AI Analyse Your Face

AI Analyse Your Face — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Manual override

  A manual override (MO) or manual analog override (MAO) is a mechanism where control is taken from an automated system and given to the user. For example, a manual override in photography refers to the ability for the human photographer to turn off the automatic aperture sizing, automatic focusing, or any other automated system on the camera. Some manual overrides can be used to veto an automated system's judgment when the system is in error. An example of this is a printer's ink level detection: in one case, a researcher found that when he overrode the system, up to 38% more pages could be printed at good quality by the printer than the automated system would have allowed. Automated systems are becoming increasingly common and integrated into everyday objects such as automobiles and domestic appliances. This development of ubiquitous computing raises general issues of policy and law about the need for manual overrides for matters of great importance such as life-threatening situations and major economic decisions. The loyalty of such autonomous devices then becomes an issue. If they follow rules installed by the manufacturer or required by law and refuse to cede control in some situations then the owners of the devices may feel disempowered, alienated and lacking true ownership. == Major incidents == China Airlines Flight 140 crashed, causing many deaths, due to a misunderstanding about the manual overrides for the autopilot. The Take-Off/Go Around system had been activated to abort a landing. It was programmed to ignore manual controls in this situation but the human pilots tried to continue the landing. The conflicting control signals from the pilots and autopilot then resulted in the aircraft stalling and crashing. The autopilot for this aircraft type was then reprogrammed so that it would never ignore a manual override.

  Read more →
• 

  How to Choose an AI Subtitle Generator

  Shopping for the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI subtitle generator slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

  Read more →
• 

  Cognitive computer

  A cognitive computer is a computer that hardwires artificial intelligence and machine learning algorithms into an integrated circuit that closely reproduces the behavior of the human brain. It generally adopts a neuromorphic engineering approach. Synonyms include neuromorphic chip and cognitive chip. In 2023, IBM's proof-of-concept NorthPole chip (optimized for 2-, 4- and 8-bit precision) achieved remarkable performance in image recognition. In 2013, IBM developed Watson, a cognitive computer that uses neural networks and deep learning techniques. The following year, it developed the 2014 TrueNorth microchip architecture which is designed to be closer in structure to the human brain than the von Neumann architecture used in conventional computers. In 2017, Intel also announced its version of a cognitive chip in "Loihi, which it intended to be available to university and research labs in 2018. Intel (most notably with its Pohoiki Beach and Springs systems), Qualcomm, and others are improving neuromorphic processors steadily. == IBM TrueNorth chip == TrueNorth was a neuromorphic CMOS integrated circuit produced by IBM in 2014. It is a manycore processor network on a chip design, with 4096 cores, each one having 256 programmable simulated neurons for a total of just over a million neurons. In turn, each neuron has 256 programmable "synapses" that convey the signals between them. Hence, the total number of programmable synapses is just over 268 million (228). Its basic transistor count is 5.4 billion. In 2023 Zhejiang University and Alibaba developed Darwin a neuromorphic chip The darwin3 chip was designed around 2023 so it is fairly modern compared to IBM's TrueNorth or Intel's LoihI. === Details === Memory, computation, and communication are handled in each of the 4096 neurosynaptic cores, TrueNorth circumvents the von Neumann-architecture bottleneck and is very energy-efficient, with IBM claiming a power consumption of 70 milliwatts and a power density that is 1/10,000th of conventional microprocessors. The SyNAPSE chip operates at lower temperatures and power because it only draws power necessary for computation. Skyrmions have been proposed as models of the synapse on a chip. The neurons are emulated using a Linear-Leak Integrate-and-Fire (LLIF) model, a simplification of the leaky integrate-and-fire model. According to IBM, it does not have a clock, operates on unary numbers, and computes by counting to a maximum of 19 bits. The cores are event-driven by using both synchronous and asynchronous logic, and are interconnected through an asynchronous packet-switched mesh network on chip (NOC). IBM developed a new network to program and use TrueNorth. It included a simulator, a new programming language, an integrated programming environment, and libraries. This lack of backward compatibility with any previous technology (e.g., C++ compilers) poses serious vendor lock-in risks and other adverse consequences that may prevent it from commercialization in the future. === Research === In 2018, a cluster of TrueNorth network-linked to a master computer was used in stereo vision research that attempted to extract the depth of rapidly moving objects in a scene. == IBM NorthPole chip == In 2023, IBM released its NorthPole chip, which is a proof-of-concept for dramatically improving performance by intertwining compute with memory on-chip, thus eliminating the Von Neumann bottleneck. It blends approaches from IBM's 2014 TrueNorth system with modern hardware designs to achieve speeds about 4,000 times faster than TrueNorth. It can run ResNet-50 or Yolo-v4 image recognition tasks about 22 times faster, with 25 times less energy and 5 times less space, when compared to GPUs which use the same 12-nm node process that it was fabricated with. It includes 224 MB of RAM and 256 processor cores and can perform 2,048 operations per core per cycle at 8-bit precision, and 8,192 operations at 2-bit precision. It runs at between 25 and 425 MHz. This is an inferencing chip, but it cannot yet handle GPT-4 because of memory and accuracy limitations == Intel Loihi chip == === Pohoiki Springs === Pohoiki Springs is a system that incorporates Intel's self-learning neuromorphic chip, named Loihi, introduced in 2017, perhaps named after the Hawaiian seamount Lōʻihi. Intel claims Loihi is about 1000 times more energy efficient than general-purpose computing systems used to train neural networks. In theory, Loihi supports both machine learning training and inference on the same silicon independently of a cloud connection, and more efficiently than convolutional neural networks or deep learning neural networks. Intel points to a system for monitoring a person's heartbeat, taking readings after events such as exercise or eating, and using the chip to normalize the data and work out the ‘normal’ heartbeat. It can then spot abnormalities and deal with new events or conditions. The first iteration of the chip was made using Intel's 14 nm fabrication process and houses 128 clusters of 1,024 artificial neurons each for a total of 131,072 simulated neurons. This offers around 130 million synapses, far less than the human brain's 800 trillion synapses, and behind IBM's TrueNorth. Loihi is available for research purposes among more than 40 academic research groups as a USB form factor. In October 2019, researchers from Rutgers University published a research paper to demonstrate the energy efficiency of Intel's Loihi in solving simultaneous localization and mapping. In March 2020, Intel and Cornell University published a research paper to demonstrate the ability of Intel's Loihi to recognize different hazardous materials, which could eventually aid to "diagnose diseases, detect weapons and explosives, find narcotics, and spot signs of smoke and carbon monoxide". === Pohoiki Beach === Intel's Loihi 2, named Pohoiki Beach, was released in September 2021 with 64 cores. It boasts faster speeds, higher-bandwidth inter-chip communications for enhanced scalability, increased capacity per chip, a more compact size due to process scaling, and improved programmability. === Hala Point === Hala Point packages 1,152 Loihi 2 processors produced on Intel 3 process node in a six-rack-unit chassis. The system supports up to 1.15 billion neurons and 128 billion synapses distributed over 140,544 neuromorphic processing cores, consuming 2,600 watts of power. It includes over 2,300 embedded x86 processors for ancillary computations. Intel claimed in 2024 that Hala Point was the world’s largest neuromorphic system. It uses Loihi 2 chips. It is claimed to offer 10x more neuron capacity and up to 12x higher performance. The Darwin3 chip exceeds these specs. Hala Point provides up to 20 quadrillion operations per second, (20 petaops), with efficiency exceeding 15 trillion (8-bit) operations s−1 W−1 on conventional deep neural networks. Hala Point integrates processing, memory and communication channels in a massively parallelized fabric, providing 16 PB s−1 of memory bandwidth, 3.5 PB s−1 of inter-core communication bandwidth, and 5 TB s−1 of inter-chip bandwidth. The system can process its 1.15 billion neurons 20 times faster than a human brain. Its neuron capacity is roughly equivalent to that of an owl brain or the cortex of a capuchin monkey. Loihi-based systems can perform inference and optimization using 100 times less energy at speeds as much as 50 times faster than CPU/GPU architectures. Intel claims that Hala Point can create LLMs. Much further research is needed == SpiNNaker == SpiNNaker (Spiking Neural Network Architecture) is a massively parallel, manycore supercomputer architecture designed by the Advanced Processor Technologies Research Group at the Department of Computer Science, University of Manchester. == Criticism == Critics argue that a room-sized computer – as in the case of IBM's Watson – is not a viable alternative to a three-pound human brain. Some also cite the difficulty for a single system to bring so many elements together, such as the disparate sources of information as well as computing resources. In 2021, The New York Times released Steve Lohr's article "What Ever Happened to IBM’s Watson?". He wrote about some costly failures of IBM Watson. One of them, a cancer-related project called the Oncology Expert Advisor, was abandoned in 2016 as a costly failure. During the collaboration, Watson could not use patient data. Watson struggled to decipher doctors’ notes and patient histories. The development of LLMs has placed a new emphasis on cognitive computers, because the Transformer technology that underpins LLMs demands huge energy for GPUs and PCs. Cognitive computers use significantly less energy, but the details of STDPs and neuron models cannot yet match the accuracy of backprop, and so ANN to SNN weight translations such as QAT and PQT or progressive quantization are becoming popular, with their own limitations.

  Read more →
• 

  Bernhard Schölkopf

  Bernhard Schölkopf (born 20 February 1968) is a German computer scientist known for his work in machine learning, especially on kernel methods and causality. He is a director at the Max Planck Institute for Intelligent Systems in Tübingen, Germany, where he heads the Department of Empirical Inference. He is also an affiliated professor at ETH Zürich, honorary professor at the University of Tübingen and Technische Universität Berlin, and chairman of the European Laboratory for Learning and Intelligent Systems (ELLIS). == Research == === Kernel methods === Schölkopf developed SVM methods achieving world record performance on the MNIST pattern recognition benchmark at the time. With the introduction of kernel PCA, Schölkopf and coauthors argued that SVMs are a special case of a much larger class of methods, and all algorithms that can be expressed in terms of dot products can be generalized to a nonlinear setting by means of what is known as reproducing kernels. Another significant observation was that the data on which the kernel is defined need not be vectorial, as long as the kernel Gram matrix is positive definite. Both insights together led to the foundation of the field of kernel methods, encompassing SVMs and many other algorithms. Kernel methods are now textbook knowledge and one of the major machine learning paradigms in research and applications. Developing kernel PCA, Schölkopf extended it to extract invariant features and to design invariant kernels and showed how to view other major dimensionality reduction methods such as LLE and Isomap as special cases. In further work with Alex Smola and others, he extended the SVM method to regression and classification with pre-specified sparsity and quantile/support estimation. He proved a representer theorem implying that SVMs, kernel PCA, and most other kernel algorithms, regularized by a norm in a reproducing kernel Hilbert space, have solutions taking the form of kernel expansions on the training data, thus reducing an infinite dimensional optimization problem to a finite dimensional one. He co-developed kernel embeddings of distributions methods to represent probability distributions in Hilbert Spaces, with links to Fraunhofer diffraction as well as applications to independence testing. === Causality === Starting in 2005, Schölkopf turned his attention to causal inference. Causal mechanisms in the world give rise to statistical dependencies as epiphenomena, but only the latter are exploited by popular machine learning algorithms. Knowledge about causal structures and mechanisms is useful by letting us predict not only future data coming from the same source, but also the effect of interventions in a system, and by facilitating transfer of detected regularities to new situations. Schölkopf and co-workers addressed (and in certain settings solved) the problem of causal discovery for the two-variable setting and connected causality to Kolmogorov complexity. Around 2010, Schölkopf began to explore how to use causality for machine learning, exploiting assumptions of independence of mechanisms and invariance. His early work on causal learning was exposed to a wider machine learning audience during his Posner lecture at NeurIPS 2011, as well as in a keynote talk at ICML 2017. He assayed how to exploit underlying causal structures in order to make machine learning methods more robust with respect to distribution shifts and systematic errors, the latter leading to the discovery of a number of new exoplanets including K2-18b, which was subsequently found to contain water vapour in its atmosphere, a first for an exoplanet in the habitable zone. == Education and employment == Schölkopf studied mathematics, physics, and philosophy in Tübingen and London. He was supported by the Studienstiftung and won the Lionel Cooper Memorial Prize for the best M.Sc. in Mathematics at the University of London. He completed a Diplom in Physics, and then moved to Bell Labs in New Jersey, where he worked with Vladimir Vapnik, who became co-adviser of his PhD thesis at TU Berlin (with Stefan Jähnichen). His thesis, defended in 1997, won the annual award of the German Informatics Association. In 2001, following positions in Berlin, Cambridge and New York, he founded the Department for Empirical Inference at the Max Planck Institute for Biological Cybernetics, which grew into a leading center for research in machine learning. In 2011, he became founding director at the Max Planck Institute for Intelligent Systems. With Alex Smola, Schölkopf co-founded the series of Machine Learning Summer Schools. He also co-founded a Cambridge-Tübingen PhD Programme and the Max Planck-ETH Center for Learning Systems. In 2016, he co-founded the Cyber Valley research consortium. He participated in the IEEE Global Initiative on "Ethically Aligned Design". Schölkopf is co-editor-in-Chief of the Journal of Machine Learning Research, a journal he helped found, being part of a mass resignation of the editorial board of Machine Learning (journal). He is among the world’s most cited computer scientists. Alumni of his lab include Ulrike von Luxburg, Carl Rasmussen, Matthias Hein, Arthur Gretton, Gunnar Rätsch, Matthias Bethge, Stefanie Jegelka, Jason Weston, Olivier Bousquet, Olivier Chapelle, Joaquin Quinonero-Candela, and Sebastian Nowozin. As of late 2023, Schölkopf is also a scientific advisor to French research group Kyutai which is being funded by Xavier Niel, Rodolphe Saadé, Eric Schmidt, and others. == Awards and recognition == Schölkopf’s awards include the Royal Society Milner Award and, shared with Isabelle Guyon and Vladimir Vapnik, the BBVA Foundation Frontiers of Knowledge Award in the Information and Communication Technologies category. He was the first scientist working in Europe to receive this award. He was elected a Fellow of the Royal Society in 2026.

  Read more →
• 

  Learnable function class

  In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

  Read more →
• 

  Markov chain central limit theorem

  In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the general form of Bienaymé's identity. == Statement == Suppose that: the sequence X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 {\textstyle X_{1}} , is the stationary distribution, so that X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent, but here we have only the weaker assumption that the process has the Markov property; and g {\textstyle g} is some (measurable) real-valued function for which var ⁡ ( g ( X 1 ) ) < + ∞ . {\textstyle \operatorname {var} (g(X_{1}))<+\infty .} Now let μ = E ⁡ ( g ( X 1 ) ) , μ ^ n = 1 n ∑ k = 1 n g ( X k ) σ 2 := lim n → ∞ var ⁡ ( n μ ^ n ) = lim n → ∞ n var ⁡ ( μ ^ n ) = var ⁡ ( g ( X 1 ) ) + 2 ∑ k = 1 ∞ cov ⁡ ( g ( X 1 ) , g ( X 1 + k ) ) . {\displaystyle {\begin{aligned}\mu &=\operatorname {E} (g(X_{1})),\\{\widehat {\mu }}_{n}&={\frac {1}{n}}\sum _{k=1}^{n}g(X_{k})\\\sigma ^{2}&:=\lim _{n\to \infty }\operatorname {var} ({\sqrt {n}}{\widehat {\mu }}_{n})=\lim _{n\to \infty }n\operatorname {var} ({\widehat {\mu }}_{n})=\operatorname {var} (g(X_{1}))+2\sum _{k=1}^{\infty }\operatorname {cov} (g(X_{1}),g(X_{1+k})).\end{aligned}}} Then as n → ∞ , {\textstyle n\to \infty ,} we have n ( μ ^ n − μ ) → D Normal ( 0 , σ 2 ) , {\displaystyle {\sqrt {n}}({\hat {\mu }}_{n}-\mu )\ {\xrightarrow {\mathcal {D}}}\ {\text{Normal}}(0,\sigma ^{2}),} where the decorated arrow indicates convergence in distribution. == Monte Carlo Setting == The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is the following: Consider a simple hard spheres model on a grid. Suppose X = { 1 , … , n 1 } × { 1 , … , n 2 } ⊆ Z 2 {\displaystyle X=\{1,\ldots ,n_{1}\}\times \{1,\ldots ,n_{2}\}\subseteq Z^{2}} . A proper configuration on X {\displaystyle X} consists of coloring each point either black or white in such a way that no two adjacent points are white. Let χ {\displaystyle \chi } denote the set of all proper configurations on X {\displaystyle X} , N χ ( n 1 , n 2 ) {\displaystyle N_{\chi }(n_{1},n_{2})} be the total number of proper configurations and π be the uniform distribution on χ {\displaystyle \chi } so that each proper configuration is equally likely. Suppose our goal is to calculate the typical number of white points in a proper configuration; that is, if W ( x ) {\displaystyle W(x)} is the number of white points in x ∈ χ {\displaystyle x\in \chi } then we want the value of E π W = ∑ x ∈ χ W ( x ) N χ ( n 1 , n 2 ) {\displaystyle E_{\pi }W=\sum _{x\in \chi }{\frac {W(x)}{N_{\chi }{\bigl (}n_{1},n_{2}{\bigr )}}}} If n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are even moderately large then we will have to resort to an approximation to E π W {\displaystyle E_{\pi }W} . Consider the following Markov chain on χ {\displaystyle \chi } . Fix p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and set X 1 = x 1 {\displaystyle X_{1}=x_{1}} where x 1 ∈ χ {\displaystyle x_{1}\in \chi } is an arbitrary proper configuration. Randomly choose a point ( x , y ) ∈ X {\displaystyle (x,y)\in X} and independently draw U ∼ U n i f o r m ( 0 , 1 ) {\displaystyle U\sim \mathrm {Uniform} (0,1)} . If u ≤ p {\displaystyle u\leq p} and all of the adjacent points are black then color ( x , y ) {\displaystyle (x,y)} white leaving all other points alone. Otherwise, color ( x , y ) {\displaystyle (x,y)} black and leave all other points alone. Call the resulting configuration X 1 {\displaystyle X_{1}} . Continuing in this fashion yields a Harris ergodic Markov chain { X 1 , X 2 , X 3 , … } {\displaystyle \{X_{1},X_{2},X_{3},\ldots \}} having π {\displaystyle \pi } as its invariant distribution. It is now a simple matter to estimate E π W {\displaystyle E_{\pi }W} with w n ¯ = ∑ i = 1 n W ( X i ) / n {\displaystyle {\overline {w_{n}}}=\sum _{i=1}^{n}W(X_{i})/n} . Also, since χ {\displaystyle \chi } is finite (albeit potentially large) it is well known that X {\displaystyle X} will converge exponentially fast to π {\displaystyle \pi } which implies that a CLT holds for w n ¯ {\displaystyle {\overline {w_{n}}}} . == Implications == Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean.

  Read more →
• 

  Muller automaton

  In automata theory, a Muller automaton is a type of an ω-automaton. The acceptance condition separates a Muller automaton from other ω-automata. The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visited infinitely often must be an element of the acceptance set. Both deterministic and non-deterministic Muller automata recognize the ω-regular languages. They are named after David E. Muller, an American mathematician and computer scientist, who invented them in 1963. == Formal definition == Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q0 is an element of Q, called the initial state. F is a set of sets of states. Formally, F ⊆ P(Q) where P(Q) is powerset of Q. F defines the acceptance condition. A accepts exactly those runs in which the set of infinitely often occurring states is an element of F In a non-deterministic Muller automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states and the initial state q0 is replaced by a set of initial states Q0. Generally, 'Muller automaton' refers to a non-deterministic Muller automaton. For more comprehensive formalisation look at ω-automaton. == Equivalence with other ω-automata == The Muller automata are equally expressive as parity automata, Rabin automata, Streett automata, and non-deterministic Büchi automata, to mention some, and strictly more expressive than the deterministic Büchi automata. The equivalence of the above automata and non-deterministic Muller automata can be shown very easily as the accepting conditions of these automata can be emulated using the acceptance condition of Muller automata and vice versa. McNaughton's theorem demonstrates the equivalence of non-deterministic Büchi automaton and deterministic Muller automaton. Thus, deterministic and non-deterministic Muller automata are equivalent in terms of the languages they can accept. == Transformation to non-deterministic Muller automata == Following is a list of automata constructions that each transforms a type of ω-automata to a non-deterministic Muller automaton. From Büchi automata If B is the set of final states in a Büchi automaton with the set of states Q, we can construct a Muller automaton with same set of states, transition function and initial state with the Muller accepting condition as F = { X | X ∈ P(Q) ∧ X ∩ B ≠ ∅}. From Rabin automata/parity automata Similarly, the Rabin conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ E j = ∅ {\displaystyle F\cap E_{j}=\emptyset } and F ∩ F j ≠ ∅ {\displaystyle F\cap F_{j}\neq \emptyset } , for some j. Note that this covers the case of parity automata too, as the parity acceptance condition can be expressed as a Rabin acceptance condition easily. From Streett automata The Streett conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ F j = ∅ ⟹ F ∩ E j = ∅ {\displaystyle F\cap F_{j}=\emptyset \implies F\cap E_{j}=\emptyset } , for all j. == Transformation to deterministic Muller automata == From Büchi automaton McNaughton's theorem provides a procedure to transform any non-deterministic Büchi automaton into a deterministic Muller automaton.

  Read more →
• 

  Rob Fergus

  Rob Fergus is a British-American computer scientist working primarily in the fields of machine learning, deep learning, representational learning, and generative models. He is a professor of computer science at Courant Institute of Mathematical Sciences at New York University (NYU) and a research scientist at DeepMind. Fergus developed ZFNet in 2013 together with M.D. Zeiler, his PhD student in NYU. Fergus co-founded Meta AI (then known as Facebook Artificial Intelligence Research (FAIR)) along with Yann Le Cun in September 2013. In 2009, Rob Fergus co-founded the Computational Intelligence, Learning, Vision, and Robotics (CILVR) Lab at NYU along with Yann Le Cun. == Awards and recognition == Rob Fergus has been recognized in academia and received the following awards: NSF Faculty Early Career Development Program (CAREER) Sloan Research Fellowship Test-of-time awards at ECCV, CVPR and ICLR == Notable PhD students == Matt Zeiler (Clarifai founder) Wojciech Zaremba (OpenAI co-founder) Denis Yarats (Perplexity co-founder) Alex Rives (EvolutionaryScale co-founder; faculty at MIT)

  Read more →
• 

  Cloud robotics

  Cloud robotics is a field of robotics that attempts to invoke cloud technologies such as cloud computing, cloud storage, and other Internet technologies centered on the benefits of converged infrastructure and shared services for robotics. When connected to the cloud, robots can benefit from the powerful computation, storage, and communication resources of a modern data center in the cloud, which can process and share information from various robots or agents (other machines, smart objects, humans, etc.). Humans can also delegate tasks to robots remotely through networks. Cloud computing technologies enable robot systems to be gain capability whilst reducing costs through cloud technologies. Thus, it is possible to build lightweight, low-cost, smarter robots with an intelligent "brain" in the cloud. The "brain" consists of data center, knowledge base, task planners, deep learning, information processing, environment models, communication support, etc. == Components == A cloud for robots potentially has at least six significant components: Building a "cloud brain" for robots, the main object of cloud robotics; Offering a global library of images, maps, and object data, often with geometry and mechanical properties, expert system, knowledge base (i.e. semantic web, data centres); Massively-parallel computation on demand for sample-based statistical modelling and motion planning, task planning, multi-robot collaboration, scheduling and coordination of system; Robot sharing of outcomes, trajectories, and dynamic control policies and robot learning support; Human sharing of open-source code, data, and designs for programming, experimentation, and hardware construction; On-demand human guidance and assistance for evaluation, learning, and error recovery; Augmented human–robot interaction through various ways (semantics knowledge base, Apple SIRI like service, etc.). == Applications == Autonomous mobile robots Google's self-driving cars are cloud robots. The cars use the network to access Google's enormous database of maps and satellite and environment model (like Streetview) and combines it with streaming data from GPS, cameras, and 3D sensors to monitor its own position within centimetres, and with past and current traffic patterns to avoid collisions. Each car can learn something about environments, roads, or driving, or conditions, and it sends the information to the Google cloud, where it can be used to improve the performance of other cars. Cloud medical robots a medical cloud (also called a healthcare cluster) consists of various services such as a disease archive, electronic medical records, a patient health management system, practice services, analytics services, clinic solutions, expert systems, etc. A robot can connect to the cloud to provide clinical service to patients, as well as deliver assistance to doctors (e.g. a co-surgery robot). Moreover, it also provides a collaboration service by sharing information between doctors and care givers about clinical treatment. Assistive robots A domestic robot can be employed for healthcare and life monitoring for elderly people. The system collects the health status of users and exchange information with cloud expert system or doctors to facilitate elderly peoples life, especially for those with chronic diseases. For example, the robots are able to provide support to prevent the elderly from falling down, emergency healthy support such as heart disease, blooding disease. Care givers of elderly people can also get notification when in emergency from the robot through network. Industrial robots As highlighted by the German government's Industry 4.0 Plan, "Industry is on the threshold of the fourth industrial revolution. Driven by the Internet, the real and virtual worlds are growing closer and closer together to form the Internet of Things. Industrial production of the future will be characterised by the strong individualisation of products under the conditions of highly flexible (large series) production, the extensive integration of customers and business partners in business and value-added processes, and the linking of production and high-quality services leading to so-called hybrid products." In manufacturing, such cloud based robot systems could learn to handle tasks such as threading wires or cables, or aligning gaskets from a professional knowledge base. A group of robots can share information for some collaborative tasks. Even more, a consumer is able to place customised product orders to manufacturing robots directly with online ordering systems. Another potential paradigm is shopping-delivery robot systems. Once an order is placed, a warehouse robot dispatches the item to an autonomous car or autonomous drone to deliver it to its recipient. == Research == RoboEarth was funded by the European Union's Seventh Framework Programme for research, technological development projects, specifically to explore the field of cloud robotics. The goal of RoboEarth is to allow robotic systems to benefit from the experience of other robots, paving the way for rapid advances in machine cognition and behaviour, and ultimately, for more subtle and sophisticated human-machine interaction. RoboEarth offers a Cloud Robotics infrastructure. RoboEarth's World-Wide-Web style database stores knowledge generated by humans – and robots – in a machine-readable format. Data stored in the RoboEarth knowledge base include software components, maps for navigation (e.g., object locations, world models), task knowledge (e.g., action recipes, manipulation strategies), and object recognition models (e.g., images, object models). The RoboEarth Cloud Engine includes support for mobile robots, autonomous vehicles, and drones, which require much computation for navigation. Rapyuta is an open source cloud robotics framework based on RoboEarth Engine developed by the robotics researcher at ETHZ. Within the framework, each robot connected to Rapyuta can have a secured computing environment (rectangular boxes) giving them the ability to move their heavy computation into the cloud. In addition, the computing environments are tightly interconnected with each other and have a high bandwidth connection to the RoboEarth knowledge repository. FogROS2 is an open-source extension to the Robot Operating System 2 (ROS 2) developed by researchers at UC Berkeley. It enables robots to offload computationally intensive tasks—such as SLAM, grasp planning, and motion planning—to cloud resources, thereby enhancing performance and reducing onboard computational requirements. FogROS2 automates the provisioning of cloud instances, deployment of ROS 2 nodes, and secure communication between robots and cloud services. The platform is designed to be compatible with existing ROS 2 applications without requiring code modifications. Further advancements include FogROS2-SGC, which facilitates secure global connectivity across different networks and locations, and FogROS2-FT, which introduces fault tolerance by replicating services across multiple cloud providers to ensure robustness against failures. KnowRob is an extensional project of RoboEarth. It is a knowledge processing system that combines knowledge representation and reasoning methods with techniques for acquiring knowledge and for grounding the knowledge in a physical system and can serve as a common semantic framework for integrating information from different sources. RoboBrain is a large-scale computational system that learns from publicly available Internet resources, computer simulations, and real-life robot trials. It accumulates everything robotics into a comprehensive and interconnected knowledge base. Applications include prototyping for robotics research, household robots, and self-driving cars. The goal is as direct as the project's name—to create a centralised, always-online brain for robots to tap into. The project is dominated by Stanford University and Cornell University. And the project is supported by the National Science Foundation, the Office of Naval Research, the Army Research Office, Google, Microsoft, Qualcomm, the Alfred P. Sloan Foundation and the National Robotics Initiative, whose goal is to advance robotics to help make the United States more competitive in the world economy. MyRobots is a service for connecting robots and intelligent devices to the Internet. It can be regarded as a social network for robots and smart objects (i.e. Facebook for robots). With socialising, collaborating and sharing, robots can benefit from those interactions too by sharing their sensor information giving insight on their perspective of their current state. COALAS is funded by the INTERREG IVA France (Channel) – England European cross-border co-operation programme. The project aims to develop new technologies for disabled people through social and technological innovation and through the users' social and psychological integrity. The objective is to produce a cognitive ambient

  Read more →
• 

  Jiliang Tang

  Jiliang Tang is a Chinese-born computer scientist and a University Foundation Professor of Computer Science and Engineering at Michigan State University, where he is the director of the Data Science and Engineering (DSE) Lab. His research expertise is in data mining and machine learning. == Education and career == He received his BEng in software engineering (2008) and MSc in computer science (2010) from the Beijing Institute of Technology, Beijing, China. His PhD is from Arizona State University (2015), under the direction of Huan Liu. After gaining his PhD, he worked as a research scientist at Yahoo Labs (2015–16) before joining Michigan State University as an assistant professor (2016). His research has mostly been published jointly with Huan Liu. It has received over thirteen thousand citations documented by Google Scholar, and has received coverage in the media. == Awards == He has received the 2020 ACM SIGKDD Rising Star Award that "aims to celebrate the early accomplishments of the SIGKDD communities' brightest new minds", NSF Career Award, and Michigan State University's Distinguished Withrow Research Award. == Selected publications == === Books === Jiliang Tang, Huan Liu. Trust in Social Media, (Synthesis digital library of engineering and computer science; Synthesis lectures on information security, privacy, and trust, # 13) Morgan & Claypool, 2015 ISBN 9781627054058 === Peer reviewed journal articles === Shu K, Sliva A, Wang S, Tang J, Liu H. Fake news detection on social media: A data mining perspective. ACM SIGKDD explorations newsletter. 2017 Sep 1;19(1):22-36. [1] Tang J, Alelyani S, Liu H. Feature selection for classification: A review. Data classification: Algorithms and applications. 2014:37. [2] Li J, Cheng K, Wang S, Morstatter F, Trevino RP, Tang J, Liu H. Feature selection: A data perspective. ACM Computing Surveys (CSUR). 2017 Dec 6;50(6):1-45. [3] Chang S, Han W, Tang J, Qi GJ, Aggarwal CC, Huang TS. Heterogeneous network embedding via deep architectures. InProceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining 2015 Aug 10 (pp. 119–128) Gao H, Tang J, Hu X, Liu H. Exploring temporal effects for location recommendation on location-based social networks. InProceedings of the 7th ACM conference on Recommender systems 2013 Oct 12 (pp. 93–100). Hu X, Tang J, Gao H, Liu H. Unsupervised sentiment analysis with emotional signals. InProceedings of the 22nd international conference on World Wide Web 2013 May 13 (pp. 607–618).

  Read more →
• 

  Top 10 AI Blog Writers Compared (2026)

  Comparing the best AI blog writer? An AI blog writer is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI blog writer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

  Read more →
• 

  Michael Kohlhase

  Michael Kohlhase (born 13 September 1964, in Erlangen) is a German computer scientist and professor at University of Erlangen–Nuremberg, where he is head of the KWARC research group (Knowledge Adaptation and Reasoning for Content). == Academic Positions == Michael Kohlhase is president of the OpenMath Society and a trustee of the Interest Group for Mathematical Knowledge Management (MKM). He was a trustee of the Conference on Automated Deduction and the CALCULEMUS Interest Group. He has been Conference Chair of CADE-21 and Program Chair of the KI-2006, MKM-2005, and CALCULEMUS-2000 conferences and has served on the Programme Committees of more than three dozen international conferences. Kohlhase holds an adjunct associate professorship at Carnegie Mellon University and was (2006–2008) vice director of the Department of Safe and Secure Cognitive Systems at German Research Centre for Artificial Intelligence (DFKI) Lab Bremen. In 2014, he became a member of the Global Digital Mathematics Library Working Group of the IMU. == Academic career == Michael Kohlhase obtained a degree in Mathematics (1989) from University of Bonn, a doctorate (1994) and habilitation (1999) in Computer Science at Saarland University. He has pursued his doctoral and post-doctoral research in extended research visits at Carnegie Mellon University, University of Amsterdam, the University of Edinburgh, and SRI International. From 2000–2003, he has conducted research and taught at the School of Computer Science at Carnegie Mellon University, where he was appointed to an adjunct associate professor. In September 2003 he was appointed as Professor of Computer Science at Jacobs University Bremen (International University Bremen until 2007), and 2006–2008 he was vice director of the Department of Safe and Secure Cognitive Systems of the German Research Centre for Artificial Intelligence (DFKI) Bremen. Since September 2016 he holds the Professorship for Knowledge Representation and Processing at University of Erlangen–Nuremberg. He has authored or edited four books and published almost 100 peer-reviewed papers. == Awards and Scholarships == 2000 3-year Heisenberg-Stipend of the Deutsche Forschungsgemeinschaft (DFG). 1996 AKI-prize, dissertation prize of the "Arbeitsgemeinschaft deutscher KI-Institute (AKI)" 1991 dissertation stipend of the Studienstiftung (German National Academic Foundation) 1986 masters stipend of Studienstiftung == Research interests == Michael Kohlhase's current research interests include Automated theorem proving and knowledge representation for mathematics, inference-based techniques for natural language processing and semantics, and computer-supported education. Much of his concrete work is based on web-based content markup formats like MathML, OpenMath, and OMDoc and systems for managing this data, e.g. semantic search engines for mathematical formulae, semantic extensions to LaTeX, or converting legacy LaTeX documents from the arXiv.

  Read more →
• 

  Machine learning in video games

  Artificial intelligence and machine learning techniques are used in video games for a wide variety of applications such as non-player character (NPC) control, procedural content generation (PCG) and deep learning-based content generation. Machine learning is a subset of artificial intelligence that uses historical data to build predictive and analytical models. This is in sharp contrast to traditional methods of artificial intelligence such as search trees and expert systems. Information on machine learning techniques in the field of games is mostly known to public through research projects as most gaming companies choose not to publish specific information about their intellectual property. The most publicly known application of machine learning in games is likely the use of deep learning agents that compete with professional human players in complex strategy games. There has been a significant application of machine learning on games such as Atari/ALE, Doom, Minecraft, StarCraft, and car racing. Other games that did not originally exists as video games, such as chess and Go have also been affected by the machine learning. == Overview of relevant machine learning techniques == === Deep learning === Deep learning is a subset of machine learning which focuses heavily on the use of artificial neural networks (ANN) that learn to solve complex tasks. Deep learning uses multiple layers of ANN and other techniques to progressively extract information from an input. Due to this complex layered approach, deep learning models often require powerful machines to train and run on. ==== Convolutional neural networks ==== Convolutional neural networks (CNN) are specialized ANNs that are often used to analyze image data. These types of networks are able to learn translation invariant patterns, which are patterns that are not dependent on location. CNNs are able to learn these patterns in a hierarchy, meaning that earlier convolutional layers will learn smaller local patterns while later layers will learn larger patterns based on the previous patterns. A CNN's ability to learn visual data has made it a commonly used tool for deep learning in games. === Recurrent neural network === Recurrent neural networks are a type of ANN that are designed to process sequences of data in order, one part at a time rather than all at once. An RNN runs over each part of a sequence, using the current part of the sequence along with memory of previous parts of the current sequence to produce an output. These types of ANN are highly effective at tasks such as speech recognition and other problems that depend heavily on temporal order. There are several types of RNNs with different internal configurations; the basic implementation suffers from a lack of long term memory due to the vanishing gradient problem, thus it is rarely used over newer implementations. ==== Long short-term memory ==== A long short-term memory (LSTM) network is a specific implementation of a RNN that is designed to deal with the vanishing gradient problem seen in simple RNNs, which would lead to them gradually "forgetting" about previous parts of an inputted sequence when calculating the output of a current part. LSTMs solve this problem with the addition of an elaborate system that uses an additional input/output to keep track of long term data. LSTMs have achieved very strong results across various fields, and were used by several monumental deep learning agents in games. === Reinforcement learning === Reinforcement learning is the process of training an agent using rewards and/or punishments. The way an agent is rewarded or punished depends heavily on the problem; such as giving an agent a positive reward for winning a game or a negative one for losing. Reinforcement learning is used heavily in the field of machine learning and can be seen in methods such as Q-learning, policy search, Deep Q-networks and others. It has seen strong performance in both the field of games and robotics. === Neuroevolution === Neuroevolution involves the use of both neural networks and evolutionary algorithms. Instead of using gradient descent like most neural networks, neuroevolution models make use of evolutionary algorithms to update neurons in the network. Researchers claim that this process is less likely to get stuck in a local minimum and is potentially faster than state of the art deep learning techniques. == Deep learning agents == Machine learning agents have been used to take the place of a human player rather than function as NPCs, which are deliberately added into video games as part of designed gameplay. Deep learning agents have achieved impressive results when used in competition with both humans and other artificial intelligence agents. === Chess === Chess is a turn-based strategy game that is considered a difficult AI problem due to the computational complexity of its board space. Similar strategy games are often solved with some form of a Minimax Tree Search. These types of AI agents have been known to beat professional human players, such as the historic 1997 Deep Blue versus Garry Kasparov match. Since then, machine learning agents have shown ever greater success than previous AI agents. === Go === Go is another turn-based strategy game which is considered an even more difficult AI problem than chess. The state space of is Go is around 10^170 possible board states compared to the 10^120 board states for Chess. Prior to recent deep learning models, AI Go agents were only able to play at the level of a human amateur. ==== AlphaGo ==== Google's 2015 AlphaGo was the first AI agent to beat a professional Go player. AlphaGo used a deep learning model to train the weights of a Monte Carlo tree search (MCTS). The deep learning model consisted of 2 ANN, a policy network to predict the probabilities of potential moves by opponents, and a value network to predict the win chance of a given state. The deep learning model allows the agent to explore potential game states more efficiently than a vanilla MCTS. The network were initially trained on games of humans players and then were further trained by games against itself. ==== AlphaGo Zero ==== AlphaGo Zero, another implementation of AlphaGo, was able to train entirely by playing against itself. It was able to quickly train up to the capabilities of the previous agent. === StarCraft series === StarCraft and its sequel StarCraft II are real-time strategy (RTS) video games that have become popular environments for AI research. Blizzard and DeepMind have worked together to release a public StarCraft 2 environment for AI research to be done on. Various deep learning methods have been tested on both games, though most agents usually have trouble outperforming the default AI with cheats enabled or skilled players of the game. ==== Alphastar ==== Alphastar was the first AI agent to beat professional StarCraft 2 players without any in-game advantages. The deep learning network of the agent initially received input from a simplified zoomed out version of the gamestate, but was later updated to play using a camera like other human players. The developers have not publicly released the code or architecture of their model, but have listed several state of the art machine learning techniques such as relational deep reinforcement learning, long short-term memory, auto-regressive policy heads, pointer networks, and centralized value baseline. Alphastar was initially trained with supervised learning, it watched replays of many human games in order to learn basic strategies. It then trained against different versions of itself and was improved through reinforcement learning. The final version was hugely successful, but only trained to play on a specific map in a protoss mirror matchup. === Dota 2 === Dota 2 is a multiplayer online battle arena (MOBA) game. Like other complex games, traditional AI agents have not been able to compete on the same level as professional human player. The only widely published information on AI agents attempted on Dota 2 is OpenAI's deep learning Five agent. ==== OpenAI Five ==== OpenAI Five utilized separate long short-term memory networks to learn each hero. It trained using a reinforcement learning technique known as Proximal Policy Learning running on a system containing 256 GPUs and 128,000 CPU cores. Five trained for months, accumulating 180 years of game experience each day, before facing off with professional players. It was eventually able to beat the 2018 Dota 2 esports champion team in a 2019 series of games. === Planetary Annihilation === Planetary Annihilation is a real-time strategy game which focuses on massive scale war. The developers use ANNs in their default AI agent. === Supreme Commander 2 === Supreme Commander 2 is a real-time strategy (RTS) video game. The game uses Multilayer Perceptrons (MLPs) to control a platoon’s reaction to encountered enemy units. Total of four MLPs are used, one for each platoon type: land, naval

  Read more →
• 

  AI Sales Assistants Reviews: What Actually Works in 2026

  Curious about the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

  Read more →
• 

  Two-way finite automaton

  In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. == Two-way deterministic finite automaton == A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value indicating whether the machine will move its position in the input to the left, right, or stay at the same position. Equivalently, 2DFAs can be seen as read-only Turing machines with no work tape, only a read-only input tape. 2DFAs were introduced in a seminal 1959 paper by Rabin and Scott, who proved them to have equivalent power to one-way DFAs. That is, any formal language which can be recognized by a 2DFA can be recognized by a DFA which only examines and consumes each character in order. Since DFAs are obviously a special case of 2DFAs, this implies that both kinds of machines recognize precisely the class of regular languages. However, the equivalent DFA for a 2DFA may require exponentially many states, making 2DFAs a much more practical representation for algorithms for some common problems. 2DFAs are also equivalent to read-only Turing machines that use only a constant amount of space on their work tape, since any constant amount of information can be incorporated into the finite control state via a product construction (a state for each combination of work tape state and control state). == Formal description == Formally, a two-way deterministic finite automaton can be described by the following 8-tuple: M = ( Q , Σ , L , R , δ , s , t , r ) {\displaystyle M=(Q,\Sigma ,L,R,\delta ,s,t,r)} where Q {\displaystyle Q} is the finite, non-empty set of states Σ {\displaystyle \Sigma } is the finite, non-empty set of input symbols L {\displaystyle L} is the left endmarker R {\displaystyle R} is the right endmarker δ : Q × ( Σ ∪ { L , R } ) → Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow Q\times \{\mathrm {left,right} \}} s {\displaystyle s} is the start state t {\displaystyle t} is the end state r {\displaystyle r} is the reject state In addition, the following two conditions must also be satisfied: For all q ∈ Q {\displaystyle q\in Q} δ ( q , L ) = ( q ′ , r i g h t ) {\displaystyle \delta (q,L)=(q^{\prime },\mathrm {right} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} δ ( q , R ) = ( q ′ , l e f t ) {\displaystyle \delta (q,R)=(q^{\prime },\mathrm {left} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} It says that there must be some transition possible when the pointer reaches either end of the input word. For all symbols σ ∈ Σ ∪ { L } {\displaystyle \sigma \in \Sigma \cup \{L\}} δ ( t , σ ) = ( t , R ) {\displaystyle \delta (t,\sigma )=(t,R)} δ ( r , σ ) = ( r , R ) {\displaystyle \delta (r,\sigma )=(r,R)} δ ( t , R ) = ( t , L ) {\displaystyle \delta (t,R)=(t,L)} δ ( r , R ) = ( r , L ) {\displaystyle \delta (r,R)=(r,L)} It says that once the automaton reaches the accept or reject state, it stays in there forever and the pointer goes to the right most symbol and cycles there infinitely. == Two-way nondeterministic finite automaton == A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Its transition function is δ : Q × ( Σ ∪ { L , R } ) → 2 Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow 2^{Q\times \{\mathrm {left,right} \}}} . Like a standard one-way NFA, a 2NFA accepts a string if at least one of the possible computations is accepting. Like the 2DFAs, the 2NFAs also accept only regular languages. == Two-way alternating finite automaton == A two-way alternating finite automaton (2AFA) is a two-way extension of an alternating finite automaton (AFA). Its state set is Q = Q ∃ ∪ Q ∀ {\displaystyle Q=Q_{\exists }\cup Q_{\forall }} where Q ∃ ∩ Q ∀ = ∅ {\displaystyle Q_{\exists }\cap Q_{\forall }=\emptyset } . States in Q ∃ {\displaystyle Q_{\exists }} and Q ∀ {\displaystyle Q_{\forall }} are called existential resp. universal. In an existential state a 2AFA nondeterministically chooses the next state like an NFA, and accepts if at least one of the resulting computations accepts. In a universal state 2AFA moves to all next states, and accepts if all the resulting computations accept. == State complexity tradeoffs == Two-way and one-way finite automata, deterministic and nondeterministic and alternating, accept the same class of regular languages. However, transforming an automaton of one type to an equivalent automaton of another type incurs a blow-up in the number of states. Christos Kapoutsis determined that transforming an n {\displaystyle n} -state 2DFA to an equivalent DFA requires n ( n n − ( n − 1 ) n ) {\displaystyle n(n^{n}-(n-1)^{n})} states in the worst case. If an n {\displaystyle n} -state 2DFA or a 2NFA is transformed to an NFA, the worst-case number of states required is ( 2 n n + 1 ) = O ( 4 n n ) {\displaystyle {\binom {2n}{n+1}}=O\left({\frac {4^{n}}{\sqrt {n}}}\right)} . Ladner, Lipton and Stockmeyer. proved that an n {\displaystyle n} -state 2AFA can be converted to a DFA with 2 n 2 n {\displaystyle 2^{n2^{n}}} states. The 2AFA to NFA conversion requires 2 Θ ( n log ⁡ n ) {\displaystyle 2^{\Theta (n\log n)}} states in the worst case, see Geffert and Okhotin. It is an open problem whether every 2NFA can be converted to a 2DFA with only a polynomial increase in the number of states. The problem was raised by Sakoda and Sipser, who compared it to the P vs. NP problem in the computational complexity theory. Berman and Lingas discovered a formal relation between this problem and the L vs. NL open problem, see Kapoutsis for a precise relation. == Sweeping automata == Sweeping automata are 2DFAs of a special kind that process the input string by making alternating left-to-right and right-to-left sweeps, turning only at the endmarkers. Sipser constructed a sequence of languages, each accepted by an n-state NFA, yet which is not accepted by any sweeping automata with fewer than 2 n {\displaystyle 2^{n}} states. == Two-way quantum finite automaton == The concept of 2DFAs was in 1997 generalized to quantum computing by John Watrous's "On the Power of 2-Way Quantum Finite State Automata", in which he demonstrates that these machines can recognize nonregular languages and so are more powerful than DFAs. == Two-way pushdown automaton == A pushdown automaton that is allowed to move either way on its input tape is called two-way pushdown automaton (2PDA); it has been studied by Hartmanis, Lewis, and Stearns (1965). Aho, Hopcroft, Ullman (1968) and Cook (1971) characterized the class of languages recognizable by deterministic (2DPDA) and non-deterministic (2NPDA) two-way pushdown automata; Gray, Harrison, and Ibarra (1967) investigated the closure properties of these languages.

  Read more →