistakes it makes during the dialogue process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. == Advantages == Error-driven learning has several advantages over other types of machine learning algorithms: They can learn from feedback and correct their mistakes, which makes them adaptive and robust to noise and changes in the data. They can handle large and high-dimensional data sets, as they do not require explicit feature engineering or prior knowledge of the data distribution. They can achieve high accuracy and performance, as they can learn complex and nonlinear relationships between the input and the output. == Limitations == Although error driven learning has its advantages, their algorithms also have the following limitations: They can suffer from overfitting, which means that they memorize the training data and fail to generalize to new and unseen data. This can be mitigated by using regularization techniques, such as adding a penalty term to the loss function, or reducing the complexity of the model. They can be sensitive to the choice of

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  Semantic compression

  In natural language processing, semantic compression is a process of compacting a lexicon used to build a textual document (or a set of documents) by reducing language heterogeneity, while maintaining text semantics. As a result, the same ideas can be represented using a smaller set of words. In most applications, semantic compression is a lossy compression. Increased prolixity does not compensate for the lexical compression and an original document cannot be reconstructed in a reverse process. == By generalization == Semantic compression is basically achieved in two steps, using frequency dictionaries and semantic network: determining cumulated term frequencies to identify target lexicon, replacing less frequent terms with their hypernyms (generalization) from target lexicon. Step 1 requires assembling word frequencies and information on semantic relationships, specifically hyponymy. Moving upwards in word hierarchy, a cumulative concept frequency is calculating by adding a sum of hyponyms' frequencies to frequency of their hypernym: c u m f ( k i ) = f ( k i ) + ∑ j c u m f ( k j ) {\displaystyle cumf(k_{i})=f(k_{i})+\sum _{j}cumf(k_{j})} where k i {\displaystyle k_{i}} is a hypernym of k j {\displaystyle k_{j}} . Then a desired number of words with top cumulated frequencies are chosen to build a target lexicon. In the second step, compression mapping rules are defined for the remaining words in order to handle every occurrence of a less frequent hyponym as its hypernym in output text. Example The below fragment of text has been processed by the semantic compression. Words in bold have been replaced by their hypernyms. They are both nest building social insects, but paper wasps and honey bees organize their colonies in very different ways. In a new study, researchers report that despite their differences, these insects rely on the same network of genes to guide their social behavior.The study appears in the Proceedings of the Royal Society B: Biological Sciences. Honey bees and paper wasps are separated by more than 100 million years of evolution, and there are striking differences in how they divvy up the work of maintaining a colony. The procedure outputs the following text: They are both facility building insect, but insects and honey insects arrange their biological groups in very different structure. In a new study, researchers report that despite their difference of opinions, these insects act the same network of genes to steer their party demeanor. The study appears in the proceeding of the institution bacteria Biological Sciences. Honey insects and insect are separated by more than hundred million years of organic processes, and there are impinging differences of opinions in how they divvy up the work of affirming a biological group. == Implicit semantic compression == A natural tendency to keep natural language expressions concise can be perceived as a form of implicit semantic compression, by omitting unmeaningful words or redundant meaningful words (especially to avoid pleonasms). == Applications and advantages == In the vector space model, compacting a lexicon leads to a reduction of dimensionality, which results in less computational complexity and a positive influence on efficiency. Semantic compression is advantageous in information retrieval tasks, improving their effectiveness (in terms of both precision and recall). This is due to more precise descriptors (reduced effect of language diversity – limited language redundancy, a step towards a controlled dictionary). As in the example above, it is possible to display the output as natural text (re-applying inflexion, adding stop words).

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  Tensor sketch

  In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms. == Mathematical definition == Mathematically, a dimensionality reduction or sketching matrix is a matrix M ∈ R k × d {\displaystyle M\in \mathbb {R} ^{k\times d}} , where k < d {\displaystyle k Read more →

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  Linear genetic programming

  "Linear genetic programming" is unrelated to "linear programming". Linear genetic programming (LGP) is a particular method of genetic programming wherein computer programs in a population are represented as a sequence of register-based instructions from an imperative programming language or machine language. The adjective "linear" stems from the fact that each LGP program is a sequence of instructions and the sequence of instructions is normally executed sequentially. Like in other programs, the data flow in LGP can be modeled as a graph that will visualize the potential multiple usage of register contents and the existence of structurally noneffective code (introns) which are two main differences of this genetic representation from the more common tree-based genetic programming (TGP) variant. Like other Genetic Programming methods, Linear genetic programming requires the input of data to run the program population on. Then, the output of the program (its behaviour) is judged against some target behaviour, using a fitness function. However, LGP is generally more efficient than tree genetic programming due to its two main differences mentioned above: Intermediate results (stored in registers) can be reused and a simple intron removal algorithm exists that can be executed to remove all non-effective code prior to programs being run on the intended data. These two differences often result in compact solutions and substantial computational savings compared to the highly constrained data flow in trees and the common method of executing all tree nodes in TGP. Furthermore, LGP naturally has multiple outputs by defining multiple output registers and easily cooperates with control flow operations. Linear genetic programming has been applied in many domains, including system modeling and system control with considerable success. Linear genetic programming should not be confused with linear tree programs in tree genetic programming, program composed of a variable number of unary functions and a single terminal. Note that linear tree GP differs from bit string genetic algorithms since a population may contain programs of different lengths and there may be more than two types of functions or more than two types of terminals. == Examples of LGP programs == Because LGP programs are basically represented by a linear sequence of instructions, they are simpler to read and to operate on than their tree-based counterparts. For example, a simple program written to solve a Boolean function problem with 3 inputs (in R1, R2, R3) and one output (in R0), could read like this: R1, R2, R3 have to be declared as input (read-only) registers, while R0 and R4 are declared as calculation (read-write) registers. This program is very simple, having just 5 instructions. But mutation and crossover operators could work to increase the length of the program, as well as the content of each of its instructions. Note that one instruction is non-effective or an intron (marked), since it does not impact the output register R0. Recognition of those instructions is the basis for the intron removal algorithm which is used analyze code prior to execution. Technically, this happens by copying an individual and then run the intron removal once. The copy with removed introns is then executed as many times as dictated by the number of training cases. Notably, the original individual is left intact, so as to continue participating in the evolutionary process. It is only the copy that is executed that is compressed by removing these "structural" introns. Another simple program, this one written in the LGP language Slash/A looks like a series of instructions separated by a slash: By representing such code in bytecode format, i.e. as an array of bytes each representing a different instruction, one can make mutation operations simply by changing an element of such an array.

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