Decision lists are a representation for Boolean functions which can be easily learned from examples. Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree. Learning decision lists can be used for attribute efficient learning, a type of machine learning. == Definition == A decision list (DL) of length r is of the form: if f1 then output b1 else if f2 then output b2 ... else if fr then output br where fi is the ith formula and bi is the ith boolean for i ∈ { 1... r } {\displaystyle i\in \{1...r\}} . The last if-then-else is the default case, which means formula fr is always equal to true. A k-DL is a decision list where all of formulas have at most k terms. Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.
Quantum image processing
Quantum image processing (QIMP) is using quantum computing or quantum information processing to create and work with quantum images. Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements. == Background == A. Y. Vlasov's work in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in and formalized in after seven years. In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits can be used to reconstruct images without using any additional information. Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups: Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications. Optics-based quantum imaging (OQI) Classically inspired quantum image processing (QIMP) A survey of quantum image representation has been published in. Furthermore, the recently published book Quantum Image Processing provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. == Quantum image representations == There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (Flexible Representation for Quantum Images), that captures the color and position at every pixel of the image, and defined as: | I ⟩ = 1 2 n ∑ i = 0 2 2 n − 1 | c i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{i=0}^{2^{2n-1}}\vert c_{i}\rangle \otimes \vert i\rangle } where | i ⟩ {\textstyle |i\rangle } is the position and | c i ⟩ = c o s θ i | 0 ⟩ + s i n θ i | 1 ⟩ {\textstyle \vert c_{i}\rangle =cos\theta _{i}\vert 0\rangle +sin\theta _{i}\vert 1\rangle } the color with a vector of angles θ i ∈ [ 0 , π / 2 ] {\textstyle \theta _{i}\in \left[0,\pi /2\right]} . As it can be seen, | c i ⟩ {\textstyle \vert c_{i}\rangle } is a regular qubit state of the form | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle \vert \psi \rangle =\alpha \vert 0\rangle +\beta \vert 1\rangle } , with basis states | 0 ⟩ = ( 1 0 ) {\textstyle \vert 0\rangle ={\begin{pmatrix}1\\0\end{pmatrix}}} and | 1 ⟩ = ( 0 1 ) {\textstyle \vert 1\rangle ={\begin{pmatrix}0\\1\end{pmatrix}}} , as well as amplitudes α {\textstyle \alpha } and β {\textstyle \beta } that satisfy | α | 2 + | β | 2 = 1 {\textstyle \left|\alpha \right|^{2}+\left|\beta \right|^{2}=1} . Another common representation is MCQI (Multi-Channel Representation for Quantum Images), that uses the RGB channels with quantum states and following FRQI definition: | I ⟩ = 1 2 n + 1 ∑ i = 0 2 2 n − 1 | C R G B i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n+1}}}\sum _{i=0}^{2^{2n-1}}\vert C_{RGB}^{i}\rangle \otimes \vert i\rangle } | C R G B i ⟩ = cos θ R i | 000 ⟩ + cos θ G i | 001 ⟩ + cos θ B i | 010 ⟩ + sin θ R i | 100 ⟩ + sin θ G i | 101 ⟩ + sin θ B i | 110 ⟩ + cos θ α | 011 ⟩ + sin θ α | 111 ⟩ {\displaystyle {\begin{aligned}{\begin{aligned}\vert C_{RGB}^{i}\rangle &={\cos \theta _{R}^{i}\vert 000\rangle }+{\cos \theta _{G}^{i}\vert 001\rangle }+{\cos \theta _{B}^{i}\vert 010\rangle }\\&\quad +{\sin \theta _{R}^{i}\vert 100\rangle }+{\sin \theta _{G}^{i}\vert 101\rangle }+{\sin \theta _{B}^{i}\vert 110\rangle }\\&\quad +{\cos {\theta _{\alpha }}\vert 011\rangle }+{\sin \theta _{\alpha }\vert 111\rangle }\end{aligned}}\end{aligned}}} Departing from the angle-based approach of FRQI and MCQI, and using a qubit sequence, NEQR (Novel Enhanced Representation for Quantum Images) is another representation approach, that uses a function f ( y , x ) = C y x q − 1 C y x q − 2 … C y x 1 C y x 0 {\textstyle f\left(y,x\right)=C_{yx}^{q-1}C_{yx}^{q-2}\ldots C_{yx}^{1}C_{yx}^{0}} to encode color values for a 2 n × 2 n {\displaystyle 2^{n}\times 2^{n}} image: | I ⟩ = 1 2 n ∑ y = 0 2 n − 1 ∑ x = 0 2 n − 1 | f ( y , x ) ⟩ | y x ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{y=0}^{2^{n}-1}\sum _{x=0}^{2^{n}-1}\vert f\left(y,x\right)\rangle \vert yx\rangle } == Quantum image manipulations == A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, quantum image segmentation, quantum image morphology, quantum image comparison, quantum image filtering, quantum image classification, quantum image stabilization, among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, encryption, and steganography etc., which form the core security technologies highlighted in this area. In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols. == Quantum image transform == By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Given an image F = ( F i , j ) M × L {\displaystyle F=(F_{i,j})_{M\times L}} , where F i , j {\displaystyle F_{i,j}} represents the pixel value at position ( i , j ) {\displaystyle (i,j)} with i = 1 , … , M {\displaystyle i=1,\dots ,M} and j = 1 , … , L {\displaystyle j=1,\dots ,L} , a vector f → {\displaystyle {\vec {f}}} with M L {\displaystyle ML} elements can be formed by letting the first M {\displaystyle M} elements of f → {\displaystyle {\vec {f}}} be the first column of F {\displaystyle F} , the next M {\displaystyle M} elements the second column, etc. A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as | g ⟩ = U ^ | f ⟩ {\displaystyle |g\rangle ={\hat {U}}|f\rangle } with the input image state | f ⟩ {\displaystyle |f\rangle } and the output image state | g ⟩ {\displaystyle |g\rangle } . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, an
CoDi
CoDi is a cellular automaton (CA) model for spiking neural networks (SNNs). CoDi is an acronym for Collect and Distribute, referring to the signals and spikes in a neural network. CoDi uses a von Neumann neighborhood modified for a three-dimensional space; each cell looks at the states of its six orthogonal neighbors and its own state. In a growth phase a neural network is grown in the CA-space based on an underlying chromosome. There are four types of cells: neuron body, axon, dendrite and blank. The growth phase is followed by a signaling- or processing-phase. Signals are distributed from the neuron bodies via their axon tree and collected from connection dendrites. These two basic interactions cover every case, and they can be expressed simply, using a small number of rules. == Cell interaction during signaling == The neuron body cells collect neural signals from the surrounding dendritic cells and apply an internally defined function to the collected data. In the CoDi model the neurons sum the incoming signal values and fire after a threshold is reached. This behavior of the neuron bodies can be modified easily to suit a given problem. The output of the neuron bodies is passed on to its surrounding axon cells. Axonal cells distribute data originating from the neuron body. Dendritic cells collect data and eventually pass it to the neuron body. These two types of cell-to-cell interaction cover all kinds of cell encounters. Every cell has a gate, which is interpreted differently depending on the type of the cell. A neuron cell uses this gate to store its orientation, i.e. the direction in which the axon is pointing. In an axon cell, the gate points to the neighbor from which the neural signals are received. An axon cell accepts input only from this neighbor, but makes its own output available to all its neighbors. In this way axon cells distribute information. The source of information is always a neuron cell. Dendritic cells collect information by accepting information from any neighbor. They give their output, (e.g. a Boolean OR operation on the binary inputs) only to the neighbor specified by their own gate. In this way, dendritic cells collect and sum neural signals, until the final sum of collected neural signals reaches the neuron cell. Each axonal and dendritic cell belongs to exactly one neuron cell. This configuration of the CA-space is guaranteed by the preceding growth phase. == Synapses == The CoDi model does not use explicit synapses, because dendrite cells that are in contact with an axonal trail (i.e. have an axon cell as neighbor) collect the neural signals directly from the axonal trail. This results from the behavior of axon cells, which distribute to every neighbor, and from the behavior of the dendrite cells, which collect from any neighbor. The strength of a neuron-neuron connection (a synapse) is represented by the number of their neighboring axon and dendrite cells. The exact structure of the network and the position of the axon-dendrite neighbor pairs determine the time delay and strength (weight) of a neuron-neuron connection. This principle infers that a single neuron-neuron connection can consist of several synapse with different time delays with independent weights. == Genetic encoding and growth of the network == The chromosome is initially distributed throughout the CA-space, so that every cell in the CA-space contains one instruction of the chromosome, i.e. one growth instruction, so that the chromosome belongs to the network as a whole. The distributed chromosome technique of the CoDi model makes maximum use of the available CA-space and enables the growth of any type of network connectivity. The local connection of the grown circuitry to its chromosome, allows local learning to be combined with the evolution of grown neural networks. Growth signals are passed to the direct neighbors of the neuron cell according to its chromosome information. The blank neighbors, which receive a neural growth signal, turn into either an axon cell or a dendrite cell. The growth signals include information containing the cell type of the cell that is to be grown from the signal. To decide in which directions axonal or dendritic trails should grow, the grown cells consult their chromosome information which encodes the growth instructions. These growth instructions can have an absolute or a relative directional encoding. An absolute encoding masks the six neighbors (i.e. directions) of a 3D cell with six bits. After a cell is grown, it accepts growth signals only from the direction from which it received its first signal. This reception direction information is stored in the gate position of each cell's state. == Implementation as a partitioned CA == The states of our CAs have two parts, which are treated in different ways. The first part of the cell-state contains the cell's type and activity level and the second part serves as an interface to the cell's neighborhood by containing the input signals from the neighbors. Characteristic of our CA is that only part of the state of a cell is passed to its neighbors, namely the signal and then only to those neighbors specified in the fixed part of the cell state. This CA is called partitioned, because the state is partitioned into two parts, the first being fixed and the second is variable for each cell. The advantage of this partitioning-technique is that the amount of information that defines the new state of a CA cell is kept to a minimum, due to its avoidance of redundant information exchange. == Implementation in hardware == Since CAs are only locally connected, they are ideal for implementation on purely parallel hardware. When designing the CoDi CA-based neural networks model, the objective was to implement them directly in hardware (FPGAs). Therefore, the CA was kept as simple as possible, by having a small number of bits to specify the state, keeping the CA rules few in number, and having few cellular neighbors. The CoDi model was implemented in the FPGA based CAM-Brain Machine (CBM) by Korkin. == History == CoDi was introduced by Gers et al. in 1998. A specialized parallel machine based on FPGA Hardware (CAM) to run the CoDi model on a large scale was developed by Korkin et al. De Garis conducted a series of experiments on the CAM-machine evaluating the CoDi model. The original model, where learning is based on evolutionary algorithms, has been augmented with a local learning rule via feedback from dendritic spikes by Schwarzer.
Artificial intelligence in Wikimedia projects
Some editors of Wikimedia projects use artificial intelligence (AI) and machine learning programs to edit existing articles or create new ones. Some applications of artificial intelligence, like using large language models (LLMs) to create new articles from scratch, have been more controversial than others for the Wikipedia community. In August 2025, English Wikipedia adopted a policy that allowed editors to nominate suspected LLM-generated articles for speedy deletion. This was followed by a March 2026 decision to prohibit the use of LLMs to generate or rewrite article content, with exceptions for copyediting one's own writing and machine translation from another language's Wikipedia. Wikipedia has also been a significant source of training data for some of the earliest artificial intelligence projects. This has received mixed reactions including concern about companies not citing Wikipedia when relying on it to answer a question as well as Wikipedia's increased costs from data scraping. == AI usage == === Earliest use of automated tools, machine learning and AI === Since 2002, bots have been allowed to run on Wikipedia but must be approved and supervised by a human. A bot created in 2002, rambot, transformed census data into short new articles about towns in the United States; the vast majority of town, city, and county articles were started by it. Fighting vandalism has been a major focus of machine learning and AI bots and tools. The 2007 ClueBot relied on simple heuristics to identify likely vandalism, while its 2010 successor, ClueBot NG, uses machine learning through an artificial neural network. Machine translation software has also been used by Wikimedia contributors for a number of years. Aaron Halfaker's Objective Revision Evaluation Service (ORES) project was launched in late 2015 as an artificial intelligence service for grading the quality of Wikipedia edits. === Generative AI and LLMs === In 2022, the public release of ChatGPT inspired more experimentation with AI and writing Wikipedia articles. A debate was sparked about whether and to what extent such large language models are suitable for such purposes in light of their tendency to generate plausible-sounding misinformation, including fake references; to generate prose that is not encyclopedic in tone; and to reproduce biases. An early experiment on December 6, 2022 by a Wikipedia contributor named Pharos occurred when he created the article "Artwork title" using ChatGPT for the initial draft. Another editor who experimented with this early version of ChatGPT said that ChatGPT's overview of "Weaponized incompetence" was decent, but that the citations were fabricated. Since 2023, work has been done to draft an English Wikipedia policy regarding ChatGPT and similar LLMs, at times recommending that users who are unfamiliar with LLMs should avoid using them due to the aforementioned risks, as well as noting the potential for libel or copyright infringement. In early 2023, the Wiki Education Foundation reported that some experienced editors found AI to be useful in starting drafts or creating new articles. It said that ChatGPT "knows" what Wikipedia articles look like and can easily generate one that is written in the style of Wikipedia, but warned that ChatGPT had a tendency to use promotional language, among other issues. In 2023, a ban on AI was deemed "too harsh" by the community given the productivity benefits it offered editors. In 2023, members of the English Wikipedia community created a WikiProject named AI Cleanup to assist in the removal of poor quality AI content from Wikipedia. Miguel García, a former Wikimedia member from Spain, said in 2024 that when ChatGPT was originally launched, the number of AI-generated articles on the site peaked. He added that the rate of AI articles has now stabilized due to the community's efforts to combat it. He said that majority of the articles that have no sources are deleted instantly or are nominated for deletion. In October 2024, a study by Princeton University found that about 5% of 3,000 newly created articles (created in August 2024) on English Wikipedia were created using AI. The study said that some of the AI articles were on innocuous topics and that AI had likely only been used to assist in writing. For some other articles, AI had been used to promote businesses or political interests. In October 2024, Ilyas Lebleu, founder of WikiProject AI Cleanup, said that they and their fellow editors noticed a pattern of unnatural writing that could be connected to ChatGPT. They added that AI is able to mass-produce content that sounds real while being completely fake, leading to the creation of hoax articles on Wikipedia that they were tasked to delete. In June 2025, the Wikimedia Foundation started testing a "Simple Article Summaries" feature which would provide AI-generated summaries of Wikipedia articles, similar to Google Search's AI Overviews. The decision was met with immediate and harsh criticism from some Wikipedia editors, who called the feature a "ghastly idea" and a "PR hype stunt." They criticized a perceived loss of trust in the site due to AI's tendency to hallucinate and questioned the necessity of the feature. The criticism led the Wikimedia Foundation to halt the rollout of Simple Article Summaries that same month while still expressing interest in integrating generative AI more into Wikipedia. The project hints at tensions within the community and with the Foundation over when to use AI.In August 2025, the English Wikipedia community created a policy that allowed users to nominate suspected AI-generated articles for speedy deletion. Editors might recognize AI-generated articles because they use citations that are not related to the subject of the article or fabricated citations or the wording has particular quirks. If an article uses language that reads like an LLM response to a user, such as "Here is your Wikipedia article on" or "Up to my last training update", the article is typically tagged for speedy deletion. Other signs of AI use include excessive use of em dashes, overuse of the word "moreover", promotional material in articles that describes something as "breathtaking" and formatting issues like using curly quotation marks instead of straight versions. During the discussion on implementing the speedy deletion policy, one user, who is an article reviewer, said that he is "flooded non-stop with horrendous drafts" created using AI. Other users said that AI articles have a large amount of "lies and fake references" and that it takes a significant amount of time to fix the issues. English Wikipedia created a guide on how to spot signs of AI-generated writing in August 2025, titled "Signs of AI writing". In January 2026, the Wiki Education Foundation continued to caution against copying and pasting outputs from generative AI into Wikipedia and to avoid it for creating new articles explaining that the text often failed verification with the sources provided. The foundation created a training module that encourages editors to use AI for identifying gaps in articles, finding access to sources and finding relevant sources. In March 2026, the English Wikipedia community prohibited the use of AI to add content to articles, with exceptions for copy editing and machine translation from another language's Wikipedia. The English Wikipedia community holds the position that LLMs often violate core content policies. == Using Wikipedia for artificial intelligence == A 2017 paper described Wikipedia as the mother lode for human-generated text available for machine learning. In the development of the Google's Perspective API that identifies toxic comments in online forums, a dataset containing hundreds of thousands of Wikipedia talk page comments with human-labelled toxicity levels was used. As of 2023, subsets of the Wikipedia corpus were considered one of the largest well-curated data sets available for AI training, used to train every LLM to-date according to Stephen Harrison. This use of Wikipedia was divisive as of 2023. The Wikimedia Foundation and many of its projects supporters worry that attribution to Wikipedia articles is missing in many large-language models like ChatGPT (as well as AI like Siri and Alexa). While Wikipedia's licensing policy lets anyone use its texts, including in modified forms, it does have the condition that credit is given, implying that using its contents in answers by AI models without clarifying the sourcing may violate its terms of use. The Foundation expressed concern that without attribution, people will not visit the site as much or be as motivated to donate to support the project if they do not know when they are benefiting from it. They also noticed an 8% decrease in visitors to Wikipedia in 2025 which they attributed both to the increased popularity of generative AI and social media. In 2025, the Wikimedia Foundation has cited absorbing increased costs associated with scra
Vivification
Vivification is an operation on a description logic knowledge base to improve performance of a semantic reasoner. Vivification replaces a disjunction of concepts C 1 ⊔ C 2 … ⊔ C n {\displaystyle C_{1}\sqcup C_{2}\ldots \sqcup C_{n}} by the least common subsumer of the concepts C 1 , C 2 , … C n {\displaystyle C_{1},C_{2},\ldots C_{n}} . The goal of this operation is to improve the performance of the reasoner by replacing a complex set of concepts with a single concept which subsumes the original concepts. For example, consider the example given in (Cohen 92): Suppose we have the concept PIANIST(Jill) ∨ ORGANIST(Jill) {\displaystyle {\textrm {PIANIST(Jill)}}\vee {\textrm {ORGANIST(Jill)}}} . This concept can be vivified into a simpler concept KEYBOARD-PLAYER(Jill) {\displaystyle {\textrm {KEYBOARD-PLAYER(Jill)}}} . This summarization leads to an approximation that may not be exactly equivalent to the original. == An approximation == Knowledge base vivification is not necessarily exact. If the reasoner is operating under the open world assumption we may get surprising results. In the previous example, if we replace the disjunction with the vivified concept, we will arrive at a surprising results. First, we find that the reasoner will no longer classify Jill as either a pianist or an organist. Even though ORGANIST {\displaystyle {\textrm {ORGANIST}}} and PIANIST {\displaystyle {\textrm {PIANIST}}} are the only two sub-classes, under the OWA we can no longer classify Jill as playing one or the other. The reason is that there may be another keyboard instrument (e.g. a harpsichord) that Jill plays but which does not have a specific subclass.
Lazy learning
(Not to be confused with the lazy learning regime, see Neural tangent kernel). In machine learning, lazy learning is a learning method in which generalization of the training data is, in theory, delayed until a query is made to the system, as opposed to eager learning, where the system tries to generalize the training data before receiving queries. The primary motivation for employing lazy learning, as in the K-nearest neighbors algorithm, used by online recommendation systems ("people who viewed/purchased/listened to this movie/item/tune also ...") is that the data set is continuously updated with new entries (e.g., new items for sale at Amazon, new movies to view at Netflix, new clips at YouTube, new music at Spotify or Pandora). Because of the continuous update, the "training data" would be rendered obsolete in a relatively short time especially in areas like books and movies, where new best-sellers or hit movies/music are published/released continuously. Therefore, one cannot really talk of a "training phase". Lazy classifiers are most useful for large, continuously changing datasets with few attributes that are commonly queried. Specifically, even if a large set of attributes exist - for example, books have a year of publication, author/s, publisher, title, edition, ISBN, selling price, etc. - recommendation queries rely on far fewer attributes - e.g., purchase or viewing co-occurrence data, and user ratings of items purchased/viewed. == Advantages == The main advantage gained in employing a lazy learning method is that the target function will be approximated locally, such as in the k-nearest neighbor algorithm. Because the target function is approximated locally for each query to the system, lazy learning systems can simultaneously solve multiple problems and deal successfully with changes in the problem domain. At the same time they can reuse a lot of theoretical and applied results from linear regression modelling (notably PRESS statistic) and control. It is said that the advantage of this system is achieved if the predictions using a single training set are only developed for few objects. This can be demonstrated in the case of the k-NN technique, which is instance-based and function is only estimated locally. == Disadvantages == Theoretical disadvantages with lazy learning include: The large space requirement to store the entire training dataset. In practice, this is not an issue because of advances in hardware and the relatively small number of attributes (e.g., as co-occurrence frequency) that need to be stored. Particularly noisy training data increases the case base unnecessarily, because no abstraction is made during the training phase. In practice, as stated earlier, lazy learning is applied to situations where any learning performed in advance soon becomes obsolete because of changes in the data. Also, for the problems for which lazy learning is optimal, "noisy" data does not really occur - the purchaser of a book has either bought another book or hasn't. Lazy learning methods are usually slower to evaluate. In practice, for very large databases with high concurrency loads, the queries are not postponed until actual query time, but recomputed in advance on a periodic basis - e.g., nightly, in anticipation of future queries, and the answers stored. This way, the next time new queries are asked about existing entries in the database, the answers are merely looked up rapidly instead of having to be computed on the fly, which would almost certainly bring a high-concurrency multi-user system to its knees. Larger training data also entail increased cost. Particularly, there is the fixed amount of computational cost, where a processor can only process a limited amount of training data points. There are standard techniques to improve re-computation efficiency so that a particular answer is not recomputed unless the data that impact this answer has changed (e.g., new items, new purchases, new views). In other words, the stored answers are updated incrementally. This approach, used by large e-commerce or media sites, has long been used in the Entrez portal of the National Center for Biotechnology Information (NCBI) to precompute similarities between the different items in its large datasets: biological sequences, 3-D protein structures, published-article abstracts, etc. Because "find similar" queries are asked so frequently, the NCBI uses highly parallel hardware to perform nightly recomputation. The recomputation is performed only for new entries in the datasets against each other and against existing entries: the similarity between two existing entries need not be recomputed. == Examples of Lazy Learning Methods == K-nearest neighbors, which is a special case of instance-based learning. Local regression. Lazy naive Bayes rules, which are extensively used in commercial spam detection software. Here, the spammers keep getting smarter and revising their spamming strategies, and therefore the learning rules must also be continually updated.
Lernmatrix
Lernmatrix (German for "learning matrix") is a special type of artificial neural network (ANN) architecture, similar to associative memory, invented around 1960 by Karl Steinbuch, a pioneer in computer science and ANNs. This model for learning systems could establish complex associations between certain sets of characteristics (e.g., letters of an alphabet) and their meanings. == Function == The Lernmatrix generally consists of n "characteristic lines" and m "meaning lines," where each characteristic line is connected to each meaning line, similar to how neurons in the brain are connected by synapses. (This can be realized in various ways – according to Steinbuch, this could be done by hardware or software). To train a Lernmatrix, values are specified on the corresponding characteristic and meaning lines (binary or real); then the connections between all pairs of characteristic and meaning lines are strengthened by the Hebb rule. A trained Lernmatrix, when given a specific input on the characteristic lines, activates the corresponding meaning lines. In modern language, it is a linear projection module. By appropriately interconnecting several Lernmatrices, a switching system can be built that, after completing certain training phases, is ultimately able to automatically determine the most probable associated meaning for an input sequence of features.