AI Coding Tools

Explore the best AI Coding Tools — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

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  Image-based modeling and rendering

  In computer graphics and computer vision, image-based modeling and rendering (IBMR) methods rely on a set of two-dimensional images of a scene to generate a three-dimensional model and then render some novel views of this scene. The traditional approach of computer graphics has been used to create a geometric model in 3D and try to reproject it onto a two-dimensional image. Computer vision, conversely, is mostly focused on detecting, grouping, and extracting features (edges, faces, etc.) present in a given picture and then trying to interpret them as three-dimensional clues. Image-based modeling and rendering allows the use of multiple two-dimensional images in order to generate directly novel two-dimensional images, skipping the manual modeling stage. == Light modeling == Instead of considering only the physical model of a solid, IBMR methods usually focus more on light modeling. The fundamental concept behind IBMR is the plenoptic illumination function which is a parametrisation of the light field. The plenoptic function describes the light rays contained in a given volume. It can be represented with seven dimensions: a ray is defined by its position ( x , y , z ) {\displaystyle (x,y,z)} , its orientation ( θ , ϕ ) {\displaystyle (\theta ,\phi )} , its wavelength ( λ ) {\displaystyle (\lambda )} and its time ( t ) {\displaystyle (t)} : P ( x , y , z , θ , ϕ , λ , t ) {\displaystyle P(x,y,z,\theta ,\phi ,\lambda ,t)} . IBMR methods try to approximate the plenoptic function to render a novel set of two-dimensional images from another. Given the high dimensionality of this function, practical methods place constraints on the parameters in order to reduce this number (typically to 2 to 4). == IBMR methods and algorithms == View morphing generates a transition between images Panoramic imaging renders panoramas using image mosaics of individual still images Lumigraph relies on a dense sampling of a scene Space carving generates a 3D model based on a photo-consistency check

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  Hyperparameter (machine learning)

  In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer). These are named hyperparameters in contrast to parameters, which are characteristics that the model learns from the data. Hyperparameters are not required by every model or algorithm. Some simple algorithms such as ordinary least squares regression require none. However, the LASSO algorithm, for example, adds a regularization hyperparameter to ordinary least squares which must be set before training. Even models and algorithms without a strict requirement to define hyperparameters may not produce meaningful results if these are not carefully chosen. However, optimal values for hyperparameters are not always easy to predict. Some hyperparameters may have no meaningful effect, or one important variable may be conditional upon the value of another. Often a separate process of hyperparameter tuning is needed to find a suitable combination for the data and task. As well as improving model performance, hyperparameters can be used by researchers to introduce robustness and reproducibility into their work, especially if it uses models that incorporate random number generation. == Considerations == The time required to train and test a model can depend upon the choice of its hyperparameters. A hyperparameter is usually of continuous or integer type, leading to mixed-type optimization problems. The existence of some hyperparameters is conditional upon the value of others, e.g. the size of each hidden layer in a neural network can be conditional upon the number of layers. === Difficulty-learnable parameters === The objective function is typically non-differentiable with respect to hyperparameters. As a result, in most instances, hyperparameters cannot be learned using gradient-based optimization methods (such as gradient descent), which are commonly employed to learn model parameters. These hyperparameters are those parameters describing a model representation that cannot be learned by common optimization methods, but nonetheless affect the loss function. An example would be the tolerance hyperparameter for errors in support vector machines. === Untrainable parameters === Sometimes, hyperparameters cannot be learned from the training data because they aggressively increase the capacity of a model and can push the loss function to an undesired minimum (overfitting to the data), as opposed to correctly mapping the richness of the structure in the data. For example, if we treat the degree of a polynomial equation fitting a regression model as a trainable parameter, the degree would increase until the model perfectly fit the data, yielding low training error, but poor generalization performance. === Tunability === Most performance variation can be attributed to just a few hyperparameters. The tunability of an algorithm, hyperparameter, or interacting hyperparameters is a measure of how much performance can be gained by tuning it. For an LSTM, while the learning rate followed by the network size are its most crucial hyperparameters, batching and momentum have no significant effect on its performance. Although some research has advocated the use of mini-batch sizes in the thousands, other work has found the best performance with mini-batch sizes between 2 and 32. === Robustness === An inherent stochasticity in learning directly implies that the empirical hyperparameter performance is not necessarily its true performance. Methods that are not robust to simple changes in hyperparameters, random seeds, or even different implementations of the same algorithm cannot be integrated into mission critical control systems without significant simplification and robustification. Reinforcement learning algorithms, in particular, require measuring their performance over a large number of random seeds, and also measuring their sensitivity to choices of hyperparameters. Their evaluation with a small number of random seeds does not capture performance adequately due to high variance. Some reinforcement learning methods, e.g. DDPG (Deep Deterministic Policy Gradient), are more sensitive to hyperparameter choices than others. == Optimization == Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined loss function on given test data. The objective function takes a tuple of hyperparameters and returns the associated loss. Typically these methods are not gradient based, and instead apply concepts from derivative-free optimization or black box optimization. == Reproducibility == Apart from tuning hyperparameters, machine learning involves storing and organizing the parameters and results, and making sure they are reproducible. In the absence of a robust infrastructure for this purpose, research code often evolves quickly and compromises essential aspects like bookkeeping and reproducibility. Online collaboration platforms for machine learning go further by allowing scientists to automatically share, organize and discuss experiments, data, and algorithms. Reproducibility can be particularly difficult for deep learning models. For example, research has shown that deep learning models depend very heavily even on the random seed selection of the random number generator.

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  Multi-armed bandit

  In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (

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  Non-human

  Non-human (also spelled nonhuman) is any entity displaying some, but not enough, human characteristics to be considered a human. The term has been used in a variety of contexts and may refer to objects that have been developed with human intelligence, such as robots or vehicles. == Organisms == === Animal rights and personhood === In the animal rights movement, it is common to distinguish between "human animals" and "non-human animals". Participants in the animal rights movement generally recognize that non-human animals have some similar characteristics to those of human persons. For example, various non-human animals have been shown to register pain, compassion, memory, and some cognitive function. Some animal rights activists argue that the similarities between human and non-human animals justify giving non-human animals rights that human society has afforded to humans, such as the right to self-preservation, and some even wish for all non-human animals or at least those that bear a fully thinking and conscious mind, such as vertebrates and some invertebrates such as cephalopods, to be given a full right of personhood. === The non-human in philosophy === Contemporary philosophers have drawn on the work of Henri Bergson, Gilles Deleuze, Félix Guattari, and Claude Lévi-Strauss (among others) to suggest that the non-human poses epistemological and ontological problems for humanist and post-humanist ethics, and have linked the study of non-humans to materialist and ethological approaches to the study of society and culture. == Software and robots == The term non-human has been used to describe computer programs and robot-like devices that display some human-like characteristics. In both science fiction and in the real world, computer programs and robots have been built to perform tasks that require human-computer interactions in a manner that suggests sentience and compassion. There is increasing interest in the use of robots in nursing homes and to provide elder care. Computer programs have been used for years in schools to provide one-on-one education with children. The Tamagotchi toy required children to provide care, attention, and nourishment to keep it "alive".

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  Inbox by Gmail

  Inbox by Gmail was an email service developed by Google. Announced on a limited invitation-only basis on October 22, 2014, it was officially released to the public on May 28, 2015. Inbox was shut down by Google on April 2, 2019. Available on the web, and through mobile apps for Android and iOS, Inbox by Gmail aimed to improve email productivity and organization through several key features. Bundles gathered emails on the same topic together; highlighted surface key details from messages, reminders and assists; and a "snooze" functionality enabled users to control when specific information would appear. Updates to the service enabled an "undo send" feature; a "Smart Reply" feature that automatically generated short reply examples for certain emails; integration with Google Calendar for event organization, previews of newsletters; and a "Save to Inbox" feature that let users save links for later use. Inbox by Gmail received generally positive reviews. At its launch, it was called "minimalist and lovely, full of layers and easy to navigate", with features deemed helpful in finding the right messages—one reviewer noted that the service felt "a lot like the future of email". However, it also received criticism, particularly for a low density of information, algorithms that needed tweaking, and because the service required users to "give up the control" of organizing their own email, meaning that "Anyone who already has a system for organizing their emails will likely find themselves fighting Google's system". Google noted in March 2016 that 10% of all replies on mobile originated from Inbox's Smart Reply feature. Google announced it would discontinue Inbox by Gmail in March 2019, with many of its features integrated into Gmail proper. == Features == Inbox by Gmail scanned the user's incoming Gmail messages for information. It gathered email messages related to the same overall topic into an organized bundle, with a title describing the bundle's content. For example, flight tickets, car rentals, and hotel reservations were grouped under "Travel", giving the user an easier overview of emails. Users could also group emails together manually, to "teach" the Inbox how the user worked. The service highlighted key details and important information in messages, such as flight itineraries, event information, photos and documents. Inbox could retrieve updated information from the Internet, including the real-time status of flights and package deliveries. Users could set reminders to bring up important messages later. When a user needed particular information, Inbox could assist the user by displaying the necessary details. Where Inbox highlights information was not needed immediately, users could "snooze" a message or reminder, with options to make the information reappear at a later time or specific location. In June 2015, Google added an "Undo Send" feature to Inbox, giving the user 10 seconds to undo sending a message. In November 2015, Google added "Smart Reply" functionality to the mobile apps. With Smart Reply, Inbox determined which emails could be answered with a short reply, generating three example responses from which the user could select one with a single tap. Smart Reply (initially available only on the Android and iOS mobile apps) was added to the Inbox website in March 2016, Google announcing that "10% of all your replies on mobile already use Smart Reply". By May 2017, Google said Smart Reply was driving about 12% of replies in inbox on mobile. In April 2016, Google updated Inbox with three new features; Google Calendar event organization, newsletter previews, and a "Save to Inbox" functionality that let the user save links for later use, rather than having to email links to themselves. In December 2017, Google introduced an "Unsubscribe" card that let users easily unsubscribe from mailing lists. The card appeared for email messages (from specific senders) that the user had not opened for a month. A few popular Inbox by Gmail features were subsequently added to Gmail: "Snoozing" of emails Nudges: Gmail could move old messages back to the top of the inbox when it thought a follow up or reply might be required. Hover actions: Placing the mouse cursor over a certain part of the message could quickly effect an action, such as archiving, without its being opened. Smart reply: This feature employed boilerplate text to suggest appropriate replies. Google reportedly wished, at a time then to be decided, to add the "bundles" feature to Gmail, which at the time was available only in Inbox for Gmail. By March 2020, many Inbox features were still missing from Gmail. == Platforms == Inbox by Gmail was announced on a limited invitation-only basis on October 22, 2014, available on the web, and through the Android and iOS mobile operating systems. It was officially released to the public on May 28, 2015. == Reception == David Pierce of The Verge praised the service, writing that it was "minimalist and lovely, full of layers and easy to navigate. It's remarkably fast and smooth on all platforms, and far better on iOS than the Gmail app". However, he criticized the app's low density of information, with only a few emails visible on the screen at a time, making it "a bit of a challenge" for users who need to go through "hundreds of emails" every day. Although positive that "Inbox feels a lot like the future of email", Pierce wrote that there was "plenty of algorithm tweaking and design condensing to do", with particular attention needed on a "compact view" for denser view of information on the screen. Sarah Mitroff of CNET also praised Inbox, writing, "Not only is it visually appealing, it's also full of features that help you find every message you need, when you need it". She added that users must "give up the control" to organize their email, and that it "won't vibe with everyone", but admitted that "if you're willing ... the app will reward you with a smarter and cleaner inbox." Mitroff noted that, initially, users had to coach the app about which bundle was appropriate for certain emails, writing, "It's a tedious process at first, by [sic] in just a few days Inbox starts to get it right." Regarding any downsides of the service, Mitroff wrote that "Inbox has a built-in strategy for managing your emails that works best on its own. Anyone who already has a system for organizing their emails will likely find themselves fighting Google's system". == Discontinuation and legacy == Google ended the service in March 2019. Google called Inbox "a great place to experiment with new ideas" and noted that many of those ideas had been migrated to Gmail. The company wanted, going forward, to focus its resources on a single email system. Several services, like Shortwave, attempted to resurrect some of the features of Inbox by Gmail to attract its old users. Similarly, Inbox Reborn, an actively maintained browser extension developed by a team of volunteer developers from around the world since 2018, aims to recreate the core features and visual style of Inbox by Gmail within the standard Gmail interface. The project continues to focus on preserving functionalities such as email bundling and streamlined workflows to provide users with a familiar productivity experience. Afterwards, most people moved to Spark, Spike, or Newton. According to a product manager at Google, a "more focused approach" regarding email was the companies goal. This is likely the reason they moved away from Inbox.

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  Resisting AI

  Resisting AI: An Anti-fascist Approach to Artificial Intelligence is a book on artificial intelligence (AI) by Dan McQuillan, published in 2022 by Bristol University Press. == Content == Resisting AI takes the form of an extended essay, which contrasts optimistic visions about AI's potential by arguing that AI may best be seen as a continuation and reinforcement of bureaucratic forms of discrimination and violence, ultimately fostering authoritarian outcomes. For McQuillan, AI's promise of objective calculability is antithetical to an egalitarian and just society. McQuillan uses the expression "AI violence" to describe how – based on opaque algorithms – various actors can discriminate against categories of people in accessing jobs, loans, medical care, and other benefits. The book suggests that AI has a political resonance with soft eugenic approaches to the valuation of life by modern welfare states, and that AI exhibits eugenic features in its underlying logic, as well as in its technical operations. The parallel is with historical eugenicists achieving saving to the state by sterilizing defectives so the state would not have to care for their offspring. The analysis of McQuillan goes beyond the known critique of AI systems fostering precarious labour markets, addressing "necropolitics", the politics of who is entitled to live, and who to die. Although McQuillan offers a brief history of machine learning at the beginning of the book – with its need for "hidden and undercompensated labour", he is concerned more with the social impacts of AI rather than with its technical aspects. McQuillan sees AI as the continuation of existing bureaucratic systems that already marginalize vulnerable groups – aggravated by the fact that AI systems trained on existing data are likely to reinforce existing discriminations, e.g. in attempting to optimize welfare distribution based on existing data patterns, ultimately creating a system of "self-reinforcing social profiling". In elaborating on the continuation between existing bureaucratic violence and AI, McQuillan connects to Hannah Arendt's concept of the thoughtless bureaucrat in Eichmann in Jerusalem: A Report on the Banality of Evil, which now becomes the algorithm that, lacking intent, cannot be accountable, and is thus endowed with an "algorithmic thoughtlessness". McQuillan defends the "fascist" in the title of the work by arguing that while not all AI is fascist, this emerging technology of control may end up being deployed by fascist or authoritarian regimes. For McQuillan, AI can support the diffusion of states of exception, as a technology impossible to properly regulate and a mechanism for multiplying exceptions more widely. An example of a scenario where AI systems of surveillance could bring discrimination to a new high is the initiative to create LGBT-free zones in Poland. Skeptical of ethical regulations to control the technology, McQuillan suggests people's councils and workers' councils, and other forms of citizens' agency to resist AI. A chapter titled "Post-Machine Learning" makes an appeal for resistance via currents of thought from feminist science (standpoint theory), post-normal science (extended peer communities), and new materialism; McQuillan encourages the reader to question the meaning of "objectivity" and calls for the necessity of alternative ways of knowing. Among the virtuous examples of resistance – possibly to be adopted by the AI workers themselves – McQuillan notes the Lucas Plan of the workers of Lucas Aerospace Corporation, in which a workforce declared redundant took control, reorienting the enterprise toward useful products. McQuillan advocates for what he calls decomputing, an opposition to the sweeping application and expansion of artificial intelligence. Similar to degrowth, the approach criticizes AI as an outgrowth of the systemic issues within capitalist systems. McQuillan argues that a different future is possible, in which distance between people is reduced rather than increased through AI intermediaries. The work of McQuillan warns against "watered-down forms of engagement" with AI, such as citizen juries, which superficially look like democratic deliberation but may actually obscure important decisions about AI that are outside the purview of the engagement situation (McQuillan 2022, 128). In an interview about the book, McQuillan describes himself as an "AI abolitionist". == Reception == The book has been praised for how it "masterfully disassembles AI as an epistemological, social, and political paradigm". On the critical side, a review in the academic journal Justice, Power and Resistance took exception to the "nightmarish visions of Big Brother" offered by McQuillan, and argued that while many elements of AI may pose concern, a critique should not be based on a caricature of what AI is, concluding that McQuillan's work is "less of a theory and more of a Manifesto". Another review notes "a disconnect between the technical aspects of AI and the socio-political analysis McQuillan provides." Although the book was published before the ChatGPT and large language model debate heated up, the book has not lost relevance to the AI discussion. It is noted for suggesting a link between beliefs in artificial intelligence and beliefs in a racialised and gendered visions of intelligence overall, whereby a certain type of rational, measurable intelligence is privileged, leading to "historical notions of hierarchies of being". The blog Reboot praised McQuillan for offering a theory of harm of AI (why AI could end up hurting people and society) that does not just encourage tackling in isolation specific predicted problems with AI-centric systems: bias, non-inclusiveness, exploitativeness, environmental destructiveness, opacity, and non-contestability. For educational policies could also look at AI following the reading of McQuillan: In his book Resisting AI, Dan McQuillan argues that "When we're thinking about the actuality of AI, we can't separate the calculations in the code from the social context of its application" .... McQuillan's particular concern is how many contemporary applications of AI are amplifying existing inequalities and injustices as well as deepening social divisions and instabilities. His book makes a powerful case for anticipating these effects and actively resisting them for the good of societies. Videos and podcasts with an interest in AI and emerging technology have discussed the book.

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  Solomonoff's theory of inductive inference

  Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical (state-space model) character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction" (as it can be approximated from below more accurately with more computational resources). It is only "incomputable" in the benign sense that no scientific consensus is able to prove that the best current scientific theory is the best of all possible theories. However, Solomonoff's theory does provide an objective criterion for deciding among the current scientific theories explaining a given set of observations. Solomonoff's induction naturally formalizes Occam's razor by assigning larger prior credences to theories that require a shorter algorithmic description. == Origin == === Philosophical === The theory is based in philosophical foundations, and was founded by Ray Solomonoff around 1960. It is a mathematically formalized combination of Occam's razor and the Principle of Multiple Explanations. All computable theories which perfectly describe previous observations are used to calculate the probability of the next observation, with more weight put on the shorter computable theories. Marcus Hutter's universal artificial intelligence builds upon this to calculate the expected value of an action. === Principle === Solomonoff's induction has been argued to be the computational formalization of pure Bayesianism. To understand, recall that Bayesianism derives the posterior probability P [ T | D ] {\displaystyle \mathbb {P} [T|D]} of a theory T {\displaystyle T} given data D {\displaystyle D} by applying Bayes rule, which yields P [ T | D ] = P [ D | T ] P [ T ] P [ D | T ] P [ T ] + ∑ A ≠ T P [ D | A ] P [ A ] {\displaystyle \mathbb {P} [T|D]={\frac {\mathbb {P} [D|T]\mathbb {P} [T]}{\mathbb {P} [D|T]\mathbb {P} [T]+\sum _{A\neq T}\mathbb {P} [D|A]\mathbb {P} [A]}}} where theories A {\displaystyle A} are alternatives to theory T {\displaystyle T} . For this equation to make sense, the quantities P [ D | T ] {\displaystyle \mathbb {P} [D|T]} and P [ D | A ] {\displaystyle \mathbb {P} [D|A]} must be well-defined for all theories T {\displaystyle T} and A {\displaystyle A} . In other words, any theory must define a probability distribution over observable data D {\displaystyle D} . Solomonoff's induction essentially boils down to demanding that all such probability distributions be computable. Interestingly, the set of computable probability distributions is a subset of the set of all programs, which is countable. Similarly, the sets of observable data considered by Solomonoff were finite. Without loss of generality, we can thus consider that any observable data is a finite bit string. As a result, Solomonoff's induction can be defined by only invoking discrete probability distributions. Solomonoff's induction then allows to make probabilistic predictions of future data F {\displaystyle F} , by simply obeying the laws of probability. Namely, we have P [ F | D ] = E T [ P [ F | T , D ] ] = ∑ T P [ F | T , D ] P [ T | D ] {\displaystyle \mathbb {P} [F|D]=\mathbb {E} _{T}[\mathbb {P} [F|T,D]]=\sum _{T}\mathbb {P} [F|T,D]\mathbb {P} [T|D]} . This quantity can be interpreted as the average predictions P [ F | T , D ] {\displaystyle \mathbb {P} [F|T,D]} of all theories T {\displaystyle T} given past data D {\displaystyle D} , weighted by their posterior credences P [ T | D ] {\displaystyle \mathbb {P} [T|D]} . === Mathematical === The proof of the "razor" is based on the known mathematical properties of a probability distribution over a countable set. These properties are relevant because the infinite set of all programs is a denumerable set. The sum S of the probabilities of all programs must be exactly equal to one (as per the definition of probability) thus the probabilities must roughly decrease as we enumerate the infinite set of all programs, otherwise S will be strictly greater than one. To be more precise, for every ϵ {\displaystyle \epsilon } > 0, there is some length l such that the probability of all programs longer than l is at most ϵ {\displaystyle \epsilon } . This does not, however, preclude very long programs from having very high probability. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion. == Mathematical guarantees == === Solomonoff's completeness === The remarkable property of Solomonoff's induction is its completeness. In essence, the completeness theorem guarantees that the expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic) data generating process. The errors can be measured using the Kullback–Leibler divergence or the square of the difference between the induction's prediction and the probability assigned by the (stochastic) data generating process. === Solomonoff's uncomputability === Unfortunately, Solomonoff also proved that Solomonoff's induction is uncomputable. In fact, he showed that computability and completeness are mutually exclusive: any complete theory must be uncomputable. The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem. == Modern applications == === Artificial intelligence === Though Solomonoff's inductive inference is not computable, several AIXI-derived algorithms approximate it in order to make it run on a modern computer. The more computing power they are given, the closer their predictions are to the predictions of inductive inference (their mathematical limit is Solomonoff's inductive inference). Another direction of inductive inference is based on E. Mark Gold's model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class S of computable functions, is there a learner (that is, recursive functional) which for any input of the form (f(0),f(1),...,f(n)) outputs a hypothesis (an index e with respect to a previously agreed on acceptable numbering of all computable functions; the indexed function may be required consistent with the given values of f). A learner M learns a function f if almost all its hypotheses are the same index e, which generates the function f; M learns S if M learns every f in S. Basic results are that all recursively enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of recursively enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards. A far reaching extension of the Gold’s approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.

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  Virtual intelligence

  Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.

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  Time series

  In mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries. Common examples include heights of ocean tides, counts of sunspots, daily temperature readings, and the closing values of stock market indices such as the Dow Jones Industrial Average. A time series is often visualized using a run chart (a type of temporal line chart), which helps identify patterns such as trends, seasonal effects, and irregular fluctuations. Time series are widely used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and many other areas of applied science and engineering that involve temporal measurements. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modeled as a stochastic process. While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series. Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility). Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language). == Methods for analysis == Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation, thereby mitigating the need to operate in the frequency domain. Additionally, time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving-average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear, and univariate and multivariate. == Panel data == A time series is one type of panel data. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate. == Analysis == There are several types of motivation and data analysis available for time series which are appropriate for different purposes. === Motivation === In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting. In the context of signal processing, control engineering and communication engineering it is used for signal detection. Other applications are in data mining, pattern recognition and machine learning, where time series analysis can be used for clustering, classification, query by content, anomaly detection as well as forecasting. === Exploratory analysis === A simple way to examine a regular time series is manually with a line chart. The datagraphic shows tuberculosis deaths in the United States, along with the yearly change and the percentage change from year to year. The total number of deaths declined in every year until the mid-1980s, after which there were occasional increases, often proportionately - but not absolutely - quite large. A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns. Visual tools that represent time series data as heat map matrices can help overcome these challenges. === Estimation, filtering, and smoothing === This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation. Its development was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. An equivalent effect may be achieved in the time domain, as in a Kalman filter; see filtering and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral analysis to examine cyclic behavior which need not be related to seasonality. For example, sunspot activity varies over 11 year cycles. Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity. Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see trend estimation and decomposition of time series === Curve fitting === Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For processes that are expected to generally grow in magnitude one of the curves in the graphic (and many others) can be fitted by estimating their parameters. The construction of economic time series involves the estimation of some components for some dates by interpolation between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines"). Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a relat

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  Manifold regularization

  In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm

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  Automated machine learning

  Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.

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  World model (artificial intelligence)

  A world model in artificial intelligence is a machine learning system that builds an internal representation of an environment. The model predicts how that environment changes over time in response to actions. Researchers design world models to help agents plan, reason, and act without constant real-world trial and error. World models differ from systems that merely classify or generate outputs. They simulate dynamics such as physics, object interactions, and causality. Early ideas date to the 1990s. Modern versions power robots, autonomous driving, and interactive video generation. == History == Jürgen Schmidhuber introduced the term world model in machine learning in 1990. He proposed recurrent neural networks that predict future states from observations and use those predictions to train agents. David Ha and Schmidhuber revived the concept in a 2018 paper. Their agents learned to drive virtual cars and play video games inside self-generated simulations. Yann LeCun advanced the idea in a 2022 position paper titled "A Path Towards Autonomous Machine Intelligence". He argued that intelligence requires predictive models of the world rather than pure pattern matching. LeCun proposed the joint embedding predictive architecture (JEPA) as a practical foundation. LeCun and collaborators developed several JEPA variants. V-JEPA 2 reached state-of-the-art performance on video understanding and physical reasoning at the time. It supports zero-shot robot control in unfamiliar environments. Introduced in March 2026, LeWorldModel trains stably end-to-end from raw pixels and uses two loss terms and avoids hand-crafted heuristics. LeCun founded Advanced Machine Intelligence Labs in 2026 to further develop world models. Google DeepMind introduced Genie in 2024. The model learned interactive environments from unlabeled internet videos. Genie 2 followed in late 2024 and added three-dimensional generation. The Genie series set benchmarks for general-purpose simulation. Genie 3 was introduced in August 2025. It produces photorealistic, real-time interactive worlds from text prompts which are displayed at 24 frames per second and explored in real time with text or image prompts. The model supports persistent three-dimensional worlds and real-time interaction. Waymo adopted Genie 3 in February 2026 and used it to create a specialized world model for autonomous driving simulation, called the Waymo World Model. It produces synchronized camera and lidar outputs and creates edge cases that real robotaxis rarely encounter. The edge cases were reported to be unusual by PCMag. General Intuition announced a $133.7 million seed round. World Labs raised $1 billion. AMI raised $1.03 billion. In April 2026, Alibaba announced Happy Oyster, its world model designed for real-time and “flowy” world model. It includes a directing mode for world building based on text and image prompts and a wandering mode for exploring the resulting world. It can generate 3-minute in-world video clips. Also in April, World Labs, co-founded by Li Fei Fei, unveiled Spark 2.0, an open-source 3D Gaussian splatting rendering engine that targets smartphone-class devices. In June 2026, Nvidia released Cosmos 3, a family of open-weight models. It combines previously independent physical reasoning, world simulation, and action generation. Cosmos 3 integrates can process and generate text, image, video, audio, and action sequences. The model employs a Mixture-of-Transformers" (MoT) approach. An autoregressive (AR) transformer handles reasoning and next-token prediction, while a diffusion transformer (DT) does multimodal generation. Encoders (ViT for vision, VAE for visual/audio, and domain-specific for actions) and generate a shared representation space using 3D multi-dimensional rotary position embedding (mRoPE) for spatial and temporal information. The family includes Cosmos3-Nano (16B parameters) for workstations; Cosmos3-Super (64B parameters) for research. == Architecture == World models process raw sensory data such as video frames or lidar scans. They compress this input into compact latent representations. The system then predicts future representations rather than pixel-by-pixel reconstructions. Many modern world models use joint embedding predictive architecture (JEPA). An encoder turns observations into embeddings. A predictor estimates one or a suite of embeddings from the current one and an action. In some cases a critic chooses one embedding as the best result. A regularizer keeps embeddings well-behaved. The model trains by minimizing prediction error in embedding space. This approach avoids the high cost of generating every detail. Some architectures add explicit components. A fast reactive path handles immediate responses. A slower deliberative path performs longer-horizon planning. Video prediction accuracy or robot success rates are key metrics, but do not always predict real-world performance. Generative world models such as Genie 3 combine these with a simulator. They accept text prompts or layouts and output consistent video, lidar, or three-dimensional scenes. World models often train with self-supervised learning. They use large unlabeled datasets of video or robot interactions. Self-supervised learning can speed learning. Reinforcement learning can fine-tune a model for specific tasks. == Applications == World models support robot learning. Agents train inside simulations and transfer skills to the physical world. This reduces the need for dangerous or expensive real-world trials. Autonomous vehicles use world models to test rare events. Waymo's system simulates tornadoes or unusual pedestrian behavior. Companies train planners without putting vehicles on public roads. Interactive entertainment benefits from world models. Genie 3 lets users generate playable environments from simple descriptions. Game studios prototype levels faster. Scientific simulation gains from these models. Researchers model physical systems or biological processes at scale. Planners in logistics or urban design test strategies inside accurate digital twins. == Comparison with large language models == Both world models and large language models (LLMs) use inferencing on their inputs to make predictions. LLMs operate on textual inputs. They predict the next token in text sequences. They excel at language-oriented tasks such as translation or summarization. However, they lack understanding of physics. World models operate on sensor inputs such as pixels. They predict state changes in that data in latent space. This design supports planning and causal reasoning. LLMs generate fluent text but often fail at consistent physical predictions. Their architecture employs transformers with refinements such as mixture of experts. World models divide an inferencing task into work performed by encoders, predictors, simulators, and other pieces. They typically handle multimodal inputs such as video, lidar, radar, and audio, guided by textual prompting. LLMs power chatbots and code assistants. World models drive embodied agents that act in dynamic environments, such as autonomous driving. The two may be combined in hybrid systems. For example, a LLM handles instructions, while a world model manages low-level control. World model proponents such as LeCun claim that because LLMs are trained only on text, they have no ability to predict anything beyond text, such as real-world events. == Benchmarks == World model benchmarks test physical understanding, long-term consistency, planning, and generalization from sensor data. Meta introduced three benchmarks for V-JEPA 2. IntPhys 2 measures a model's ability to detect physics violations. It presents pairs of videos that diverge when one breaks physical rules. Humans score near 100% accuracy. V-JEPA 2 achieves little better than random chance on many conditions. Minimal Video Pairs (MVPBench) tests physical understanding through multiple-choice questions based on short video clips. It probes object interactions and causality. Something-Something tests action recognition. Epic-Kitchens-100 tests human action anticipation. DeepMind benchmark: Interactive evaluation measures consistency over minutes of interaction, memory of off-screen objects, and response to user actions or text prompts. Waymo benchmark: Output generation quality: Metrics include realism, controllability (via text prompts), and usefulness for training planners in simulated worlds. However, pixel reconstruction error rate with episodic rewards often fails. Other: Epic-Kitchens-100 (often measured with Recall@5) Ego4D 50 Salads, Breakfast, etc. Potential benchmarks: Zero-shot transfer to robots Long-horizon planning Implausible prediction rate

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  Wix.com

  Wix.com Ltd. (Hebrew: וויקס.קום, romanized: wix.com) or simply Wix is an Israeli software company, publicly listed in the US, that provides cloud-based web development services. It offers tools for creating HTML5 websites for desktop and mobile platforms using online drag-and-drop editing. Along with its headquarters and other offices in Israel, Wix also has offices in Brazil, Canada, Germany, India, Ireland, Japan, Lithuania, Poland, the Netherlands, the United States, Ukraine, and Singapore. Users can add applications for social media, e-commerce, online marketing, contact forms, e-mail marketing, and community forums to their websites. The Wix website builder is built on a freemium business model, earning its revenues through premium upgrades. According to the W3Techs technology survey website, Wix was used by 2.5% of websites as of September 2023; at the end of May 2025, it was 3.8%. == History == === Corporate affairs === Wix was founded in 2006 by Israeli developers Avishai Abrahami, Nadav Abrahami, and Giora Kaplan. With its main offices in Tel Aviv, Wix was backed by investors Insight Venture Partners, Mangrove Capital Partners, Bessemer Venture Partners, DAG Ventures, and Benchmark Capital. By April 2010, Wix had 3.5 million users and raised US$10 million in Series C funding provided by Benchmark Capital and existing investors Bessemer Venture Partners and Mangrove Capital Partners. In March 2011, Wix had 8.5 million users and raised US$40 million in Series D funding, bringing its total funding to that date to US$61 million. By August 2013, the Wix platform had more than 34 million registered users. On 5 November 2013, Wix had an initial public offering on NASDAQ, raising about US$127 million for the company and some share holders. In 2016, Mark Tluszcz became the chair of the board of directors. In 2020, Wix's revenue increased to $989 million, a 30% rise year-on-year, primarily due to the shift of businesses online during the coronavirus pandemic. The company added over 31 million new registered users in 2020, reaching a total of 196.7 million by year's end. Wix added approximately 1 million net new premium subscriptions in 2020, surpassing $1 billion in annual collections for the first time. By the end of the year, there were 5.5 million premium subscriptions, a 22% increase compared to the end of 2019. As of its most recent reporting in June 2024, Wix has over 260 million users worldwide. === Product development === ==== 2000s ==== Wix entered an open beta phase in 2007 using a platform based on Adobe Flash. ==== 2010s ==== In June 2011, Wix launched the Facebook store module, making its first step into social commerce. In March 2012, Wix launched a new HTML5 site builder, replacing the Adobe Flash technology. In October 2012, Wix launched an app market for users to sell applications built with the company's automated web development technology. In August 2014, Wix launched Wix Hotels, a booking system for hotels, bed and breakfasts, and vacation rentals that use Wix websites. In June 2016, Wix introduced Wix ADI (Artificial Design Intelligence), a platform that uses artificial intelligence to design websites. ==== 2020s ==== In 2020, Wix launched an additional CMS, EditorX, which included additional CSS features to the original builder. In July 2023, Wix announced that it would be building on its ADI technology to create an AI powered website generator In October 2023, Wix launched the Wix Studio website builder. Co-founder and CEO, Avishai Abrahami described the platform as a “product for agencies”. In March 2024, the AI web builder, which uses a chatbot to help users create content was launched to the public. In March 2025, the digital publisher CNET has identified Wix as the "Best overall website builder overall." In August 2025, Wix announced it would launch banking services—including checking accounts and loans for small businesses—via a partnership with Israeli fintech Unit Finance, as it sought to diversify amid what it described as threats to its core website-building business from artificial intelligence. In January 2026, Wix launched Wix Harmony. Wix harmony is an AI website builder that uses agentic technology, generative design and vibe coding—with manual editing features for additional control. In May 2026, Wix announced layoffs affecting approximately 1,000 employees, or 20% of its workforce. CEO Avishai Abrahami cited two factors: the need to restructure around artificial intelligence and the appreciation of the Israeli shekel against the US dollar, which increased the cost of its Israel-based workforce relative to its dollar-denominated revenue. === Acquisitions === In April 2014, Wix announced the acquisition of Appixia, an Israeli startup for creating native mobile commerce (mCommerce) apps. In October 2014, Wix announced its acquisition of OpenRest, a developer of online ordering systems for restaurants. In April 2015, Wix acquired Moment.me, a mobile website builder for events and marketing tools for social lead generation. On 23 February 2017, Wix acquired the online art community DeviantArt for US$36 million. In January 2017, the company acquired Flok, a provider of customer loyalty programs tools. In February 2020, Wix acquired Inkfrog for eBay sellers, a web design company that provides customized business management software for eBay sellers. On 2 March 2021, Wix acquired SpeedETab, a Miami-based restaurant online technology provider. In May 2021, Wix acquired Rise.ai, a gift card and customer re-engagement package for online brands. A month later, Wix acquired Modalyst, a marketplace and drop-shipping platform. In May 2025, Wix acquired Hour One, a startup specializing in AI-powered video creation tools, to enhance its generative AI capabilities. In June 2025, the company acquired Base44, owned by independent entrepreneur Maor Shlomo, with the intention of integrating Base44's artificial intelligence capabilities and conversational interface into Wix's website and app building platform. == Description == Wix uses a freemium business model. Users can create websites for free then must purchase premium packages to connect their sites to their own domains, remove Wix ads, access the form builder, add e-commerce capabilities, or buy extra data storage and bandwidth. Wix provides customizable website templates and a drag-and-drop HTML5 website builder that includes apps, graphics, image galleries, fonts, vectors, animations, and other options. Users also may opt to create their web sites from scratch. In October 2013, Wix introduced a mobile editor for mobile viewing customization. Wix App Market offers both free and subscription-based applications, with a revenue split of 80% for the developer and 20% for Wix. Customers can integrate third-party applications into their own web sites, such as photograph feeds, blogging, music playlists, online community, e-mail marketing, and file management. Custom JavaScript code can be inserted into Wix webpages using the Velo API. == Controversies == === Use of WordPress code === In October 2016, there was a controversy over Wix's use of WordPress's GPL-licensed code. In response, Avishai Abrahami, Wix's CEO, published a response describing which open-source code was used and how Wix says it collaborates with the open-source community. However, it was subsequently noted that collaboration with the open-source community was not sufficient under the terms of the GPL license, which requires any code built on GPL-licensed code to be released under the same license. === Censorship === On 31 May 2021, 2021 Hong Kong Charter, a Wix-hosted website run by exiled Hong Kong activists, was shut down at the request of the Hong Kong Police. This was the first known case of Hong Kong's National Security Law being used to censor content on an overseas website. Wix later apologized for "mistakenly removing the website" and reinstated the website after it had been down for four days. In October 2023, Wix fired an employee in Dublin, Ireland, for having made social media posts critical of Israel. This incident led to criticism of Wix from members of the Oireachtas (the Irish parliament) and from the head of the Irish government, Taoiseach Leo Varadkar, who said it was "not okay to dismiss somebody because of their political views". Deputy head of government, Tánaiste Micheál Martin, also condemned their dismissal, stating "we tolerate debate with freedom of speech, freedom of opinion, and people have different opinions on these issues." The dismissed employee, Courtney Carey, successfully sued the company for unfair dismissal. Wix did not contest the charge, admitting liability. === Outreach abroad === In October 2023, The Irish Times reported that an Israeli advertising agency advised Wix staff how they can tailor posts for "outreach abroad". This included advice for Wix employees to “show Westernity” in social media posts supporting Israel, stating that “unlike the Gazans,

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  Wetware computer

  A wetware computer is an organic computer (which can also be known as an artificial organic brain or a neurocomputer) composed of organic material "wetware" such as "living" neurons. Wetware computers composed of neurons are different than conventional computers because they use biological materials, and offer the possibility of substantially more energy-efficient computing. While a wetware computer is still largely conceptual, there has been limited success with construction and prototyping, which has acted as a proof of the concept's realistic application to computing in the future. The most notable prototypes have stemmed from the research completed by biological engineer William Ditto during his time at the Georgia Institute of Technology. His work constructing a simple neurocomputer capable of basic addition from leech neurons in 1999 was a significant discovery for the concept. This research was a primary example driving interest in creating these artificially constructed, but still organic brains. == Origins and theoretical foundations == The term wetware came from cyberpunk fiction, notably through Gibson's Neuromancer, but was quickly taken up in scientific literature to explain computation by biological material. Theories of early biological computation borrowed from Alan Turing's morphogenesis model, which showed that chemical interactions could produce complex patterns without centralized control. Hopfield's associative memory networks also provided a foundation for biological information systems with fault tolerance and self-organization. == Major characteristics and processes == Biological wetware systems demonstrate dynamic reconfigurability underpinned by neuroplasticity and enable continuous learning and adaptation. Reaction-diffusion-based computing and molecular logic gates allow spatially parallel information processing unachievable in conventional systems. These systems also show fault tolerance and self-repair at the cellular and network level. The development of cerebral organoids—miniature lab-grown brains—demonstrates spontaneous learning behavior and suggests biological tissue as a viable computational substrate. == Overview == The concept of wetware is an application of specific interest to the field of computer manufacturing. Moore's law, which states that the number of transistors which can be placed on a silicon chip is doubled roughly every two years, has acted as a goal for the industry for decades, but as the size of computers continues to decrease, the ability to meet this goal has become more difficult, threatening to reach a plateau. Due to the difficulty in reducing the size of computers because of size limitations of transistors and integrated circuits, wetware provides an unconventional alternative. A wetware computer composed of neurons is an ideal concept because, unlike conventional materials which operate in binary (on/off), a neuron can shift between thousands of states, constantly altering its chemical conformation, and redirecting electrical pulses through over 200,000 channels in any of its many synaptic connections. Because of this large difference in the possible settings for any one neuron, compared to the binary limitations of conventional computers, the space limitations are far fewer. == Background == The concept of wetware is distinct and unconventional and draws slight resonance with both hardware and software from conventional computers. While hardware is understood as the physical architecture of traditional computational devices, comprising integrated circuits and supporting infrastructure, software represents the encoded architecture of storage and instructions. Wetware is a separate concept that uses the formation of organic molecules, mostly complex cellular structures (such as neurons), to create a computational device such as a computer. In wetware, the ideas of hardware and software are intertwined and interdependent. The molecular and chemical composition of the organic or biological structure would represent not only the physical structure of the wetware but also the software, being continually reprogrammed by the discrete shifts in electrical pulses and chemical concentration gradients as the molecules change their structures to communicate signals. The responsiveness of a cell, proteins, and molecules to changing conformations, both within their structures and around them, ties the idea of internal programming and external structure together in a way that is alien to the current model of conventional computer architecture. The structure of wetware represents a model where the external structure and internal programming are interdependent and unified; meaning that changes to the programming or internal communication between molecules of the device would represent a physical change in the structure. The dynamic nature of wetware borrows from the function of complex cellular structures in biological organisms. The combination of "hardware" and "software" into one dynamic, and interdependent system which uses organic molecules and complexes to create an unconventional model for computational devices is a specific example of applied biorobotics. === The cell as a model of wetware === Cells in many ways can be seen as their form of naturally occurring wetware, similar to the concept that the human brain is the preexisting model system for complex wetware. In his book Wetware: A Computer in Every Living Cell (2009) Dennis Bray explains his theory that cells, which are the most basic form of life, are just a highly complex computational structure, like a computer. To simplify one of his arguments a cell can be seen as a type of computer, using its structured architecture. In this architecture, much like a traditional computer, many smaller components operate in tandem to receive input, process the information, and compute an output. In an overly simplified, non-technical analysis, cellular function can be broken into the following components: Information and instructions for execution are stored as DNA in the cell, RNA acts as a source for distinctly encoded input, processed by ribosomes and other transcription factors to access and process the DNA and to output a protein. Bray's argument in favor of viewing cells and cellular structures as models of natural computational devices is important when considering the more applied theories of wetware to biorobotics. === Biorobotics === Wetware and biorobotics are closely related concepts, which both borrow from similar overall principles. A biorobotic structure can be defined as a system modeled from a preexisting organic complex or model such as cells (neurons) or more complex structures like organs (brain) or whole organisms. Unlike wetware, the concept of biorobotics is not always a system composed of organic molecules, but instead could be composed of conventional material which is designed and assembled in a structure similar or derived from a biological model. Biorobotics have many applications and are used to address the challenges of conventional computer architecture. Conceptually, designing a program, robot, or computational device after a preexisting biological model such as a cell, or even a whole organism, provides the engineer or programmer the benefits of incorporating into the structure the evolutionary advantages of the model. == Effects on users == Wetware technologies such as BCIs and neuromorphic chips offer new possibilities for user autonomy. For those with disabilities, such systems could restore motor or sensory functions and enhance quality of life. However, these technologies raise ethical questions: cognitive privacy, consent over biological data, and risk of exploitation. Without proper oversight, wetware technologies may also widen inequality, favoring those with access to cognitive enhancements. Open governance frameworks and ethical AI design grounded in neuro ethics will be essential. With the development of wetware devices, disparities in access could exacerbate social inequalities, benefiting those who have resources to enhance cognitive or physical abilities. It is necessary to create strong ethical frameworks, inclusive development practices, and open systems of governance to reduce risks and make sure that wetware advances are beneficial to all segments of society. == Applications and goals == === Basic neurocomputer composed of leech neurons === In 1999 William Ditto and his team of researchers at Georgia Institute of Technology and Emory University created a basic form of a wetware computer capable of simple addition by harnessing leech neurons. Leeches were used as a model organism due to the large size of their neuron, and the ease associated with their collection and manipulation. However, these results have never been published in a peer-reviewed journal, prompting questions about the validity of the claims. The computer was able to complete basic addition through electrical probes

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  Hierarchical control system

  A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. == Overview == A human-built system with complex behavior is often organized as a hierarchy. For example, a command hierarchy has among its notable features the organizational chart of superiors, subordinates, and lines of organizational communication. Hierarchical control systems are organized similarly to divide the decision making responsibility. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas sensations and command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a hierarchical control system are related to its layers. Each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer. The lower layers have local tasks, goals, and sensations, and their activities are planned and coordinated by higher layers which do not generally override their decisions. The layers form a hybrid intelligent system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning. A hierarchical task network is a good fit for planning in a hierarchical control system. Besides artificial systems, an animal's control systems are proposed to be organized as a hierarchy. In perceptual control theory, which postulates that an organism's behavior is a means of controlling its perceptions, the organism's control systems are suggested to be organized in a hierarchical pattern as their perceptions are constructed so. == Control system structure == The accompanying diagram is a general hierarchical model which shows functional manufacturing levels using computerised control of an industrial control system. Referring to the diagram; Level 0 contains the field devices such as flow and temperature sensors, and final control elements, such as control valves Level 1 contains the industrialised Input/Output (I/O) modules, and their associated distributed electronic processors. Level 2 contains the supervisory computers, which collate information from processor nodes on the system, and provide the operator control screens. Level 3 is the production control level, which does not directly control the process, but is concerned with monitoring production and monitoring targets Level 4 is the production scheduling level. == Applications == === Manufacturing, robotics and vehicles === Among the robotic paradigms is the hierarchical paradigm in which a robot operates in a top-down fashion, heavy on planning, especially motion planning. Computer-aided production engineering has been a research focus at NIST since the 1980s. Its Automated Manufacturing Research Facility was used to develop a five layer production control model. In the early 1990s DARPA sponsored research to develop distributed (i.e. networked) intelligent control systems for applications such as military command and control systems. NIST built on earlier research to develop its Real-Time Control System (RCS) and Real-time Control System Software which is a generic hierarchical control system that has been used to operate a manufacturing cell, a robot crane, and an automated vehicle. In November 2007, DARPA held the Urban Challenge. The winning entry, Tartan Racing employed a hierarchical control system, with layered mission planning, motion planning, behavior generation, perception, world modelling, and mechatronics. === Artificial intelligence === Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a particular goal of the software agent (i.e. system as a whole), and higher layers are increasingly more abstract. Each layer's goal subsumes that of the underlying layers, e.g. the decision to move forward by the eat-food layer takes into account the decision of the lowest obstacle-avoidance layer. Behavior need not be planned by a superior layer, rather behaviors may be triggered by sensory inputs and so are only active under circumstances where they might be appropriate. Reinforcement learning has been used to acquire behavior in a hierarchical control system in which each node can learn to improve its behavior with experience. James Albus, while at NIST, developed a theory for intelligent system design named the Reference Model Architecture (RMA), which is a hierarchical control system inspired by RCS. Albus defines each node to contain these components. Behavior generation is responsible for executing tasks received from the superior, parent node. It also plans for, and issues tasks to, the subordinate nodes. Sensory perception is responsible for receiving sensations from the subordinate nodes, then grouping, filtering, and otherwise processing them into higher level abstractions that update the local state and which form sensations that are sent to the superior node. Value judgment is responsible for evaluating the updated situation and evaluating alternative plans. World Model is the local state that provides a model for the controlled system, controlled process, or environment at the abstraction level of the subordinate nodes. At its lowest levels, the RMA can be implemented as a subsumption architecture, in which the world model is mapped directly to the controlled process or real world, avoiding the need for a mathematical abstraction, and in which time-constrained reactive planning can be implemented as a finite-state machine. Higher levels of the RMA however, may have sophisticated mathematical world models and behavior implemented by automated planning and scheduling. Planning is required when certain behaviors cannot be triggered by current sensations, but rather by predicted or anticipated sensations, especially those that come about as result of the node's actions.

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