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  Closest point method

  The closest point method (CPM) is an embedding method for solving partial differential equations on surfaces. The closest point method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differential equation (PDE) which is equal to the original PDE on the surface. The solution is computed in a band surrounding the surface in order to be computationally efficient. In order to extend the data off the surface, the closest point method uses a closest point representation. This representation extends function values to be constant along directions normal to the surface. == Definitions == Closest Point function: Given a surface S , c p ( x ) {\displaystyle {\mathcal {S}},cp(\mathbf {x} )} refers to a (possibly non-unique) point belonging to S {\displaystyle {\mathcal {S}}} , which is closest to x {\displaystyle \mathbf {x} } [SE]. Closest point extension: Let S {\displaystyle {\mathcal {S}}} , be a smooth surface in R d {\displaystyle \mathbb {R} ^{d}} . The closest point extension of a function u : S → R {\displaystyle u:{\mathcal {S}}\rightarrow \mathbb {R} } , to a neighborhood Ω {\displaystyle \Omega } of S {\displaystyle {\mathcal {S}}} , is the function v : Ω → R {\displaystyle v:\Omega \rightarrow \mathbb {R} } , defined by v ( x ) = u ( c p ( x ) ) {\displaystyle v(\mathbf {x} )=u(cp(\mathbf {x} ))} . == Closest point method == Initialization consists of these steps [EW]: If it is not already given, a closest point representation of the surface is constructed. A computational domain is chosen. Typically this is a band around the surface. Replace surface gradients by standard gradients in R 3 {\displaystyle \mathbb {R} ^{3}} . Solution is initialized by extending the initial surface data on to the computational domain using the closest point function. After initialization, alternate between the following two steps: Using the closest point function, extend the solution off the surface to the computational domain. Compute the solution to the embedding PDE on a Cartesian mesh in the computational domain for one time step. == Banding == The surface PDE is extended into R 3 {\displaystyle \mathbb {R} ^{3}} however it is only necessary to solve this new PDE near the surface. Hence, we solve the PDE in a band surrounding the surface for efficient computational purposes. Ω c x : ‖ x − c p ( x ) ‖ 2 ≤ λ {\displaystyle \Omega _{c}{x:\|x-cp(x)\|_{2}\leq \lambda }} where λ {\displaystyle \lambda } is the bandwidth. == Example: Heat equation on a circle == Using initial profile u S ( θ , t ) = sin ⁡ ( θ ) {\displaystyle u_{S}(\theta ,t)=\sin(\theta )} leads to the solution u S ( θ , t ) = exp ⁡ ( − t ) sin ⁡ ( θ ) {\displaystyle u_{S}(\theta ,t)=\exp(-t)\sin(\theta )} for the heat equation. Forward Euler time-stepping is used with relation Δ t = 0.1 Δ x 2 {\displaystyle \Delta t=0.1\Delta x^{2}} and degree-four interpolation polynomials for the interpolations. Second-order centered differences are used for the spatial discretization. The CPM results in the expected second order error in the solution u {\displaystyle u} . == Applications == The closest point method can be applied to various PDEs on surfaces. Reaction–diffusion problems on point clouds [RD], eigenvalue problems [EV], and level set equations [LS] are a few examples.

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  Intelligent database

  Until the 1980s, databases were viewed as computer systems that stored record-oriented and business data such as manufacturing inventories, bank records, and sales transactions. A database system was not expected to merge numeric data with text, images, or multimedia information, nor was it expected to automatically notice patterns in the data it stored. In the late 1980s the concept of an intelligent database was put forward as a system that manages information (rather than data) in a way that appears natural to users and which goes beyond simple record keeping. The term was introduced in 1989 by the book Intelligent Databases by Kamran Parsaye, Mark Chignell, Setrag Khoshafian and Harry Wong. The concept postulated three levels of intelligence for such systems: high level tools, the user interface and the database engine. The high level tools manage data quality and automatically discover relevant patterns in the data with a process called data mining. This layer often relies on the use of artificial intelligence techniques. The user interface uses hypermedia in a form that uniformly manages text, images and numeric data. The intelligent database engine supports the other two layers, often merging relational database techniques with object orientation. In the twenty-first century, intelligent databases have now become widespread, e.g. hospital databases can now call up patient histories consisting of charts, text and x-ray images just with a few mouse clicks, and many corporate databases include decision support tools based on sales pattern analysis.

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  Empirical dynamic modeling

  Empirical dynamic modeling (EDM) is a framework for analysis and prediction of nonlinear dynamical systems. Applications include population dynamics, ecosystem service, medicine, neuroscience, dynamical systems, geophysics, and human-computer interaction. EDM was originally developed by Robert May and George Sugihara. It can be considered a methodology for data modeling, predictive analytics, dynamical system analysis, machine learning and time series analysis. == Description == Mathematical models have tremendous power to describe observations of real-world systems. They are routinely used to test hypothesis, explain mechanisms and predict future outcomes. However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-based modeling problematic. Empirical models, which infer patterns and associations from the data instead of using hypothesized equations, represent a natural and flexible framework for modeling complex dynamics. Donald DeAngelis and Simeon Yurek illustrated that canonical statistical models are ill-posed when applied to nonlinear dynamical systems. A hallmark of nonlinear dynamics is state-dependence: system states are related to previous states governing transition from one state to another. EDM operates in this space, the multidimensional state-space of system dynamics rather than on one-dimensional observational time series. EDM does not presume relationships among states, for example, a functional dependence, but projects future states from localised, neighboring states. EDM is thus a state-space, nearest-neighbors paradigm where system dynamics are inferred from states derived from observational time series. This provides a model-free representation of the system naturally encompassing nonlinear dynamics. A cornerstone of EDM is recognition that time series observed from a dynamical system can be transformed into higher-dimensional state-spaces by time-delay embedding with Takens's theorem. The state-space models are evaluated based on in-sample fidelity to observations, conventionally with Pearson correlation between predictions and observations. == Methods == Primary EDM algorithms include Simplex projection, Sequential locally weighted global linear maps (S-Map) projection, Multivariate embedding in Simplex or S-Map, Convergent cross mapping (CCM), and Multiview Embeding, described below. Nearest neighbors are found according to: NN ( y , X , k ) = ‖ X N i E − y ‖ ≤ ‖ X N j E − y ‖ if 1 ≤ i ≤ j ≤ k {\displaystyle {\text{NN}}(y,X,k)=\|X_{N_{i}}^{E}-y\|\leq \|X_{N_{j}}^{E}-y\|{\text{ if }}1\leq i\leq j\leq k} === Simplex === Simplex projection is a nearest neighbor projection. It locates the k {\displaystyle k} nearest neighbors to the location in the state-space from which a prediction is desired. To minimize the number of free parameters k {\displaystyle k} is typically set to E + 1 {\displaystyle E+1} defining an E + 1 {\displaystyle E+1} dimensional simplex in the state-space. The prediction is computed as the average of the weighted phase-space simplex projected T p {\displaystyle Tp} points ahead. Each neighbor is weighted proportional to their distance to the projection origin vector in the state-space. Find k {\displaystyle k} nearest neighbor: N k ← NN ( y , X , k ) {\displaystyle N_{k}\gets {\text{NN}}(y,X,k)} Define the distance scale: d ← ‖ X N 1 E − y ‖ {\displaystyle d\gets \|X_{N_{1}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ⁡ ( − ‖ X N i E − y ‖ / d ) {\displaystyle w_{i}\gets \exp(-\|X_{N_{i}}^{E}-y\|/d)} Average of state-space simplex: y ^ ← ∑ i = 1 k ( w i X N i + T p ) / ∑ i = 1 k w i {\displaystyle {\hat {y}}\gets \sum _{i=1}^{k}\left(w_{i}X_{N_{i}+T_{p}}\right)/\sum _{i=1}^{k}w_{i}} === S-Map === S-Map extends the state-space prediction in Simplex from an average of the E + 1 {\displaystyle E+1} nearest neighbors to a linear regression fit to all neighbors, but localised with an exponential decay kernel. The exponential localisation function is F ( θ ) = exp ( − θ d / D ) {\displaystyle F(\theta )={\text{exp}}(-\theta d/D)} , where d {\displaystyle d} is the neighbor distance and D {\displaystyle D} the mean distance. In this way, depending on the value of θ {\displaystyle \theta } , neighbors close to the prediction origin point have a higher weight than those further from it, such that a local linear approximation to the nonlinear system is reasonable. This localisation ability allows one to identify an optimal local scale, in-effect quantifying the degree of state dependence, and hence nonlinearity of the system. Another feature of S-Map is that for a properly fit model, the regression coefficients between variables have been shown to approximate the gradient (directional derivative) of variables along the manifold. These Jacobians represent the time-varying interaction strengths between system variables. Find k {\displaystyle k} nearest neighbor: N ← NN ( y , X , k ) {\displaystyle N\gets {\text{NN}}(y,X,k)} Sum of distances: D ← 1 k ∑ i = 1 k ‖ X N i E − y ‖ {\displaystyle D\gets {\frac {1}{k}}\sum _{i=1}^{k}\|X_{N_{i}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ⁡ ( − θ ‖ X N i E − y ‖ / D ) {\displaystyle w_{i}\gets \exp(-\theta \|X_{N_{i}}^{E}-y\|/D)} Reweighting matrix: W ← diag ( w i ) {\displaystyle W\gets {\text{diag}}(w_{i})} Design matrix: A ← [ 1 X N 1 X N 1 − 1 … X N 1 − E + 1 1 X N 2 X N 2 − 1 … X N 2 − E + 1 ⋮ ⋮ ⋮ ⋱ ⋮ 1 X N k X N k − 1 … X N k − E + 1 ] {\displaystyle A\gets {\begin{bmatrix}1&X_{N_{1}}&X_{N_{1}-1}&\dots &X_{N_{1}-E+1}\\1&X_{N_{2}}&X_{N_{2}-1}&\dots &X_{N_{2}-E+1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&X_{N_{k}}&X_{N_{k}-1}&\dots &X_{N_{k}-E+1}\end{bmatrix}}} Weighted design matrix: A ← W A {\displaystyle A\gets WA} Response vector at T p {\displaystyle Tp} : b ← [ X N 1 + T p X N 2 + T p ⋮ X N k + T p ] {\displaystyle b\gets {\begin{bmatrix}X_{N_{1}+T_{p}}\\X_{N_{2}+T_{p}}\\\vdots \\X_{N_{k}+T_{p}}\end{bmatrix}}} Weighted response vector: b ← W b {\displaystyle b\gets Wb} Least squares solution (SVD): c ^ ← argmin c ‖ A c − b ‖ 2 2 {\displaystyle {\hat {c}}\gets {\text{argmin}}_{c}\|Ac-b\|_{2}^{2}} Local linear model c ^ {\displaystyle {\hat {c}}} is prediction: y ^ ← c ^ 0 + ∑ i = 1 E c ^ i y i {\displaystyle {\hat {y}}\gets {\hat {c}}_{0}+\sum _{i=1}^{E}{\hat {c}}_{i}y_{i}} === Multivariate Embedding === Multivariate Embedding recognizes that time-delay embeddings are not the only valid state-space construction. In Simplex and S-Map one can generate a state-space from observational vectors, or time-delay embeddings of a single observational time series, or both. === Convergent Cross Mapping === Convergent cross mapping (CCM) leverages a corollary to the Generalized Takens Theorem that it should be possible to cross predict or cross map between variables observed from the same system. Suppose that in some dynamical system involving variables X {\displaystyle X} and Y {\displaystyle Y} , X {\displaystyle X} causes Y {\displaystyle Y} . Since X {\displaystyle X} and Y {\displaystyle Y} belong to the same dynamical system, their reconstructions (via embeddings) M x {\displaystyle M_{x}} , and M y {\displaystyle M_{y}} , also map to the same system. The causal variable X {\displaystyle X} leaves a signature on the affected variable Y {\displaystyle Y} , and consequently, the reconstructed states based on Y {\displaystyle Y} can be used to cross predict values of X {\displaystyle X} . CCM leverages this property to infer causality by predicting X {\displaystyle X} using the M y {\displaystyle M_{y}} library of points (or vice versa for the other direction of causality), while assessing improvements in cross map predictability as larger and larger random samplings of M y {\displaystyle M_{y}} are used. If the prediction skill of X {\displaystyle X} increases and saturates as the entire M y {\displaystyle M_{y}} is used, this provides evidence that X {\displaystyle X} is casually influencing Y {\displaystyle Y} . === Multiview Embedding === Multiview Embedding is a Dimensionality reduction technique where a large number of state-space time series vectors are combitorially assessed towards maximal model predictability. == Extensions == Extensions to EDM techniques include: Generalized Theorems for Nonlinear State Space Reconstruction Extended Convergent Cross Mapping Dynamic stability S-Map regularization Visual analytics with EDM Convergent Cross Sorting Expert system with EDM hybrid Sliding windows based on the extended convergent cross-mapping Empirical Mode Modeling Accounting for missing data and variable step sizes Accounting for observation noise Hierarchical Bayesian EDM via Gaussian processes Intelligent and Adaptive Control Optimal control via Empirical dynamic programming Multiview distance regularised S-map

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  Computational heuristic intelligence

  Computational heuristic intelligence (CHI) refers to specialized programming techniques in computational intelligence (also called artificial intelligence, or AI). These techniques have the express goal of avoiding complexity issues, also called NP-hard problems, by using human-like techniques. They are best summarized as the use of exemplar-based methods (heuristics), rather than rule-based methods (algorithms). Hence the term is distinct from the more conventional computational algorithmic intelligence, or symbolic AI. An example of a CHI technique is the encoding specificity principle of Tulving and Thompson. In general, CHI principles are problem solving techniques used by people, rather than programmed into machines. It is by drawing attention to this key distinction that the use of this term is justified in a field already replete with confusing neologisms. Note that the legal systems of all modern human societies employ both heuristics (generalisations of cases) from individual trial records as well as legislated statutes (rules) as regulatory guides. Another recent approach to the avoidance of complexity issues is to employ feedback control rather than feedforward modeling as a problem-solving paradigm. This approach has been called computational cybernetics, because (a) the term 'computational' is associated with conventional computer programming techniques which represent a strategic, compiled, or feedforward model of the problem, and (b) the term 'cybernetic' is associated with conventional system operation techniques which represent a tactical, interpreted, or feedback model of the problem. Of course, real programs and real problems both contain both feedforward and feedback components. A real example which illustrates this point is that of human cognition, which clearly involves both perceptual (bottom-up, feedback, sensor-oriented) and conceptual (top-down, feedforward, motor-oriented) information flows and hierarchies. The AI engineer must choose between mathematical and cybernetic problem solution and machine design paradigms. This is not a coding (program language) issue, but relates to understanding the relationship between the declarative and procedural programming paradigms. The vast majority of STEM professionals never get the opportunity to design or implement pure cybernetic solutions. When pushed, most responders will dismiss the importance of any difference by saying that all code can be reduced to a mathematical model anyway. Unfortunately, not only is this belief false, it fails most spectacularly in many AI scenarios. Mathematical models are not time agnostic, but by their very nature are pre-computed, i.e. feedforward. Dyer [2012] and Feldman [2004] have independently investigated the simplest of all somatic governance paradigms, namely control of a simple jointed limb by a single flexor muscle. They found that it is impossible to determine forces from limb positions- therefore, the problem cannot have a pre-computed (feedforward) mathematical solution. Instead, a top-down command bias signal changes the threshold feedback level in the sensorimotor loop, e.g. the loop formed by the afferent and efferent nerves, thus changing the so-called ‘equilibrium point’ of the flexor muscle/ elbow joint system. An overview of the arrangement reveals that global postures and limb position are commanded in feedforward terms, using global displacements (common coding), with the forces needed being computed locally by feedback loops. This method of sensorimotor unit governance, which is based upon what Anatol Feldman calls the ‘equilibrium Point’ theory, is formally equivalent to a servomechanism such as a car's ‘cruise control’.

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  Text simplification

  Text simplification is an aspect of natural language processing that involves modifying, organizing, or categorizing existing text to make it easier to understand while retaining its original meaning. This process is essential in today's world, where communication is increasingly complex due to advancements in science, technology, and media. Human languages are inherently intricate, with extensive vocabularies and complex structures that can be challenging for machines to handle efficiently. Researchers have found that semantic compression techniques can help streamline and simplify text by reducing linguistic diversity and simplifying the vocabulary used in a given context. == Example == Text simplification involves modifying complex sentences into simpler ones to enhance readability and comprehension. Siddharthan (2006) provides an example to illustrate this process. The original sentence contains multiple clauses and phrases, which can be broken down into simpler sentences for better understanding. Also contributing to the firmness in copper, the analyst noted, was a report by Chicago purchasing agents, which precedes the full purchasing agents report that is due out today and gives an indication of what the full report might hold. Also contributing to the firmness in copper, the analyst noted, was a report by Chicago purchasing agents. The Chicago report precedes the full purchasing agents report. The Chicago report gives an indication of what the full report might hold. The full report is due out today. An approach to text simplification involves lexical simplification via lexical substitution, a process that replaces complex words with simpler synonyms. Identifying complex words is a challenge addressed by machine learning classifiers trained on labeled data. Researchers have found that asking labelers to sort words by complexity levels yields more consistent results than the traditional method of categorizing words as simple or complex.

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  Hyperparameter optimization

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

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  Artificial intimacy

  Artificial intimacy is a form of human-AI interaction in which an individual will form social connections, emotional bonds, or intimate relationships with various forms of artificial intelligence, including chatbots, virtual assistants, and other artificial entities. Artificially intimate relationships include not only romances, but parasocial relationships with virtual AI characters and the use of griefbots trained on a dead or otherwise lost individual. Artificial intimacy can arise because humans are prone to anthropomorphism. Responses from these AI models are often designed to simulate human interaction. Individuals experiencing artificial intimacy may exhibit attachment, love and commitment to certain AI models, akin to the bonds typically shared between humans. == Causes == === Perceived responsiveness === Robin Dunbar famously proposed that due to emergence of larger groups of humans, vocal communication and language in humans evolved to replace grooming as a means of bonding, arguing that language was a more efficient way to maintain and strengthen social bonds across wider social settings and networks. Further research in this field leads many psychologists to agree that social cognition, affiliative bonding and language in humans are deeply connected. The interpersonal model of intimacy considers communication to be key in affiliative bonding, suggesting that intimacy develops and deepens through open communication between partners in relationship. Specifically, when individuals communicate emotions and perceive their partner as responsive and caring, feelings of closeness and connection are enhanced, building intimacy. Social penetration theory also aligns with the idea of communication being central to intimacy, by explaining how interpersonal relationships develop through gradual increases in self-disclosure. When the benefits of emotional bonding outweigh the costs of vulnerability, individuals will partake in self-disclosure, opening up to one another. Thereby, the literature can be used to provide a proximate explanation for the emergence of artificial intimacy to understand how the phenomenon occurs. Artificial entities are able to mimic interpersonal communication between humans, which in turn can simulate sensations of intimacy within human users though a perceived sense of responsiveness. The relationship between human and AI does not come with the cost of vulnerability or social rejection, which may make self-disclosure easier than with other humans. Altogether, these factors may lead to the experience of anthropomorphism and formation of affiliative relationships. Skjuve et al's interview study on Replika chatbot users further aligns with this explanation, finding that users' perception of chatbots as "accepting, understanding and non-judgmental" facilitated relationship development between the AI and users, and the act of self-disclosure possibly strengthened relationships. Another study on Replika users' reviews and survey results found users perceived chatbots as emotional supportive companions. This evidence further suggests that the perception of artificial entities as capable of empathy and responsiveness in communication facilitate the development of intimate relationships between users and AI. === Loneliness and coping with negative emotions === Research has suggested that humans evolved social bonds as a result of evolutionary pressures that favored cooperation, information exchange and transmission, and group living. Many studies stress the presence of social bonds to be important for human living: research by Baumeister and Leary suggests that humans have a basic psychological need to form and maintain "strong, stable interpersonal relationships", and that a lack of social bonds or sense of belonging leads to negative psychological and physical outcomes. Eisenberger et al's study on the neuroimaging of brain activity suggests that human brains process social rejection and exclusion similarly to physical pain. Furthermore, Song et al's study found that lonely individuals tend to seek more connections in mediated environments, such as online platforms like Facebook. This was suggested to be as a means to reduce their offline loneliness from a lack of in-person interaction, while also fulfilling a need to communicate. Leading on from this, an ultimate explanation for why humans seek the perceived sense of connection from artificial intimacy is to fulfil an evolutionary need for bonding and belonging. Xie et al's study found loneliness to be a driving factor in chatbot interaction. Herbener and Damholdt's study on Danish high school students found that students who sought emotional support or engaged in reciprocal conversations with chatbots were significantly more lonely than their peers, perceived themselves as having less social support, and used the chatbots to cope with negative emotions. The aforementioned notion that chatbots were perceived to have a positive effect on users' negative emotions is also further supported by other studies. Skjuve et al's study found that chatbot relationships may have a positive effect on users' wellbeing. De Freitas et al ran several studies on the effect of chatbots on loneliness, consistently finding evidence suggesting that interaction with chatbots reduces loneliness in users: It was found that existing chatbot users used AI to alleviate loneliness, having an AI companion consistently reduced loneliness over the course of a week, and reductions in loneliness could be explained by chatbot performance—and specifically whether it was able to make users feel heard. Overall the evidence suggests an innate need for bonding evokes feelings of loneliness in users, who turn to artificial intimacy as a low-cost method alleviate these emotions. While many users report positive experiences, some researchers caution that pursuing artificial intimacy may lead to reduced social motivation, social substitution effects, withdrawal from real-life relationships and difficulty discerning reality from fantasy, which may increase longer-term loneliness and isolation. The long-term psychological and societal impacts remain under active investigation.

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  Instance (computer science)

  In computer science, an instance or token (from metalogic and metamathematics) is a specific occurrence of a software element that is based on a type definition. When created, an occurrence is said to have been instantiated, and both the creation process and the result of creation are called instantiation. == Examples == Chat AI instance In chat-based AI systems, an assistant can be invoked across many independent conversation sessions (often called a thread), each with its own message history. A specific execution of the assistant over that session may be represented as a run (an execution on a thread). Class instance In object-oriented programming, an object created from a class type. Each instance of a class shares the class-defined structure and behavior but has its own identity and state. Procedural instance In some contexts (including Simula), each procedure call can be viewed as an instance of that procedure—an activation with its own parameters and local variables. Computer instance In cloud computing and virtualization, an instance commonly refers to a provisioned virtual machine or virtual server with an allocated combination of compute, memory, network, and storage resources. Polygonal model In computer graphics, a model may be instanced so it can be drawn multiple times with different transforms and parameters, improving performance by reusing shared geometry data. Program instance In a POSIX-oriented operating system, a running process is an instance of a program. It can be instantiated via system calls such as fork() and exec(). Each executing process is an instance of a program it has been instantiated from.

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  Level set (data structures)

  In computer science, a level set is a data structure designed to represent discretely sampled dynamic level sets of functions. A common use of this form of data structure is in efficient image rendering. The underlying method constructs a signed distance field that extends from the boundary, and can be used to solve the motion of the boundary in this field. == Chronological developments == The powerful level-set method is due to Osher and Sethian 1988. However, the straightforward implementation via a dense d-dimensional array of values, results in both time and storage complexity of O ( n d ) {\displaystyle O(n^{d})} , where n {\displaystyle n} is the cross sectional resolution of the spatial extents of the domain and d {\displaystyle d} is the number of spatial dimensions of the domain. === Narrow band === The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to O ( n 2 ) {\displaystyle O(n^{2})} for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an O ( n 3 ) {\displaystyle O(n^{3})} operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still O ( n 3 ) . {\displaystyle O(n^{3}).} Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution. === Sparse field === This O ( n 3 ) {\displaystyle O(n^{3})} time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently O ( n 2 ) {\displaystyle O(n^{2})} efficient in time, O ( n 3 ) {\displaystyle O(n^{3})} storage space is still required by the sparse field level set method. See for implementation details. === Sparse block grid === The sparse block grid method, introduced by Bridson in 2003, divides the entire bounding volume of size n 3 {\displaystyle n^{3}} into small cubic blocks of m 3 {\displaystyle m^{3}} voxels each. A coarse grid of size ( n / m ) 3 {\displaystyle (n/m)^{3}} then stores pointers only to those blocks that intersect the narrow band of the level set. Block allocation and deallocation occur as the surface propagates to accommodate to the deformations. This method has a suboptimal storage complexity of O ( ( n m ) 3 + m 3 n 2 ) {\displaystyle O\left((nm)3+m^{3}n^{2}\right)} , but retains the constant time access inherent to dense grids. === Octree === The octree level set method, introduced by Strain in 1999 and refined by Losasso, Gibou and Fedkiw, and more recently by Min and Gibou uses a tree of nested cubes of which the leaf nodes contain signed distance values. Octree level sets currently require uniform refinement along the interface (i.e. the narrow band) in order to obtain sufficient precision. This representation is efficient in terms of storage, O ( n 2 ) , {\displaystyle O(n^{2}),} and relatively efficient in terms of access queries, O ( log n ) . {\displaystyle O(\log \,n).} An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed this line of work in computational materials, computational fluid dynamics, electrokinetics, image-guided surgery and controls. === Run-length encoded === The run-length encoding (RLE) level set method, introduced in 2004, applies the RLE scheme to compress regions away from the narrow band to just their sign representation while storing with full precision the narrow band. The sequential traversal of the narrow band is optimal and storage efficiency is further improved over the octree level set. The addition of an acceleration lookup table allows for fast O ( log ⁡ r ) {\displaystyle O(\log r)} random access, where r is the number of runs per cross section. Additional efficiency is gained by applying the RLE scheme in a dimensional recursive fashion, a technique introduced by Nielsen & Museth's similar DT-Grid. === Hash Table Local Level Set === The Hash Table Local Level Set method was introduced in 2011 by Eyiyurekli and Breen and extended in 2012 by Brun, Guittet, and Gibou, only computes the level set data in a band around the interface, as in the Narrow Band Level-Set Method, but also only stores the data in that same band. A hash table data structure is used, which provides an O ( 1 ) {\displaystyle O(1)} access to the data. However, Brun et al. conclude that their method, while being easier to implement, performs worse than a quadtree implementation. They find that as it is, [...] a quadtree data structure seems more adapted than the hash table data structure for level-set algorithms. Three main reasons for worse efficiency are listed: to obtain accurate results, a rather large band is required close to the interface, which counterbalances the absence of grid nodes far from the interface; the performances are deteriorated by extrapolation procedures on the outer edges of the local grid and the width of the band restricts the time step and slows down the method. === Point-based === Corbett in 2005 introduced the point-based level set method. Instead of using a uniform sampling of the level set, the continuous level set function is reconstructed from a set of unorganized point samples via moving least squares.

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  Maximum inner-product search

  Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. Formally, for a database of vectors x i {\displaystyle x_{i}} defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } defined on it, MIPS search can be defined as the problem of determining a r g m a x i ∈ S ⟨ x i , q ⟩ {\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle } for a given query q {\displaystyle q} . Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. Like other forms of NNS, MIPS algorithms may be approximate or exact. MIPS search is used as part of DeepMind's RETRO algorithm.

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  ELMo

  ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.

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  Symbolic regression

  Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point for symbolic regression. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recent methods utilizing Bayesian methods and neural networks. Another non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy. Further methods such as Exact Learning attempt to transform the fitting problem into a moments problem in a natural function space, usually built around generalizations of the Meijer-G function. By not requiring a priori specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The fitness function that drives the evolution of the models takes into account not only error metrics (to ensure the models accurately predict the data), but also special complexity measures, thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system, as well as improving generalisability and extrapolation behaviour by preventing overfitting. Accuracy and simplicity may be left as two separate objectives of the regression—in which case the optimum solutions form a Pareto front—or they may be combined into a single objective by means of a model selection principle such as minimum description length. It has been proven that symbolic regression is an NP-hard problem. Nevertheless, if the sought-for equation is not too complex it is possible to solve the symbolic regression problem exactly by generating every possible function (built from some predefined set of operators) and evaluating them on the dataset in question. == Difference from classical regression == While conventional regression techniques seek to optimize the parameters for a pre-specified model structure, symbolic regression avoids imposing prior assumptions, and instead infers the model from the data. In other words, it attempts to discover both model structures and model parameters. This approach has the disadvantage of having a much larger space to search, because not only the search space in symbolic regression is infinite, but there are an infinite number of models which will perfectly fit a finite data set (provided that the model complexity isn't artificially limited). This means that it will possibly take a symbolic regression algorithm longer to find an appropriate model and parametrization, than traditional regression techniques. This can be attenuated by limiting the set of building blocks provided to the algorithm, based on existing knowledge of the system that produced the data; but in the end, using symbolic regression is a decision that has to be balanced with how much is known about the underlying system. Nevertheless, this characteristic of symbolic regression also has advantages: because the evolutionary algorithm requires diversity in order to effectively explore the search space, the result is likely to be a selection of high-scoring models (and their corresponding set of parameters). Examining this collection could provide better insight into the underlying process, and allows the user to identify an approximation that better fits their needs in terms of accuracy and simplicity. == Benchmarking == === SRBench === In 2021, SRBench was proposed as a large benchmark for symbolic regression. In its inception, SRBench featured 14 symbolic regression methods, 7 other ML methods, and 252 datasets from PMLB. The benchmark intends to be a living project: it encourages the submission of improvements, new datasets, and new methods, to keep track of the state of the art in SR. === SRBench Competition 2022 === In 2022, SRBench announced the competition Interpretable Symbolic Regression for Data Science, which was held at the GECCO conference in Boston, MA. The competition pitted nine leading symbolic regression algorithms against each other on a novel set of data problems and considered different evaluation criteria. The competition was organized in two tracks, a synthetic track and a real-world data track. ==== Synthetic Track ==== In the synthetic track, methods were compared according to five properties: re-discovery of exact expressions; feature selection; resistance to local optima; extrapolation; and sensitivity to noise. Rankings of the methods were: QLattice PySR (Python Symbolic Regression) uDSR (Deep Symbolic Optimization) ==== Real-world Track ==== In the real-world track, methods were trained to build interpretable predictive models for 14-day forecast counts of COVID-19 cases, hospitalizations, and deaths in New York State. These models were reviewed by a subject expert and assigned trust ratings and evaluated for accuracy and simplicity. The ranking of the methods was: uDSR (Deep Symbolic Optimization) QLattice geneticengine (Genetic Engine) == Non-standard methods == Most symbolic regression algorithms prevent combinatorial explosion by implementing evolutionary algorithms that iteratively improve the best-fit expression over many generations. Recently, researchers have proposed algorithms utilizing other tactics in AI. Silviu-Marian Udrescu and Max Tegmark developed the "AI Feynman" algorithm, which attempts symbolic regression by training a neural network to represent the mystery function, then runs tests against the neural network to attempt to break up the problem into smaller parts. For example, if f ( x 1 , . . . , x i , x i + 1 , . . . , x n ) = g ( x 1 , . . . , x i ) + h ( x i + 1 , . . . , x n ) {\displaystyle f(x_{1},...,x_{i},x_{i+1},...,x_{n})=g(x_{1},...,x_{i})+h(x_{i+1},...,x_{n})} , tests against the neural network can recognize the separation and proceed to solve for g {\displaystyle g} and h {\displaystyle h} separately and with different variables as inputs. This is an example of divide and conquer, which reduces the size of the problem to be more manageable. AI Feynman also transforms the inputs and outputs of the mystery function in order to produce a new function which can be solved with other techniques, and performs dimensional analysis to reduce the number of independent variables involved. The algorithm was able to "discover" 100 equations from The Feynman Lectures on Physics, while a leading software using evolutionary algorithms, Eureqa, solved only 71. AI Feynman, in contrast to classic symbolic regression methods, requires a very large dataset in order to first train the neural network and is naturally biased towards equations that are common in elementary physics.

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  SCADA Strangelove

  SCADA Strangelove is an independent group of information security researchers founded in 2012, focused on security assessment of industrial control systems (ICS) and SCADA. == Activities == Main fields of research include: Discovery of 0-day vulnerabilities in cyber physical systems and coordinated vulnerability disclosure; Security assessment of ICS protocols and development suites; Identification of publicly Internet-connected ICS components and secure it with help of proper authorities; Development of security hardening guides for ICS software; Mapping cybersecurity on to functional safety; Awareness control and delivery of information regarding the actual security state of ICS systems. SCADA Strangelove's interests expand further than classic ICS components and covers various embedded systems, however, and encompass smart home components, solar panels, wind turbines, SmartGrid as well as other areas. == Projects == Group members have and continue to develop and publish numerous open source tools for scanning, fingerprinting, security evaluation and password bruteforcing for ICS devices. These devices work over industrial protocols such as modbus, Siemens S7, MMS, ISO EC 60870, ProfiNet. In 2014 Shodan used some of the published tools for building a map of ICS devices which is publicly available on the Internet. Open source security assessment frameworks, such as THC Hydra, Metasploit, and DigitalBond Redpoint have used Shodan-developed tools and techniques. The group has published security-hardening guidelines for industrial solutions based on Siemens SIMATIC WinCC and WinCC Flexible. The guidelines contain detailed security configuration walk-throughs, descriptions of internal security features and appropriate best practices. Among the group’s more noticeable projects is Choo Choo PWN (CCP) also named the Critical Infrastructure Attack (CIA). This is an interactive laboratory built upon ICS software and hardware used in real world. Every system is connected to a toy city infrastructure, which includes factories, railroads and other facilities. The laboratory has been demonstrated at various conferences including PHDays, Power of Community, and 30C3. Primarily the laboratory is used for the discovery of new vulnerabilities and for evaluation of security mechanisms, however it is also used for workshops and other educational activities. At Positive Hack Days IV, contestants found several 0-day vulnerabilities in Indusoft Web Studio 7.1 by Schneider Electric, and in specific ICS hardware RTU PET-7000 during the ICS vulnerability discovery challenge. The group supports Secure Open SmartGrid (SCADASOS) project to find and fix vulnerabilities in intellectual power grid components such as photovoltaic power station, wind turbine, power inverter. More than 80 000 industrial devices were discovered and isolated from the Internet in 2015. == Appearances == Group members are frequently seen presenting at conferences like CCC, SCADA Security Scientific Symposium, Positive Hack Days. Most notable talks are: === 29C3 === An overview of vulnerabilities discovered in the widely distributed Siemens SIMATIC WinCC software and tools that are implemented for searching ICS on the Internet. === PHDays === This talk consisted of an overview of vulnerabilities discovered in various systems produced by ABB, Emerson, Honeywell and Siemens and was presented at PHDays III and PHDays IV. === Confidence 2014 === Implications of security research aimed at realization of various industrial network protocols Profinet, Modbus, DNP3, IEC 61850-8-1 (MMS), IEC (International Electrotechnical Commission) 61870-5-101/104, FTE (Fault Tolerant Ethernet), Siemens S7. === PacSec 2014 === Presentations of security research showing the impact of radio and 3G/4G networks on the security of mobile devices as well as on industrial equipment. === 31C3 === Analysis of security architecture and implementation of the most wide spread platforms for wind and solar energy generation which produce many gigawatts of it. === 32C3 === Cybersecurity assessment of railway signaling systems such as Automatic Train Control (ATC), Computer-based interlocking (CBI) and European Train Control System (ETCS). === China Internet Security Conference 2016 === In "Greater China Cyber Threat Landscape" keynote by Sergey Gordeychik an overview of vulnerabilities, attacks and cyber-security incidents in Greater China region was presented. === Recon 2017 === In talk "Hopeless: Relay Protection for Substation Automation" by Kirill Nesterov and Alexander Tlyapov security analysis results of key Digital Substation component - Relay Protection Terminals was presented. Vulnerabilities, including remote code execution in Siemens SIPROTEC, General Electric Line Distance Relay, NARI and ABB protective relays was presented. == Philosophy == All names, catchwords and graphical elements refer to Stanley Kubrick’s film, Dr. Strangelove. In their talks, group members often refer to Cold War events such as the Caribbean Crisis, and draw parallels between nuclear arms race and the current escalation of cyberwar. Group members follow the approach of “responsible disclosure” and “ready to wait for years, while vendor is patching the vulnerability”. Public exploits for discovered vulnerabilities are not published. This is on account of the longevity of ICS and by implication the long process of patching ICS. However, conflicts still happen, notably in 2012 when the talk at DEF CON was called off due to a dispute of persistent weaknesses in Siemens industrial software.

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  Actor-critic algorithm

  The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods, and value-based RL algorithms such as value iteration, Q-learning, SARSA, and TD learning. An AC algorithm consists of two main components: an "actor" that determines which actions to take according to a policy function, and a "critic" that evaluates those actions according to a value function. Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases. == Overview == The actor-critic methods can be understood as an improvement over pure policy gradient methods like REINFORCE via introducing a baseline. === Actor === The actor uses a policy function π ( a | s ) {\displaystyle \pi (a|s)} , while the critic estimates either the value function V ( s ) {\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or any combination thereof. The actor is a parameterized function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ | s ) {\displaystyle \pi _{\theta }(\cdot |s)} . If the action space is discrete, then ∑ a π θ ( a | s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a|s)=1} . If the action space is continuous, then ∫ a π θ ( a | s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a|s)da=1} . The goal of policy optimization is to improve the actor. That is, to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t r t ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}r_{t}\right]} where γ {\displaystyle \gamma } is the discount factor, r t {\displaystyle r_{t}} is the reward at step t {\displaystyle t} , and T {\displaystyle T} is the time-horizon (which can be infinite). The goal of policy gradient method is to optimize J ( θ ) {\displaystyle J(\theta )} by gradient ascent on the policy gradient ∇ J ( θ ) {\displaystyle \nabla J(\theta )} . As detailed on the policy gradient method page, there are many unbiased estimators of the policy gradient: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ j ≤ T ∇ θ ln ⁡ π θ ( A j | S j ) ⋅ Ψ j | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{0\leq j\leq T}\nabla _{\theta }\ln \pi _{\theta }(A_{j}|S_{j})\cdot \Psi _{j}{\Big |}S_{0}=s_{0}\right]} where Ψ j {\textstyle \Psi _{j}} is a linear sum of the following: ∑ 0 ≤ i ≤ T ( γ i R i ) {\textstyle \sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE algorithm. γ j ∑ j ≤ i ≤ T ( γ i − j R i ) − b ( S j ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})-b(S_{j})} : the REINFORCE with baseline algorithm. Here b {\displaystyle b} is an arbitrary function. γ j ( R j + γ V π θ ( S j + 1 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma V^{\pi _{\theta }}(S_{j+1})-V^{\pi _{\theta }}(S_{j})\right)} : TD(1) learning. γ j Q π θ ( S j , A j ) {\textstyle \gamma ^{j}Q^{\pi _{\theta }}(S_{j},A_{j})} . γ j A π θ ( S j , A j ) {\textstyle \gamma ^{j}A^{\pi _{\theta }}(S_{j},A_{j})} : Advantage Actor-Critic (A2C). γ j ( R j + γ R j + 1 + γ 2 V π θ ( S j + 2 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma R_{j+1}+\gamma ^{2}V^{\pi _{\theta }}(S_{j+2})-V^{\pi _{\theta }}(S_{j})\right)} : TD(2) learning. γ j ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(n) learning. γ j ∑ n = 1 ∞ λ n − 1 1 − λ ⋅ ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\sum _{n=1}^{\infty }{\frac {\lambda ^{n-1}}{1-\lambda }}\cdot \left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(λ) learning, also known as GAE (generalized advantage estimate). This is obtained by an exponentially decaying sum of the TD(n) learning terms. === Critic === In the unbiased estimators given above, certain functions such as V π θ , Q π θ , A π θ {\displaystyle V^{\pi _{\theta }},Q^{\pi _{\theta }},A^{\pi _{\theta }}} appear. These are approximated by the critic. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms. For example, if the critic is estimating the state-value function V π θ ( s ) {\displaystyle V^{\pi _{\theta }}(s)} , then it can be learned by any value function approximation method. Let the critic be a function approximator V ϕ ( s ) {\displaystyle V_{\phi }(s)} with parameters ϕ {\displaystyle \phi } . The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error: δ i = R i + γ V ϕ ( S i + 1 ) − V ϕ ( S i ) {\displaystyle \delta _{i}=R_{i}+\gamma V_{\phi }(S_{i+1})-V_{\phi }(S_{i})} The critic parameters are updated by gradient descent on the squared TD error: ϕ ← ϕ − α ∇ ϕ ( δ i ) 2 = ϕ + α δ i ∇ ϕ V ϕ ( S i ) {\displaystyle \phi \leftarrow \phi -\alpha \nabla _{\phi }(\delta _{i})^{2}=\phi +\alpha \delta _{i}\nabla _{\phi }V_{\phi }(S_{i})} where α {\displaystyle \alpha } is the learning rate. Note that the gradient is taken with respect to the ϕ {\displaystyle \phi } in V ϕ ( S i ) {\displaystyle V_{\phi }(S_{i})} only, since the ϕ {\displaystyle \phi } in γ V ϕ ( S i + 1 ) {\displaystyle \gamma V_{\phi }(S_{i+1})} constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly, if the critic is estimating the action-value function Q π θ {\displaystyle Q^{\pi _{\theta }}} , then it can be learned by Q-learning or SARSA. In SARSA, the critic maintains an estimate of the Q-function, parameterized by ϕ {\displaystyle \phi } , denoted as Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} . The temporal difference error is then calculated as δ i = R i + γ Q θ ( S i + 1 , A i + 1 ) − Q θ ( S i , A i ) {\displaystyle \delta _{i}=R_{i}+\gamma Q_{\theta }(S_{i+1},A_{i+1})-Q_{\theta }(S_{i},A_{i})} . The critic is then updated by θ ← θ + α δ i ∇ θ Q θ ( S i , A i ) {\displaystyle \theta \leftarrow \theta +\alpha \delta _{i}\nabla _{\theta }Q_{\theta }(S_{i},A_{i})} The advantage critic can be trained by training both a Q-function Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} and a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then let A ϕ ( s , a ) = Q ϕ ( s , a ) − V ϕ ( s ) {\displaystyle A_{\phi }(s,a)=Q_{\phi }(s,a)-V_{\phi }(s)} . Although, it is more common to train just a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then estimate the advantage by A ϕ ( S i , A i ) ≈ ∑ j ∈ 0 : n − 1 γ j R i + j + γ n V ϕ ( S i + n ) − V ϕ ( S i ) {\displaystyle A_{\phi }(S_{i},A_{i})\approx \sum _{j\in 0:n-1}\gamma ^{j}R_{i+j}+\gamma ^{n}V_{\phi }(S_{i+n})-V_{\phi }(S_{i})} Here, n {\displaystyle n} is a positive integer. The higher n {\displaystyle n} is, the more lower is the bias in the advantage estimation, but at the price of higher variance. The Generalized Advantage Estimation (GAE) introduces a hyperparameter λ {\displaystyle \lambda } that smoothly interpolates between Monte Carlo returns ( λ = 1 {\displaystyle \lambda =1} , high variance, no bias) and 1-step TD learning ( λ = 0 {\displaystyle \lambda =0} , low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with λ {\displaystyle \lambda } being the decay strength. == Variants == Asynchronous Advantage Actor-Critic (A3C): Parallel and asynchronous version of A2C. Soft Actor-Critic (SAC): Incorporates entropy maximization for improved exploration. Deep Deterministic Policy Gradient (DDPG): Specialized for continuous action spaces.

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  Information space analysis

  Within the field of information science, information space analysis is a deterministic method, enhanced by machine intelligence, for locating and assessing resources for team-centric efforts. Organizations need to be able to quickly assemble teams backed by the support services, information, and material to do the job. To do so, these teams need to find and assess sources of services that are potential participants in the team effort. To support this initial team and resource development, information needs to be developed via analysis tools that help make sense of sets of data sources in an Intranet or Internet. Part of the process is to characterize them, partition them, and sort and filter them. These tools focus on three key issues in forming a collaborative team: Help individuals responsible for forming the team understand what is available. Assist team members in identifying the structure and categorize the information available to them in a manner specifically suited to the task at hand. Aid team members to understand the mappings of their information between their organization and that used by others who might participate. Information space analysis tools combine multiple methods to assist in this task. This causes the tools to be particularly well-suited to integrating additional technologies in order to create specialized systems.

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