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  • Meta-learning (computer science)

    Meta-learning (computer science)

    Meta-learning is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017, the term had not found a standard interpretation, however the main goal is to use such metadata to understand how automatic learning can become flexible in solving learning problems, hence to improve the performance of existing learning algorithms or to learn (induce) the learning algorithm itself, hence the alternative term learning to learn. Flexibility is important because each learning algorithm is based on a set of assumptions about the data, its inductive bias. This means that it will only learn well if the bias matches the learning problem. A learning algorithm may perform very well in one domain, but not on the next. This poses strong restrictions on the use of machine learning or data mining techniques, since the relationship between the learning problem (often some kind of database) and the effectiveness of different learning algorithms is not yet understood. By using different kinds of metadata, like properties of the learning problem, algorithm properties (like performance measures), or patterns previously derived from the data, it is possible to learn, select, alter or combine different learning algorithms to effectively solve a given learning problem. Critiques of meta-learning approaches bear a strong resemblance to the critique of metaheuristic, a possibly related problem. A good analogy to meta-learning, and the inspiration for Jürgen Schmidhuber's early work (1987) and Yoshua Bengio et al.'s work (1991), considers that genetic evolution learns the learning procedure encoded in genes and executed in each individual's brain. In an open-ended hierarchical meta-learning system using genetic programming, better evolutionary methods can be learned by meta evolution, which itself can be improved by meta meta evolution, etc. == Definition == A proposed definition for a meta-learning system combines three requirements: The system must include a learning subsystem. Experience is gained by exploiting meta knowledge extracted in a previous learning episode on a single dataset, or from different domains. Learning bias must be chosen dynamically. Bias refers to the assumptions that influence the choice of explanatory hypotheses and not the notion of bias represented in the bias-variance dilemma. Meta-learning is concerned with two aspects of learning bias. Declarative bias specifies the representation of the space of hypotheses, and affects the size of the search space (e.g., represent hypotheses using linear functions only). Procedural bias imposes constraints on the ordering of the inductive hypotheses (e.g., preferring smaller hypotheses). == Common approaches == There are three common approaches: using (cyclic) networks with external or internal memory (model-based) learning effective distance metrics (metrics-based) explicitly optimizing model parameters for fast learning (optimization-based). === Model-Based === Model-based meta-learning models updates its parameters rapidly with a few training steps, which can be achieved by its internal architecture or controlled by another meta-learner model. ==== Memory-Augmented Neural Networks ==== A Memory-Augmented Neural Network, or MANN for short, is claimed to be able to encode new information quickly and thus to adapt to new tasks after only a few examples. ==== Meta Networks ==== Meta Networks (MetaNet) learns a meta-level knowledge across tasks and shifts its inductive biases via fast parameterization for rapid generalization. === Metric-Based === The core idea in metric-based meta-learning is similar to nearest neighbors algorithms, which weight is generated by a kernel function. It aims to learn a metric or distance function over objects. The notion of a good metric is problem-dependent. It should represent the relationship between inputs in the task space and facilitate problem solving. ==== Convolutional Siamese Neural Network ==== Siamese neural network is composed of two twin networks whose output is jointly trained. There is a function above to learn the relationship between input data sample pairs. The two networks are the same, sharing the same weight and network parameters. ==== Matching Networks ==== Matching Networks learn a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. ==== Relation Network ==== The Relation Network (RN), is trained end-to-end from scratch. During meta-learning, it learns to learn a deep distance metric to compare a small number of images within episodes, each of which is designed to simulate the few-shot setting. ==== Prototypical Networks ==== Prototypical Networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class. Compared to recent approaches for few-shot learning, they reflect a simpler inductive bias that is beneficial in this limited-data regime, and achieve satisfied results. === Optimization-Based === What optimization-based meta-learning algorithms intend for is to adjust the optimization algorithm so that the model can be good at learning with a few examples. ==== LSTM Meta-Learner ==== LSTM-based meta-learner is to learn the exact optimization algorithm used to train another learner neural network classifier in the few-shot regime. The parametrization allows it to learn appropriate parameter updates specifically for the scenario where a set amount of updates will be made, while also learning a general initialization of the learner (classifier) network that allows for quick convergence of training. ==== Temporal Discreteness ==== Model-Agnostic Meta-Learning (MAML) is a fairly general optimization algorithm, compatible with any model that learns through gradient descent. ==== Reptile ==== Reptile is a remarkably simple meta-learning optimization algorithm, given that both of its components rely on meta-optimization through gradient descent and both are model-agnostic. == Examples == Some approaches which have been viewed as instances of meta-learning: Recurrent neural networks (RNNs) are universal computers. In 1993, Jürgen Schmidhuber showed how "self-referential" RNNs can in principle learn by backpropagation to run their own weight change algorithm, which may be quite different from backpropagation. In 2001, Sepp Hochreiter & A.S. Younger & P.R. Conwell built a successful supervised meta-learner based on Long short-term memory RNNs. It learned through backpropagation a learning algorithm for quadratic functions that is much faster than backpropagation. Researchers at Deepmind (Marcin Andrychowicz et al.) extended this approach to optimization in 2017. In the 1990s, Meta Reinforcement Learning or Meta RL was achieved in Schmidhuber's research group through self-modifying policies written in a universal programming language that contains special instructions for changing the policy itself. There is a single lifelong trial. The goal of the RL agent is to maximize reward. It learns to accelerate reward intake by continually improving its own learning algorithm which is part of the "self-referential" policy. An extreme type of Meta Reinforcement Learning is embodied by the Gödel machine, a theoretical construct which can inspect and modify any part of its own software which also contains a general theorem prover. It can achieve recursive self-improvement in a provably optimal way. Model-Agnostic Meta-Learning (MAML) was introduced in 2017 by Chelsea Finn et al. Given a sequence of tasks, the parameters of a given model are trained such that few iterations of gradient descent with few training data from a new task will lead to good generalization performance on that task. MAML "trains the model to be easy to fine-tune." MAML was successfully applied to few-shot image classification benchmarks and to policy-gradient-based reinforcement learning. Variational Bayes-Adaptive Deep RL (VariBAD) was introduced in 2019. While MAML is optimization-based, VariBAD is a model-based method for meta reinforcement learning, and leverages a variational autoencoder to capture the task information in an internal memory, thus conditioning its decision making on the task. When addressing a set of tasks, most meta learning approaches optimize the average score across all tasks. Hence, certain tasks may be sacrificed in favor of the average score, which is often unacceptable in real-world applications. By contrast, Robust Meta Reinforcement Learning (RoML) focuses on improving low-score tasks, increasing robustness to the selection of task. RoML works as a meta-algorithm, as it can be applied on top of other meta learning algorithms (such as MAML and VariBAD) to increase their robustness. It is applicable to both supervised meta learning and meta reinforcement learning. Discovering meta-knowledge works by inducing knowledge

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  • Apache cTAKES

    Apache cTAKES

    Apache cTAKES: clinical Text Analysis and Knowledge Extraction System is an open-source Natural Language Processing (NLP) system that extracts clinical information from electronic health record unstructured text. It processes clinical notes, identifying types of clinical named entities — drugs, diseases/disorders, signs/symptoms, anatomical sites and procedures. Each named entity has attributes for the text span, the ontology mapping code, context (family history of, current, unrelated to patient), and negated/not negated. cTAKES was built using the UIMA Unstructured Information Management Architecture framework and OpenNLP natural language processing toolkit. == Components == Components of cTAKES are specifically trained for the clinical domain, and create rich linguistic and semantic annotations that can be utilized by clinical decision support systems and clinical research. These components include: Named Section identifier Sentence boundary detector Rule-based tokenizer Formatted list identifier Normalizer Context dependent tokenizer Part-of-speech tagger Phrasal chunker Dictionary lookup annotator Context annotator Negation detector Uncertainty detector Subject detector Dependency parser patient smoking status identifier Drug mention annotator == History == Development of cTAKES began at the Mayo Clinic in 2006. The development team, led by Dr. Guergana Savova and Dr. Christopher Chute, included physicians, computer scientists and software engineers. After its deployment, cTAKES became an integral part of Mayo's clinical data management infrastructure, processing more than 80 million clinical notes. When Dr. Savova's moved to Boston Children's Hospital in early 2010, the core development team grew to include members there. Further external collaborations include: University of Colorado Brandeis University University of Pittsburgh University of California at San Diego Such collaborations have extended cTAKES' capabilities into other areas such as Temporal Reasoning, Clinical Question Answering, and coreference resolution for the clinical domain. In 2010, cTAKES was adopted by the i2b2 program and is a central component of the SHARP Area 4. In 2013, cTAKES released their first release as an Apache Software Foundation incubator project: cTAKES 3.0. In March 2013, cTAKES became an Apache Software Foundation Top Level Project (TLP).

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  • Ancient text corpora

    Ancient text corpora

    Ancient text corpora are the entire collection of texts from the period of ancient history, defined in this article as the period from the beginning of writing up to 300 AD. These corpora are important for the study of literature, history, linguistics, and other fields, and are a fundamental component of the world's cultural heritage. Chinese, Latin, and Greek are examples of ancient languages with significant text corpora, although much of these corpora are known to us via transmission (frequently via medieval manuscript copies) rather than in their original form. These texts – both transmitted and original – provide valuable insights into the history and culture of different regions of the world, and have been studied for centuries by scholars and researchers. Other ancient texts – particularly stone inscriptions and papyrus scrolls – have been published following archaeological research, notably the cuneiform corpus of c.10 million words and the c.5 million words in ancient Egyptian. Through advances in technology and digitization, ancient text corpora are more accessible than ever before. Tools such as the Perseus Digital Library and the Digital Corpus of Sanskrit have made it easier for researchers to access and analyze these texts. == Quantifying the corpora == Two types of ancient texts are known to modern scholars – those that have only survived in younger manuscripts, but whose great age is undisputed (this applies to the bulk of the Chinese, Brahmi, Greek, Latin, Hebrew and Avestan tradition), and those known from original inscriptions, papyri and other manuscripts. Counting of the words in each corpus presents significant methodological challenges – in principle, every single occurrence of a word in the text is counted separately, but in the case of parallel transmission of literary texts, only a single transmission is taken into account. Just as the Book of the Dead and the coffin texts are only included once in the number given for the Egyptian, the Greek and Latin literary works should only be counted according to one manuscript. If, on the other hand, tombs, royal inscriptions or economic documents of certain ancient languages often show a more or less identical form, this is not evaluated as a purely "parallel tradition". Attached prepositions are counted as separate words, except in the case of the definite article in Hebrew, Aramaic and Greek since it has no equivalent in most languages, so its frequency would significantly affect the comparability of numbers. === Languages with known size estimates === === South Asian === Sanskrit (Vedic Sanskrit and Classical Sanskrit) Indus script (3,800 items, c.20,000 characters) Brahmi script Old Tamil Early Indian epigraphy and Indian epic poetry Kharosthi Pali literature List of historic Indian texts === Mesoamerican === Olmec hieroglyphs Maya script === East Asian === Old Chinese Chinese classics The pre-Qin corpus: a collection of ancient Chinese texts written before the Qin dynasty (221 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. The pre-Han corpus: a collection of ancient Chinese texts written before the Han dynasty (202 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. See the Chinese Text Project Chinese bronze inscriptions, Oracle bone script, Seal script, Clerical script === Central Iranian languages === Prior to 300 AD, the Central Iranian languages are mainly in the form of Sassanid stone inscriptions in the two closely related idioms Middle Persian (Pahlavi scripts and Inscriptional Parthian), there are 5000 for the corpus of Middle Persian (mostly 3rd, but also 4th/5th centuries) and for the corpus of Parthian (3rd century) 3000 words. To what extent some of the Manichaean Middle Persian literary texts may date back to the 3rd century is difficult to estimate; Mani is said to have personally written the Shabuhragan totaling about 5000 words. In any case, if we combine Middle Persian and Parthian, we come to over 10,000 words. === Proto-Sinaitic === Proto-Sinaitic script has no more than about 400 letters (number of words is unknown since the script has not been fully interpreted). To a similar extent, there are probably approximately contemporaneous Proto-Canaanite inscriptions (ibid.). === Anatolian === Luwian cuneiform, approx. 3000 words the Palaic language few hundred words. Hieroglyphic Luwian the Lycian alphabet (the best attested Anatolian successor language written in alphabetic script) with about 5000 words The Lydian alphabet 109 inscriptions comprising about 1500 words The Phrygian alphabet the in-tomb inscriptions from the 2nd and 3rd centuries AD (approx. 1000 words) and in the so-called "old Phrygian" inscriptions less than 300 words The Carian alphabets whose texts, mainly from Egypt, contain around 600 words. === Old Italic === the Umbrian language attested essentially by the sacrificial instructions of the Iguvinian Tables with 5000 words the Oscan language (ibid.) with 2000 words the Messapic language with probably a good 1000 words (the estimate is difficult because most texts in this hardly understandable language do not use word separators) the Venetic language a few hundred words the Faliscan language a few hundred words Cisalpine Celtic inscriptions amount to approximately 2000 words, to which are added a number of glosses by classical authors === Iberia === Iberian scripts, more rarely written in Greek or Latin script, approx. 2500 words Celtiberian script, which refers to Celtic language testimonies in Iberian, but also in Latin script from Spain (approx. 1000 words) Southwest Paleohispanic script, 78 inscriptions, a few hundred words Lusitanian language, three monuments in Latin script, approx. 60 words === Germanic Northern Europe === Runic inscriptions dated before the 4th century amount to about 30 pieces, which contain no more than 50 words in total === Africa === Geʽez script: comparatively few inscriptions with a total of around 1,000 words before 300 AD. Following Christianization in the 4th century, more extensive texts are known. Libyco-Berber alphabet: over 1,000 inscriptions from the Maghreb, which are dated to Roman times. Most texts do not use a word separator; Peust estimates that the total number of words could be around 5,000 Meroitic script (Ancient Nubian): about 900 texts are known, which Peust estimates may contain approximately 10,000 words, albeit with uncertainty from the fact that the word separator is not used consistently in the Meroitic script. === Aegean === The Cretan Linear A inscriptions that have not yet been deciphered are available in about 2500 texts, which contain a total of around 20,000 characters. The total number of words can hardly be determined; Peust tentatively put it in the same order of magnitude as in Meroitic. In addition to the Linear A texts, there are also inscriptions Cretan hieroglyphs of a few hundred characters and texts written in the Greek alphabet, but not in Greek, with a few dozen words Cypriot syllabary in the first millennium BC, in which mostly Greek texts were recorded. The relevant texts comprise around 100 to 200 words. === Micro corpora === There are a significant number of ancient micro-corpus languages. Estimating the total number of attested ancient languages may be as difficult as estimating their corpus size. For example, Greek and Latin sources hand down an enormous amount of foreign-language glosses, the seriousness of which is not always certain. == Preservation and curation == Historic preservation and maintaining ancient text corpora presents several challenges, including issues with preservation, translation, and digitization. Many ancient texts have been lost over time, and those that survive may be damaged or fragmented. Translating ancient languages and scripts requires specialized expertise, and digitizing texts can be time-consuming and resource-intensive. == Corpus linguistics == The field of corpus linguistics studies language as expressed in text corpora. This includes the analysis of word frequency, collocations, grammar, and semantics. Ancient text corpora provide a valuable resource for corpus linguistics research, enabling scholars to explore the evolution of language and culture over time.

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  • Levenshtein automaton

    Levenshtein automaton

    In computer science, a Levenshtein automaton for a string w and a number n is a finite-state automaton that can recognize the set of all strings whose Levenshtein distance from w is at most n. That is, a string x is in the formal language recognized by the Levenshtein automaton if and only if x can be transformed into w by at most n single-character insertions, deletions, and substitutions. == Applications == Levenshtein automata may be used for spelling correction, by finding words in a given dictionary that are close to a misspelled word. In this application, once a word is identified as being misspelled, its Levenshtein automaton may be constructed, and then applied to all of the words in the dictionary to determine which ones are close to the misspelled word. If the dictionary is stored in compressed form as a trie, the time for this algorithm (after the automaton has been constructed) is proportional to the number of nodes in the trie, significantly faster than using dynamic programming to compute the Levenshtein distance separately for each dictionary word. It is also possible to find words in a regular language, rather than a finite dictionary, that are close to a given target word, by computing the Levenshtein automaton for the word, and then using a Cartesian product construction to combine it with an automaton for the regular language, giving an automaton for the intersection language. Alternatively, rather than using the product construction, both the Levenshtein automaton and the automaton for the given regular language may be traversed simultaneously using a backtracking algorithm. Levenshtein automata are used in Lucene for full-text searches that can return relevant documents even if the query is misspelled. == Construction == For any fixed constant n, the Levenshtein automaton for w and n may be constructed in time O(|w|). Mitankin studies a variant of this construction called the universal Levenshtein automaton, determined only by a numeric parameter n, that can recognize pairs of words (encoded in a certain way by bitvectors) that are within Levenshtein distance n of each other. Touzet proposed an effective algorithm to build this automaton. Yet a third finite automaton construction of Levenshtein (or Damerau–Levenshtein) distance are the Levenshtein transducers of Hassan et al., who show finite state transducers implementing edit distance one, then compose these to implement edit distances up to some constant.

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  • Statistical shape analysis

    Statistical shape analysis

    Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. Important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate mean shapes from (possibly random) samples, to estimate shape variability within samples, to perform clustering and to test for differences between shapes. One of the main methods used is principal component analysis (PCA). Statistical shape analysis has applications in various fields, including medical imaging, computer vision, computational anatomy, sensor measurement, and geographical profiling. == Landmark-based techniques == In the point distribution model, a shape is determined by a finite set of coordinate points, known as landmark points. These landmark points often correspond to important identifiable features such as the corners of the eyes. Once the points are collected some form of registration is undertaken. This can be a baseline methods used by Fred Bookstein for geometric morphometrics in anthropology. Or an approach like Procrustes analysis which finds an average shape. David George Kendall investigated the statistical distribution of the shape of triangles, and represented each triangle by a point on a sphere. He used this distribution on the sphere to investigate ley lines and whether three stones were more likely to be co-linear than might be expected. Statistical distribution like the Kent distribution can be used to analyse the distribution of such spaces. Alternatively, shapes can be represented by curves or surfaces representing their contours, by the spatial region they occupy. == Shape deformations == Differences between shapes can be quantified by investigating deformations transforming one shape into another. In particular a diffeomorphism preserves smoothness in the deformation. This was pioneered in D'Arcy Thompson's On Growth and Form before the advent of computers. Deformations can be interpreted as resulting from a force applied to the shape. Mathematically, a deformation is defined as a mapping from a shape x to a shape y by a transformation function Φ {\displaystyle \Phi } , i.e., y = Φ ( x ) {\displaystyle y=\Phi (x)} . Given a notion of size of deformations, the distance between two shapes can be defined as the size of the smallest deformation between these shapes. Diffeomorphometry is the focus on comparison of shapes and forms with a metric structure based on diffeomorphisms, and is central to the field of Computational anatomy. Diffeomorphic registration, introduced in the 90's, is now an important player with existing codes bases organized around ANTS, DARTEL, DEMONS, LDDMM, StationaryLDDMM, and FastLDDMM are examples of actively used computational codes for constructing correspondences between coordinate systems based on sparse features and dense images. Voxel-based morphometry (VBM) is an important technology built on many of these principles. Methods based on diffeomorphic flows are also used. For example, deformations could be diffeomorphisms of the ambient space, resulting in the LDDMM (Large Deformation Diffeomorphic Metric Mapping) framework for shape comparison.

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  • Top 10 AI Marketing Tools Compared (2026)

    Top 10 AI Marketing Tools Compared (2026)

    Comparing the best AI marketing tool? An AI marketing tool 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 marketing tool slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Lise Getoor

    Lise Getoor

    Lise Getoor is an American computer scientist who is a distinguished professor and Baskin Endowed chair in the Computer Science and Engineering department, at the University of California, Santa Cruz, and an adjunct professor in the Computer Science Department at the University of Maryland, College Park. Her primary research interests are in machine learning and reasoning with uncertainty, applied to graphs and structured data. She also works in data integration, social network analysis and visual analytics. She has edited a book on Statistical relational learning that is a main reference in this domain. She has published many highly cited papers in academic journals and conference proceedings. She has also served as action editor for the Machine Learning Journal, JAIR associate editor, and TKDD associate editor. She received her Ph.D. from Stanford University, her M.S. from UC Berkeley, and her B.S. from UC Santa Barbara. Prior to joining University of California, Santa Cruz, she was a professor at the University of Maryland, College Park until November 2013. == Recognition == Getoor has multiple best paper awards, an NSF Career Award, and is an Association for the Advancement of Artificial Intelligence (AAAI) Fellow. In 2019, she was elected as an ACM Fellow "for contributions to machine learning, reasoning under uncertainty, and responsible data science", was selected as a Distinguished Alumna of the UC Santa Barbara Computer Science Department, was awarded the UCSC WiSE Chancellor's Achievement Award for Diversity, and was selected to give the UC Santa Cruz Faculty Research Lecture 2018-19, one of the highest recognitions given to UC faculty. She was named an IEEE Fellow in 2021, "for contributions to machine learning and reasoning under uncertainty". In October 2022, Getoor was elected a Fellow of the American Association for the Advancement of Science (AAAS). In 2024, she was named a Fellow of the American Academy of Arts and Sciences (AAA&S). Also in 2024, she received the ACM SIGKDD Innovation Award recognizing individuals with outstanding technical innovations in the field of Knowledge Discovery and Data Mining that have had a lasting impact in advancing the theory and practice of the field. == Personal life == Getoor's father was mathematician Ronald Getoor (1929–2017).

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  • Markov information source

    Markov information source

    In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain. == Formal definition == An information source is a sequence of random variables ranging over a finite alphabet Γ {\displaystyle \Gamma } , having a stationary distribution. A Markov information source is then a (stationary) Markov chain M {\displaystyle M} , together with a function f : S → Γ {\displaystyle f:S\to \Gamma } that maps states S {\displaystyle S} in the Markov chain to letters in the alphabet Γ {\displaystyle \Gamma } . A unifilar Markov source is a Markov source for which the values f ( s k ) {\displaystyle f(s_{k})} are distinct whenever each of the states s k {\displaystyle s_{k}} are reachable, in one step, from a common prior state. Unifilar sources are notable in that many of their properties are far more easily analyzed, as compared to the general case. == Applications == Markov sources are commonly used in communication theory, as a model of a transmitter. Markov sources also occur in natural language processing, where they are used to represent hidden meaning in a text. Given the output of a Markov source, whose underlying Markov chain is unknown, the task of solving for the underlying chain is undertaken by the techniques of hidden Markov models, such as the Viterbi algorithm.

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  • Belief–desire–intention model

    Belief–desire–intention model

    For popular psychology, the belief–desire–intention (BDI) model of human practical reasoning was developed by Michael Bratman as a way of explaining future-directed intention. BDI is fundamentally reliant on folk psychology (the 'theory theory'), which is the notion that our mental models of the world are theories. It was used as a basis for developing the belief–desire–intention software model. == Applications == BDI was part of the inspiration behind the BDI software architecture, which Bratman was also involved in developing. Here, the notion of intention was seen as a way of limiting time spent on deliberating about what to do, by eliminating choices inconsistent with current intentions. BDI has also aroused some interest in psychology. BDI formed the basis for a computational model of childlike reasoning CRIBB.

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  • Separating words problem

    Separating words problem

    In theoretical computer science, the separating words problem is the problem of finding the smallest deterministic finite automaton that behaves differently on two given strings, meaning that it accepts one of the two strings and rejects the other string. It is an open problem how large such an automaton must be, in the worst case, as a function of the length of the input strings. == Example == The two strings 0010 and 1000 may be distinguished from each other by a three-state automaton in which the transitions from the start state go to two different states, both of which are terminal in the sense that subsequent transitions from these two states always return to the same state. The state of this automaton records the first symbol of the input string. If one of the two terminal states is accepting and the other is rejecting, then the automaton will accept only one of the strings 0010 and 1000. However, these two strings cannot be distinguished by any automaton with fewer than three states. == Simplifying assumptions == For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also differ. Any automaton that distinguishes the binary strings can be translated into an automaton that distinguishes the original strings, without any increase in the number of states. It may also be assumed that the two strings have equal length. For strings of unequal length, there always exists a prime number p whose value is logarithmic in the smaller of the two input lengths, such that the two lengths are different modulo p. An automaton that counts the length of its input modulo p can be used to distinguish the two strings from each other in this case. Therefore, strings of unequal lengths can always be distinguished from each other by automata with few states. == History and bounds == The problem of bounding the size of an automaton that distinguishes two given strings was first formulated by Goralčík & Koubek (1986), who showed that the automaton size is always sublinear. Later, Robson (1989) proved the upper bound O(n2/5(log n)3/5) on the automaton size that may be required. This was improved by Chase (2020) to O(n1/3(log n)7). There exist pairs of inputs that are both binary strings of length n for which any automaton that distinguishes the inputs must have size Ω(log n). Closing the gap between this lower bound and Chase's upper bound remains an open problem. Jeffrey Shallit has offered a prize of 100 British pounds for any improvement to Robson's upper bound. == Special cases == Several special cases of the separating words problem are known to be solvable using few states: If two binary words have differing numbers of zeros or ones, then they can be distinguished from each other by counting their Hamming weights modulo a prime of logarithmic size, using a logarithmic number of states. More generally, if a pattern of length k appears a different number of times in the two words, they can be distinguished from each other using O(k log n) states. If two binary words differ from each other within their first or last k positions, they can be distinguished from each other using k + O(1) states. This implies that almost all pairs of binary words can be distinguished from each other with a logarithmic number of states, because only a polynomially small fraction of pairs have no difference in their initial O(log n) positions. If two binary words have Hamming distance d, then there exists a prime p with p = O(d log n) and a position i at which the two strings differ, such that i is not equal modulo p to the position of any other difference. By computing the parity of the input symbols at positions congruent to i modulo p, it is possible to distinguish the words using an automaton with O(d log n) states.

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  • Project Bergamot

    Project Bergamot

    Project Bergamot is a joint project between several European universities and Mozilla for the development of machine translation software based on artificial neural networks, which is intended for local execution on end-user devices. The software library that was created and the associated language models were made available to the general public as Free Software. Execution requires a x86 CPU with SSE4.1 instruction set extensions. In 2022, Devin Coldewey of TechCrunch judged the translation quality to be "more than adequate", but considered Firefox Translations to be not yet fully mature. == Usage == Mozilla used the Bergamot Translator to expand its web browser Firefox with a feature for translating web pages, which was previously considered an important gap in Firefox' feature set. It is often compared to the much older corresponding feature in Google Chrome, which utilizes a cloud-based background service. In contrast, Firefox Translations does not require any data to leave the user's computer, resulting in advantages in terms of data protection, availability and possibly response times. There is just the installation of a new language model that needs to take place the first time a new language is encountered. Greater independence from large technology companies and their interests is also mentioned as an important advantage. Mozilla thus strengthened its position as an alternative software vendor with a particular focus on data protection and security. Mozilla followed up with the similar feature of speech recognition for spoken user input, based on whisperfile. On the other hand, slow translation times have been observed, especially on older devices. Also, Firefox Translations initially supported far fewer language pairs than other major translation services and is only gradually adding new models. On that matter, the training pipeline is also made available to interested parties to enable the creation of missing language models. TranslateLocally is a Firefox-independent translation software based on the Bergamot Translator. It is also available as an (Electron-based) standalone application or as an extension for Chromium-based web browsers. == History == Mozilla had already tried to get a (cloud-based) web content translation feature into Firefox a few years before Project Bergamot, but had failed because of the financial challenge. Microsoft had already delivered offline capabilities for its translation software in 2018. Google soon followed suit, Apple two years later. The software is based on the free translation framework Marian, which the University of Edinburgh had previously developed in cooperation with Microsoft, and is itself based on the Nematus toolkit that was presented in 2017. Under the leadership of the University of Edinburgh, a development consortium was formed with the Mozilla Corporation and the additional European universities of Prague, Sheffield and Tartu. In 2018, it was able to get 3 million euros of funding from the EU's Horizon 2020 programme. Firefox Translations was initially provided as an add-on. A first functional demonstration prototype was presented in October 2019. Beta version 117 had the feature integrated directly into the browser, the official release was in version 118 from September 2023. Both the add-on module and as part of Firefox, the code and the models are subject to the version 2 of the Mozilla Public License. Since 2022, the EU-funded HPLT project creates new language models. It involves additional partners, including the universities of Helsinki, Turku, Oslo and other partners from Spain, Norway and the Czech Republic.

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  • Best AI Paragraph Rewriters in 2026

    Best AI Paragraph Rewriters in 2026

    In search of the best AI paragraph rewriter? An AI paragraph rewriter is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI paragraph rewriter slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Co–Star

    Co–Star

    Co–Star is an American astrological social networking service founded in 2017, and headquartered in New York City. Users enter the date, time and place they were born to generate an astrological chart and daily horoscopes, which can be compared with those of other users. == History == The concept for Co-Star began in 2015 when Banu Guler created an astrological chart as a gift. The idea later developed into a mobile application with collaborators Anna Kopp and Ben Weitzman. The app publicly launched in 2017. The app includes astrological readings, charts, and daily push notifications that have been noted for their unconventional tone. In early 2018, the company raised a $750,000 pre-seed round from Female Founders Fund. In 2019, Co–Star raised a $5.2 million seed round from Maveron, Aspect, and 14W. In January 2020, Co–Star for Android was launched to a 120,000-person waitlist—two years after their iOS version. In April 2021, the company announced a $15 million Series A, led by Spark Capital. As of that date, Co–Star reported more than 20 million downloads and increased adoption among young women in the United States. == Features == Co–Star employs artificial intelligence to analyze publicly accessible NASA JPL data and find patterns in a user's transits. Co–Star's algorithm maps human-written snippets of text to planetary movements to display personalized content for each user. That content has been called “slightly robotic,” “wildly beautiful,” “truly insane," “brutally honest,” and compared to “a free therapy session.” In July 2023, Co–Star released an in-app service called The Void that allows users to ask open-ended questions and receive answers informed by Co–Star's astrological database.

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  • Jürgen Schmidhuber

    Jürgen Schmidhuber

    Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist noted for his work in the field of artificial intelligence, specifically artificial neural networks. He has been described by media outlets as a leading pioneer of modern artificial intelligence. He is a scientific director of the Dalle Molle Institute for Artificial Intelligence Research in Switzerland. He is also director of the Artificial Intelligence Initiative and professor of the Computer Science program in the Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE) division at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He is best known for his work on long short-term memory (LSTM), a type of neural network architecture which was the dominant technique for various natural language processing tasks in research and commercial applications in the 2010s. He also introduced principles of dynamic neural networks, meta-learning, generative adversarial networks and linear transformers, all of which are widespread in modern AI. == Career == Schmidhuber completed his undergraduate (1987) and PhD (1991) studies at the Technical University of Munich in Munich, Germany. His PhD advisors were Wilfried Brauer and Klaus Schulten. He taught there from 2004 until 2009. From 2009 to 2021, he was a professor of artificial intelligence at the Università della Svizzera Italiana in Lugano, Switzerland. He has served as the director of Dalle Molle Institute for Artificial Intelligence Research (IDSIA), a Swiss AI lab, since 1995. Since 2021, he has also been the director of the AI Initiative at the King Abdullah University of Science and Technology (KAUST). In 2014, Schmidhuber formed a company, NNAISENSE, to work on commercial applications of artificial intelligence in fields such as finance, heavy industry and self-driving cars. Sepp Hochreiter, Jaan Tallinn, and Marcus Hutter are advisers to the company. Sales were under US$11 million in 2016; however, Schmidhuber states that the current emphasis is on research and not revenue. NNAISENSE raised its first round of capital funding in January 2017. Schmidhuber's overall goal is to create an all-purpose AI by training a single AI in sequence on a variety of narrow tasks, but as of 2026 he has said that the focus of NNAISENSE has shifted from artificial general intelligence to asset management. == Research == In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths in artificial neural networks. To overcome this problem, Schmidhuber (1991) proposed a hierarchy of recurrent neural networks (RNNs) pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales, facilitating downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network. In 1993, a chunker solved a deep learning task whose depth exceeded 1000. In 1991, Schmidhuber published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in the creation of the generative adversarial network, which Schmidhuber describes as a special case of artificial curiosity where the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. Schmidhuber supervised the 1991 diploma thesis of his student Sepp Hochreiter which he considered "one of the most important documents in the history of machine learning". It studied the neural history compressor and analyzed and overcame the vanishing gradient problem. This led to the creation of long short-term memory (LSTM), a type of recurrent neural network. The name LSTM was introduced in a tech report in 1995, leading to the most cited LSTM publication, published in 1997 and co-authored by Hochreiter and Schmidhuber. The standard LSTM architecture was introduced in 2000 by Felix Gers, Schmidhuber, and Fred Cummins. Today's "vanilla LSTM" using backpropagation through time was published with his student Alex Graves in 2005, and its connectionist temporal classification (CTC) training algorithm in 2006. CTC was applied to end-to-end speech recognition with LSTM. In 2014, the state of the art was training “very deep neural network” with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In May 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. In Dec 2015, the residual neural network (ResNet) was published, which is a variant of the highway network. In 1992, Schmidhuber published fast weights programmer, an alternative to recurrent neural networks. It has a slow feedforward neural network that learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns, and the fast weights network itself operates over inputs. This was later shown to be equivalent to the unnormalized linear transformer. In 2011, Schmidhuber's team at IDSIA with his postdoc Dan Ciresan also achieved dramatic speedups of convolutional neural networks (CNNs) using graphics processing units (GPUs), based on CNN designs introduced much earlier by Kunihiko Fukushima. An earlier CNN on GPU by Chellapilla et al. (2006) was 4 times faster than an equivalent implementation on CPU. The deep CNN of Dan Ciresan et al. (2011) at IDSIA was 60 times faster and achieved the first superhuman performance in a computer vision contest in August 2011. Between 15 May 2011 and 10 September 2012, these CNNs won four more image competitions and improved the state of the art on multiple image benchmarks. The approach has become central to the field of computer vision. == Credit disputes == Schmidhuber has controversially argued that he and other researchers have been denied adequate recognition for their contribution to the field of deep learning, in favour of Geoffrey Hinton, Yoshua Bengio and Yann LeCun, who shared the 2018 Turing Award for their work in deep learning. He wrote a "scathing" 2015 article arguing that Hinton, Bengio and LeCun "heavily cite each other" but "fail to credit the pioneers of the field". In a statement to the New York Times, Yann LeCun wrote that "Jürgen is manically obsessed with recognition and keeps claiming credit he doesn't deserve for many, many things... It causes him to systematically stand up at the end of every talk and claim credit for what was just presented, generally not in a justified manner." Schmidhuber replied that LeCun did this "without any justification, without providing a single example", and published details of numerous priority disputes with Hinton, Bengio and LeCun. The term "schmidhubered" has been jokingly used in the AI community to describe Schmidhuber's habit of publicly challenging the originality of other researchers' work, a practice seen by some in the AI community as a "rite of passage" for young researchers. Some suggest that Schmidhuber's significant accomplishments have been underappreciated due to his confrontational personality. == Recognition == Schmidhuber received the Helmholtz Award of the International Neural Network Society in 2013, and the Neural Networks Pioneer Award of the IEEE Computational Intelligence Society in 2016 for "pioneering contributions to deep learning and neural networks." He is a member of the European Academy of Sciences and Arts. He has been referred to as the "father of modern AI", the "father of generative AI", and the "father of deep learning". Schmidhuber himself, however, has called Alexey Grigorevich Ivakhnenko the "father of deep learning", and gives credit to many even earlier AI pioneers. The New York Times ran a profile under the headline "When A.I. Matures, It May Call Jürgen Schmidhuber 'Dad'", highlighting his early work on deep learning and his long‑term vision for self‑improving AI. == Views == Schmidhuber is a proponent of open source AI, and believes that they will become competitive against commercial closed-source AI. Since the 1970s, Schmidhuber wanted to create "intelligent machines that could learn and improve on their own and become smarter than him within his lifetime." He differentiates between two types of AIs: tool AI, such as those for improving healthcare, and autonomous AIs that set their own goals, perform their own research, and explore the universe. He has worked on both types for de

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  • Clement Farabet

    Clement Farabet

    Clément Farabet is a computer scientist and AI expert known for his contributions to the field of deep learning. He served as a research scientist at the New York University. He serves as the Vice President of Research at Google DeepMind and previously served as the VP of AI Infrastructure at NVIDIA. His scholarly work received over 11,000 citations with an h-index of 21. == Education == In 2008, Farabet earned a master's degree in electrical engineering with honors from Institut national des sciences appliquées (INSA) de Lyon, France. In 2010, Farabet received his PhD at Université Paris-Est, co-advised by Professors Laurent Najman and Yann LeCun. His thesis focused on real-time image understanding and introduced multi-scale convolutional networks and graph-based techniques for efficient segmentations of class prediction maps. He successfully defended his thesis in 2013. == Career == In 2008, after completing his Master's degree, Farabet joined Professor Yann LeCun's laboratory at the Courant Institute of Mathematical Sciences at New York University. His Master's thesis work on reconfigurable hardware for deep neural networks resulted in a patent. He continued his collaboration with Yann LeCun, and in 2009, he began working with Yale University's e-Lab, led by Eugenio Culurciello. This collaboration eventually led to the creation of TeraDeep. He began his career as a researcher, contributing to the development of LuaTorch, one of the first AI frameworks, which later evolved into PyTorch, widely recognized and adopted globally. == Startups == Farabet co-founded MadBits, a startup with a focus on web-scale image understanding. The company was acquired by Twitter in 2014. Following this acquisition, Farabet co-founded Twitter Cortex, a team dedicated to building Twitter's deep learning platform for various applications, including recommendations, search, spam detection, and NSFW content and ads. == Publications == Farabet, Clement; Couprie, Camille; Najman, Laurent; LeCun, Yann (August 2013). "Learning Hierarchical Features for Scene Labeling". IEEE Transactions on Pattern Analysis and Machine Intelligence. 35 (8): 1915–1929. Bibcode:2013ITPAM..35.1915F. doi:10.1109/TPAMI.2012.231. PMID 23787344. S2CID 206765110. LeCun, Yann; Kavukcuoglu, Koray; Farabet, Clement (2010). "Convolutional networks and applications in vision". Proceedings of 2010 IEEE International Symposium on Circuits and Systems. pp. 253–256. doi:10.1109/ISCAS.2010.5537907. ISBN 978-1-4244-5308-5. S2CID 7625356. Collobert, Ronan; Kavukcuoglu, K.; Farabet, C. (2011). "Torch7: A Matlab-like Environment for Machine Learning". Neural Information Processing Systems. Couprie, Camille; Farabet, Clément; Najman, Laurent; LeCun, Yann (16 January 2013). "Indoor Semantic Segmentation using depth information". arXiv:1301.3572 [cs.CV]. Farabet, Clement (2011). "NeuFlow: A runtime reconfigurable dataflow processor for vision". CVPR 2011 Workshops. pp. 109–116. doi:10.1109/CVPRW.2011.5981829. ISBN 978-1-4577-0529-8. S2CID 851574. Farabet, Clement (2009). "CNP: An FPGA-based processor for Convolutional Networks". 2009 International Conference on Field Programmable Logic and Applications. pp. 32–37. doi:10.1109/FPL.2009.5272559. S2CID 5339694. Farabet, Clement (2010). "Hardware accelerated convolutional neural networks for synthetic vision systems". Proceedings of 2010 IEEE International Symposium on Circuits and Systems. pp. 257–260. doi:10.1109/ISCAS.2010.5537908. ISBN 978-1-4244-5308-5. S2CID 6542026.

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