AI Art Museum Los Angeles

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  Semantic compression

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 Words in bold have been replaced by their hypernyms.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

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  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

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  Web intelligence

  Web intelligence is the area of scientific research and development that explores the roles and makes use of artificial intelligence and information technology for new products, services and frameworks that are empowered by the World Wide Web. The term was coined in a paper written by Ning Zhong, Jiming Liu Yao and Y.Y. Ohsuga in the Computer Software and Applications Conference in 2000. == Research == The research about the web intelligence covers many fields – including data mining (in particular web mining), information retrieval, pattern recognition, predictive analytics, the semantic web, web data warehousing – typically with a focus on web personalization and adaptive websites.

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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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  Brain technology

  Brain technology, or self-learning know-how systems, defines a technology that employs latest findings in neuroscience. [see also neuro implants] The term was first introduced by the Artificial Intelligence Laboratory in Zurich, Switzerland, in the context of the Roboy project. Brain Technology can be employed in robots, know-how management systems and any other application with self-learning capabilities. In particular, Brain Technology applications allow the visualization of the underlying learning architecture often coined as "know-how maps". == Research and applications == The first demonstrations of BC in humans and animals took place in the 1960s when Grey Walter demonstrated use of non-invasively recorded encephalogram (EEG) signals from a human subject to control a slide projector (Graimann et al., 2010). Soon after Jacques J. Vidal coined the term brain–computer interface (BCI) in 1971, the Defense Advanced Research Projects Agency (DARPA) first starting funding brain–computer interface research and has since funded several brain–computer interface projects. That market is expected to reach a value of $1.72 billion by 2022. Brain–computer interfaces record brain activity, transmit the information out of the body, signal-process the data via algorithms, and convert them into command control signals. In 2012, a landmark study in Nature, led by pioneer Leigh Hochberg, MD, PhD, demonstrated that two people with tetraplegia were able to control robotic arms through thought when connected to the BrainGate neural interface system. The two participants were able to reach for and grasp objects in three-dimensional space, and one participant used the system to serve herself coffee for the first time since becoming paralyzed nearly 15 years prior. And in October 2020, two patients were able to wirelessly control an operating system to text, email, shop and bank using direct thought through the Stentrode brain computer interface (Journal of NeuroInterventional Surgery) in a study led by Thomas Oxley. This was the first time a brain–computer interface was implanted via the patient's blood vessels, eliminating the need for open brain surgery. Currently a number of groups are exploring a range of experimental devices using brain–computer interfaces, which have the potential to fundamentally change the way of life for patients with paralysis and a wide range of neurological disorders. These include: as Elon Musk, Facebook, and the University of California in San Francisco. The systems. This technology is also being explored as a neuromodulation device and may ultimately help diagnose and treat a range of brain pathologies, such as epilepsy and Parkinson's disease.

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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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  Proximal gradient methods for learning

  Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \ell _{1}} regularization (also known as Lasso) of the form min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , where x i ∈ R d and y i ∈ R . {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},\quad {\text{ where }}x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as sparsity (in the case of lasso) or group structure (in the case of group lasso). == Relevant background == Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form min x ∈ H F ( x ) + R ( x ) , {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x),} where F {\displaystyle F} is convex and differentiable with Lipschitz continuous gradient, R {\displaystyle R} is a convex, lower semicontinuous function which is possibly nondifferentiable, and H {\displaystyle {\mathcal {H}}} is some set, typically a Hilbert space. The usual criterion of x {\displaystyle x} minimizes F ( x ) + R ( x ) {\displaystyle F(x)+R(x)} if and only if ∇ ( F + R ) ( x ) = 0 {\displaystyle \nabla (F+R)(x)=0} in the convex, differentiable setting is now replaced by 0 ∈ ∂ ( F + R ) ( x ) , {\displaystyle 0\in \partial (F+R)(x),} where ∂ φ {\displaystyle \partial \varphi } denotes the subdifferential of a real-valued, convex function φ {\displaystyle \varphi } . Given a convex function φ : H → R {\displaystyle \varphi :{\mathcal {H}}\to \mathbb {R} } an important operator to consider is its proximal operator prox φ : H → H {\displaystyle \operatorname {prox} _{\varphi }:{\mathcal {H}}\to {\mathcal {H}}} defined by prox φ ⁡ ( u ) = arg ⁡ min x ∈ H φ ( x ) + 1 2 ‖ u − x ‖ 2 2 , {\displaystyle \operatorname {prox} _{\varphi }(u)=\operatorname {arg} \min _{x\in {\mathcal {H}}}\varphi (x)+{\frac {1}{2}}\|u-x\|_{2}^{2},} which is well-defined because of the strict convexity of the ℓ 2 {\displaystyle \ell _{2}} norm. The proximal operator can be seen as a generalization of a projection. We see that the proximity operator is important because x ∗ {\displaystyle x^{}} is a minimizer to the problem min x ∈ H F ( x ) + R ( x ) {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x)} if and only if x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) , {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right),} where γ > 0 {\displaystyle \gamma >0} is any positive real number. === Moreau decomposition === One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let φ : X → R {\displaystyle \varphi :{\mathcal {X}}\to \mathbb {R} } be a lower semicontinuous, convex function on a vector space X {\displaystyle {\mathcal {X}}} . We define its Fenchel conjugate φ ∗ : X → R {\displaystyle \varphi ^{}:{\mathcal {X}}\to \mathbb {R} } to be the function φ ∗ ( u ) := sup x ∈ X ⟨ x , u ⟩ − φ ( x ) . {\displaystyle \varphi ^{}(u):=\sup _{x\in {\mathcal {X}}}\langle x,u\rangle -\varphi (x).} The general form of Moreau's decomposition states that for any x ∈ X {\displaystyle x\in {\mathcal {X}}} and any γ > 0 {\displaystyle \gamma >0} that x = prox γ φ ⁡ ( x ) + γ prox φ ∗ / γ ⁡ ( x / γ ) , {\displaystyle x=\operatorname {prox} _{\gamma \varphi }(x)+\gamma \operatorname {prox} _{\varphi ^{}/\gamma }(x/\gamma ),} which for γ = 1 {\displaystyle \gamma =1} implies that x = prox φ ⁡ ( x ) + prox φ ∗ ⁡ ( x ) {\displaystyle x=\operatorname {prox} _{\varphi }(x)+\operatorname {prox} _{\varphi ^{}}(x)} . The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections. In certain situations it may be easier to compute the proximity operator for the conjugate φ ∗ {\displaystyle \varphi ^{}} instead of the function φ {\displaystyle \varphi } , and therefore the Moreau decomposition can be applied. This is the case for group lasso. == Lasso regularization == Consider the regularized empirical risk minimization problem with square loss and with the ℓ 1 {\displaystyle \ell _{1}} norm as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},} where x i ∈ R d and y i ∈ R . {\displaystyle x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} The ℓ 1 {\displaystyle \ell _{1}} regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such ℓ 1 {\displaystyle \ell _{1}} regularization problems are interesting because they induce sparse solutions, that is, solutions w {\displaystyle w} to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{0},} where ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", which is the number of nonzero entries of the vector w {\displaystyle w} . Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors. === Solving for L1 proximity operator === For simplicity we restrict our attention to the problem where λ = 1 {\displaystyle \lambda =1} . To solve the problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\|w\|_{1},} we consider our objective function in two parts: a convex, differentiable term F ( w ) = 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 {\displaystyle F(w)={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}} and a convex function R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} . Note that R {\displaystyle R} is not strictly convex. Let us compute the proximity operator for R ( w ) {\displaystyle R(w)} . First we find an alternative characterization of the proximity operator prox R ⁡ ( x ) {\displaystyle \operatorname {prox} _{R}(x)} as follows: u = prox R ⁡ ( x ) ⟺ 0 ∈ ∂ ( R ( u ) + 1 2 ‖ u − x ‖ 2 2 ) ⟺ 0 ∈ ∂ R ( u ) + u − x ⟺ x − u ∈ ∂ R ( u ) . {\displaystyle {\begin{aligned}u=\operatorname {prox} _{R}(x)\iff &0\in \partial \left(R(u)+{\frac {1}{2}}\|u-x\|_{2}^{2}\right)\\\iff &0\in \partial R(u)+u-x\\\iff &x-u\in \partial R(u).\end{aligned}}} For R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} it is easy to compute ∂ R ( w ) {\displaystyle \partial R(w)} : the i {\displaystyle i} th entry of ∂ R ( w ) {\displaystyle \partial R(w)} is precisely ∂ | w i | = { 1 , w i > 0 − 1 , w i < 0 [ − 1 , 1 ] , w i = 0. {\displaystyle \partial |w_{i}|={\begin{cases}1,&w_{i}>0\\-1,&w_{i}<0\\\left[-1,1\right],&w_{i}=0.\end{cases}}} Using the recharacterization of the proximity operator given above, for the choice of R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} and γ > 0 {\displaystyle \gamma >0} we have that prox γ R ⁡ ( x ) {\displaystyle \operatorname {prox} _{\gamma R}(x)} is defined entrywise by ( prox γ R ⁡ ( x ) ) i = { x i − γ , x i > γ 0 , | x i | ≤ γ x i + γ , x i < − γ , {\displaystyle \left(\operatorname {prox} _{\gamma R}(x)\right)_{i}={\begin{cases}x_{i}-\gamma ,&x_{i}>\gamma \\0,&|x_{i}|\leq \gamma \\x_{i}+\gamma ,&x_{i}<-\gamma ,\end{cases}}} which is known as the soft thresholding operator S γ ( x ) = prox γ ‖ ⋅ ‖ 1 ⁡ ( x ) {\displaystyle S_{\gamma }(x)=\operatorname {prox} _{\gamma \|\cdot \|_{1}}(x)} . === Fixed point iterative schemes === To finally solve the lasso problem we consider the fixed point equation shown earlier: x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) . {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right).} Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial w 0 ∈ R d {\displaystyle w^{0}\in \mathbb {R} ^{d}} , and for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } define w k + 1 = S γ ( w k − γ ∇ F ( w k ) ) . {\displaystyle w^{k+1}=S_{\gamma }\left(w^{k}-\gamma \nabla F\l

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  Artificial brain

  An artificial brain (or artificial mind) is software and hardware with cognitive abilities similar to those of the animal or human brain. Research investigating "artificial brains" and brain emulation plays three important roles in science: An ongoing attempt by neuroscientists to understand how the human brain works, known as cognitive neuroscience. A thought experiment in the philosophy of artificial intelligence, demonstrating that it is possible, at least in theory, to create a machine that has all the capabilities of a human being. A long-term project to create machines exhibiting behavior comparable to those of animals with complex central nervous system such as mammals and most particularly humans. The ultimate goal of creating a machine exhibiting human-like behavior or intelligence is sometimes called strong AI. An example of the first objective is the project reported by Aston University in Birmingham, England where researchers are using biological cells to create "neurospheres" (small clusters of neurons) in order to develop new treatments for diseases including Alzheimer's, motor neurone and Parkinson's disease. The second objective is a reply to arguments such as John Searle's Chinese room argument, Hubert Dreyfus's critique of AI or Roger Penrose's argument in The Emperor's New Mind. These critics argued that there are aspects of human consciousness or expertise that can not be simulated by machines. One reply to their arguments is that the biological processes inside the brain can be simulated to any degree of accuracy. This reply was made as early as 1950, by Alan Turing in his classic paper "Computing Machinery and Intelligence". The third objective is generally called artificial general intelligence by researchers. However, Ray Kurzweil prefers the term "strong AI". In his book The Singularity is Near, he focuses on whole brain emulation using conventional computing machines as an approach to implementing artificial brains, and claims (on grounds of computer power continuing an exponential growth trend) that this could be done by 2025. Henry Markram, director of the Blue Brain project (which is attempting brain emulation), made a similar claim (2020) at the Oxford TED conference in 2009. == Approaches to brain simulation == W. Ross Ashby's pioneering work in cybernetics provided an early mathematical framework for understanding adaptive brain-like systems. In his 1952 book Design for a Brain, Ashby proposed that the brain could be modeled as an ultrastable system that maintains equilibrium through continuous adaptation to environmental perturbations. His approach used differential equations and state-space models to describe how neural systems could exhibit purposeful behavior through feedback mechanisms. Ashby's homeostat, a physical machine built in 1948, demonstrated these principles through an electromechanical device with four interconnected units that automatically adjusted their parameters to maintain stability when disturbed. The homeostat represented one of the first attempts to build an artificial system exhibiting brain-like adaptive behavior, influencing subsequent work in adaptive systems, neural networks, and artificial intelligence. Although direct human brain emulation using artificial neural networks on a high-performance computing engine is a commonly discussed approach, there are other approaches. An alternative artificial brain implementation could be based on Holographic Neural Technology (HNeT) non linear phase coherence/decoherence principles. The analogy has been made to quantum processes through the core synaptic algorithm which has strong similarities to the quantum mechanical wave equation. EvBrain is a form of evolutionary software that can evolve "brainlike" neural networks, such as the network immediately behind the retina. In November 2008, IBM received a US$4.9 million grant from the Pentagon for research into creating intelligent computers. The Blue Brain project is being conducted with the assistance of IBM in Lausanne. The project is based on the premise that it is possible to artificially link the neurons "in the computer" by placing thirty million synapses in their proper three-dimensional position. Some proponents of strong AI speculated in 2009 that computers in connection with Blue Brain and Soul Catcher may exceed human intellectual capacity by around 2015, and that it is likely that we will be able to download the human brain at some time around 2050. While Blue Brain is able to represent complex neural connections on the large scale, the project does not achieve the link between brain activity and behaviors executed by the brain. In 2012, project Spaun (Semantic Pointer Architecture Unified Network) attempted to model multiple parts of the human brain through large-scale representations of neural connections that generate complex behaviors in addition to mapping. Spaun's design recreates elements of human brain anatomy. The model, consisting of approximately 2.5 million neurons, includes features of the visual and motor cortices, GABAergic and dopaminergic connections, the ventral tegmental area (VTA), substantia nigra, and others. The design allows for several functions in response to eight tasks, using visual inputs of typed or handwritten characters and outputs carried out by a mechanical arm. Spaun's functions include copying a drawing, recognizing images, and counting. There are good reasons to believe that, regardless of implementation strategy, the predictions of realising artificial brains in the near future are optimistic. In particular brains (including the human brain) and cognition are not currently well understood, and the scale of computation required is unknown. Another near term limitation is that all current approaches for brain simulation require orders of magnitude larger power consumption compared with a human brain. The human brain consumes about 20 W of power, whereas current supercomputers may use as much as 1 MW—i.e., an order of 100,000 more. == Artificial brain thought experiment == Some critics of brain simulation believe that it is simpler to create general intelligent action directly without imitating nature. Some commentators have used the analogy that early attempts to construct flying machines modeled them after birds, but that modern aircraft do not look like birds.

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  Photo-consistency

  In computer vision, photo-consistency determines whether a given voxel is occupied. A voxel is considered to be photo consistent when its color appears to be similar to all the cameras that can see it. Most voxel coloring or space carving techniques require using photo consistency as a check condition in Image-based modeling and rendering applications. == Usage == 3D Volumetric Reconstruction. Image registration. Multi-view reconstruction.

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  AI nationalism

  AI nationalism is the idea that nations should develop and control their own artificial intelligence technologies to advance their own interests and ensure technological sovereignty. This concept is gaining traction globally, leading countries to implement new laws, form strategic alliances, and invest significantly in domestic AI capabilities. == Global trends and national strategies == In 2018, British technology investor Ian Hogarth published an influential essay titled AI Nationalism. He argued that as AI gains more power and its economic and military significance expands, governments will take measures to bolster their own domestic AI industries, and predicted that the advancement of machine learning systems would lead to what he termed "AI nationalism." He anticipated that this rise in AI would accelerate a global arms race, resulting in more closed economies, restrictions on foreign acquisitions, and limitations on the movement of talent. Hogarth predicted that AI policy would become a central focus of government agendas. He also criticized Britain’s approach to AI strategy, citing the sale of London-based DeepMind—one of the leading AI laboratories, acquired by Google for a relatively modest £400 million in 2014—as a significant misstep. AI nationalism is chiefly reflected in the escalating rhetoric of an artificial intelligence arms race, portraying AI development as a zero-sum game where the winner gains significant economic, political, and military advantages. This mindset, as highlighted in a 2017 Pentagon report, warns that sharing AI technology could erode technological supremacy and enhance rivals' capabilities. The winner-takes-all mentality of AI nationalism poses risks including unsafe AI development, increased geopolitical tension, and potential military aggression (such as cyberattacks or targeting AI professionals). Several countries, including Canada, France, and India, have formulated national strategies to advance their positions in AI. In the United States, a leading player in the global AI arena, trade policies have been enacted to restrict China's access to critical microchips, reflecting a strategic effort to maintain a technological edge. The United States’ National Security Commission on Artificial Intelligence (NSCAI) frames AI development as a critical aspect of a broader technology competition crucial for national success. It emphasizes the need to outpace China in AI to maintain strategic advantage, reflecting AI nationalism by linking geopolitical power directly to advancements in AI. France has seen notable governmental support for local AI startups, particularly those specializing in language technologies that cater to French and other non-English languages. In Saudi Arabia, Crown Prince Mohammed bin Salman is investing billions in AI research and development. The country has actively collaborated with major technology firms such as Amazon, IBM, and Microsoft to establish itself as a prominent AI hub. == Historical and cultural context == AI nationalism is seen as deeply connected to historical racism and imperialism. It is viewed not merely as a technological competition but as a contest over racial and civilizational superiority. Historically, technological achievements were often used to justify colonialism and racial hierarchies, with Western societies perceiving their advancements as evidence of superiority. In the context of AI, this historical context continues to shape views on intelligence and development. Some argue that AI nationalism reinforces the idea of fundamental civilizational divides, especially between the Western world and China. This perspective often frames China's progress in AI as a direct challenge to Western values, presenting the AI competition as a struggle over values. AI nationalism is said to draw from long-standing anti-Asian stereotypes, such as the "Yellow Peril," which portray Asian nations as threats to Western civilization. This viewpoint links Asian technological advances with dehumanization and artificiality, reflecting persistent anxieties about China's growing role in the global tech landscape. == Implications == AI nationalism is seen as a component of a broader trend towards the fragmentation of the internet, where digital services are increasingly influenced by local regulations and national interests. This shift is creating a new technological landscape in which the impact of artificial intelligence on individuals' lives can vary significantly depending on their geographic location. J. Paul Goode argues that AI nationalism may exacerbate existing societal divisions by promoting the development of systems that embed cultural biases, thereby privileging certain groups while disadvantaging others.

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  Knowledge graph embedding

  In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q Read more →

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  Meta-learning (computer science)

  Meta-learning is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017, the term had not found a standard interpretation, however the main goal is to use such metadata to understand how automatic learning can become flexible in solving learning problems, hence to improve the performance of existing learning algorithms or to learn (induce) the learning algorithm itself, hence the alternative term learning to learn. Flexibility is important because each learning algorithm is based on a set of assumptions about the data, its inductive bias. This means that it will only learn well if the bias matches the learning problem. A learning algorithm may perform very well in one domain, but not on the next. This poses strong restrictions on the use of machine learning or data mining techniques, since the relationship between the learning problem (often some kind of database) and the effectiveness of different learning algorithms is not yet understood. By using different kinds of metadata, like properties of the learning problem, algorithm properties (like performance measures), or patterns previously derived from the data, it is possible to learn, select, alter or combine different learning algorithms to effectively solve a given learning problem. Critiques of meta-learning approaches bear a strong resemblance to the critique of metaheuristic, a possibly related problem. A good analogy to meta-learning, and the inspiration for Jürgen Schmidhuber's early work (1987) and Yoshua Bengio et al.'s work (1991), considers that genetic evolution learns the learning procedure encoded in genes and executed in each individual's brain. In an open-ended hierarchical meta-learning system using genetic programming, better evolutionary methods can be learned by meta evolution, which itself can be improved by meta meta evolution, etc. == Definition == A proposed definition for a meta-learning system combines three requirements: The system must include a learning subsystem. Experience is gained by exploiting meta knowledge extracted in a previous learning episode on a single dataset, or from different domains. Learning bias must be chosen dynamically. Bias refers to the assumptions that influence the choice of explanatory hypotheses and not the notion of bias represented in the bias-variance dilemma. Meta-learning is concerned with two aspects of learning bias. Declarative bias specifies the representation of the space of hypotheses, and affects the size of the search space (e.g., represent hypotheses using linear functions only). Procedural bias imposes constraints on the ordering of the inductive hypotheses (e.g., preferring smaller hypotheses). == Common approaches == There are three common approaches: using (cyclic) networks with external or internal memory (model-based) learning effective distance metrics (metrics-based) explicitly optimizing model parameters for fast learning (optimization-based). === Model-Based === Model-based meta-learning models updates its parameters rapidly with a few training steps, which can be achieved by its internal architecture or controlled by another meta-learner model. ==== Memory-Augmented Neural Networks ==== A Memory-Augmented Neural Network, or MANN for short, is claimed to be able to encode new information quickly and thus to adapt to new tasks after only a few examples. ==== Meta Networks ==== Meta Networks (MetaNet) learns a meta-level knowledge across tasks and shifts its inductive biases via fast parameterization for rapid generalization. === Metric-Based === The core idea in metric-based meta-learning is similar to nearest neighbors algorithms, which weight is generated by a kernel function. It aims to learn a metric or distance function over objects. The notion of a good metric is problem-dependent. It should represent the relationship between inputs in the task space and facilitate problem solving. ==== Convolutional Siamese Neural Network ==== Siamese neural network is composed of two twin networks whose output is jointly trained. There is a function above to learn the relationship between input data sample pairs. The two networks are the same, sharing the same weight and network parameters. ==== Matching Networks ==== Matching Networks learn a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. ==== Relation Network ==== The Relation Network (RN), is trained end-to-end from scratch. During meta-learning, it learns to learn a deep distance metric to compare a small number of images within episodes, each of which is designed to simulate the few-shot setting. ==== Prototypical Networks ==== Prototypical Networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class. Compared to recent approaches for few-shot learning, they reflect a simpler inductive bias that is beneficial in this limited-data regime, and achieve satisfied results. === Optimization-Based === What optimization-based meta-learning algorithms intend for is to adjust the optimization algorithm so that the model can be good at learning with a few examples. ==== LSTM Meta-Learner ==== LSTM-based meta-learner is to learn the exact optimization algorithm used to train another learner neural network classifier in the few-shot regime. The parametrization allows it to learn appropriate parameter updates specifically for the scenario where a set amount of updates will be made, while also learning a general initialization of the learner (classifier) network that allows for quick convergence of training. ==== Temporal Discreteness ==== Model-Agnostic Meta-Learning (MAML) is a fairly general optimization algorithm, compatible with any model that learns through gradient descent. ==== Reptile ==== Reptile is a remarkably simple meta-learning optimization algorithm, given that both of its components rely on meta-optimization through gradient descent and both are model-agnostic. == Examples == Some approaches which have been viewed as instances of meta-learning: Recurrent neural networks (RNNs) are universal computers. In 1993, Jürgen Schmidhuber showed how "self-referential" RNNs can in principle learn by backpropagation to run their own weight change algorithm, which may be quite different from backpropagation. In 2001, Sepp Hochreiter & A.S. Younger & P.R. Conwell built a successful supervised meta-learner based on Long short-term memory RNNs. It learned through backpropagation a learning algorithm for quadratic functions that is much faster than backpropagation. Researchers at Deepmind (Marcin Andrychowicz et al.) extended this approach to optimization in 2017. In the 1990s, Meta Reinforcement Learning or Meta RL was achieved in Schmidhuber's research group through self-modifying policies written in a universal programming language that contains special instructions for changing the policy itself. There is a single lifelong trial. The goal of the RL agent is to maximize reward. It learns to accelerate reward intake by continually improving its own learning algorithm which is part of the "self-referential" policy. An extreme type of Meta Reinforcement Learning is embodied by the Gödel machine, a theoretical construct which can inspect and modify any part of its own software which also contains a general theorem prover. It can achieve recursive self-improvement in a provably optimal way. Model-Agnostic Meta-Learning (MAML) was introduced in 2017 by Chelsea Finn et al. Given a sequence of tasks, the parameters of a given model are trained such that few iterations of gradient descent with few training data from a new task will lead to good generalization performance on that task. MAML "trains the model to be easy to fine-tune." MAML was successfully applied to few-shot image classification benchmarks and to policy-gradient-based reinforcement learning. Variational Bayes-Adaptive Deep RL (VariBAD) was introduced in 2019. While MAML is optimization-based, VariBAD is a model-based method for meta reinforcement learning, and leverages a variational autoencoder to capture the task information in an internal memory, thus conditioning its decision making on the task. When addressing a set of tasks, most meta learning approaches optimize the average score across all tasks. Hence, certain tasks may be sacrificed in favor of the average score, which is often unacceptable in real-world applications. By contrast, Robust Meta Reinforcement Learning (RoML) focuses on improving low-score tasks, increasing robustness to the selection of task. RoML works as a meta-algorithm, as it can be applied on top of other meta learning algorithms (such as MAML and VariBAD) to increase their robustness. It is applicable to both supervised meta learning and meta reinforcement learning. Discovering meta-knowledge works by inducing knowledge

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  Anomaly detection

  In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behavior. Such examples may arouse suspicions of being generated by a different mechanism, or appear inconsistent with the remainder of that set of data. Anomaly detection finds application in many domains including cybersecurity, medicine, machine vision, statistics, neuroscience, law enforcement and financial fraud to name only a few. Anomalies were initially searched for clear rejection or omission from the data to aid statistical analysis, for example to compute the mean or standard deviation. They were also removed to better predictions from models such as linear regression, and more recently their removal aids the performance of machine learning algorithms. However, in many applications anomalies themselves are of interest and are the observations most desirous in the entire data set, which need to be identified and separated from noise or irrelevant outliers. Three broad categories of anomaly detection techniques exist. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier. However, this approach is rarely used in anomaly detection due to the general unavailability of labelled data and the inherent unbalanced nature of the classes. Semi-supervised anomaly detection techniques assume that some portion of the data is labelled. This may be any combination of the normal or anomalous data, but more often than not, the techniques construct a model representing normal behavior from a given normal training data set, and then test the likelihood of a test instance to be generated by the model. Unsupervised anomaly detection techniques assume the data is unlabelled and are by far the most commonly used due to their wider and relevant application. == Definition == Many attempts have been made in the statistical and computer science communities to define an anomaly. The most prevalent ones include the following, and can be categorised into three groups: those that are ambiguous, those that are specific to a method with pre-defined thresholds usually chosen empirically, and those that are formally defined: === Ill defined === An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism. Anomalies are instances or collections of data that occur very rarely in the data set and whose features differ significantly from most of the data. An outlier is an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data. An anomaly is a point or collection of points that is relatively distant from other points in multi-dimensional space of features. Anomalies are patterns in data that do not conform to a well-defined notion of normal behaviour. === Specific === Let T be observations from a univariate Gaussian distribution and O a point from T. Then the z-score for O is greater than a pre-selected threshold if and only if O is an outlier. == History == === Intrusion detection === The concept of intrusion detection, a critical component of anomaly detection, has evolved significantly over time. Initially, it was a manual process where system administrators would monitor for unusual activities, such as a vacationing user's account being accessed or unexpected printer activity. This approach was not scalable and was soon superseded by the analysis of audit logs and system logs for signs of malicious behavior. By the late 1970s and early 1980s, the analysis of these logs was primarily used retrospectively to investigate incidents, as the volume of data made it impractical for real-time monitoring. The affordability of digital storage eventually led to audit logs being analyzed online, with specialized programs being developed to sift through the data. These programs, however, were typically run during off-peak hours due to their computational intensity. The 1990s brought the advent of real-time intrusion detection systems capable of analyzing audit data as it was generated, allowing for immediate detection of and response to attacks. This marked a significant shift towards proactive intrusion detection. As the field has continued to develop, the focus has shifted to creating solutions that can be efficiently implemented across large and complex network environments, adapting to the ever-growing variety of security threats and the dynamic nature of modern computing infrastructures. == Applications == Anomaly detection is applicable in a very large number and variety of domains, and is an important subarea of unsupervised machine learning. As such it has applications in cyber-security, intrusion detection, fraud detection, fault detection, system health monitoring, event detection in sensor networks, detecting ecosystem disturbances, defect detection in images using machine vision, medical diagnosis and law enforcement. === Intrusion detection === Anomaly detection was proposed for intrusion detection systems (IDS) by Dorothy Denning in 1986. Anomaly detection for IDS is normally accomplished with thresholds and statistics, but can also be done with soft computing, and inductive learning. Types of features proposed by 1999 included profiles of users, workstations, networks, remote hosts, groups of users, and programs based on frequencies, means, variances, covariances, and standard deviations. The counterpart of anomaly detection in intrusion detection is misuse detection. === Fintech fraud detection === Anomaly detection is vital in fintech for fraud prevention. === Preprocessing === Preprocessing data to remove anomalies can be an important step in data analysis, and is done for a number of reasons. Statistics such as the mean and standard deviation are more accurate after the removal of anomalies, and the visualisation of data can also be improved. In supervised learning, removing the anomalous data from the dataset often results in a statistically significant increase in accuracy. === Video surveillance === Anomaly detection has become increasingly vital in video surveillance to enhance security and safety. With the advent of deep learning technologies, methods using Convolutional Neural Networks (CNNs) and Simple Recurrent Units (SRUs) have shown significant promise in identifying unusual activities or behaviors in video data. These models can process and analyze extensive video feeds in real-time, recognizing patterns that deviate from the norm, which may indicate potential security threats or safety violations. An important aspect for video surveillance is the development of scalable real-time frameworks. Such pipelines are required for processing multiple video streams with low computational resources. === IT infrastructure === In IT infrastructure management, anomaly detection is crucial for ensuring the smooth operation and reliability of services. These are complex systems, composed of many interactive elements and large data quantities, requiring methods to process and reduce this data into a human and machine interpretable format. Techniques like the IT Infrastructure Library (ITIL) and monitoring frameworks are employed to track and manage system performance and user experience. Detected anomalies can help identify and pre-empt potential performance degradations or system failures, thus maintaining productivity and business process effectiveness. === IoT systems === Anomaly detection is critical for the security and efficiency of Internet of Things (IoT) systems. It helps in identifying system failures and security breaches in complex networks of IoT devices. The methods must manage real-time data, diverse device types, and scale effectively. Garg et al. have introduced a multi-stage anomaly detection framework that improves upon traditional methods by incorporating spatial clustering, density-based clustering, and locality-sensitive hashing. This tailored approach is designed to better handle the vast and varied nature of IoT data, thereby enhancing security and operational reliability in smart infrastructure and industrial IoT systems. === Petroleum industry === Anomaly detection is crucial in the petroleum industry for monitoring critical machinery. A 2015 paper proposed a novel segmentation algorithm using support vector machines to analyze sensor data for real-time anomaly detection. === Oil and gas pipeline monitoring === In the oil and gas sector, anomaly detection is not just crucial for maintenance and safety, but also for environmental protection. Aljameel et al. propose an advanced machine learning-based model for detecting minor leaks in oil and gas pipelines, a task traditional methods may miss.

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  Automated medical scribe

  Automated medical scribes (also called artificial intelligence scribes, AI scribes, digital scribes, virtual scribes, ambient AI scribes, AI documentation assistants, and digital/virtual/smart clinical assistants) are tools for transcribing medical speech, such as patient consultations and dictated medical notes. Many also produce summaries of consultations. Automated medical scribes based on large language models (LLMs, commonly called "AI", short for "artificial intelligence") increased drastically in popularity in 2024. There are privacy and antitrust concerns. Accuracy concerns also exist, and intensify in situations in which tools try to go beyond transcribing and summarizing, and are asked to format information by its meaning, since LLMs do not deal well with meaning (see weak artificial intelligence). Medics using these scribes are generally expected to understand the ethical and legal considerations, and supervise the outputs. The privacy protections of automated medical scribes vary widely. While it is possible to do all the transcription and summarizing locally, with no connection to the internet, most closed-source providers require that data be sent to their own servers over the internet, processed there, and the results sent back (as with digital voice assistants). Some retailers say their tools use zero-knowledge encryption (meaning that the service provider can't access the data). Others explicitly say that they use patient data to train their AIs, or rent or resell it to third parties; the nature of privacy protections used in such situations is unclear, and they are likely not to be fully effective. Most providers have not published any safety or utility data in academic journals, and are not responsive to requests from medical researchers studying their products. == Privacy == Some providers unclear about what happens to user data. Some may sell data to third parties. Some explicitly send user data to for-profit tech companies for secondary purposes, which may not be specified. Some require users to sign consents to such reuse of their data. Some ingest user data to train the software, promising to anonymize it; however, deanonymization may be possible (that is, it may become obvious who the patient is). It is intrinsically impossible to prevent an LLM from correlating its inputs; they work by finding similar patterns across very large data sets. Some information on the patient will be known from other sources (for instance, information that they were injured in an incident on a certain day might be available from the news media; information that they attended specific appointment locations at specific times is probably available to their cellphone provider/apps/data brokers; information about when they had a baby is probably implied by their online shopping records; and they might mention lifestyle changes to their doctor and on a forum or blog). The software may correlate such information with the "anonymized" clinical consultation record, and, asked about the named patient, provide information which they only told their doctor privately. Because a patient's record is all about the same patient, it is all unavoidably linked; in very many cases, medical histories are intrinsically identifiable. Depending on how common a condition and what other data is available, K-anonymity may be useless. Differential privacy could theoretically preserve privacy. Data broker companies like Google, Amazon, Apple and Microsoft have produced or bought up medical scribes, some of which use user data for secondary purposes, which has led to antitrust concerns. Transfer of patient records for AI training has, in the past, prompted legal action. Open-source programs typically do all the transcription locally, on the doctor's own computer. Open-source software is widely used in healthcare, with some national public healthcare bodies holding hack days. === Data resale and commercialization === Several AI medical scribe providers include terms in their service agreements that allow the reuse, sale, or commercialization of de-identified or user-submitted data. Although such data are generally described as anonymized or aggregated, these practices have raised ethical concerns among clinicians and privacy advocates regarding secondary uses of medical information beyond clinical documentation. Freed, an AI transcription and scribe platform, states in its Terms of Use that it may "collect, use, publish, disseminate, sell, transfer, and otherwise exploit" de-identified and aggregated data derived from user inputs. OpenEvidence similarly states that it may "collect, use, transfer, sell, and disclose non-personal information and customer usage data for any purpose including commercial uses." Doximity, which offers an AI-enabled medical scribe as part of its physician platform, grants itself a "nonexclusive, irrevocable, worldwide, perpetual, unlimited, assignable, sublicensable, royalty-free" license to "copy, prepare derivative works from, improve, distribute, publish, ... analyze, index, tag, [and] commercialize" content submitted by users, subject to its privacy policy. Because these terms allow broad secondary use—including sale, licensing, model-training, derivative works, and commercial exploitation of de-identified or user-submitted data—some commentators have recommended that clinicians review data-handling provisions carefully when adopting AI-scribe tools, particularly in clinical environments where patient privacy and regulatory compliance are critical. === Encryption === Multifactor authentication for access to the data is expected practice. Typically, Diffie–Hellman key exchange is used for encryption; this is the standard method commonly used for things like online banking. This encryption is expensive but not impossible to break; it is not generally considered safe against eavesdroppers with the resources of a nation-state. If content is encrypted between the client and the service provider's remote server (transport cryptography), then the server has an unencrypted copy. This is necessary if the data is used by the service provider (for instance, to train the software). Zero-knowledge encryption implies that the only unencrypted copy is at the client, and the server cannot decrypt the data any more easily than a monster-in-the-middle attacker. == Platforms == Scribes may operate on desktops, laptop, or mobile computers, under a variety of operating systems. These vary in their risks; for instance, mobiles can be lost. The underlying mobile or desktop operating systems are also part of the trusted computing base, and if they are not secure, the software relying on them cannot be secure either. Some AI medical scribe platforms are designed to operate as cloud-based applications that generate structured clinical documentation from clinician–patient conversations. These systems may offer features such as real-time transcription, document generation, and integration with electronic health record (EHR) systems. == Confabulation, omissions, and other errors == Like other LLMs, medical-scribe LLMs are prone to hallucinations, where they make up content based on statistically associations between their training data and the transcription audio. LLMs do not distinguish between trying to transcribe the audio and guessing what words will come next, but perform both processes mixed together. They are especially likely to take short silences or non-speech noises and invent some sort of speech to transcribe them as. LLM medical scribes have been known to confabulate racist and otherwise prejudiced content; this is partly because the training datasets of many LLMs contain pseudoscientific texts about medical racism. They may misgender patients. A survey found that most doctors preferred, in principle, that scribes be trained on data reviewed by medical subject experts. Relevant, accurate training data increases the probability of an accurate transcription, but does not guarantee accuracy. Software trained on thousands of real clinical conversations generated transcripts with lower word error rates. Software trained on manually-transcribed training data did better than software trained with automatically transcribed training data such as YouTube captions. Autoscribes omit parts of the conversation classes as irrelevant. The may wrongly classify pertinent information as irrelevant and omit it. They may also confuse historic and current symptoms, or otherwise misclassify information. They may also simply wrongly transcribe the speech, writing something incorrect instead. If clinicians do not carefully check the recording, such mistakes could make their way into their medical records and cause patient harms. == Patient consent == Professional organizations generally require that scribes be used only with patient consent; some bodies may require written consent. Medics must also abide by local surveillance laws, which may criminalize recording pri

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  Agent verification

  Agent verification is activity to gain assurances that purposeful artificial constructs act in accordance with their specifications. While primitive forms of inorganic agents have been used in manufacturing for centuries, the study of artificial agents did not begin until the mid 20th century. Foundational work on such agents was closely bound with the emergence of artificial intelligence as an academic discipline. Early agents deployed for industrial control systems and in computing were often controlled by quite simple logic however, not involving artificial intelligence as such. When deployed as part of a multi-agent system, even such simple agents could require special agent orientated testing methods, as their collective behaviour was challenging to verify with traditional testing techniques. Difficulties in providing assurances that agents will not behave in dangerous ways became more prevalent after the introduction of LLM agents, especially after the rapid acceleration of their deployment in 2025. The verification of agent behaviour can be conducted by formal or informal methods. Informal verification requires less mathematical skill. But when agents are part of systems where errors have significant risks — such as danger to human life, environmental damage or major financial loss — formal verification is preferred. Both regulators and system designers themselves like formal verification as it provides a high degree of mathematical certainty. It is not however always possible to formally test all aspects of an agent based system's behaviour, especially where newer LLM based agents are concerned, due in part to their high degree of autonomy. Accordingly, agent verification for low impact deployments might be carried out only with informal methods, while for high impact deployments, it may be performed with a mix of formal and informal techniques. == Terminology == In academia, the term agent verification is often defined to mean activity concerned with gaining assurance that the agent behaves in accordance with its specification - whether by processes such as testing or simulation. 'Verification' is typically contrasted with 'validation', the latter meaning activity concerned with checking that the specification itself meets user or real world needs. Such definitions are not universally adhered to however - for example, in some workplaces and documents, the words 'verification' and 'validation' can be used synonymously. Efforts to gain confidence in Agents have intensified sharply since 2025 due to the rapid roll out of LLM agents; different terms are sometimes used in the commercial sector. Here the term 'agent verification' can be used in the same sense as it is in academia, but sometimes the same activity can be covered by more ambiguous and wider ranging terms such as 'Agent governance' , 'Agent observability' or 'AI agent policing'. == History == === Classical agents === The theoretical underpinnings for artificial (inorganic) agents emerged in the mid 20th century, with establishment of cybernetics and artificial intelligence. Oliver Selfridge's 1958 Pandemonium - A Paradigm for Learning paper was an important early theoretical contribution in establishing agent oriented architecture. Practical implementations of agents for real world applications began to become widespread in the 1990s, after the introduction of the belief–desire–intention software model (BDI), and agent-oriented programming. Pure digital agents were deployed in computer infrastructure for purposes such as monitoring, while agents connected to real-world sensors and actuators were increasingly used in industrial control systems. While the concept of artificial agents was interwoven with early artificial intelligence studies right from the start, early agents lacked general purpose reasoning capabilities, often only having simple if then logic. Even a device as simple as a thermostat, which has a sensor and a means of acting, can be considered a proto agent in this sense. Verifying the behaviours of a simple single agent system is not generally especially difficult, but it can be a different matter when several simple agents coexist in the same system. Craig Reynolds's work on boids showed that relatively complex, "intelligent" behaviour can emerge from a number of such simple agents working together in a Multi-agent system (MAS). By the 1990s, even the behaviour of a single agent system could sometimes be quite complex; in accordance with the Belief–desire–intention software model, agents could have believes that might evolve over time. Agents were increasingly introduced that were controlled by quite large decision tree models, which had new vulnerabilities to adversarial attack. It was becoming increasingly apparent that traditional software verification methods had limitations for testing such agents, or even for the more primitive type of agents when they were deployed as part of a MAS. It was the use of agents for industrial control systems, sometimes associated with robotics, that lent urgency to the practice of agent verification. Informal testing might be acceptable for digital agents used say to monitor whether each of an organisation's computers are properly licensed. But with an increasing potential for faulty agents to result in a failure that might cause a large fire to break out at a chemical manufacturing plant, a botched medical operation, or even a crashed aircraft, the need to develop reliable means of verifying behaviour of such agents was considered urgent. The Foundation for Intelligent Physical Agents was established in 1996. From the late 90s, a growing number of industry and university based scientists began working on the problem, with researchers publishing papers on the verification of both single and multi agent systems. Much of this work showed how formal verification techniques like model checking could be used to gain a high level of assurance that agent based systems would conform with their specification. A 2018 systematic review covering 231 studies found that model checking was the most common technique for agent verification, with theorem proving the second most commonly used formal verification method. In the first two decades of the 20th century, agents run by AI became more common, with Siri and Alexa being well known examples. But such agents still lacked general reasoning capabilities and did not pose new pressing problems for agent verification. === General purpose reasoning agents === The advent of LLMs created huge potential for further use of artificial agents, as agents based on them could have general purpose cognitive abilities. Agents run by LLMs (and occasionally non-LLM foundation models) have similar vulnerability to adversarial attack as those run by decision tree models. The wider scope of actions for LLM agents has created new challenges for their verification, over and above those present for classical agents. For example, the LLM's neural network endows it with infinite domains, an especial challenge for traditional formal verification techniques. Academics began to study the problems involved in verifying LLM agents from 2018. Deployment of such agents began to accelerate in late 2023 after OpenAI's "function-calling" API was made available, and especially after Anthropic's late 2024 introduction of Model Context Protocol (MCP), a standardised way for LLM agents to gain contextual awareness, and to act on the world by calling various external tools. The rapid rollout of LLM agents following MCP's release has seen the task of agent verification receive increased attention within academia, and also from the private sector. In 2024 and 2025 several startups focusing on LLM agent verification have been founded in both Europe and the US to meet growing demand. == Approaches == === Formal verification === Formal verification involves proving the correctness of some or all aspects of a system using mathematical methods. Such methods can range from manual formal proof, to verification assisted with automated theorem provers like Isabelle. For agent verification, model checking is by far the most frequently used formal verification method; for pre-LLM models it was often complemented with techniques using computation tree logic. Another common method is theorem proving. Formal verification provides a higher degree of confidence than informal methods, but it is not always used, even when it is possible. Sometimes a person or organisation developing software agents won't have the necessary skills, or may not see it as worth the effort if the agent(s) will not have the ability to cause much harm even if they malfunction. When agents are deployed in systems where errors could have serious consequences, the ability of formal verification methods to provide mathematical certainty tends to be strongly preferred by both regulators and designers themselves. But even for high impact systems, formal verificatio

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