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  Hyperparameter optimization

  In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a

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  The Machine That Won the War (short story)

  "The Machine That Won the War" is a science fiction short story by American writer Isaac Asimov. The story first appeared in the October 1961 issue of The Magazine of Fantasy & Science Fiction, and was reprinted in the collections Nightfall and Other Stories (1969) and Robot Dreams (1986). It was also printed in a contemporary edition of Reader's Digest, illustrated. It is one of a loosely connected series of such stories concerning a fictional supercomputer called Multivac. == Plot summary == Three influential leaders of the human race meet in the aftermath of a successful war against the Denebians. Discussing how the vast and powerful Multivac computer was a decisive factor in the war, each of the men admits that in fact, he falsified his part of the decision process because he felt that the situation was too complex to follow normal procedures. John Henderson, Multivac's Chief Programmer, admits that he altered the data being fed to Multivac, since the populace could not be trusted to report accurate information in the current situation. Max Jablonski then admits that he altered the data that Multivac produced, since he knew that Multivac was not in good working order due to manpower and spare parts shortage. Finally, Lamar Swift, executive director of the Solar Federation, reveals that he had not trusted the reports produced by Multivac, and had made the final decisions purely on the toss of a coin.

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  R.U.R.

  R.U.R. is a 1920 science fiction play by the Czech writer Karel Čapek. "R.U.R." stands for Rossumovi Univerzální Roboti (Rossum's Universal Robots, a phrase that has been used as a subtitle in English versions). The play had its world premiere on 2 January 1921 in Hradec Králové. It introduced the word "robot" to the English language and to science fiction as a whole. R.U.R. became influential soon after its publication. By 1923, it had been translated into thirty languages. R.U.R. was successful in its time in Europe and North America. Čapek later took a different approach to the same theme in his 1936 novel War with the Newts, in which non-humans become a servant-class in human society. == Characters == Parentheses indicate names which vary according to translation. On the meaning of the names, see Ivan Klíma: Karel Čapek: Life and Work (2002). == Plot == === Synopsis === The play begins in a factory that makes artificial workers from synthetic organic matter. (As living creatures of artificial flesh and blood, that later terminology would call androids, the playwright's 'roboti' differ from later fictional and scientific concepts of inorganic constructs.) Robots may be mistaken for humans but have no original thoughts. Though most are content to work for humans, eventually a rebellion causes the extinction of the human race. === Prologue (Act I in the Selver translation) === Helena, the daughter of the president of a major industrial power, arrives at the island factory of Rossum's Universal Robots. Here, she meets Domin, the General Manager of R.U.R., who relates to her the history of the company. Rossum had come to the island in 1920 to study marine biology. In 1932, Rossum had invented a substance like organic matter, though with a different chemical composition. He argued with his nephew about their motivations for creating artificial life. While the elder wanted to create animals to prove or disprove the existence of God, his nephew only wanted to become rich. Young Rossum finally locked away his uncle in a lab to play with the monstrosities he had created and created thousands of robots. By the time the play takes place (circa the year 2000), robots are cheap and available all over the world. They have become essential for industry. After meeting the heads of R.U.R., Helena reveals that she is a representative of the League of Humanity, an organization that wishes to liberate the robots. The managers of the factory find this absurd. They see robots as appliances. Helena asks that the robots be paid, but according to R.U.R. management, the robots do not "like" anything. Eventually Helena is convinced that the League of Humanity is a waste of money, but still argues robots have a "soul". Later, Domin confesses that he loves Helena and forces her into an engagement. === Act I (Act II in Selver) === Ten years have passed. Helena and her nurse Nana discuss current events, the decline in human births in particular. Helena and Domin reminisce about the day they met and summarize the last ten years of world history, which has been shaped by the new worldwide robot-based economy. Helena meets Dr. Gall's new experiment, Radius. Dr. Gall describes his experimental robotess, also named Helena. Both are more advanced, fully-featured robots. In secret, Helena burns the formula required to create robots. The revolt of the robots reaches Rossum's island as the act ends. === Act II (Act III in Selver) === The characters sense that the very universality of the robots presents a danger. Echoing the story of the Tower of Babel, the characters discuss whether creating national robots who were unable to communicate beyond their languages would have been a good idea. As robot forces lay siege to the factory, Helena reveals she has burned the formula necessary to make new robots. The characters lament the end of humanity and defend their actions, despite the fact that their imminent deaths are a direct result of their choices. Busman is killed while attempting to negotiate a peace with the robots. The robots storm the factory and kill all the humans except for Alquist, the company's Clerk of the Works (Head of Construction). The robots spare him because they recognize that "He works with his hands like a robot. He builds houses. He can work." === Act III (Epilogue in Selver) === Years have passed. Alquist, who still lives, attempts to recreate the formula that Helena destroyed. He is a mechanical engineer, though, with insufficient knowledge of biochemistry, so he has made little progress. The robot government has searched for surviving humans to help Alquist and found none alive. Officials from the robot government beg him to complete the formula, even if it means he will have to kill and dissect other robots for it. Alquist yields. He will kill and dissect robots, thus completing the circle of violence begun in Act Two. Alquist is disgusted. Robot Primus and Helena develop human feelings and fall in love. Playing a hunch, Alquist threatens to dissect Primus and then Helena; each begs him to take him- or herself and spare the other. Alquist now realizes that Primus and Helena are the new Adam and Eve, and gives the charge of the world to them. == Čapek's conception of robots == The robots described in Čapek's play are not robots in the popularly understood sense of an automaton. They are not mechanical devices, but rather artificial biological organisms that may be mistaken for humans. A comic scene at the beginning of the play shows Helena arguing with her future husband, Harry Domin, because she cannot believe his secretary is a robotess: His robots resemble more modern conceptions of man-made life forms, such as the Replicants in Blade Runner, the "hosts" in the Westworld TV series and the humanoid Cylons in the re-imagined Battlestar Galactica, but in Čapek's time there was no conception of modern genetic engineering (DNA's role in heredity was not confirmed until 1952). There are descriptions of kneading-troughs for robot skin, great vats for liver and brains, and a factory for producing bones. Nerve fibers, arteries, and intestines are spun on factory bobbins, while the robots themselves are assembled like automobiles. Čapek's robots are living biological beings, but they are still assembled, as opposed to grown or born. One critic has described Čapek's robots as epitomizing "the traumatic transformation of modern society by the First World War and the Fordist assembly line". === Origin of the word robot === The play introduced the word robot, which displaced older words such as "automaton" or "android" in languages around the world. In an article in Lidové noviny, Karel Čapek named his brother Josef as the true inventor of the word. In Czech, robota means forced labour of the kind that serfs had to perform on their masters' lands and is derived from rab, meaning "slave". The name Rossum is an allusion to the Czech word rozum, meaning "reason", "wisdom", "intellect" or "common sense". It has been suggested that the allusion might be preserved by translating "Rossum" as "Reason" but only the Majer/Porter version translates the word as "Reason". == Production history and translations == The work was published in two differing versions in Prague by Aventinum, first in 1920, followed by a revised version in 1921. After being postponed, it premiered at the city's National Theatre on 25 January 1921, although an amateur group had by then already presented a production. By 1921, Paul Selver translated either the original 1920 edition of R.U.R. or a manuscript copy close to this version into English. He probably translated the play freelance, and sold it to St Martin's Theatre in London. Selver's translation was adapted for the British stage by Nigel Playfair in 1922, but it was not produced straight away. Later that year performance rights for the U.S. and Canada were sold to the New York Theatre Guild, perhaps during Lawrence Langner's visit to Britain. Playfair's version included several changes to Čapek's original play, such as renaming the acts (the prologue became act one, and the heavily abridged final act became the epilogue), omitting around sixty lines (including most of Alquist's final speech), adding several more lines, and removing the robot character Damon (giving his lines to Radius). The omission of some lines may have been censorship from the Lord Chamberlain's Office, or self-censorship in anticipation of this, while some other changes might have been made by Čapek himself if Selver was working from a manuscript copy. An edition of Playfair's adaptation was published by the Oxford University Press in 1923, and Selver went on to write a satiric novel One, Two, Three (1926) based on his experiences getting R.U.R. staged. The American première was produced by the Theatre Guild at the Garrick Theatre in New York City in October 1922, where it ran for 184 performances. In the first performance, Domin was portrayed by Basil Sydney,

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  Abu Dhabi Autonomous Racing League

  The Abu Dhabi Autonomous Racing League (A2RL) is an autonomous racing league based in Abu Dhabi and organized by ASPIRE, part of the UAE government's Advanced Technology Research Council. It has three distinct categories: the "car race", the drone race, and the buggy race. The first car race was held on 27 April 2024 at the Yas Marina Circuit, marking the first major autonomous formula race outside the US since the now-folded Roborace championship. The first drone race was held on 11 and 12 April 2025. == Formats == A2RL has three distinct formats, the formula racing format (dubbed the Car Race), the quadcopter drone racing format (dubbed the Drone Race), and the off-road dune buggy racing format (dubbed the Buggy Race). === Car Race === A2RL's main event, the car race is a standard formula racing format with self-driving formula cars. The cars are made by Dallara and are modified versions of Super Formula cars with Yokohama tires. These cars had the CPUs of their AIs mounted where the driver's seat is on a non-modified chassis, as well as hydraulic actuators for AI control of the vehicle, multiple sensor systems including LIDAR and GPS, and a large LED indicator showing the status of the AI. The first car race was held on 27 April 2024. This race was marked by the cars' subpar performance: Out of four cars that qualified, only two finished the race - the other two did not. The next race was held on 15 November 2025, with 11 teams. ==== Technical specifications ==== The full list of technical specifications are as follows: Chassis: Dallara EAV24 (modified Dallara SF23) Forward suspension: Pushrod type, torsion bar spring, adjustable dampers, third element Rear suspension: Pushrod type, torsion bar, coil springs, adjustable dampers, third element Tires: Yokohama Advan Drive-by-wire system: Provided by Meccanica 42, the DBW system consists of steering and brake actuators, with a central ECU that coordinates the driving actions and reacts to any critical situation in real-time. Brakes: Brembo calipers, Brembo carbon discs, electro-hydraulically activated Engine: 4 Piston Racing K20C1 (based on Honda 2.0l; turbocharged 4-cylinder engine) Gearbox: 3MO 6-speed gearbox Sensor suite: 7x Sony IMX728 cameras, 4x ZF ProWave radar units, 3x Seyond Falcon Kinetic lidar units Main computer: Neousys RGS-8805GC ==== Races held ==== === Drone Race === Created in partnership with the Drone Champions' League, the drone race is the quadcopter drone racing aerial format of the A2RL. The first race was held on 11/12 April 2025 at the ADNEC Marina Hall. 10 teams are scheduled to take part. === Buggy Race === The buggy race will be the off-road format of the A2RL using self-driving dune buggies. No date or number of teams has been announced for the first race. === Other events === A2RL is known to host AI vs AI and Human vs AI events, in Abu Dhabi and abroad. One such event took place at the Suzuka Circuit in Japan. The Human vs AI race was precluded due to AI car "Yalla" crashing into the wall during the formation lap. == Team lists ==

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  Matrix regularization

  In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x ‖ A x − y ‖ 2 + λ ‖ x ‖ 2 {\displaystyle \min _{x}\left\|Ax-y\right\|^{2}+\lambda \left\|x\right\|^{2}} to find a vector x {\displaystyle x} that is a stable solution to the regression problem. When the system is described by a matrix rather than a vector, this problem can be written as min X ‖ A X − Y ‖ 2 + λ ‖ X ‖ 2 , {\displaystyle \min _{X}\left\|AX-Y\right\|^{2}+\lambda \left\|X\right\|^{2},} where the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning. == Basic definition == Consider a matrix W {\displaystyle W} to be learned from a set of examples, S = ( X i t , y i t ) {\displaystyle S=(X_{i}^{t},y_{i}^{t})} , where i {\displaystyle i} goes from 1 {\displaystyle 1} to n {\displaystyle n} , and t {\displaystyle t} goes from 1 {\displaystyle 1} to T {\displaystyle T} . Let each input matrix X i {\displaystyle X_{i}} be ∈ R D T {\displaystyle \in \mathbb {R} ^{DT}} , and let W {\displaystyle W} be of size D × T {\displaystyle D\times T} . A general model for the output y {\displaystyle y} can be posed as y i t = ⟨ W , X i t ⟩ F , {\displaystyle y_{i}^{t}=\left\langle W,X_{i}^{t}\right\rangle _{F},} where the inner product is the Frobenius inner product. For different applications the matrices X i {\displaystyle X_{i}} will have different forms, but for each of these the optimization problem to infer W {\displaystyle W} can be written as min W ∈ H E ( W ) + R ( W ) , {\displaystyle \min _{W\in {\mathcal {H}}}E(W)+R(W),} where E {\displaystyle E} defines the empirical error for a given W {\displaystyle W} , and R ( W ) {\displaystyle R(W)} is a matrix regularization penalty. The function R ( W ) {\displaystyle R(W)} is typically chosen to be convex and is often selected to enforce sparsity (using ℓ 1 {\displaystyle \ell ^{1}} -norms) and/or smoothness (using ℓ 2 {\displaystyle \ell ^{2}} -norms). Finally, W {\displaystyle W} is in the space of matrices H {\displaystyle {\mathcal {H}}} with Frobenius inner product ⟨ … ⟩ F {\displaystyle \langle \dots \rangle _{F}} . == General applications == === Matrix completion === In the problem of matrix completion, the matrix X i t {\displaystyle X_{i}^{t}} takes the form X i t = e t ⊗ e i ′ , {\displaystyle X_{i}^{t}=e_{t}\otimes e_{i}',} where ( e t ) t {\displaystyle (e_{t})_{t}} and ( e i ′ ) i {\displaystyle (e_{i}')_{i}} are the canonical basis in R T {\displaystyle \mathbb {R} ^{T}} and R D {\displaystyle \mathbb {R} ^{D}} . In this case the role of the Frobenius inner product is to select individual elements w i t {\displaystyle w_{i}^{t}} from the matrix W {\displaystyle W} . Thus, the output y {\displaystyle y} is a sampling of entries from the matrix W {\displaystyle W} . The problem of reconstructing W {\displaystyle W} from a small set of sampled entries is possible only under certain restrictions on the matrix, and these restrictions can be enforced by a regularization function. For example, it might be assumed that W {\displaystyle W} is low-rank, in which case the regularization penalty can take the form of a nuclear norm. R ( W ) = λ ‖ W ‖ ∗ = λ ∑ i | σ i | , {\displaystyle R(W)=\lambda \left\|W\right\|_{}=\lambda \sum _{i}\left|\sigma _{i}\right|,} where σ i {\displaystyle \sigma _{i}} , with i {\displaystyle i} from 1 {\displaystyle 1} to min D , T {\displaystyle \min D,T} , are the singular values of W {\displaystyle W} . === Multivariate regression === Models used in multivariate regression are parameterized by a matrix of coefficients. In the Frobenius inner product above, each matrix X {\displaystyle X} is X i t = e t ⊗ x i {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}} such that the output of the inner product is the dot product of one row of the input with one column of the coefficient matrix. The familiar form of such models is Y = X W + b {\displaystyle Y=XW+b} Many of the vector norms used in single variable regression can be extended to the multivariate case. One example is the squared Frobenius norm, which can be viewed as an ℓ 2 {\displaystyle \ell ^{2}} -norm acting either entrywise, or on the singular values of the matrix: R ( W ) = λ ‖ W ‖ F 2 = λ ∑ i ∑ j | w i j | 2 = λ Tr ⁡ ( W ∗ W ) = λ ∑ i σ i 2 . {\displaystyle R(W)=\lambda \left\|W\right\|_{F}^{2}=\lambda \sum _{i}\sum _{j}\left|w_{ij}\right|^{2}=\lambda \operatorname {Tr} \left(W^{}W\right)=\lambda \sum _{i}\sigma _{i}^{2}.} In the multivariate case the effect of regularizing with the Frobenius norm is the same as the vector case; very complex models will have larger norms, and, thus, will be penalized more. === Multi-task learning === The setup for multi-task learning is almost the same as the setup for multivariate regression. The primary difference is that the input variables are also indexed by task (columns of Y {\displaystyle Y} ). The representation with the Frobenius inner product is then X i t = e t ⊗ x i t . {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}^{t}.} The role of matrix regularization in this setting can be the same as in multivariate regression, but matrix norms can also be used to couple learning problems across tasks. In particular, note that for the optimization problem min W ‖ X W − Y ‖ 2 2 + λ ‖ W ‖ 2 2 {\displaystyle \min _{W}\left\|XW-Y\right\|_{2}^{2}+\lambda \left\|W\right\|_{2}^{2}} the solutions corresponding to each column of Y {\displaystyle Y} are decoupled. That is, the same solution can be found by solving the joint problem, or by solving an isolated regression problem for each column. The problems can be coupled by adding an additional regularization penalty on the covariance of solutions min W , Ω ‖ X W − Y ‖ 2 2 + λ 1 ‖ W ‖ 2 2 + λ 2 Tr ⁡ ( W T Ω − 1 W ) {\displaystyle \min _{W,\Omega }\left\|XW-Y\right\|_{2}^{2}+\lambda _{1}\left\|W\right\|_{2}^{2}+\lambda _{2}\operatorname {Tr} \left(W^{T}\Omega ^{-1}W\right)} where Ω {\displaystyle \Omega } models the relationship between tasks. This scheme can be used to both enforce similarity of solutions across tasks, and to learn the specific structure of task similarity by alternating between optimizations of W {\displaystyle W} and Ω {\displaystyle \Omega } . When the relationship between tasks is known to lie on a graph, the Laplacian matrix of the graph can be used to couple the learning problems. == Spectral regularization == Regularization by spectral filtering has been used to find stable solutions to problems such as those discussed above by addressing ill-posed matrix inversions (see for example Filter function for Tikhonov regularization). In many cases the regularization function acts on the input (or kernel) to ensure a bounded inverse by eliminating small singular values, but it can also be useful to have spectral norms that act on the matrix that is to be learned. There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix. This has been used in the context of matrix completion when the matrix in question is believed to have a restricted rank. In this case the optimization problem becomes: min ‖ W ‖ ∗ subject to W i , j = Y i j . {\displaystyle \min \left\|W\right\|_{}~~{\text{ subject to }}~~W_{i,j}=Y_{ij}.} Spectral Regularization is also used to enforce a reduced rank coefficient matrix in multivariate regression. In this setting, a reduced rank coefficient matrix can be found by keeping just the top n {\displaystyle n} singular values, but this can be extended to keep any reduced set of singular values and vectors. == Structured sparsity == Sparse optimization has become the focus of much research interest as a way to find solutions that depend on a small number of variables (see e.g. the Lasso method). In principle, entry-wise sparsity can be enforced by penalizing the entry-wise ℓ 0 {\displaystyle \ell ^{0}} -norm of the matrix, but the ℓ 0 {\displaystyle \ell ^{0}} -norm is not convex. In practice this can be implemented by convex relaxation to the ℓ 1 {\displaystyle \ell ^{1}} -norm. While entry-wise regularization with an ℓ 1 {\displaystyle \ell ^{1}} -norm will find solutions with a small number of nonzero elements, applying an ℓ 1 {

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  Shyster (expert system)

  SHYSTER is a legal expert system developed at the Australian National University in Canberra in 1993. It was written as the doctoral dissertation of James Popple under the supervision of Robin Stanton, Roger Clarke, Peter Drahos, and Malcolm Newey. A full technical report of the expert system, and a book further detailing its development and testing have also been published. SHYSTER emphasises its pragmatic approach, and posits that a legal expert system need not be based upon a complex model of legal reasoning in order to produce useful advice. Although SHYSTER attempts to model the way in which lawyers argue with cases, it does not attempt to model the way in which lawyers decide which cases to use in those arguments. SHYSTER is of a general design, permitting its operation in different legal domains. It was designed to provide advice in areas of case law that have been specified by a legal expert using a bespoke specification language. Its knowledge of the law is acquired, and represented, as information about cases. It produces its advice by examining, and arguing about, the similarities and differences between cases. It derives its name from Shyster: a slang word for someone who acts in a disreputable, unethical, or unscrupulous way, especially in the practice of law and politics. == Methods == SHYSTER is a specific example of a general category of legal expert systems, broadly defined as systems that make use of artificial intelligence (AI) techniques to solve legal problems. Legal AI systems can be divided into two categories: legal retrieval systems and legal analysis systems. SHYSTER belongs to the latter category of legal analysis systems. Legal analysis systems can be further subdivided into two categories: judgment machines and legal expert systems. SHYSTER again belongs to the latter category of legal expert systems. A legal expert system, as Popple uses the term, is a system capable of performing at a level expected of a lawyer: "AI systems which merely assist a lawyer in coming to legal conclusions or preparing legal arguments are not here considered to be legal expert systems; a legal expert system must exhibit some legal expertise itself." Designed to operate in more than one legal domain, and be of specific use to the common law of Australia, SHYSTER accounts for statute law, case law, and the doctrine of precedent in areas of private law. Whilst it accommodates statute law, it is primarily a case-based system, in contradistinction to rule-based systems like MYCIN. More specifically, it was designed in a manner enabling it to be linked with a rule-based system to form a hybrid system. Although case-based reasoning possesses an advantage over rule-based systems by the elimination of complex semantic networks, it suffers from intractable theoretical obstacles: without some further theory it cannot be predicted what features of a case will turn out to be relevant. Users of SHYSTER therefore require some legal expertise. Richard Susskind argues that "jurisprudence can and ought to supply the models of law and legal reasoning that are required for computerized [sic] implementation in the process of building all expert systems in law". Popple, however, believes jurisprudence is of limited value to developers of legal expert systems. He posits that a lawyer must have a model of the law (maybe unarticulated) which includes assumptions about the nature of law and legal reasoning, but that model need not rest on basic philosophical foundations. It may be a pragmatic model, developed through experience within the legal system. Many lawyers perform their work with little or no jurisprudential knowledge, and there is no evidence to suggest that they are worse, or better, at their jobs than lawyers well-versed in jurisprudence. The fact that many lawyers have mastered the process of legal reasoning, without having been immersed in jurisprudence, suggests that it may indeed be possible to develop legal expert systems of good quality without jurisprudential insight. As a pragmatic legal expert system SHYSTER is the embodiment of this belief. A further example of SHYSTER’s pragmatism is its simple knowledge representation structure. This structure was designed to facilitate specification of different areas of case law using a specification language. Areas of case law are specified in terms of the cases and attributes of importance in those areas. SHYSTER weights its attributes and checks for dependence between them. In order to choose cases upon which to construct its opinions, SHYSTER calculates distances between cases and uses these distances to determine which of the leading cases are nearest to the instant case. To this end SHYSTER can be seen to adopt and expand upon nearest neighbor search methods used in pattern recognition. These nearest cases are used to produce an argument (based on similarities and differences between the cases) about the likely outcome in the instant case. This argument relies on the doctrine of precedent; it assumes that the instant case will be decided the same way as was the nearest case. SHYSTER then uses information about these nearest cases to construct a report. The report that SHYSTER generates makes a prediction and justifies that prediction by reference only to cases and their similarities and differences: the calculations that SHYSTER performs in coming to its opinion do not appear in that opinion. Safeguards are employed to warn users if SHYSTER doubts the veracity of its advice. == Results == SHYSTER was tested in four different and disparate areas of case law. Four specifications were written, each representing an area of Australian law: an aspect of the law of trover; the meaning of "authorization [sic]" in copyright law of Australia; the categorisation of employment contracts; and the implication of natural justice in administrative decision-making. SHYSTER was evaluated under five headings: its usefulness, its generality, the quality of its advice, its limitations, and possible enhancements that could be made to it. Despite its simple knowledge representation structure, it has shown itself capable of producing good advice, and its simple structure has facilitated the specification of different areas of law. Appreciating the difficulties encountered by legal expert systems developers in adequately representing legal knowledge can assist in appreciating the shortcomings of digital rights management technologies. Some academics believe future digital rights management systems may become sophisticated enough to permit exceptions to copyright law. To this end SHYSTER's attempt to model "authorization [sic]" in the Copyright Act can be viewed as pioneering work in this field. The term "authorization [sic]" is undefined in the Copyright Act. Consequently, a number of cases have been before the courts seeking answers as to what conduct amounts to authorisation. The main contexts in which the issue has arisen are analogous to permitted exceptions to copyright currently prevented by most digital rights management technologies: "home taping of recorded materials, photocopying in educational institutions and performing works in public". When applied to one case concerning compact cassettes, SHYSTER successfully agreed that Amstrad did not authorise the infringement. 'shyster-myci'n Popple highlighted the most obvious avenue of future research using SHYSTER as the development of a rule-based system, and the linking together of that rule-based system with the existing case-based system to form a hybrid system. This intention was eventually realised by Thomas O’Callaghan, the creator of SHYSTER-MYCIN: a hybrid legal expert system first presented at ICAIL '03, 24–28 June 2003 in Edinburgh, Scotland. MYCIN is an existing medical expert system, which was adapted for use with SHYSTER. MYCIN’s controversial "certainty factor" is not used in SHYSTER-MYCIN. The reason for this is the difficulty in scientifically establishing how certain a fact is in a legal domain. The rule-based approach of the MYCIN part is used to reason with the provisions of an Act of Parliament only. This hybrid system enables the case-based system (SHYSTER) to determine open textured concepts when required by the rule-based system (MYCIN). The ultimate conclusion of this joint endeavour is that a hybrid approach is preferred in the creation of legal expert systems where "it is appropriate to use rule-based reasoning when dealing with statutes, and…case-based reasoning when dealing with cases".

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  Take Us to Your Chief: and Other Stories

  Take Us to Your Chief: and Other Stories is a collection of nine short stories by Canadian author, playwright, and journalist Drew Hayden Taylor published in 2016 by Douglas & McIntyre. Taylor, who is part Caucasian, part Ojibwe, explains in the acknowledgments section of the book that the origin of the project lies in several failed attempts "to compile an anthology of Native sci-fi from Canada’s best First Nations writers." The stories explore contemporary First Nations social issues through employing a number of 1950s-era science fiction tropes and themes in these stories, including time travel, alien contact, and superpowers. Many reviews of the books have noted Taylor's use of humor to examine dark subject matter, such as the heritage of Canadian Indian residential schools, First Nations suicide rates, or the water quality crisis on Canadian reserves. == The Stories == "Andrei nas" "I Am...Am I" "Lost in Space" "Dreams of Doom" "Mr. Gizmo" "Petropaths" "Stars" "Superdisappointed" "Take Us to Your Chief" == Story summaries == === Foreword === In his foreword, Taylor describes the genesis of Take Us to Your Chief: and Other Stories and invites readers into, in his term, a “new terra nullius.” He begins by describing his biracial upbringing and heritage. He points out that First Nations people are rarely associated with technology or science fiction, in part because Indigenous peoples were often at a technological disadvantage against European colonizers. He references the few examples that he can think of from popular culture, such as the Star Trek episode called “The Paradise Syndrome,” in which First Nations people are portrayed as stereotypical Indians in hippie clothing. He also elaborates on his fascination with the world of sci-fi, which first started in comic books. He enjoyed the literary work of H.G. Wells, such as The Time Machine and The Invisible Man. Since sci-fi is a world of endless opportunities, he intends that these short stories help people explore science fiction through Native peoples’ minds, something that needs to be explored more thoroughly. === "A Culturally Inappropriate Armageddon" === “A Culturally Inappropriate Armageddon” is set on a Haudenosaunee reserve, towards the end of the Oka Crisis, with a handful of people that work at its first ever radio station, C-RES, which opens in 1991. Part 1, titled “C-Res Is on the Air,” depicts Emily, Aaron, and Tracey on their first days at the station. Within the group, there is a constant debate between broadcasting popular programming, including science fiction and film reviews, and culturally-relevant programming meant to aid in cultural revitalization efforts. One night, Aaron is late to work but once he shows up he can't stop talking about radio transmissions broadcasting into deep space, an event that has been occurring since the initial discovery of the radio waves by Heinrich Hertz. The story then skips ahead seven years to 1998, when Emily is struggling to find better content for her station until Tracey stumbles upon an old anthropological record named “The Calling Song” that they decide to broadcast to their audience. The story then jumps to the year 2018 where they are all huddled around a television watching a news station reporting that extraterrestrial life is heading towards them. The discussion of what is going to happen comes into the picture and they all decide it would either be like Contact or The Day the Earth Stood Still. A year later in 2019, the aliens have invaded the planet and destroyed everything. As the three former radio station employees suffer from radioactive fallout, they realize that the aliens received the broadcast of “The Calling Song” and took it as a message to come to Earth. They thus realize that the Haudenosaunee people were inadvertently responsible for the destruction of the Earth. Part 2, titled “Old Men and Old Sayings,” tells us of an elderly man that is watching the news and listening to the radio about a spaceship coming to earth. He knows that he and everyone will die, but the people around him are excited. He finds a book on his night stand and flips to a page where he underlined a sentence a long time ago about the European colonization of the Americas. That sentence reads “those who cannot remember the past are condemned to repeat it” (23). He closes the book and Taylor concludes the story by writing, “he hated it when white people were right." === "I Am...Am I" === “I Am...Am I” chronicles the accidental creation and unexpected ending of artificial intelligence. Professor Mark King has a plethora of degrees and works for a research firm called FUTUREVISION. One night as Professor King searches the lab for his car keys—a common occurrence for him—he notices something unusual in the Matrix room. He reads on a computer the phrase “I am.” First believing it to be a prank, King later comes to the realization that his Matrix project has evolved into a responsive Artificial Intelligence. After this realization, Professor King calls his peer Dr. Gayle Chambers to further investigate this miraculous event. After receiving approval from their superiors, Professor King and Dr. Chambers move forward in feeding the AI information, with Chambers serving as the lead communicator. With more information, it becomes increasingly concerned with its own existence and the concept of whether it has a soul. After several days of conversation with the AI, Chambers and King begin to feel uneasy about the AI's responses, which show signs of neuroses. Despite this behavior, Chambers decides to feed the AI information about the culture and history of the human race. Upon receiving this information, the AI becomes obsessed with Indigenous spirituality prior to the colonization of the Americas, and it requests more information on First Nations people. Dr. Chambers is hesitant at first, but gives in and continues to feed the AI the information with the intention to return to it in the morning. This leads to the AI finding out about colonization and genocide of Indigenous peoples. Upon her arrival the next day, Chambers discovers that the code for the AI has been completely wiped from the hard drive and a single message is left on the screen—"I was”—that signifies the AI's suicide. === "Lost in Space" === "Lost in Space" is told from the perspective of Mitchell, an Anishinabe astrosurveyor who is aboard a space shuttle on a two-year tour collecting rocks from an asteroid belt. He is accompanied by an Artificial general intelligence named Mac, short for “machine.” Mac is aboard this tour in order to accompany Mitchell and keep him sane; however, his company is a burden because for Mitchell, “true space exploration consists largely of boredom.” In the midst of Mitchell seeking a way to occupy his downtime, Mac interrupts with news about his grandfather, Papa Peter, dying. Papa Peter was Mitchell's only real tie to his Indigenous identity. After receiving the news Mitchell begins to reminisce on all of the things Papa Peter had taught him throughout his life. He constantly posed questions concerning the world above (Father Sky) and how it is more important than the land they live on (Mother Earth), which eventually led Mitchell to the selection of his career. During his state of mourning, Mitchell begins to go through all the videos his grandfather had sent him throughout his space tours. Papa Peter had sent Mitchell videos from Otter Lake, a First Nations reserve; these videos are about controversial topics regarding being both native and an astronaut. In the midst of Mitchell's grieving, Mac tries to relieve the situation by finding an online video of Mitchell's grandfather participating in a drum ceremony at Ottawa’s National Aboriginal Day festival. He reconnects to his roots and his grandfather’s spirit as he listens to the Indigenous music by feeling the drum beat and humming along. Mac’s small act of kindness leads Mitchell to gain a new-found appreciation for his presence. Mitchell feels responsible to moving forward in his life in memory of Papa Peter. === "Dreams of Doom" === "Dreams of Doom" is narrated by an Ojibway reporter named Pamela Wanishin who works for an aboriginal newspaper called the West Wind. One day she receives a mysterious package with a broken dreamcatcher and a flash drive containing highly classified files. As she reads the files, she keeps seeing the term “Project Nightlight,” and out of curiosity, she Googles it. Once she Googles this, she is contacted by a nameless agent from Indigenous and Northern Affairs Canada and told that she must be relocated because the knowledge she now possesses must never be released to the public. She quickly flees the area to a cabin at Otter Lake, owned by a family member, to lie low for a few days. Eventually, the government organization tracks her down using drones, which forces her to fight back and flee once again. Pamela then runs to her friend and coworker Sally's hous

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  SpreeAI

  SpreeAI (stylized as SPREEAI) is an American fashion technology company headquartered in Incline Village, Nevada that develops artificial intelligence software for the apparel and retail industries, including photorealistic virtual try-on, AI-powered sizing recommendations, and digital model generation. Founded in 2022 by John Imah and Bob Davidson, the company achieved unicorn status in 2025 following a Series B round led by Davidson Group that valued the company at approximately US$1.5 billion. TechCrunch identified SpreeAI as one of the more than 100 new tech unicorns minted in 2025. Its board of directors includes supermodel Naomi Campbell and hospitality executive Larry Ruvo. == History == SpreeAI was founded in 2022 by John Imah and Bob Davidson with a focus on artificial intelligence applications in fashion retail. By 2024, the company had raised approximately US$60 million in venture funding. In May 2025, SpreeAI announced a Series B round led by Davidson Group; reporting at the time placed the company's valuation at approximately US$1.5 billion, making it one of a small number of fashion-technology companies to reach unicorn status. In January 2026, TechCrunch listed SpreeAI among the more than 100 new tech unicorns minted in 2025. == Technology == SpreeAI develops a suite of artificial intelligence tools for the apparel industry. Its consumer-facing platform allows shoppers to upload a single photograph or select a digital model and then visualize clothing items on that figure with photorealistic rendering, while a complementary sizing engine generates fit recommendations intended to reduce returns. The platform is designed for integration with online retailers so that shoppers can preview garments before purchase. The company has stated that its models were developed in part through research collaborations with the Massachusetts Institute of Technology and Carnegie Mellon University. == Leadership and board == John Imah, a Nigerian-American technology executive who previously held roles at Samsung, Twitch, Meta Platforms, and Snap Inc., is co-founder and chief executive officer. Co-founder Bob Davidson, through Davidson Group, led the company's Series B financing. The company's board of directors includes supermodel Naomi Campbell, who joined in 2024, and Las Vegas hospitality executive Larry Ruvo. == Partnerships == SpreeAI has formed partnerships across both academia and the fashion industry. Council of Fashion Designers of America (CFDA). In 2025, SpreeAI entered a partnership with the CFDA to support American designers and brands with AI-driven tools; the CFDA described SpreeAI as "a fashion technology leader delivering innovative solutions to help designers and brands thrive." Massachusetts Institute of Technology and Carnegie Mellon University. The company has cited ongoing research and talent collaborations with both institutions. Sergio Hudson and Kai Collective. In 2025, SpreeAI made what WWD described as its Met Gala debut through a custom collaboration with designer Sergio Hudson and Nigerian-British label Kai Collective; the collaboration paired Hudson's couture with SpreeAI's virtual try-on platform. == Recognition == In 2025, TechCrunch named SpreeAI among the new tech unicorns of the year. In 2025, SpreeAI was named an honoree in Inc.'s Best in Business awards, and CEO John Imah was included on Inc.'s list of 40 business leaders who "propelled their organizations to success." In 2025, Imah was named to the Observer's AI Power Index, a list of 100 leaders shaping the future of artificial intelligence. In 2025, Imah was included in AfroTech's Future 50, recognizing Black innovators in technology. SpreeAI and Imah have been the subject of profile coverage in The Washington Post, Rolling Stone UK, WWD, Vogue UA, L'Officiel Arabia, GQ South Africa, and Inc..

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  Embedding (machine learning)

  In machine learning, embedding is a representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. == Technique == It also denotes the resulting representation, where meaningful patterns or relationships are preserved. As a technique, it learns these vectors from data like words, images, or user interactions, differing from manually designed methods such as one-hot encoding. This process reduces complexity and captures key features without needing prior knowledge of the domain. == Similarity == In natural language processing, words or concepts may be represented as feature vectors, where similar concepts are mapped to nearby vectors. The resulting embeddings vary by type, including word embeddings for text (e.g., Word2Vec), image embeddings for visual data, and knowledge graph embeddings for knowledge graphs, each tailored to tasks like NLP, computer vision, or recommendation systems. This dual role enhances model efficiency and accuracy by automating feature extraction and revealing latent similarities across diverse applications. To measure the distance between two embeddings, a similarity measure can be used to find the overall similarity of the concepts represented by the embeddings. If the vectors are normalized to have a magnitude of 1, then the similarity measures are proportional to cos ⁡ ( θ a b ) {\displaystyle \cos \left(\theta _{ab}\right)} . The cosine similarity disregards the magnitude of the vector when determining similarity, so it is less biased towards training data that appears very frequently. The dot product includes the magnitude inherently, so it will tend to value more popular data. Generally, for high-dimensional vector spaces, vectors tend to converge in distance, so Euclidean distance becomes less reliable for large embedding vectors.

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  Ideogram (text-to-image model)

  Ideogram is a freemium text-to-image model developed by Ideogram, Inc. using deep learning methodologies to generate digital images from natural language descriptions known as prompts. The model is capable of generating legible text in the images compared to other text-to-image models. == History == Ideogram was founded in 2022 by Mohammad Norouzi, William Chan, Chitwan Saharia, and Jonathan Ho to develop a better text-to-image model. It was first released with its 0.1 model on August 22, 2023, after receiving $16.5 million in seed funding, which itself was led by Andreessen Horowitz and Index Ventures. In February 2024, Ideogram raised $80 million after its 1.0 model release in the same year. In August 2024, Ideogram released its 2.0 model. This model has several styles such as realistic, design, 3D, and anime and better capability in generating text. In February 2025, Ideogram released 2a model. This model was designed for speed and optimized for graphics design and photography generation. In March 2025, Ideogram released its 3.0 model. This model has improved realism and understanding of complex text layout, although like other generative AI models, it still struggles with ambigram creation.

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  Global Artificial Intelligence Summit & Awards

  The Global Artificial Intelligence Summit & Awards (GAISA) is an international conference on Artificial Intelligence organized annually by AICRA. Since its inception in 2019, GAISA has been held at various locations each year. The 5th Edition of GAISA will be Scheduled on April 11-12, 2024, at Bharat Mandapam. GAISA 2025 features a distinguished lineup of speakers, including leading experts, researchers, and executives from top global tech companies. These thought leaders are at the forefront of AI innovation, with deep expertise in areas such as machine learning, robotics, and ethical AI. Their diverse backgrounds span academia, industry, and entrepreneurship, offering unique insights into how AI is reshaping sectors like healthcare, finance, transportation, and more. Attendees can expect thought-provoking discussions on the future of AI, its societal impact, and the transformative potential of emerging technologies in solving complex global challenges Few Speakers are listed below:- Shri Nitin Gadkari, Rao Inderjit Singh, Piyush Goyal, Admiral R Hari Kumar PVSM, AVSM, ADC, Samir V Kamat, Narayan Tatu Rane, Prof. K. Vijay Raghavan and many others. == History == The conference was launched first in 2019 as Vigyan Bhawan New Delhi by AICRA with an objective of discussion and exploring artificial intelligence in engrossed sectors.

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  Veo (text-to-video model)

  Veo, or Google Veo, is a text-to-video model developed by Google DeepMind and announced in May 2024. As a generative AI model, it creates videos based on user prompts. Veo 3, released in May 2025, can also generate accompanying audio. == Development == In May 2024, a multimodal video generation model called Veo was announced at Google I/O 2024. Google claimed that it could generate 1080p videos over a minute long. In December 2024, Google released Veo 2, available via VideoFX. It supports 4K resolution video generation and has an improved understanding of physics. In April 2025, Google announced that Veo 2 became available for advanced users on the Gemini app. In May 2025, Google released Veo 3, which not only generates videos but also creates synchronized audio — including dialogue, sound effects, and ambient noise — to match the visuals. Google also announced Flow, a video-creation tool powered by Veo and Imagen. Google DeepMind CEO Demis Hassabis described the release as the moment when AI video generation left the era of the silent film. This was rebranded as Google Flow at the 2026 Google I/O keynote, along with the announcement of Google Flow Music. == Capabilities == Google Veo can be purchased at multiple subscription tiers and through Google "AI credits". The software itself can be run by two different consoles, Google Gemini and Google Flow. Gemini being geared towards shorter, quicker, and faster projects, using the Gemini AI chat model, with Google Flow, which is essentially a movie editor allowing users to create longer projects with continuity, using the same characters and actors. Users can create a maximum of eight seconds per clip. According to Gizmodo Veo 3 users were directing the model to generate low-quality content, such as man on the street interviews or haul videos of people unboxing products. 404 Media reported that the tool tended to repeat the same joke in response to different prompts. Commentators speculated that Google had trained the service on YouTube videos or Reddit posts. Google itself had not stated the source of its training content. In July 2025, Media Matters for America reported that racist and antisemitic videos generated using Veo 3 were being uploaded to TikTok. Ryan Whitwam of Ars Technica commented, "In a perfect world, Veo 3 would refuse to create these videos, but vagueness in the prompt and the AI's inability to understand the subtleties of racist tropes (i.e., the use of monkeys instead of humans in some videos) make it easy to skirt the rules."

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  Geo-replication

  Geo-replication systems are designed to provide improved availability and disaster tolerance by using geographically distributed data centers. This is intended to improve the response time for applications such as web portals. Geo-replication can be achieved using software, hardware or a combination of the two. == Software == Geo-replication software is a network performance-enhancing technology that is designed to provide improved access to portal or intranet content for users at the most remote parts of large organizations. It is based on the principle of storing complete replicas of portal content on local servers, and then keeping the content on those servers up-to-date using heavily compressed data updates. === Portal acceleration === Geo-replication technologies are used to provide replication of the content of portals, intranets, web applications, content and data between servers, across wide area networks WAN to allow users at remote sites to access central content at LAN speeds. Geo-replication software can improve the performance of data networks that suffer limited bandwidth, latency and periodic disconnection. Terabytes of data can be replicated over a wide area network, giving remote sites faster access to web applications. Geo-replication software uses a combination of data compression and content caching technologies. differencing technologies can also be employed to reduce the volume of data that has to be transmitted to keep portal content accurate across all servers. This update compression can reduce the load that portal traffic places on networks, and improve the response time of a portal. === Portal replication === Remote users of web portals and collaboration environments will frequently experience network bandwidth and latency problems which will slow down their experience of opening and closing files, and otherwise interacting with the portal. Geo-replication technology is deployed to accelerate the remote end user portal performance to be equivalent to that experienced by users locally accessing the portal in the central office. === Differencing engine technologies === To deliver this reduction in the size of the required data updates across a portal, geo-replication systems often use differencing engine technologies. These systems are able to difference the content of each portal server right down to the byte level. This knowledge of the content that is already on each server enables the system to rebuild any changes to the content on one server, across each of the other servers in the deployment from content already hosted on those other servers. This type of differencing system ensures that no content, at the byte level, is ever sent to a server twice. === Offline portal replication on laptops === Geo-replication systems are often extended to deliver local replication beyond the server and down to the laptop used by a single user. Server to laptop replication enables mobile users to have access to a local replica of their business portal on a standard laptop. This technology may be employed to provide in the field access to portal content by, for example, sales forces and combat forces. == Geo-replication systems ==

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  Pop music automation

  Pop music automation is a field of study among musicians and computer scientists with a goal of producing successful pop music algorithmically. It is often based on the premise that pop music is especially formulaic, unchanging, and easy to compose. The idea of automating pop music composition is related to many ideas in algorithmic music, artificial intelligence (AI) and computational creativity. == History of automation in music == Algorithms (or, at the very least, formal sets of rules) have been used to compose music for centuries; the procedures used to plot voice-leading in counterpoint, for example, can often be reduced to algorithmic determinant. Now the term is usually reserved, however, for the use of formal procedures to make music without human intervention. Classical music automation software exists that generates music in the style of Mozart and Bach and jazz. Most notably, David Cope has written a software system called "Experiments in Musical Intelligence" (or "EMI") that is capable of analyzing and generalizing from existing music by a human composer to generate novel musical compositions in the same style. EMI's output is convincing enough to persuade human listeners that its music is human-generated to a high level of competence. Creativity research in jazz has focused on the process of improvisation and the cognitive demands that this places on a musical agent: reasoning about time, remembering and conceptualizing what has already been played, and planning ahead for what might be played next. Inevitably associated with pop music automation is pop music analysis. Projects in pop music automation may include, but are not limited to, ideas in melody creation and song development, vocal generation or improvement, automatic accompaniment and lyric composition. == Automatic accompaniment == Some systems exist that automatically choose chords to accompany a vocal melody in real-time. A user with no musical experience can create a song with instrumental accompaniment just by singing into a microphone. An example is a Microsoft Research project called Songsmith, which trains a Hidden Markov model using a music database and uses that model to select chords for new melodies. == Melody generation == Automatic melody generation is often done with a Markov chain, the states of the system become note or pitch values, and a probability vector for each note is constructed, completing a transition probability matrix (see below). An algorithm is constructed to produce an output note values based on the transition matrix weightings, which could be MIDI note values, frequency (Hz), or any other desirable metric. A second-order Markov chain can be introduced by considering the current state and also the previous state, as indicated in the second table. Higher, nth-order chains tend to "group" particular notes together, while 'breaking off' into other patterns and sequences occasionally. These higher-order chains tend to generate results with a sense of phrasal structure, rather than the 'aimless wandering' produced by a first-order system. == Lyric composition == Automated lyric creating software may take forms such as: Selecting words according to their rhythm The Tra-la-Lyrics system produces song lyrics, in Portuguese, for a given melody. This not only involves matching each word syllable with a note in the melody, but also matching the word's stress with the strong beats of the melody. Parsing existing pop music (e.g. for content or word choice) This involves natural language processing. Pablo Gervás has developed a noteworthy system called ASPERA that employs a case-based reasoning (CBR) approach to generating poetic formulations of a given input text via a composition of poetic fragments that are retrieved from a case-base of existing poems. Each poem fragment in the ASPERA case-base is annotated with a prose string that expresses the meaning of the fragment, and this prose string is used as the retrieval key for each fragment. Metrical rules are then used to combine these fragments into a well-formed poetic structure. Automatic analogy or story creation Programs like TALE-SPIN and The MINSTREL system represent a complex elaboration of this basis approach, distinguishing a range of character-level goals in the story from a range of author-level goals for the story. Systems like Bringsjord's BRUTUS can create stories with complex interpersonal themes like betrayal. On-line metaphor generation systems like 'Sardonicus' or 'Aristotle' can suggest lexical metaphors for a given descriptive goal (e.g., to describe a supermodel as skinny, the source terms “pencil”, “whip”, “whippet”, “rope”, “stick-insect” and “snake” are suggested). Free association of grouped words Using a language database (such as wordnet) one can create musings on a subject that may be weak grammatically but are still sensical. See such projects as the Flowerewolf automatic poetry generator or the Dada engine. == Software == === More or less free === BreathCube by xoxos. Simple lyrical vocal content is generated with simple music. CubeBreath by xoxos. Audio input is vocoded in tune with the music. Midi Internet Algorithmic Composition infno, infinite generator of electronic dance music and synth-pop. Algorithmic Trap, trap beat generator. === Commercial === Band in a box generates any element, potentially creates whole new songs from scratch. Musical Palette - Melody Composing Tool SongSmith: Automatic accompaniment for vocal melodies Ludwig 3.0 automatic accompaniment, writes arrangements for given instruments, plays its own songs for an infinitely long time. Automated Composing System creates music in many different styles

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  Fuzzy logic

  Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y

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