Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory and algorithmic inductive inference. Algorithmic learning theory is different from statistical learning theory in that it does not make use of statistical assumptions and analysis. Both algorithmic and statistical learning theory are concerned with machine learning and can thus be viewed as branches of computational learning theory. == Distinguishing characteristics == Unlike statistical learning theory and most statistical theory in general, algorithmic learning theory does not assume that data are random samples, that is, that data points are independent of each other. This makes the theory suitable for domains where observations are (relatively) noise-free but not random, such as language learning and automated scientific discovery. The fundamental concept of algorithmic learning theory is learning in the limit: as the number of data points increases, a learning algorithm should converge to a correct hypothesis on every possible data sequence consistent with the problem space. This is a non-probabilistic version of statistical consistency, which also requires convergence to a correct model in the limit, but allows a learner to fail on data sequences with probability measure 0 . Algorithmic learning theory investigates the learning power of Turing machines. Other frameworks consider a much more restricted class of learning algorithms than Turing machines, for example, learners that compute hypotheses more quickly, for instance in polynomial time. An example of such a framework is probably approximately correct learning . == Learning in the limit == The concept was introduced in E. Mark Gold's seminal paper "Language identification in the limit". The objective of language identification is for a machine running one program to be capable of developing another program by which any given sentence can be tested to determine whether it is "grammatical" or "ungrammatical". The language being learned need not be English or any other natural language - in fact the definition of "grammatical" can be absolutely anything known to the tester. In Gold's learning model, the tester gives the learner an example sentence at each step, and the learner responds with a hypothesis, which is a suggested program to determine grammatical correctness. It is required of the tester that every possible sentence (grammatical or not) appears in the list eventually, but no particular order is required. It is required of the learner that at each step the hypothesis must be correct for all the sentences so far. A particular learner is said to be able to "learn a language in the limit" if there is a certain number of steps beyond which its hypothesis no longer changes. At this point it has indeed learned the language, because every possible sentence appears somewhere in the sequence of inputs (past or future), and the hypothesis is correct for all inputs (past or future), so the hypothesis is correct for every sentence. The learner is not required to be able to tell when it has reached a correct hypothesis, all that is required is that it be true. Gold showed that any language which is defined by a Turing machine program can be learned in the limit by another Turing-complete machine using enumeration. This is done by the learner testing all possible Turing machine programs in turn until one is found which is correct so far - this forms the hypothesis for the current step. Eventually, the correct program will be reached, after which the hypothesis will never change again (but note that the learner does not know that it won't need to change). Gold also showed that if the learner is given only positive examples (that is, only grammatical sentences appear in the input, not ungrammatical sentences), then the language can only be guaranteed to be learned in the limit if there are only a finite number of possible sentences in the language (this is possible if, for example, sentences are known to be of limited length). Language identification in the limit is a highly abstract model. It does not allow for limits of runtime or computer memory which can occur in practice, and the enumeration method may fail if there are errors in the input. However the framework is very powerful, because if these strict conditions are maintained, it allows the learning of any program known to be computable. This is because a Turing machine program can be written to mimic any program in any conventional programming language. See Church-Turing thesis. == Other identification criteria == Learning theorists have investigated other learning criteria, such as the following. Efficiency: minimizing the number of data points required before convergence to a correct hypothesis. Mind Changes: minimizing the number of hypothesis changes that occur before convergence. Mind change bounds are closely related to mistake bounds that are studied in statistical learning theory. Kevin Kelly has suggested that minimizing mind changes is closely related to choosing maximally simple hypotheses in the sense of Occam’s Razor. == Annual conference == Since 1990, there is an International Conference on Algorithmic Learning Theory (ALT), called Workshop in its first years (1990–1997). Between 1992 and 2016, proceedings were published in the LNCS series. Starting from 2017, they are published by the Proceedings of Machine Learning Research. The 34th conference will be held in Singapore in Feb 2023. The topics of the conference cover all of theoretical machine learning, including statistical and computational learning theory, online learning, active learning, reinforcement learning, and deep learning.
Differentiable imaging
Differentiable imaging is a method within computational imaging that incorporates differentiable programming to design imaging systems. It treats the entire imaging process - from light passing through optical components to the numerical reconstruction—as a differentiable programming problem. This approach links optical hardware with numerical reconstruction, enabling joint optimization of both parts through differentiable programming. Differentiable imaging additionally extends the scope of computational imaging beyond image reconstruction, such as by aiding in characterization of optical components. == Background == Computational imaging combines optical hardware and computational algorithms to capture and reconstruct information that conventional imaging system cannot. This is achieved from a combination of the imaging system and the software used in the image reconstruction. Since the captured information may not directly show the image of the target, these systems often rely on numerical models that describe how light encodes the target. In practice, such models may deviate from the physical systems due to uncertainties such as noise, misalignments, manufacturing imperfections, environmental variations, etc. These uncertainties can cause a mismatch between the physical system and its numerical model, which may degrade reconstruction quality and limit the effectiveness of the hardware–software co-design. Uncertainty quantification is also studied in other hybrid physical–numerical systems, such as digital twin. While numerical modeling imaging systems date back to the several decades, such as the multislice method in electron microscopy or X-Ray nanotomography, differentiable imaging emphasizes jointly modeling uncertainties and solving inverse problems with image reconstruction simultaneously. Differentiable imaging transforms the traditional encoding model y = f ( x ) {\textstyle y=f(x)} into a more comprehensive formulation y = f ( x , θ ) {\textstyle y=f(x,\theta )} , where θ {\displaystyle \theta } represents a parameter set of mismatches between physical systems and numerical models. The forward model captures the entire imaging pipeline through a series of interconnected component functions: y = f ( x , θ ) , f = f n o i s e ∘ f c ∘ f o c ∘ f x ∘ f o i ∘ f i , {\displaystyle y=f(x,\theta ),\qquad f=f_{noise}\circ f_{c}\circ f_{oc}\circ f_{x}\circ f_{oi}\circ f_{i},} where the function composition operator ∘ {\displaystyle \circ } connects each system component, and θ = { θ c , θ o c , … } {\displaystyle \theta =\{\theta _{c},\theta _{oc},\ldots \}} encompasses uncertainty system parameters. Each component corresponds to specific physical processes within the imaging system, from illumination through object interactions to sensor behavior and noises. This forward model enables the formulation of an inverse problem that simultaneously optimizes system parameters while reconstructing images: x ∗ , θ ∗ = argmin x , θ L ( f ( x , θ ) , y ) + ∑ n = 1 N β n R n ( x ) {\displaystyle x^{},\theta ^{}={\text{argmin}}_{x,\theta }{\mathcal {L}}(f(x,\theta ),y)+\sum _{n=1}^{N}\beta _{n}{\mathcal {R}}_{n}(x)} s . t . x ∈ Ω x , θ ∈ Ω θ {\displaystyle s.t.\quad x\in \Omega _{x},\theta \in \Omega _{\theta }} Here, L ( f ( x , θ ) , y ) {\displaystyle {\mathcal {L}}(f(x,\theta ),y)} represents the fidelity term that quantifies the discrepancy between the model predictions and measured data. The whole process of the y = f ( x , θ ) {\displaystyle y=f(x,\theta )} is constructed as a computer graph based on differentiable programming, and the inverse problem is solved with gradient based algorithm, while the gradient is calculated with automatic differentiation. == Applications == One application of differentiable imaging is uncertainty management, which seeks to quantify and mitigate the impact of factors induce reality-numerical mismatch. Explicitly accounting for uncertainties can improve reconstruction accuracy and system robustness. Examples include: Model-related uncertainties: unknown or unmeasurable variables—for instance, optical system quantities that differ from the design specifications Data and system uncertainties: artifacts introduced during image acquisition, such as low-quality data, noise, or hardware imperfections Manufacturing uncertainties: variability in the production of imaging hardware—such as slight deviations in lens curvature or sensor alignment—that alters the physical system's behavior
How to Choose an AI Blog Writer
Curious about the best AI blog writer? An AI blog writer 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 blog writer 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.
Victor Yngve
Victor Huse Yngve (July 5, 1920 – January 15, 2012) was a professor of linguistics at the University of Chicago and the Massachusetts Institute of Technology (1953-1965). He was one of the earliest researchers in computational linguistics and natural language processing, the use of computers to analyze and process languages. He created the first program to produce random but well-formed output sentences, given a text, a children's book called Engineer Small and the Little Train. Most importantly, he showed in computer processing terms why the human brain can only process sentences of a certain kind of complexity, ones that do not exceed a "depth limit" (which has nothing to do with length) of the kind established independently by George Miller with his depth limit of "seven plus or minus two" sentence constituents in memory at any given time. Yngve was also the author of COMIT, the first string processing language (compare SNOBOL, TRAC, and Perl), which was developed on the IBM 700/7000 series computers by Yngve and collaborators at MIT from 1957-1965. Yngve created the language for supporting computerized research in the field of linguistics, and more specifically, the area of machine translation for natural language processing. In his 1970 paper "On Getting a Word in Edgewise", Yngve coined the term 'back channel behavior' to describe the conversational phenomenon that to this day is known in the linguistic literature as back-channeling. According to Duncan, Yngve's paper also suggested the term turn-taking, independently of Erving Goffman (Duncan, 1972: 283).
Ben Goertzel
Ben Goertzel is a computer scientist, artificial intelligence (AI) researcher, and businessman. He helped popularize the term artificial general intelligence (AGI). == Early life and education == Three of Goertzel's Jewish great-grandparents immigrated to New York from Lithuania and Poland (in the Russian Empire). Goertzel's father is Ted Goertzel, a former professor of sociology at Rutgers University. Goertzel left high school after the tenth grade to attend Bard College at Simon's Rock, where he graduated with a bachelor's degree in Quantitative Studies. Goertzel graduated with a PhD in mathematics from Temple University under the supervision of Avi Lin in 1990, at age 23. == Career == Goertzel is the founder and CEO of SingularityNET, a project which was founded to distribute artificial intelligence data via blockchains. He is a leading developer of the OpenCog framework for artificial general intelligence. Goertzel was an associate and grant recipient of Jeffrey Epstein. He received a $100,000 grant from the Jeffrey Epstein Foundation for artificial general intelligence research in 2001. When interviewed by The New York Times about Epstein in 2019, Goertzel said, "I have no desire to talk about Epstein right now... The stuff I'm reading about him in the papers is pretty disturbing and goes way beyond what I thought his misdoings and kinks were. Yecch." === Sophia the Robot === Goertzel was the Chief Scientist of Hanson Robotics, the company that created the Sophia robot. As of 2018, Sophia's architecture includes scripting software, a chat system, and OpenCog, an AI system designed for general reasoning. Experts in the field have treated the project mostly as a PR stunt, stating that Hanson's claims that Sophia was "basically alive" are "grossly misleading" because the project does not involve AI technology, while computer scientist Yann LeCun, then Meta's chief AI scientist, made several unflattering remarks including calling the project "complete bullshit". === Views on AI === In May 2007, Goertzel spoke at a Google tech talk about his approach to creating artificial general intelligence. He defines intelligence as the ability to detect patterns in the world and in the agent itself, measurable in terms of emergent behavior of "achieving complex goals in complex environments". A "baby-like" artificial intelligence is initialized, then trained as an agent in a simulated or virtual world such as Second Life to produce a more powerful intelligence. Knowledge is represented in a network whose nodes and links carry probabilistic truth values as well as "attention values", with the attention values resembling the weights in a neural network. Several algorithms operate on this network, the central one being a combination of a probabilistic inference engine and a custom version of evolutionary programming. The 2012 documentary The Singularity by independent filmmaker Doug Wolens discussed Goertzel's views on AGI. In 2023 Goertzel postulated that artificial intelligence could replace up to 80 percent of human jobs in the coming years "without having an AGI, by my guess. Not with ChatGPT exactly as a product. But with systems of that nature". At the Web Summit 2023 in Rio de Janeiro, Goertzel spoke out against efforts to curb AI research and that AGI is only a few years away. Goertzel's belief is that AGI will be a net positive for humanity by assisting with societal problems such as, but not limited to, climate change.
Structured-light 3D scanner
A structured-light 3D scanner is a device used to capture the three-dimensional shape of an object by projecting light patterns, such as grids or stripes, onto its surface. The deformation of these patterns is recorded by cameras and processed using specialized algorithms to generate a detailed 3D model. Structured-light 3D scanning is widely employed in fields such as industrial design, quality control, cultural heritage preservation, augmented reality gaming, and medical imaging. Compared to laser-based 3D scanning, structured-light scanners use non-coherent light sources, such as LEDs or projectors, which enable faster data acquisition and eliminate potential safety concerns associated with lasers. However, the accuracy of structured-light scanning can be influenced by external factors, including ambient lighting conditions and the reflective properties of the scanned object. == Principle == Projecting a narrow band of light onto a three-dimensional surface creates a line of illumination that appears distorted when viewed from perspectives other than that of the projector. This distortion can be analyzed to reconstruct the geometry of the surface, a technique known as light sectioning. Projecting patterns composed of multiple stripes or arbitrary fringes simultaneously enables the acquisition of numerous data points at once, improving scanning speed. While various structured light projection techniques exist, parallel stripe patterns are among the most commonly used. By analyzing the displacement of these stripes, the three-dimensional coordinates of surface details can be accurately determined. === Generation of light patterns === Two major methods of stripe pattern generation have been established: Laser interference and projection. The laser interference method works with two wide planar laser beam fronts. Their interference results in regular, equidistant line patterns. Different pattern sizes can be obtained by changing the angle between these beams. The method allows for the exact and easy generation of very fine patterns with unlimited depth of field. Disadvantages are high cost of implementation, difficulties providing the ideal beam geometry, and laser typical effects like speckle noise and the possible self interference with beam parts reflected from objects. Typically, there is no means of modulating individual stripes, such as with Gray codes. The projection method uses incoherent light and basically works like a video projector. Patterns are usually generated by passing light through a digital spatial light modulator, typically based on one of the three currently most widespread digital projection technologies, transmissive liquid crystal, reflective liquid crystal on silicon (LCOS) or digital light processing (DLP; moving micro mirror) modulators, which have various comparative advantages and disadvantages for this application. Other methods of projection could be and have been used, however. Patterns generated by digital display projectors have small discontinuities due to the pixel boundaries in the displays. Sufficiently small boundaries however can practically be neglected as they are evened out by the slightest defocus. A typical measuring assembly consists of one projector and at least one camera. For many applications, two cameras on opposite sides of the projector have been established as useful. Invisible (or imperceptible) structured light uses structured light without interfering with other computer vision tasks for which the projected pattern will be confusing. Example methods include the use of infrared light or of extremely high framerates alternating between two exact opposite patterns. === Calibration === Geometric distortions by optics and perspective must be compensated by a calibration of the measuring equipment, using special calibration patterns and surfaces. A mathematical model is used for describing the imaging properties of projector and cameras. Essentially based on the simple geometric properties of a pinhole camera, the model also has to take into account the geometric distortions and optical aberration of projector and camera lenses. The parameters of the camera as well as its orientation in space can be determined by a series of calibration measurements, using photogrammetric bundle adjustment. === Analysis of stripe patterns === There are several depth cues contained in the observed stripe patterns. The displacement of any single stripe can directly be converted into 3D coordinates. For this purpose, the individual stripe has to be identified, which can for example be accomplished by tracing or counting stripes (pattern recognition method). Another common method projects alternating stripe patterns, resulting in binary Gray code sequences identifying the number of each individual stripe hitting the object. An important depth cue also results from the varying stripe widths along the object surface. Stripe width is a function of the steepness of a surface part, i.e. the first derivative of the elevation. Stripe frequency and phase deliver similar cues and can be analyzed by a Fourier transform. Finally, the wavelet transform has recently been discussed for the same purpose. In many practical implementations, series of measurements combining pattern recognition, Gray codes and Fourier transform are obtained for a complete and unambiguous reconstruction of shapes. Another method also belonging to the area of fringe projection has been demonstrated, utilizing the depth of field of the camera. It is also possible to use projected patterns primarily as a means of structure insertion into scenes, for an essentially photogrammetric acquisition. === Precision and range === The optical resolution of fringe projection methods depends on the width of the stripes used and their optical quality. It is also limited by the wavelength of light. An extreme reduction of stripe width proves inefficient due to limitations in depth of field, camera resolution and display resolution. Therefore, the phase shift method has been widely established: A number of at least 3, typically about 10 exposures are taken with slightly shifted stripes. The first theoretical deductions of this method relied on stripes with a sine wave shaped intensity modulation, but the methods work with "rectangular" modulated stripes, as delivered from LCD or DLP displays as well. By phase shifting, surface detail of e.g. 1/10 the stripe pitch can be resolved. Current optical stripe pattern profilometry hence allows for detail resolutions down to the wavelength of light, below 1 micrometer in practice or, with larger stripe patterns, to approx. 1/10 of the stripe width. Concerning level accuracy, interpolating over several pixels of the acquired camera image can yield a reliable height resolution and also accuracy, down to 1/50 pixel. Arbitrarily large objects can be measured with accordingly large stripe patterns and setups. Practical applications are documented involving objects several meters in size. Typical accuracy figures are: Planarity of a 2-foot (0.61 m) wide surface, to 10 micrometres (0.00039 in). Shape of a motor combustion chamber to 2 micrometres (7.9×10−5 in) (elevation), yielding a volume accuracy 10 times better than with volumetric dosing. Shape of an object 2 inches (51 mm) large, to about 1 micrometre (3.9×10−5 in) Radius of a blade edge of e.g. 10 micrometres (0.00039 in), to ±0.4 μm === Navigation === As the method can measure shapes from only one perspective at a time, complete 3D shapes have to be combined from different measurements in different angles. This can be accomplished by attaching marker points to the object and combining perspectives afterwards by matching these markers. The process can be automated, by mounting the object on a motorized turntable on robotic inspection cell, or CNC positioning device. Markers can as well be applied on a positioning device instead of the object itself. The 3D data gathered can be used to retrieve CAD (computer aided design) data and models from existing components (reverse engineering), hand formed samples or sculptures, natural objects or artifacts. === Challenges === As with all optical methods, reflective or transparent surfaces raise difficulties. Reflections cause light to be reflected either away from the camera or right into its optics. In both cases, the dynamic range of the camera can be exceeded. Transparent or semi-transparent surfaces also cause major difficulties. In these cases, coating the surfaces with a thin opaque lacquer just for measuring purposes is a common practice. A recent method handles highly reflective and specular objects by inserting a 1-dimensional diffuser between the light source (e.g., projector) and the object to be scanned. Alternative optical techniques have been proposed for handling perfectly transparent and specular objects. Double reflections and inter-reflections can cause the stripe pattern to be overlaid with unwanted ligh
Corinna Cortes
Corinna Cortes (born 31 March 1961) is a Danish computer scientist known for her contributions to machine learning. She is a Vice President at Google Research in New York City. Cortes is an ACM Fellow and a recipient of the Paris Kanellakis Award for her work on theoretical foundations of support vector machines. == Early life and education == Corinna Cortes was born in 1961 in Denmark. Cortes received her Master of Science degree in physics from University of Copenhagen in 1989. She received her PhD in computer science from the University of Rochester in 1993 for research supervised by Randal C. Nelson. == Career and research == Cortes joined AT&T Bell Labs as a researcher in 1993. Since 2003, she has served as Vice President of Google Research, New York City, and since 2011, as adjunct professor at the UCPH Department of Computer Science. She is serves as an editorial board member of the journal Machine Learning. Cortes' research covers a wide range of topics in machine learning, including support vector machines (SVM) and data mining. SVM is one of the most frequently used algorithms in machine learning, which is used in many practical applications, including medical diagnosis and weather forecasting. At AT&T, Cortes was a contributor to the design of Hancock programming language. === Awards and honours === In 2008, she jointly with Vladimir Vapnik received the Paris Kanellakis Award for the development of a highly effective algorithm for supervised learning known as support vector machines (SVM). She was named an ACM Fellow in 2023 for theoretical and practical contributions to machine learning, industrial leadership and service to the field. == Personal life == Corinna has two children and is also a competitive runner.