Inferential Theory of Learning (ITL) is an area of machine learning which describes inferential processes performed by learning agents. ITL has been continuously developed by Ryszard S. Michalski, starting in the 1980s. The first known publication of ITL was in 1983. In the ITL learning process is viewed as a search (inference) through hypotheses space guided by a specific goal. The results of learning need to be stored. Stored information will later be used by the learner for future inferences. Inferences are split into multiple categories including conclusive, deduction, and induction. In order for an inference to be considered complete it was required that all categories must be taken into account. This is how the ITL varies from other machine learning theories like Computational Learning Theory and Statistical Learning Theory; which both use singular forms of inference. == Usage == The most relevant published usage of ITL was in scientific journal published in 2012 and used ITL as a way to describe how agent-based learning works. According to the journal "The Inferential Theory of Learning (ITL) provides an elegant way of describing learning processes by agents".
StyleGAN
The Style Generative Adversarial Network, or StyleGAN for short, is an extension to the GAN architecture introduced by Nvidia researchers in December 2018, and made source available in February 2019. StyleGAN depends on Nvidia's CUDA software, GPUs, and Google's TensorFlow, or Meta AI's PyTorch, which supersedes TensorFlow as the official implementation library in later StyleGAN versions. The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. Nvidia introduced StyleGAN3, described as an "alias-free" version, on June 23, 2021, and made source available on October 12, 2021. == History == A direct predecessor of the StyleGAN series is the Progressive GAN, published in 2017. In December 2018, Nvidia researchers distributed a preprint with accompanying software introducing StyleGAN, a GAN for producing an unlimited number of (often convincing) portraits of fake human faces. StyleGAN was able to run on Nvidia's commodity GPU processors. In February 2019, Uber engineer Phillip Wang used the software to create the website This Person Does Not Exist, which displayed a new face on each web page reload. Wang himself has expressed amazement, given that humans are evolved to specifically understand human faces, that nevertheless StyleGAN can competitively "pick apart all the relevant features (of human faces) and recompose them in a way that's coherent." In September 2019, a website called Generated Photos published 100,000 images as a collection of stock photos. The collection was made using a private dataset shot in a controlled environment with similar light and angles. Similarly, two faculty at the University of Washington's Information School used StyleGAN to create Which Face is Real?, which challenged visitors to differentiate between a fake and a real face side by side. The faculty stated the intention was to "educate the public" about the existence of this technology so they could be wary of it, "just like eventually most people were made aware that you can Photoshop an image". The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. In 2021, a third version was released, improving consistency between fine and coarse details in the generator. Dubbed "alias-free", this version was implemented with PyTorch. === Illicit use === In December 2019, Facebook took down a network of accounts with false identities, and mentioned that some of them had used profile pictures created with machine learning techniques. == Architecture == === Progressive GAN === Progressive GAN is a method for training GAN for large-scale image generation stably, by growing a GAN generator from small to large scale in a pyramidal fashion. Like SinGAN, it decomposes the generator as G = G 1 ∘ G 2 ∘ ⋯ ∘ G N {\displaystyle G=G_{1}\circ G_{2}\circ \cdots \circ G_{N}} , and the discriminator as D = D N ∘ D N − 1 ∘ ⋯ ∘ D 1 {\displaystyle D=D_{N}\circ D_{N-1}\circ \cdots \circ D_{1}} . During training, at first only G N , D N {\displaystyle G_{N},D_{N}} are used in a GAN game to generate 4x4 images. Then G N − 1 , D N − 1 {\displaystyle G_{N-1},D_{N-1}} are added to reach the second stage of GAN game, to generate 8x8 images, and so on, until we reach a GAN game to generate 1024x1024 images. To avoid discontinuity between stages of the GAN game, each new layer is "blended in" (Figure 2 of the paper). For example, this is how the second stage GAN game starts: Just before, the GAN game consists of the pair G N , D N {\displaystyle G_{N},D_{N}} generating and discriminating 4x4 images. Just after, the GAN game consists of the pair ( ( 1 − α ) + α ⋅ G N − 1 ) ∘ u ∘ G N , D N ∘ d ∘ ( ( 1 − α ) + α ⋅ D N − 1 ) {\displaystyle ((1-\alpha )+\alpha \cdot G_{N-1})\circ u\circ G_{N},D_{N}\circ d\circ ((1-\alpha )+\alpha \cdot D_{N-1})} generating and discriminating 8x8 images. Here, the functions u , d {\displaystyle u,d} are image up- and down-sampling functions, and α {\displaystyle \alpha } is a blend-in factor (much like an alpha in image composing) that smoothly glides from 0 to 1. === StyleGAN === StyleGAN is designed as a combination of Progressive GAN with neural style transfer. The key architectural choice of StyleGAN-1 is a progressive growth mechanism, similar to Progressive GAN. Each generated image starts as a constant 4 × 4 × 512 {\displaystyle 4\times 4\times 512} array, and repeatedly passed through style blocks. Each style block applies a "style latent vector" via affine transform ("adaptive instance normalization"), similar to how neural style transfer uses Gramian matrix. It then adds noise, and normalize (subtract the mean, then divide by the variance). At training time, usually only one style latent vector is used per image generated, but sometimes two ("mixing regularization") in order to encourage each style block to independently perform its stylization without expecting help from other style blocks (since they might receive an entirely different style latent vector). After training, multiple style latent vectors can be fed into each style block. Those fed to the lower layers control the large-scale styles, and those fed to the higher layers control the fine-detail styles. Style-mixing between two images x , x ′ {\displaystyle x,x'} can be performed as well. First, run a gradient descent to find z , z ′ {\displaystyle z,z'} such that G ( z ) ≈ x , G ( z ′ ) ≈ x ′ {\displaystyle G(z)\approx x,G(z')\approx x'} . This is called "projecting an image back to style latent space". Then, z {\displaystyle z} can be fed to the lower style blocks, and z ′ {\displaystyle z'} to the higher style blocks, to generate a composite image that has the large-scale style of x {\displaystyle x} , and the fine-detail style of x ′ {\displaystyle x'} . Multiple images can also be composed this way. === StyleGAN2 === StyleGAN2 improves upon StyleGAN in two ways. One, it applies the style latent vector to transform the convolution layer's weights instead, thus solving the "blob" problem. The "blob" problem roughly speaking is because using the style latent vector to normalize the generated image destroys useful information. Consequently, the generator learned to create a "distraction" by a large blob, which absorbs most of the effect of normalization (somewhat similar to using flares to distract a heat-seeking missile). Two, it uses residual connections, which helps it avoid the phenomenon where certain features are stuck at intervals of pixels. For example, the seam between two teeth may be stuck at pixels divisible by 32, because the generator learned to generate teeth during stage N-5, and consequently could only generate primitive teeth at that stage, before scaling up 5 times (thus intervals of 32). This was updated by the StyleGAN2-ADA ("ADA" stands for "adaptive"), which uses invertible data augmentation. It also tunes the amount of data augmentation applied by starting at zero, and gradually increasing it until an "overfitting heuristic" reaches a target level, thus the name "adaptive". === StyleGAN3 === StyleGAN3 improves upon StyleGAN2 by solving the "texture sticking" problem, which can be seen in the official videos. They analyzed the problem by the Nyquist–Shannon sampling theorem, and argued that the layers in the generator learned to exploit the high-frequency signal in the pixels they operate upon. To solve this, they proposed imposing strict lowpass filters between each generator's layers, so that the generator is forced to operate on the pixels in a way faithful to the continuous signals they represent, rather than operate on them as merely discrete signals. They further imposed rotational and translational invariance by using more signal filters. The resulting StyleGAN-3 is able to generate images that rotate and translate smoothly, and without texture sticking.
Really Simple Licensing
Really Simple Licensing (RSL) is an open content licensing standard that allows web publishers to set terms for web crawlers gathering training data for generative AI use. It was launched on September 10, 2025 and is managed by the nonprofit RSL Collective, co-founded by RSS co-creator Eckart Walther and former Ask.com CEO Doug Leeds. Participating companies at launch include Reddit, Yahoo, and Medium. Publishers can implement the RSL standard by adding licensing terms to their robots.txt files.
Algorithmic accountability
Algorithmic accountability refers to the allocation of responsibility for the consequences of real-world actions influenced by algorithms used in decision-making processes. Ideally, algorithms should be designed to eliminate bias from their decision-making outcomes. This means they ought to evaluate only relevant characteristics of the input data, avoiding distinctions based on attributes that are generally inappropriate in social contexts, such as an individual's ethnicity in legal judgments. However, adherence to this principle is not always guaranteed, and there are instances where individuals may be adversely affected by algorithmic decisions. Responsibility for any harm resulting from a machine's decision may lie with the algorithm itself or with the individuals who designed it, particularly if the decision resulted from bias or flawed data analysis inherent in the algorithm's design. == Algorithm usage == Algorithms are widely utilized across various sectors of society that incorporate computational techniques in their control systems. These applications span numerous industries, including but not limited to medical, transportation, and payment services. In these contexts, algorithms perform functions such as: Approving or denying credit card applications; Approving or denying immigrant visas; Determining which taxpayers will be audited on their income taxes; Managing systems that control self-driving cars on a highway; Scoring individuals as potential criminals for use in legal proceedings; Search engines that match and rank database and internet search results; Recommendation systems that filter which news, entertainment, or purchase items are featured in a feed; Market-making algorithms that match sellers and buyers, such as in transportation (ride-hailing) or financial platforms. However, the implementation of these algorithms can be complex and opaque. Generally, algorithms function as "black boxes," meaning that the specific processes an input undergoes during execution are often not transparent, with users typically only seeing the resulting output. This lack of transparency raises concerns about potential biases within the algorithms, as the parameters influencing decision-making may not be well understood. The outputs generated can lead to perceptions of bias, especially if individuals in similar circumstances receive different results. According to Nicholas Diakopoulos: But these algorithms can make mistakes. They have biases. Yet they sit in opaque black boxes, their inner workings, their inner “thoughts” hidden behind layers of complexity. We need to get inside that black box, to understand how they may be exerting power on us, and to understand where they might be making unjust mistakes == Wisconsin Supreme Court case == Algorithms are prevalent across various fields and significantly influence decisions that affect the population at large. Their underlying structures and parameters often remain unknown to those impacted by their outcomes. A notable case illustrating this issue is a recent ruling by the Wisconsin Supreme Court concerning "risk assessment" algorithms used in criminal justice. The court determined that scores generated by such algorithms, which analyze multiple parameters from individuals, should not be used as a determining factor for arresting an accused individual. Furthermore, the court mandated that all reports submitted to judges must include information regarding the accuracy of the algorithm used to compute these scores. This ruling is regarded as a noteworthy development in how society should manage software that makes consequential decisions, highlighting the importance of reliability, particularly in complex settings like the legal system. The use of algorithms in these contexts necessitates a high degree of impartiality in processing input data. However, experts note that there is still considerable work to be done to ensure the accuracy of algorithmic results. Questions about the transparency of data processing continue to arise, which raises issues regarding the appropriateness of the algorithms and the intentions of their designers. == Controversies == A notable instance of potential algorithmic bias is highlighted in an article by The Washington Post regarding the ride-hailing service Uber. An analysis of collected data revealed that estimated waiting times for users varied based on the neighborhoods in which they resided. Key factors influencing these discrepancies included the predominant ethnicity and average income of the area. Specifically, neighborhoods with a majority white population and higher economic status tended to have shorter waiting times, while those with more diverse ethnic compositions and lower average incomes experienced longer waits. It’s important to clarify that this observation reflects a correlation identified in the data, rather than a definitive cause-and-effect relationship. No value judgments are made regarding the behavior of the Uber app in these cases. In TechCrunch website, Hemant Taneja wrote: Concern about “black box” algorithms that govern our lives has been spreading. New York University’s Information Law Institute hosted a conference on algorithmic accountability, noting: “Scholars, stakeholders, and policymakers question the adequacy of existing mechanisms governing algorithmic decision-making and grapple with new challenges presented by the rise of algorithmic power in terms of transparency, fairness, and equal treatment.” Yale Law School’s Information Society Project is studying this, too. “Algorithmic modeling may be biased or limited, and the uses of algorithms are still opaque in many critical sectors,” the group concluded. == Possible solutions == Discussions among experts have sought viable solutions to understand the operations of algorithms, often referred to as "black boxes." It is generally proposed that companies responsible for developing and implementing these algorithms should ensure their reliability by disclosing the internal processes of their systems. Hemant Taneja, writing for TechCrunch, emphasizes that major technology companies, such as Google, Amazon, and Uber, must actively incorporate algorithmic accountability into their operations. He suggests that these companies should transparently monitor their own systems to avoid stringent regulatory measures. One potential approach is the introduction of regulations in the tech sector to enforce oversight of algorithmic processes. However, such regulations could significantly impact software developers and the industry as a whole. It may be more beneficial for companies to voluntarily disclose the details of their algorithms and decision-making parameters, which could enhance the trustworthiness of their solutions. Another avenue discussed is the possibility of self-regulation by the companies that create these algorithms, allowing them to take proactive steps in ensuring accountability and transparency in their operations. In TechCrunch website, Hemant Taneja wrote: There’s another benefit — perhaps a huge one — to software-defined regulation. It will also show us a path to a more efficient government. The world’s legal logic and regulations can be coded into software and smart sensors can offer real-time monitoring of everything from air and water quality, traffic flows and queues at the DMV. Regulators define the rules, technologist create the software to implement them and then AI and ML help refine iterations of policies going forward. This should lead to much more efficient, effective governments at the local, national and global levels.
Fuzzy architectural spatial analysis
Fuzzy architectural spatial analysis (FASA) (also fuzzy inference system (FIS) based architectural space analysis or fuzzy spatial analysis) is a spatial analysis method of analysing the spatial formation and architectural space intensity within any architectural organization. Fuzzy architectural spatial analysis is used in architecture, interior design, urban planning and similar spatial design fields. == Overview == Fuzzy architectural spatial analysis was developed by Burcin Cem Arabacioglu (2010) from the architectural theories of space syntax and visibility graph analysis, and is applied with the help of a fuzzy system with a Mamdani inference system based on fuzzy logic within any architectural space. Fuzzy architectural spatial analysis model analyses the space by considering the perceivable architectural element by their boundary and stress characteristics and intensity properties. The method is capable of taking all sensorial factors into account during analyses in conformably with the perception process of architectural space which is a multi-sensorial act.
Solomonoff's theory of inductive inference
Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical (state-space model) character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction" (as it can be approximated from below more accurately with more computational resources). It is only "incomputable" in the benign sense that no scientific consensus is able to prove that the best current scientific theory is the best of all possible theories. However, Solomonoff's theory does provide an objective criterion for deciding among the current scientific theories explaining a given set of observations. Solomonoff's induction naturally formalizes Occam's razor by assigning larger prior credences to theories that require a shorter algorithmic description. == Origin == === Philosophical === The theory is based in philosophical foundations, and was founded by Ray Solomonoff around 1960. It is a mathematically formalized combination of Occam's razor and the Principle of Multiple Explanations. All computable theories which perfectly describe previous observations are used to calculate the probability of the next observation, with more weight put on the shorter computable theories. Marcus Hutter's universal artificial intelligence builds upon this to calculate the expected value of an action. === Principle === Solomonoff's induction has been argued to be the computational formalization of pure Bayesianism. To understand, recall that Bayesianism derives the posterior probability P [ T | D ] {\displaystyle \mathbb {P} [T|D]} of a theory T {\displaystyle T} given data D {\displaystyle D} by applying Bayes rule, which yields P [ T | D ] = P [ D | T ] P [ T ] P [ D | T ] P [ T ] + ∑ A ≠ T P [ D | A ] P [ A ] {\displaystyle \mathbb {P} [T|D]={\frac {\mathbb {P} [D|T]\mathbb {P} [T]}{\mathbb {P} [D|T]\mathbb {P} [T]+\sum _{A\neq T}\mathbb {P} [D|A]\mathbb {P} [A]}}} where theories A {\displaystyle A} are alternatives to theory T {\displaystyle T} . For this equation to make sense, the quantities P [ D | T ] {\displaystyle \mathbb {P} [D|T]} and P [ D | A ] {\displaystyle \mathbb {P} [D|A]} must be well-defined for all theories T {\displaystyle T} and A {\displaystyle A} . In other words, any theory must define a probability distribution over observable data D {\displaystyle D} . Solomonoff's induction essentially boils down to demanding that all such probability distributions be computable. Interestingly, the set of computable probability distributions is a subset of the set of all programs, which is countable. Similarly, the sets of observable data considered by Solomonoff were finite. Without loss of generality, we can thus consider that any observable data is a finite bit string. As a result, Solomonoff's induction can be defined by only invoking discrete probability distributions. Solomonoff's induction then allows to make probabilistic predictions of future data F {\displaystyle F} , by simply obeying the laws of probability. Namely, we have P [ F | D ] = E T [ P [ F | T , D ] ] = ∑ T P [ F | T , D ] P [ T | D ] {\displaystyle \mathbb {P} [F|D]=\mathbb {E} _{T}[\mathbb {P} [F|T,D]]=\sum _{T}\mathbb {P} [F|T,D]\mathbb {P} [T|D]} . This quantity can be interpreted as the average predictions P [ F | T , D ] {\displaystyle \mathbb {P} [F|T,D]} of all theories T {\displaystyle T} given past data D {\displaystyle D} , weighted by their posterior credences P [ T | D ] {\displaystyle \mathbb {P} [T|D]} . === Mathematical === The proof of the "razor" is based on the known mathematical properties of a probability distribution over a countable set. These properties are relevant because the infinite set of all programs is a denumerable set. The sum S of the probabilities of all programs must be exactly equal to one (as per the definition of probability) thus the probabilities must roughly decrease as we enumerate the infinite set of all programs, otherwise S will be strictly greater than one. To be more precise, for every ϵ {\displaystyle \epsilon } > 0, there is some length l such that the probability of all programs longer than l is at most ϵ {\displaystyle \epsilon } . This does not, however, preclude very long programs from having very high probability. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion. == Mathematical guarantees == === Solomonoff's completeness === The remarkable property of Solomonoff's induction is its completeness. In essence, the completeness theorem guarantees that the expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic) data generating process. The errors can be measured using the Kullback–Leibler divergence or the square of the difference between the induction's prediction and the probability assigned by the (stochastic) data generating process. === Solomonoff's uncomputability === Unfortunately, Solomonoff also proved that Solomonoff's induction is uncomputable. In fact, he showed that computability and completeness are mutually exclusive: any complete theory must be uncomputable. The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem. == Modern applications == === Artificial intelligence === Though Solomonoff's inductive inference is not computable, several AIXI-derived algorithms approximate it in order to make it run on a modern computer. The more computing power they are given, the closer their predictions are to the predictions of inductive inference (their mathematical limit is Solomonoff's inductive inference). Another direction of inductive inference is based on E. Mark Gold's model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class S of computable functions, is there a learner (that is, recursive functional) which for any input of the form (f(0),f(1),...,f(n)) outputs a hypothesis (an index e with respect to a previously agreed on acceptable numbering of all computable functions; the indexed function may be required consistent with the given values of f). A learner M learns a function f if almost all its hypotheses are the same index e, which generates the function f; M learns S if M learns every f in S. Basic results are that all recursively enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of recursively enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards. A far reaching extension of the Gold’s approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.
Xaitment
xaitment is a German-based company that develops and sells artificial intelligence (AI) software to video game developers and simulation developers. The company was founded in 2004 by Dr. Andreas Gerber, and is a spin-off of the German Research Centre for Artificial Intelligence, or DFKI. xaitment has its main office in Quierschied, Germany, and field offices in San Francisco and China. == Products == xaitment currently sells two AI software modules: xaitMap and xaitControl. xaitMap provides runtime libraries and graphical tools for navigation mesh generation (also called NavMesh generation), pathfinding, dynamic collision avoidance, and individual and crowd movement. xaitControl is a finite-state machine for game logic and character behavior modeling that also includes a real-time debugger. On January 11, 2012, xaitment announced that it making its source code for these modules available to "all current and future US and European licensees". On February 22, 2012 xaitment released two new plug-ins, xaitMap and xaitControl for the Unity Game Engine. The full versions are available for PC (Windows and Linux), PlayStation 3, Xbox 360 and Wii. The pathfinding plug-in is available with a Windows dev environment, but can deployed on iOS, Mac, Android and the Unity Web Player. == Partners == xaitment's AI software is currently integrated into the Unity game engine, Havok's Vision Engine, Bohemia Interactive's VBS2 Simulation Engine, GameBase's Gamebryo game engine. == Customers == xaitment sells its AI software products to video game developers and military and civil simulation developers. Current customers include Tencent, gamania, TML Studios, Emobi Games, IP Keys and others. A full list of customers can be found on xaitment's website.