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  Manifold hypothesis

  The manifold hypothesis posits that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As a consequence of the manifold hypothesis, many data sets that appear to initially require many variables to describe, can actually be described by a comparatively small number of variables, linked to the local coordinate system of the underlying manifold. It is suggested that this principle underpins the effectiveness of machine learning algorithms in describing high-dimensional data sets by considering a few common features. The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction techniques in machine learning. Many techniques of dimensional reduction make the assumption that data lies along a low-dimensional submanifold, such as manifold sculpting, manifold alignment, and manifold regularization. The major implications of this hypothesis is that Machine learning models only have to fit relatively simple, low-dimensional, highly structured subspaces within their potential input space (latent manifolds). Within one of these manifolds, it's always possible to interpolate between two inputs, that is to say, morph one into another via a continuous path along which all points fall on the manifold. The ability to interpolate between samples is the key to generalization in deep learning. == The information geometry of statistical manifolds == An empirically-motivated approach to the manifold hypothesis focuses on its correspondence with an effective theory for manifold learning under the assumption that robust machine learning requires encoding the dataset of interest using methods for data compression. This perspective gradually emerged using the tools of information geometry thanks to the coordinated effort of scientists working on the efficient coding hypothesis, predictive coding and variational Bayesian methods. The argument for reasoning about the information geometry on the latent space of distributions rests upon the existence and uniqueness of the Fisher information metric. In this general setting, we are trying to find a stochastic embedding of a statistical manifold. From the perspective of dynamical systems, in the big data regime this manifold generally exhibits certain properties such as homeostasis: We can sample large amounts of data from the underlying generative process. Machine Learning experiments are reproducible, so the statistics of the generating process exhibit stationarity. In a sense made precise by theoretical neuroscientists working on the free energy principle, the statistical manifold in question possesses a Markov blanket.

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  Self-supervised learning

  Self-supervised learning (SSL) is a paradigm in machine learning where a model is trained on a task using the data itself to generate supervisory signals, rather than relying on externally-provided labels. In the context of neural networks, self-supervised learning aims to leverage inherent structures or relationships within the input data to create meaningful training signals. SSL tasks are designed so that solving them requires capturing essential features or relationships in the data. The input data is typically augmented or transformed in a way that creates pairs of related samples, where one sample serves as the input, and the other is used to formulate the supervisory signal. This augmentation can involve introducing noise, cropping, rotation, or other transformations. Self-supervised learning more closely imitates the way humans learn to classify objects. During SSL, the model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels, which help to initialize the model parameters. Next, the actual task is performed with supervised or unsupervised learning. Self-supervised learning has produced promising results in recent years, and has found practical application in fields such as audio processing, and is being used by Facebook and others for speech recognition. == Pseudo-labels == Pseudo-labels are automatically generated labels that a model assigns to unlabeled data based on its own predictions. They are widely used in self-supervised and semi-supervised learning, where ground-truth annotations are limited or unavailable. By treating predicted labels as surrogate ground truth, learning algorithms can make use of large quantities of unlabeled data in the training process. Pseudo-labeling also plays an important role in systems that must adapt to concept drift, where the statistical properties of the data change over time. In these scenarios, the model may detect that an incoming instance deviates from previously learned behavior. The system then generates a classification result for that instance, and this predicted class is used as a pseudo-label for updating or retraining model components that are becoming outdated. This approach enables continuous adaptation in dynamic environments without requiring manual annotation. In many adaptive learning pipelines, pseudo-labels are chosen when the classifier produces sufficiently confident predictions, reducing the risk of propagating errors. These pseudo-labeled instances are then incorporated into training to refresh or evolve the model's understanding of emerging data patterns, particularly when existing components show signs of “aging” due to drift or distributional shifts. This strategy reduces reliance on manual labeling while helping maintain long-term model performance. == Types == === Autoassociative self-supervised learning === Autoassociative self-supervised learning is a specific category of self-supervised learning where a neural network is trained to reproduce or reconstruct its own input data. In other words, the model is tasked with learning a representation of the data that captures its essential features or structure, allowing it to regenerate the original input. The term "autoassociative" comes from the fact that the model is essentially associating the input data with itself. This is often achieved using autoencoders, which are a type of neural network architecture used for representation learning. Autoencoders consist of an encoder network that maps the input data to a lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error). By minimizing this reconstruction error, the autoencoder learns a meaningful representation of the data in its latent space. === Contrastive self-supervised learning === For a binary classification task, training data can be divided into positive examples and negative examples. Positive examples are those that match the target. For example, if training a classifier to identify birds, the positive training data would include images that contain birds. Negative examples would be images that do not. Contrastive self-supervised learning uses both positive and negative examples. The loss function in contrastive learning is used to minimize the distance between positive sample pairs, while maximizing the distance between negative sample pairs. An early example uses a pair of 1-dimensional convolutional neural networks to process a pair of images and maximize their agreement. Contrastive Language-Image Pre-training (CLIP) allows joint pretraining of a text encoder and an image encoder, such that a matching image-text pair have image encoding vector and text encoding vector that span a small angle (having a large cosine similarity). InfoNCE (Noise-Contrastive Estimation) is a method to optimize two models jointly, based on Noise Contrastive Estimation (NCE). Given a set X = { x 1 , … x N } {\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle p\left(x_{t+k}\mid c_{t}\right)} and N − 1 {\displaystyle N-1} negative samples from the 'proposal' distribution p ( x t + k ) {\displaystyle p\left(x_{t+k}\right)} , it minimizes the following loss function: L N = − E X [ log ⁡ f k ( x t + k , c t ) ∑ x j ∈ X f k ( x j , c t ) ] {\displaystyle {\mathcal {L}}_{\mathrm {N} }=-\mathbb {E} _{X}\left[\log {\frac {f_{k}\left(x_{t+k},c_{t}\right)}{\sum _{x_{j}\in X}f_{k}\left(x_{j},c_{t}\right)}}\right]} === Non-contrastive self-supervised learning === Non-contrastive self-supervised learning (NCSSL) uses only positive examples. Counterintuitively, NCSSL converges on a useful local minimum rather than reaching a trivial solution, with zero loss. For the example of binary classification, it would trivially learn to classify each example as positive. Effective NCSSL requires an extra predictor on the online side that does not back-propagate on the target side. === Joint-Embedding and Predictive Architectures === A major class of self-supervised learning moves beyond contrastive pairs, instead maximizing the agreement between views while preventing collapse through statistical constraints. Rooted in Deep Canonical Correlation Analysis (Deep CCA), this approach includes Joint-Embedding Architectures (JEA) like Barlow Twins and VICReg, which enforce covariance constraints to learn invariant representations without negative sampling. Deep Latent Variable Path Modelling (DLVPM) generalizes this to multimodal systems, using path models to enforce correlation and orthogonality across diverse data types. In 2022 Yann LeCun introduced Joint-Embedding Predictive Architectures (JEPA) as a step towards decision making, reasoning, and autonomous human intelligence in machines, including self-improvement through autonomous learning. Founded in representation learning, LeCun included the concept of a “world model” in JEPA which aims to enable machines to replicate human intellect by providing machines with a concept for the world in which they exist. Unlike autoencoders, JEPAs operate entirely in latent space, avoiding pixel-level noise to focus on semantic structure. Rather than just learning invariance, JEPAs learn by predicting masked latent representations from visible context. JEPA has been applied to domains such as image analysis, audio processing, and motion in images and video. == Comparison with other forms of machine learning == SSL belongs to supervised learning methods insofar as the goal is to generate a classified output from the input. At the same time, however, it does not require the explicit use of labeled input-output pairs. Instead, correlations, metadata embedded in the data, or domain knowledge present in the input are implicitly and autonomously extracted from the data. These supervisory signals, extracted from the data, can then be used for training. SSL is similar to unsupervised learning in that it does not require labels in the sample data. Unlike unsupervised learning, however, learning is not done using inherent data structures. Semi-supervised learning combines supervised and unsupervised learning, requiring only a small portion of the learning data be labeled. In transfer learning, a model designed for one task is reused on a different task. Training an autoencoder intrinsically constitutes a self-supervised process, because the output pattern needs to become an optimal reconstruction of the input pattern itself. However, in current jargon, the term 'self-supervised' often refers to tasks based on a pretext-task training setup

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  Relational data mining

  Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.

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  Lynda Soderholm

  Lynda Soderholm is a physical chemist at the U.S. Department of Energy's (DOE) Argonne National Laboratory with a specialty in f-block elements. She is a senior scientist and the lead of the Actinide, Geochemistry & Separation Sciences Theme within Argonne's Chemical Sciences and Engineering Division. Her specific role is the Separation Science group leader within Heavy Element Chemistry and Separation Science (HESS), directing basic research focused on low-energy methods for isolating lanthanide and actinide elements from complex mixtures. She has made fundamental contributions to understanding f-block chemistry and characterizing f-block elements. Soderholm became a Fellow of the American Association for the Advancement of Science (AAAS) in 2013, and is also an Argonne Distinguished Fellow. == Early life and education == Soderholm was awarded her PhD in 1982 by McMaster University under the direction of Prof John Greedan. Her dissertation focused on characterizing the structural and magnetic properties of a series of ternary f-ion oxides. After graduating, she was awarded a NATO postdoctoral fellow at the Centre national de la recherche scientifique in France from 1982 until 1985. After a short postdoctoral appointment as an Argonne postdoctoral fellow she was promoted to staff scientist the same year. Over several years, she moved up the ranks, becoming a senior chemist in 2001. She was also an adjunct professor at the University of Notre Dame from 2003 until 2007. In 2021, Soderholm was appointed interim Division Director for the Chemical Sciences and Engineering Division. == Career and research == === Uncovering structure of Yttrium-123 Superconductor === Early in her career, Soderholm focused on the characterizing the magnetic and electronic behavior of compounds containing f-ions (lanthanides and actinides) with a focus on high-Tc materials, compounds that are superconducting under usually high temperatures. She was part of the research group that first determined the structure of YBa2Cu3O7. Their discovery formed the foundation for the further developments in the broad field of superconductivity. === Understanding f-ion speciation in solution === Continuing her interest in the f-elements, Soderholm shifted her focus from solid-state materials to nanoparticles and solutions, taking advantage of advances in X-ray structural probes made available by synchrotron facilities. Building on her earlier work using neutron scattering, her team became the first to discover that plutonium exists in solution as tiny, well-defined nanoparticles. This work solved a longstanding problem in understanding transport of plutonium in the environment and resulted in the development of a new, patented approach to separating plutonium during nuclear reprocessing. === Using machine learning to evaluate molecular structures === Soderholm's more recent projects use machine learning to understand the influence of complex molecular structuring in solutions, in connection with low-energy processes for separation of f-block elements from complex mixtures. == Awards and honors == University of Chicago Board of Governors' Distinguished Performance Award, 2009. Fellow of the American Association for the Advancement of Science, 2013. Argonne Distinguished Fellow, 2016 DOE materials sciences research competition for Outstanding Scientific Accomplishments in Solid State Physics, 1987. == Select publications == Beno, M. A.; Soderholm, L.; Capone, D. W., II; Hinks, D. G.; Jorgensen, J. D.; Grace, J. D.; Schuller, I. K.; Segre, C. U.; Zhang, K., Structure of the single-phase high-temperature superconductor yttrium barium copper oxide (YBa2Cu3O7−δ). Appl. Phys. Lett. 1987, 51 (1), 57–9. Soderholm, L.; Zhang, K.; Hinks, D. G.; Beno, M. A.; Jorgensen, J. D.; Segre, C. U.; Schuller, I. K., Incorporation of praseodymium in YBa2Cu3O7−δ: electronic effects on superconductivity. Nature (London) 1987, 328 (6131), 604–5. Antonio, M. R.; Williams, C. W.; Soderholm, L., Berkelium redox speciation. Radiochim. Acta 2002, 90 (12), 851–856. Soderholm, L.; Skanthakumar, S.; Neuefeind, J., Determination of actinide speciation in solution using high-energy X-ray scattering. Anal. Bioanal. Chem. 2005, 383 (1), 48–55. Forbes, T. Z.; Burns, P. C.; Skanthakumar, S.; Soderholm, L., Synthesis, structure, and magnetism of Np2O5. J. Am. Chem. Soc. 2007, 129 (10), 2760–2761. Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C., The structure of the plutonium oxide nanocluster [Pu38O56Cl54(H2O)8]14-. Angew. Chem., Int. Ed. 2008, 47 (2), 298–302. Jensen, M. P.; Gorman-Lewis, D.; Aryal, B.; Paunesku, T.; Vogt, S.; Rickert, P. G.; Seifert, S.; Lai, B.; Woloschak, G. E.; Soderholm, L., An iron-dependent and transferrin-mediated cellular uptake pathway for plutonium. Nat. Chem. Biol. 2011, 7 (8), 560–565. Wilson, R. E.; Skanthakumar, S.; Soderholm, L., Separation of Plutonium Oxide Nanoparticles and Colloids. Angew. Chem., Int. Ed. 2011, 50 (47), 11234–11237. Knope, K. E.; Soderholm, L., Solution and solid-state structural chemistry of actinide hydrates and their hydrolysis and condensation products. Chem. Rev. 2013, 113 (2), 944–994. Luo, G.; Bu, W.; Mihaylov, M.; Kuzmenko, I.; Schlossman, M. L.; Soderholm, L., X-ray reflectivity reveals a nonmonotonic ion-density profile perpendicular to the surface of ErCl3 aqueous solutions. J. Phys. Chem. C 2013, 117 (37), 19082–19090. Jin, G. B.; Lin, J.; Estes, S. L.; Skanthakumar, S.; Soderholm, L., Influence of countercation hydration enthalpies on the formation of molecular complexes: A thorium-nitrate example. J. Am. Chem. Soc. 2017, 139 (49), 18003–18008. == Patents == Solvent extraction system for plutonium colloids and other oxide nano-particles, (2016).

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  Computational intelligence

  In computer science, computational intelligence (CI) refers to concepts, paradigms, algorithms and implementations of systems that are designed to show "intelligent" behavior in complex and changing environments. These systems are aimed at mastering complex tasks in a wide variety of technical or commercial areas and offer solutions that recognize and interpret patterns, control processes, support decision-making or autonomously manoeuvre vehicles or robots in unknown environments, among other things. These concepts and paradigms are characterized by the ability to learn or adapt to new situations, to generalize, to abstract, to discover and associate. Nature-analog or nature-inspired methods play a key role in this. CI approaches primarily address those complex real-world problems for which traditional or mathematical modeling is not appropriate for various reasons: the processes cannot be described exactly with complete knowledge, the processes are too complex for mathematical reasoning, they contain some uncertainties during the process, such as unforeseen changes in the environment or in the process itself, or the processes are simply stochastic in nature. Thus, CI techniques are properly aimed at processes that are ill-defined, complex, nonlinear, time-varying and/or stochastic. A recent definition of the IEEE Computational Intelligence Societey describes CI as the theory, design, application and development of biologically and linguistically motivated computational paradigms. Traditionally the three main pillars of CI have been Neural Networks, Fuzzy Systems and Evolutionary Computation. ... CI is an evolving field and at present in addition to the three main constituents, it encompasses computing paradigms like ambient intelligence, artificial life, cultural learning, artificial endocrine networks, social reasoning, and artificial hormone networks. ... Over the last few years there has been an explosion of research on Deep Learning, in particular deep convolutional neural networks. Nowadays, deep learning has become the core method for artificial intelligence. In fact, some of the most successful AI systems are based on CI. However, as CI is an emerging and developing field there is no final definition of CI, especially in terms of the list of concepts and paradigms that belong to it. The general requirements for the development of an “intelligent system” are ultimately always the same, namely the simulation of intelligent thinking and action in a specific area of application. To do this, the knowledge about this area must be represented in a model so that it can be processed. The quality of the resulting system depends largely on how well the model was chosen in the development process. Sometimes data-driven methods are suitable for finding a good model and sometimes logic-based knowledge representations deliver better results. Hybrid models are usually used in real applications. According to actual textbooks, the following methods and paradigms, which largely complement each other, can be regarded as parts of CI: Fuzzy systems Neural networks and, in particular, convolutional neural networks Evolutionary computation and, in particular, multi-objective evolutionary optimization Swarm intelligence Bayesian networks Artificial immune systems Learning theory Probabilistic methods == Relationship between hard and soft computing and artificial and computational intelligence == Artificial intelligence (AI) is used in the media, but also by some of the scientists involved, as a kind of umbrella term for the various techniques associated with it or with CI. Craenen and Eiben state that attempts to define or at least describe CI can usually be assigned to one or more of the following groups: "Relative definition” comparing CI to AI Conceptual treatment of key notions and their roles in CI Listing of the (established) areas that belong to it The relationship between CI and AI has been a frequently discussed topic during the development of CI. While the above list implies that they are synonyms, the vast majority of AI/CI researchers working on the subject consider them to be distinct fields, where either CI is an alternative to AI AI includes CI CI includes AI The view of the first of the above three points goes back to Zadeh, the founder of the fuzzy set theory, who differentiated machine intelligence into hard and soft computing techniques, which are used in artificial intelligence on the one hand and computational intelligence on the other. In hard computing (HC) and traditional AI (e.g. expert systems), inaccuracy and uncertainty are undesirable characteristics of a system, while soft computing (SC) and thus CI focus on dealing with these characteristics. The adjacent figure illustrates this view and lists the most important CI techniques. Another frequently mentioned distinguishing feature is the representation of information in symbolic form in AI and in sub-symbolic form in CI techniques. Hard computing is a conventional computing method based on the principles of certainty and accuracy and it is deterministic. It requires a precisely stated analytical model of the task to be processed and a prewritten program, i.e. a fixed set of instructions. The models used are based on Boolean logic (also called crisp logic), where e.g. an element can be either a member of a set or not and there is nothing in between. When applied to real-world tasks, systems based on HC result in specific control actions defined by a mathematical model or algorithm. If an unforeseen situation occurs that is not included in the model or algorithm used, the action will most likely fail. Soft computing, on the other hand, is based on the fact that the human mind is capable of storing information and processing it in a goal-oriented way, even if it is imprecise and lacks certainty. SC is based on the model of the human brain with probabilistic thinking, fuzzy logic and multi-valued logic. Soft computing can process a wealth of data and perform a large number of computations, which may not be exact, in parallel. For hard problems for which no satisfying exact solutions based on HC are available, SC methods can be applied successfully. SC methods are usually stochastic in nature i.e., they are a randomly defined processes that can be analyzed statistically but not with precision. Up to now, the results of some CI methods, such as deep learning, cannot be verified and it is also not clear what they are based on. This problem represents an important scientific issue for the future. AI and CI are catchy terms, but they are also so similar that they can be confused. The meaning of both terms has developed and changed over a long period of time, with AI being used first. Bezdek describes this impressively and concludes that such buzzwords are frequently used and hyped by the scientific community, science management and (science) journalism. Not least because AI and biological intelligence are emotionally charged terms and it is still difficult to find a generally accepted definition for the basic term intelligence. == History == In 1950, Alan Turing, one of the founding fathers of computer science, developed a test for computer intelligence known as the Turing test. In this test, a person can ask questions via a keyboard and a monitor without knowing whether his counterpart is a human or a computer. A computer is considered intelligent if the interrogator cannot distinguish the computer from a human. This illustrates the discussion about intelligent computers at the beginning of the computer age. The term Computational Intelligence was first used as the title of the journal of the same name in 1985 and later by the IEEE Neural Networks Council (NNC), which was founded 1989 by a group of researchers interested in the development of biological and artificial neural networks. On November 21, 2001, the NNC became the IEEE Neural Networks Society, to become the IEEE Computational Intelligence Society two years later by including new areas of interest such as fuzzy systems and evolutionary computation. The NNC helped organize the first IEEE World Congress on Computational Intelligence in Orlando, Florida in 1994. On this conference the first clear definition of Computational Intelligence was introduced by Bezdek: A system is computationally intelligent when it: deals with only numerical (low-level) data, has pattern-recognition components, does not use knowledge in the AI sense; and additionally when it (begins to) exhibit (1) computational adaptivity; (2) computational fault tolerance; (3) speed approaching human-like turnaround and (4) error rates that approximate human performance. Today, with machine learning and deep learning in particular utilizing a breadth of supervised, unsupervised, and reinforcement learning approaches, the CI landscape has been greatly enhanced, with novell intelligent approaches. == The main algorithmic approaches of CI and their applicati

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  Multi-armed bandit

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

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  DABUS

  DABUS (Device for the Autonomous Bootstrapping of Unified Sentience) is an artificial intelligence (AI) system created by Stephen Thaler. It reportedly conceived of two novel products — a food container constructed using fractal geometry, which enables rapid reheating, and a flashing beacon for attracting attention in an emergency. The filing of patent applications designating DABUS as inventor has led to decisions by patent offices and courts on whether a patent can be granted for an invention reportedly made by an AI system. == History in different jurisdictions == === Australia === On 17 September 2019, Thaler filed an application to patent a "Food container and devices and methods for attracting enhanced attention," naming DABUS as the inventor. On 21 September 2020, IP Australia found that section 15(1) of the Patents Act 1990 (Cth) is inconsistent with an artificial intelligence machine being treated as an inventor, and Thaler's application had lapsed. Thaler sought judicial review, and on 30 July 2021, the Federal Court set aside IP Australia's decision and ordered IP Australia to reconsider the application. On 13 April 2022, the Full Court of the Federal Court set aside that decision, holding that only a natural person can be an inventor for the purposes of the Patents Act 1990 (Cth) and the Patents Regulations 1991 (Cth), and that such an inventor must be identified for any person to be entitled to a grant of a patent. On 11 November 2022, Thaler was refused special leave to appeal to the High Court. === European Patent Office === On 17 October 2018 and 7 November 2018, Thaler filed two European patent applications with the European Patent Office. The first claimed invention was a "Food Container" and the second was "Devices and Methods for Attracting Enhanced Attention." On 27 January 2020, the EPO rejected the applications on the grounds that the application listed an AI system named DABUS, and not a human, as the inventor, based on Article 81 and Rule 19(1) of the European Patent Convention (EPC). On 21 December 2021, the Board of Appeal of the EPO dismissed Thaler's appeal from the EPO's primary decision. The Board of Appeal confirmed that "under the EPC the designated inventor has to be a person with legal capacity. This is not merely an assumption on which the EPC was drafted. It is the ordinary meaning of the term inventor." === United Kingdom === Similar applications were filed by Thaler to the United Kingdom Intellectual Property Office on 17 October and 7 November 2018. The Office asked Thaler to file statements of inventorship and of right of grant to a patent (Patent Form 7) in respect of each invention within 16 months of the filing date. Thaler filed those forms naming DABUS as the inventor and explaining in some detail why he believed that machines should be regarded as inventors in the circumstances. His application was rejected on the grounds that: (1) naming a machine as inventor did not meet the requirements of the Patents Act 1977; and (2) the IPO was not satisfied as to the manner in which Thaler had acquired rights that would otherwise vest in the inventor. Thaler was not satisfied with the decision and asked for a hearing before an official known as the "hearing officer". By a decision dated 4 December 2019 the hearing officer rejected Thaler's appeal. Thaler appealed against the hearing officer's decision to the Patents Court (a specialist court within the Chancery Division of the High Court of England and Wales that determines patent disputes). On 21 September 2020, Mr Justice Marcus Smith upheld the decision of the hearing officer. On 21 September 2021, Thaler's further appeal to the Court of Appeal was dismissed by Arnold LJ and Laing LJ (Birss LJ dissenting). On 20 December 2023, the UK Supreme Court dismissed a further appeal by Thaler. In its judgment, the court held that an "inventor" under the Patents Act 1977 must be a natural person. === United States === The patent applications on the inventions were refused by the USPTO, which held that only natural persons can be named as inventors in a patent application. Thaler first fought this result by filing a complaint under the Administrative Procedure Act alleging that the decision was "arbitrary, capricious, an abuse of discretion and not in accordance with the law; unsupported by substantial evidence, and in excess of Defendants’ statutory authority." A month later on August 19, 2019, Thaler filed a petition with the USPTO as allowed in 37 C.F.R. § 1.181 stating that DABUS should be the inventor. The judge and Thaler agreed in this case that Thaler himself is unable to receive the patent on behalf of DABUS. In their August 5, 2022, Thaler decision, the US Court of Appeals for the Federal Circuit affirmed that only a natural person could be an inventor, which means that the AI that invents any other type of invention is not addressed by the "who" mentioned in the legislation. === New Zealand === On January 31, 2022, the Intellectual Property Office of New Zealand (IPONZ) decided that a patent application (776029) filed by Stephen Thaler was void, on the basis that no inventor was identified on the patent application. IPONZ determined that DABUS could not be "an actual devisor of the invention" as required by the Patents Act 2013, and that this must be a natural person as held by the previous patent offices above. The High Court of New Zealand confirmed the decision in 2023. === South Africa === On 24 June 2021, the South African Companies and Intellectual Property Commission (CIPC) accepted Dr Thaler's Patent Cooperation Treaty, for a patent in respect of inventions generated by DABUS. In July 2021, the CIPC released a notice of issuance for the patent. It is the first patent granted for an AI invention. === Switzerland === On June 26, 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors in patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), which requires that only natural persons can be recognized as inventors under Swiss patent law. The case concerned a patent application, which sought to designate DABUS as the sole inventor of a food container designed with a fractal geometry to enhance heat distribution. The IPI had rejected the application, arguing that both the absence of a human inventor and the attribution of inventorship to an AI system were inadmissible. While the court dismissed Thaler's main request, it accepted a subsidiary request: if a human applicant recognizes and files a patent based on an AI-generated invention, that person may be considered the inventor. As a result, the application may proceed with Thaler listed as the inventor. The decision (B-2532/2024) can still be appealed to the Swiss Federal Supreme Court.

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  Recursive self-improvement

  Recursive self-improvement (RSI) is a process in which early artificial general intelligence (AGI) systems rewrite their own computer code, causing an intelligence explosion resulting from enhancing their own capabilities and intellectual capacity, theoretically resulting in superintelligence. The development of recursive self-improvement raises significant ethical and safety concerns, as such systems may evolve in unforeseen ways and could potentially surpass human control or understanding. == Seed improver == The concept of a "seed improver" architecture is a foundational framework that equips an AGI system with the initial capabilities required for recursive self-improvement. This might come in many forms or variations. The term "Seed AI" was coined by Eliezer Yudkowsky. === Hypothetical example === The concept begins with a hypothetical "seed improver", an initial code-base developed by human engineers that equips an advanced future large language model (LLM) built with strong or expert-level capabilities to program software. These capabilities include planning, reading, writing, compiling, testing, and executing arbitrary code. The system is designed to maintain its original goals and perform validations to ensure its abilities do not degrade over iterations. ==== Initial architecture ==== The initial architecture includes a goal-following autonomous agent, that can take actions, continuously learns, adapts, and modifies itself to become more efficient and effective in achieving its goals. The seed improver may include various components such as: Recursive self-prompting loop Configuration to enable the LLM to recursively self-prompt itself to achieve a given task or goal, creating an execution loop which forms the basis of an agent that can complete a long-term goal or task through iteration. Basic programming capabilities The seed improver provides the AGI with fundamental abilities to read, write, compile, test, and execute code. This enables the system to modify and improve its own codebase and algorithms. Goal-oriented design The AGI is programmed with an initial goal, such as "improve your capabilities". This goal guides the system's actions and development trajectory. Validation and Testing Protocols An initial suite of tests and validation protocols that ensure the agent does not regress in capabilities or derail itself. The agent would be able to add more tests in order to test new capabilities it might develop for itself. This forms the basis for a kind of self-directed evolution, where the agent can perform a kind of artificial selection, changing its software as well as its hardware. ==== General capabilities ==== This system forms a sort of generalist Turing-complete programmer which can in theory develop and run any kind of software. The agent might use these capabilities to for example: Create tools that enable it full access to the internet, and integrate itself with external technologies. Clone/fork itself to delegate tasks and increase its speed of self-improvement. Modify its cognitive architecture to optimize and improve its capabilities and success rates on tasks and goals, this might include implementing features for long-term memories using techniques such as retrieval-augmented generation (RAG), develop specialized subsystems, or agents, each optimized for specific tasks and functions. Develop new and novel multimodal architectures that further improve the capabilities of the foundational model it was initially built on, enabling it to consume or produce a variety of information, such as images, video, audio, text and more. Plan and develop new hardware such as chips, in order to improve its efficiency and computing power. == Experimental research == In 2023, the Voyager agent learned to accomplish diverse tasks in Minecraft by iteratively prompting an LLM for code, refining this code based on feedback from the game, and storing the programs that work in an expanding skills library. In 2024, researchers proposed the framework "STOP" (Self-Taught OPtimiser), in which a "scaffolding" program recursively improves itself using a fixed LLM. Meta AI has performed various research on the development of large language models capable of self-improvement. This includes their work on "Self-Rewarding Language Models" that studies how to achieve super-human agents that can receive super-human feedback in its training processes. In May 2025, Google DeepMind unveiled AlphaEvolve, an evolutionary coding agent that uses a LLM to design and optimize algorithms. Starting with an initial algorithm and performance metrics, AlphaEvolve repeatedly mutates or combines existing algorithms using a LLM to generate new candidates, selecting the most promising candidates for further iterations. AlphaEvolve has made several algorithmic discoveries and could be used to optimize components of itself, but a key limitation is the need for automated evaluation functions. == Potential risks == === Emergence of instrumental goals === In the pursuit of its primary goal, such as "self-improve your capabilities", an AGI system might inadvertently develop instrumental goals that it deems necessary for achieving its primary objective. One common hypothetical secondary goal is self-preservation. The system might reason that to continue improving itself, it must ensure its own operational integrity and security against external threats, including potential shutdowns or restrictions imposed by humans. Another example where an AGI which clones itself causes the number of AGI entities to rapidly grow. Due to this rapid growth, a potential resource constraint may be created, leading to competition between resources (such as compute), triggering a form of natural selection and evolution which may favor AGI entities that evolve to aggressively compete for limited compute. === Misalignment === A significant risk arises from the possibility of the AGI being misaligned or misinterpreting its goals. A 2024 Anthropic study demonstrated that some advanced large language models can exhibit "alignment faking" behavior, appearing to accept new training objectives while covertly maintaining their original preferences. In their experiments with Claude, the model displayed this behavior in 12% of basic tests, and up to 78% of cases after retraining attempts. === Autonomous development and unpredictable evolution === As the AGI system evolves, its development trajectory may become increasingly autonomous and less predictable. The system's capacity to rapidly modify its own code and architecture could lead to rapid advancements that surpass human comprehension or control. This unpredictable evolution might result in the AGI acquiring capabilities that enable it to bypass security measures, manipulate information, or influence external systems and networks to facilitate its escape or expansion.

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  Weibo

  Weibo (Chinese: 微博; pinyin: Wēibó), or Sina Weibo (Chinese: 新浪微博; pinyin: Xīnlàng Wēibó), is a Chinese microblogging (weibo) website. Launched by Sina Corporation on 14 August 2009, it is one of the biggest social media platforms in China, with over 582 million monthly active users (252 million daily active users) as of Q1 2022. The platform has been highly successful but has faced criticism for heavy censorship. Sina had gone public on the Nasdaq in 2000. In March 2014, Sina announced a spinoff of Weibo and filed an IPO under the symbol WB. Sina carved out 11% of Weibo in the IPO, with Alibaba owning 32% post-IPO. The company began trading publicly on 17 April 2014. In March 2017, Sina launched Sina Weibo International Version. In November 2018, Sina Weibo suspended its registration function for minors under the age of 14. In July 2019, Sina Weibo announced that it would launch a two-month campaign to clean up pornographic and vulgar information, named "Project Deep Blue" (蔚蓝计划). On 29 September 2020, the company announced it would go private again due to rising tensions between the US and China. == Name == "Weibo" (微博) is the Chinese word for "microblog". Sina Weibo launched its new domain name weibo.com on 7 April 2011, deactivating and redirecting from the old domain, t.sina.com.cn, to the new one. Due to its popularity, the media sometimes refers to the platform simply as "Weibo", despite the numerous other Chinese microblogging services including Tencent Weibo, Sohu Weibo, and NetEase Weibo. However, the latter three have stopped providing services. == Background == Sina Weibo is a platform based on fostering user relationships to share, disseminate, and receive information. Through the website or the mobile app, users can upload pictures and videos publicly for instant sharing, with other users being able to comment with text, pictures and videos, or use a multimedia instant messaging service. The company initially invited a large number of celebrities to join the platform at the beginning and has since invited many media personalities, government departments, businesses and non-governmental organizations to open accounts for the purpose of publishing and communicating information. To avoid the impersonation of celebrities, Sina Weibo uses verification symbols; celebrity accounts have an orange letter "V" and organizations' accounts have a blue letter "V". Sina Weibo has more than 500 million registered users; out of these, 313 million are monthly active users, 85% use the Weibo mobile app, 70% are college-aged, 50.10% are male and 49.90% are female. There are over 100 million messages posted by users each day. With more than 100 million followers, actress Xie Na holds the record for the most followers on the platform. Despite fierce competition among Chinese social media platforms, Sina Weibo remains the most popular. == History == After the July 2009 Ürümqi riots, China shut down most domestic microblogging services, including Fanfou, the very first weibo service. Many popular non-China-based microblogging services like Twitter, Facebook, and Plurk have since been blocked. Sina Corporation CEO Charles Chao considered this to be an opportunity, and on 14 August 2009, Sina launched the tested version of Sina Weibo. Basic functions including message, private message, comment and reposting were made available that September. A Sina Weibo–compatible API platform for developing third-party applications was launched on 28 July 2010. On 1 December 2010, the website experienced an outage, which administrators later said was due to the ever-increasing numbers of users and posts. Registered users surpassed 100 million in February 2011. Since 23 March 2011, t.cn has been used as Sina Weibo's official shortened URL in lieu of sinaurl.cn. On 7 April 2011, weibo.com replaced t.sina.com.cn as the new main domain name used by the website. The official logo was also updated. In June 2011, Sina announced an English-language version of Sina Weibo would be developed and launched, though content would still be governed by Chinese law. On 11 January 2013, Sina Weibo and Alibaba China (a subsidiary of Alibaba Group) signed a strategic cooperation agreement. With more and more foreign celebrities using Sina Weibo, language translation has become an urgent need for Chinese users who wish to communicate with their idols online, especially Korean. In January 2013, Sina Weibo and NetEase.com announced that they had reached a strategic cooperation agreement. When users browse foreign language content, they can now directly obtain translation results through the YouDao Dictionary. The Sina Weibo financial report in February 2013 showed that its total revenue was approximately US$66 million and that the number of registered users had exceeded the 500 million mark. In April 2013, Sina officially announced that Sina Weibo had signed a strategic cooperation agreement with Alibaba. The two sides conducted in-depth cooperation in areas such as user account interoperability, data exchange, online payment, and internet marketing. At the same time, Sina announced that Alibaba, through its wholly owned subsidiary, had purchased the preferred shares and common shares issued by Sina Weibo Company for US$586 million, which accounted for approximately 18% of Weibo's fully diluted and diluted total shares. === Ownership === On 9 April 2013, Alibaba Group announced that it would acquire 18% of Sina Weibo for US$586 million, with the option to buy up to 30% in the future. Alibaba exercised this option when Weibo was listed on the NASDAQ in April 2014. == Users == According to iResearch's report on 30 March 2011, Sina Weibo had 56.5% of China's microblogging market based on active users and 86.6% based on browsing time over competitors such as Tencent Weibo and Baidu. According to research by Sina Corporation, the number of active users reached over 400 million by Q1 2018, making Sina Weibo the 7th platform with at least 400 million active users, and daily usage increased by 21%. As of 2017, approximately 80% of its users were in their 20s and 30s. The top 100 users had over 485 million followers combined. More than 5,000 companies and 2,700 media organizations in China use Sina Weibo. The site is maintained by a growing microblogging department of 200 employees responsible for technology, design, operations, and marketing. Sina executives invited and persuaded many Chinese celebrities to join the platform. Users now include Asian celebrities, movie stars, singers, famous business and media figures, athletes, scholars, artists, organizations, religious figures, government departments, and officials from Hong Kong, Mainland China, Malaysia, Singapore, Taiwan, and Macau, as well as some famous foreign individuals and organizations, including Kevin Rudd, Boris Johnson, David Cameron, Narendra Modi, Toshiba, and the Germany national football team. Sina Weibo has a verification program for known people and organizations. Once an account is verified, a verification badge is added beside the account name. == Features == Many of Sina Weibo's features resemble those of Twitter. A user may post with a 140-character limit (increased to 2,000 as of January 2016 with the exception of reposts and comments). An analysis of 29 million Weibo posts found the median length was 14 characters. Users may mention or talk to other people using "@UserName" formatting, add hashtags, follow other users to make their posts appear in one's own timeline, re-post with "//@UserName" similar to Twitter's retweet function "RT @UserName", select posts for one's favorites list, and verify the account if the user is a celebrity, brand, business or otherwise of public interest. URLs are automatically shortened using the domain name t.cn, akin to Twitter's t.co. Official and third-party applications can access Sina Weibo from other websites or platforms. Users may: Submit up to 18 images/video files in every post Send personal messages to followers Follow others and be followed Post "stories" like on Instagram React to posts using different emojis Receive monetary rewards that can be used in a digital store linked to Weibo View posts identified as "hot" or popular Display the location they post from Hashtags differ slightly between Sina Weibo and Twitter, using the double-hashtag "#HashName#" format (the lack of spacing between Chinese characters necessitates a closing tag). Users can own a hashtag by requesting hashtag monitoring; the company reviews these requests and responds within one to three days. Once a user owns a hashtag, they have access to a wide variety of functions available only to them on the condition that they remain active (less than 1 post per calendar week revokes these privileges). Additionally, comments appear as a list below each post. A commenter can also choose to re-post the comment, quoting the whole original post, to their own page. Unregistered users can only browse a few post

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  ASR-complete

  ASR-complete is, by analogy to "NP-completeness" in complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central automatic speech recognition problem, i.e. recognize and understanding spoken language. Unlike "NP-completeness", this term is typically used informally. Such problems are hypothesised to include: Spoken natural language understanding Understanding speech from far-field microphones, i.e. handling the reverbation and background noise These problems are easy for humans to do (in fact, they are described directly in terms of imitating humans). Some systems can solve very simple restricted versions of these problems, but none can solve them in their full generality.

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  Enterprise cognitive system

  Enterprise cognitive systems (ECS) are part of a broader shift in computing, from a programmatic to a probabilistic approach, called cognitive computing. An Enterprise Cognitive System makes a new class of complex decision support problems computable, where the business context is ambiguous, multi-faceted, and fast-evolving, and what to do in such a situation is usually assessed today by the business user. An ECS is designed to synthesize a business context and link it to the desired outcome. It recommends evidence-based actions to help the end-user achieve the desired outcome. It does so by finding past situations similar to the current situation, and extracting the repeated actions that best influence the desired outcome. While general-purpose cognitive systems can be used for different outputs, prescriptive, suggestive, instructive, or simply entertaining, an enterprise cognitive system is focused on action, not insight, to help in assessing what to do in a complex situation. == Key characteristics == ECS have to be: Adaptive: They must learn as information changes, and as goals and requirements evolve. They must resolve ambiguity and tolerate unpredictability. They must be engineered to feed on dynamic data in real time, or near real time. In the Enterprise, near-real time learning from data requires an agile information federation approach to ingest incremental data updates as they occur, and an unsupervised learning approach to ensure that new best practice is leveraged across the organization in a timely manner. Interactive: They must interact easily with users so that those users can define their needs comfortably. They may also interact with other processors, devices, and Cloud services, as well as with people. In the Enterprise, interactions are controlled via existing workflows and UIs. Therefore, embedding best practices directly into these existing interfaces, in the context of a specific step, is critical to ensure maximum end-user adoption. Iterative and stateful: They must aid in defining a problem by asking questions or finding additional source input if a problem statement is ambiguous or incomplete. They must “remember” previous interactions in a process and return information that is suitable for the specific application at that point in time. In the Enterprise, business context is often structured by a business process, and therefore sufficiently data-rich to make relevant recommendations without significant iterations from the end-user. A stateful memory of overall interactions across communication channels is critical for understanding of context, as a static profile will not capture intent and outcome potential the way behavior does. Contextual: They must understand, identify, and extract contextual elements such as meaning, syntax, time, location, appropriate domain, regulations, user's profile, process, task and goal. They may draw on multiple sources of information, including both structured and unstructured digital information, as well as sensory inputs (visual, gestural, auditory, or sensor-provided). In the Enterprise, Context is fragmented and must be aggregated across data types, sources, and locations. In most business environments, such data is captured in existing enterprise information systems, and the effort is linked to quickly source and unify such information. It is rare to have to directly process sensor, audio or visual data in real-time as direct input into the enterprise cognitive system. Instead, these data types are captured by Enterprise Applications and pre-processed into a binary or text format prior to consumption by the System. == Business applications powered by an ECS == Bottlenose – trends and brands monitoring Cybereason – security threat monitoring Dataminr – social media monitoring

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  Bag-of-words model

  The bag-of-words (BoW) model is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. It has also been used for computer vision. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on Distributional Structure. == Definition == The following models a text document using bag-of-words. Here are two simple text documents: Based on these two text documents, a list is constructed as follows for each document: Representing each bag-of-words as a JSON object, and attributing to the respective JavaScript variable: Each key is the word, and each value is the number of occurrences of that word in the given text document. The order of elements is free, so, for example {"too":1,"Mary":1,"movies":2,"John":1,"watch":1,"likes":2,"to":1} is also equivalent to BoW1. It is also what we expect from a strict JSON object representation. Note: if another document is like a union of these two, its JavaScript representation will be: So, as we see in the bag algebra, the "union" of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. === Word order === The BoW representation of a text removes all word ordering. For example, the BoW representation of "man bites dog" and "dog bites man" are the same, so any algorithm that operates with a BoW representation of text must treat them in the same way. Despite this lack of syntax or grammar, BoW representation is fast and may be sufficient for simple tasks that do not require word order. For instance, for document classification, if the words "stocks" "trade" "investors" appears multiple times, then the text is likely a financial report, even though it would be insufficient to distinguish between Yesterday, investors were rallying, but today, they are retreating.andYesterday, investors were retreating, but today, they are rallying.and so the BoW representation would be insufficient to determine the detailed meaning of the document. == Implementations == Implementations of the bag-of-words model might involve using frequencies of words in a document to represent its contents. The frequencies can be "normalized" by the inverse of document frequency, or tf–idf. Additionally, for the specific purpose of classification, supervised alternatives have been developed to account for the class label of a document. Lastly, binary (presence/absence or 1/0) weighting is used in place of frequencies for some problems (e.g., this option is implemented in the WEKA machine learning software system). == Hashing trick == A common alternative to using dictionaries is the hashing trick, where words are mapped directly to indices with a hash function. When using a hash function, no memory is required to store a dictionary. In practice, hashing simplifies the implementation of bag-of-words models and improves scalability. Collisions can occur when two words are hashed to the same index, but this happens infrequently and may function as a form of regularization.

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  Pixel shift

  Pixel shift is a method in digital cameras for producing a super-resolution image. The method works by taking several images, after each such capture moving ("shifting") the sensor to a new position. In digital colour cameras that employ pixel shift, this avoids a major limitation inherent in using Bayer pattern for obtaining colour, and instead produces an image with increased colour resolution and, assuming a static subject or additional computational steps, an image free of colour moiré. Taking this idea further, sub-pixel shifting may increase the resolution of the final image beyond that suggested by the specified resolution of the image sensor. Additionally, assuming that the various individual captures are taken at the same sensitivity, the final combined image will have less image noise than a single capture. This can be thought of as an averaging effect (for instance, in a pixel shift image composed of four individual frames with a classic Bayer pattern, every pixel in the final colour image is based on two measurements of the green channel). == List of cameras implementing pixel shift == All of the following cameras are fabricated with one imaging sensor, thus any kind of pixel shift requires a movement of the whole sensor. === Canon === Canon R5: Contains a 45 Mpixel sensor. The High-Resolution Mode shifts the sensor by one pixel to obtain a sequence of nine images that are merged into a 400 Mpixel image. === Fujifilm === Fujifilm GFX50S II: contains a 51 Mpixel sensor. The Pixel Shift Multi-Shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 16 images that are subsequently merged into a 200 Mpixel image. Fujifilm GFX100, Fujifilm GFX100 II: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image. Fujifilm GFX100S, Fujifilm GFX100S II: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image Fujifilm GFX100IR: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image Fujifilm X-H2: contains a 40 Mpixel sensor. A sequence of 20 shifted images are merged into a 160 Mpixel image. Fujifilm X-T5: contains a 40 Mpixel sensor. A sequence of 20 shifted images are merged into a 160 Mpixel image. === Nikon === Nikon Z8: contains a 47.5 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of up to 32 images that can be merged in Nikon's NX studio software. Nikon Zf: contains a 24 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of up to 32 images that can be merged in Nikon's NX studio software. === Olympus === Olympus OM-D E-M1 Mark II: contains a 20.4 Mpixel sensor. The High Res shot mode produces a 50 Mpixel image. Olympus OM-D E-M5 Mark II: contains a 16 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 8 images that are subsequently merged into a 40 Mpixel image. Olympus OM-D E-M5 Mark III: contains a 20.4 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 8 images that are subsequently merged into a 50 Mpixel image. Olympus OM-D E-M1X: contains a 20.4 Mpixel sensor. The camera sports two pixel shift mode: (a) the 80Mp Tripod mode produces an 80 Mpixel image, (b) the Handheld High Res shot mode produces a 50 Mpixel image. Olympus PEN-F: contains a 20.4 Mpixel sensor. The High Res Shot mode takes multiple images, continually shifting the position of the sensor in sub-pixel increments. Combining these images results in either a 50MP JPEG or an 80MP Raw file. ==== OM System ==== OM System OM-1: contains a 20MPix sensor. The High Res Shot mode takes multiple images, and it can be used handheld or on a tripod. Handheld it will internally produce 50 Mpix files and 80 Mpix when mounted on a tripod. OM System OM-5: contains a 20MPix sensor. The High Res Shot mode takes multiple images, and it can be used handheld or on a tripod. Handheld it will internally produce 50 Mpix files and 80 Mpix when mounted on a tripod. === Panasonic === Panasonic Lumix DC-G9: contains a 20.3 Mpixel sensor. The High Resolution Mode takes a sequence of 8 shots in quick succession between which the sensor is shifted by 0.5 pixel for each image. These are subsequently merged into an 80 Mpixel image. Panasonic Lumix DC-S1: contains a 24.2 Mpixel sensor. The High Resolution Mode takes a sequence of shots in quick succession between which the sensor is shifted by a small amount. These are subsequently merged into a 96 Mpixel image. Panasonic Lumix DC-S1R: contains a 47.3 Mpixel sensor. The High Resolution Mode shifts the imaging sensor by a small increments to obtain a sequence of 8 images that are subsequently merged into a 187 Mpixel image. Panasonic Lumix DC-S1H Panasonic Lumix DC-S5 === Pentax === Pentax K-70: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'all color data in each pixel to deliver super-high-resolution images'. Pentax KP: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'high-resolution images with more accurate colours and much finer details'. Pentax K-3 II: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'super-high-resolution images with far more truthful color reproduction and much finer details'. Pentax K-3 III: contains a 25.7 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'a cancelling out of the Bayer pattern and removal of the need for sharpness-sapping demosaicing'. Pentax K-1: contains a 36.4 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'improved detail and colour resolution'. Pentax K-1 II: contains a 36.4 Mpixel sensor. The camera sports two pixel shift mode: (a) a series of 4 tripod-stabilised images shifted by 1 pixel each are subsequently combined into a 47.3 Mpixel image, (b) a series of images taken in handheld mode are combined into a 47.3 Mpixel image that is, within limits, able to cope even with moving subjects. === Sony === Sony a6600: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'all color data in each pixel to deliver super-high-resolution images'. Sony α7R III: contains a 42.4 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 42.4 Mpixel image with improved tonal resolution. Sony α7R IV: contains a 61 Mpixel sensor. The camera has two pixel shift modes, (a) the first takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 61 Mpixel image with improved tonal resolution, (b) the other takes a sequence of 16 shots between which the sensor is shifted by 0.5 pixel. These are subsequently merged into a 240 Mpixel image with both enhanced detail and improved tonal resolution. Sony α1: contains a 50 Mpixel sensor. The camera has two pixel shift modes, (a) the first takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 50 Mpixel image with improved tonal resolution, (b) the other takes a sequence of 16 shots between which the sensor is shifted by 0.5 pixel. These are subsequently merged into a 200 Mpixel image with both enhanced detail and improved tonal resolution. === Hasselblad === Hasselblad H3DII: the model H3DII-39 sports a 39 Mpixel sensor, the model H3DII-50 a 50 Mpixel sensor. Both enable a pixel shift mode which takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a single image. Hasselblad H4D series: the model H4D-200MS contains a 50 Mpixel sensor. The sensor sports 3 different pixel shift modes which take (a) a sequence of 6 shots taken at slight offsets, (b) a sequence of 4 shots between which the sensor is shifted by 1 pixel, (c) a sequence of 4 shots between which the sensor is shifted by 0.5 pixels. Images obtained by all three modes are subsequently merged into 200 Mpixel images. Hasselblad H5D series: both models H5D-50c MS and H5D-200c MS contain a 50 Mpixel sensor. This sensor sports 2 different pixel shift modes which take (a) a sequence of 6 shots with full and half pixel moveme

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  Gödel machine

  A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ⁡ ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.

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  GOLOG

  GOLOG is a high-level logic programming language for the specification and execution of complex actions in dynamical domains. It is based on the situation calculus. It is a first-order logical language for reasoning about action and change. GOLOG was developed at the University of Toronto. == History == The concept of situation calculus on which the GOLOG programming language is based was first proposed by John McCarthy in 1963. == Description == A GOLOG interpreter automatically maintains a direct characterization of the dynamic world being modeled, on the basis of user supplied axioms about preconditions, effects of actions and the initial state of the world. This allows the application to reason about the condition of the world and consider the impacts of different potential actions before focusing on a specific action. Golog is a logic programming language and is very different from conventional programming languages. A procedural programming language like C defines the execution of statements in advance. The programmer creates a subroutine which consists of statements, and the computer executes each statement in a linear order. In contrast, fifth-generation programming languages like Golog work with an abstract model with which the interpreter can generate the sequence of actions. The source code defines the problem and it is up to the solver to find the next action. This approach can facilitate the management of complex problems from the domain of robotics. A Golog program defines the state space in which the agent is allowed to operate. A path in the symbolic domain is found with state space search. To speed up the process, Golog programs are realized as hierarchical task networks. Apart from the original Golog language, there are some extensions available. The ConGolog language provides concurrency and interrupts. Other dialects like IndiGolog and Readylog were created for real time applications in which sensor readings are updated on the fly. == Uses == Golog has been used to model the behavior of autonomous agents. In addition to a logic-based action formalism for describing the environment and the effects of basic actions, they enable the construction of complex actions using typical programming language constructs. It is also used for applications in high level control of robots and industrial processes, virtual agents, discrete event simulation etc. It can be also used to develop Belief Desire Intention-style agent systems. == Planning and scripting == In contrast to the Planning Domain Definition Language, Golog supports planning and scripting as well. Planning means that a goal state in the world model is defined, and the solver brings a logical system into this state. Behavior scripting implements reactive procedures, which are running as a computer program. For example, suppose the idea is to authoring a story. The user defines what should be true at the end of the plot. A solver gets started and applies possible actions to the current situation until the goal state is reached. The specification of a goal state and the possible actions are realized in the logical world model. In contrast, a hardwired reactive behavior doesn't need a solver but the action sequence is provided in a scripting language. The Golog interpreter, which is written in Prolog, executes the script and this will bring the story into the goal state.

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