AI Chatbot Generator

AI Chatbot Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Deep learning

  In machine learning, deep learning (DL) focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and revolves around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Early forms of neural networks were inspired by information processing and distributed communication nodes in biological systems, particularly the human brain. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose. == Overview == Most modern deep learning models are based on multi-layered neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines. Fundamentally, deep learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an image recognition model, the raw input may be an image (represented as a tensor of pixels). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face. Importantly, a deep learning process can learn which features to optimally place at which level on its own. Prior to deep learning, machine learning techniques often involved hand-crafted feature engineering to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model discovers useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction. The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited. No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function. Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively. Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks. The term deep learning was introduced to the machine learning community by Rina Dechter in 1986, and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons. The etymology of the term is more complicated. == Interpretations == Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference. The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit. The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop. == History == === Before 1980 === There are two types of artificial neural network (ANN): feedforward neural network (FNN) or multilayer perceptron (MLP) and recurrent neural networks (RNN). RNNs have cycles in their connectivity structure, whereas FNNs do not. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was republished by John Hopfield in 1982. Other early recurrent neural networks were published by Kaoru Nakano in 1971. Already in 1948, Alan Turing produced work on "Intelligent Machinery" that was not published in his lifetime, containing "ideas related to artificial evolution and learning RNNs". Frank Rosenblatt (1958) proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight). The book cites an earlier network by R. D. Joseph (1960) "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive multilayer perceptrons with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion. The first working deep learning algorithm was the Group method of data handling, a method to train arbitrarily deep neural networks, published by Alexey Ivakhnenko and Lapa in 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron to handle more complex, nonlinear, and hierarchical relationships. A 1971 paper described a deep network with eight layers trained by this method, which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates". The first deep learning multilayer perceptron trained by stochastic gradient descent was published in 1967 by Shun'ichi

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  Pronunciation assessment

  Automatic pronunciation assessment uses computer speech recognition to determine how accurately speech has been pronounced, instead of relying on a human instructor or proctor. It is also called speech verification, pronunciation evaluation, and pronunciation scoring. This technology is used to grade speech quality, for language testing, for computer-aided pronunciation teaching (CAPT) in computer-assisted language learning (CALL), for speaking skill remediation, and for accent reduction. Pronunciation assessment is different from dictation or automatic transcription, because instead of determining unknown speech, it verifies learners' pronunciation of known word(s), often from prior transcription of the same utterance; ideally scoring the intelligibility of the learners' speech. Sometimes pronunciation assessment evaluates the prosody of the learners' speech, such as intonation, pitch, tempo, rhythm, and syllable and word stress, although those are usually not essential for being understood in most languages. Pronunciation assessment is also used in reading tutoring, for example in products from Google, Microsoft, and Amira Learning. Automatic pronunciation assessment can also be used to help diagnose and treat speech disorders such as apraxia. == Intelligibility == Intelligibility refers to how well a learner's utterance is understood by a listener, rather than how much it sounds like a native speaker. This is separate from measures of fluency, such as so-called "Goodness of Pronunciation" (GoP) scores, which estimate how closely an utterance aligns with those of native speakers. Intelligibility is widely regarded as the most important communicative goal in pronunciation teaching and assessment. For example, in the Common European Framework of Reference for Languages (CEFR) assessment criteria for "overall phonological control", intelligibility outweighs formally correct pronunciation at all levels. Studies in applied linguistics have shown that accent reduction does not always increase intelligibility because listeners can often comprehend heavily accented speech without difficulty. Pronunciation assessment systems often rely on acoustic methods such as GoP which compare learner speech to reference models to produce phoneme-level scores, which are in turn aggregated to produce word and phrase scores. While these methods are effective for identifying deviations from native speakers' utterances, they do not effectively measure how understandable speech is to human listeners. Intelligibility is influenced by broader linguistic and contextual factors such as stress placement, speech rate, and coarticulation, which are not represented in purely segmental scores. The earliest work on pronunciation assessment avoided measuring genuine listener intelligibility, a shortcoming corrected in 2011 at the Toyohashi University of Technology, and included in the Versant high-stakes English fluency assessment from Pearson and mobile apps from 17zuoye Education & Technology, but still missing in 2023 products from Google Search, Microsoft, Educational Testing Service, Speechace, and ELSA. Assessing authentic listener intelligibility is essential for avoiding inaccuracies from accent bias, especially in high-stakes assessments; from words with multiple correct pronunciations; and from phoneme coding errors in machine-readable pronunciation dictionaries. In 2022, researchers found that some newer speech-to-text systems, based on end-to-end reinforcement learning to map audio signals directly into words, produce word and phrase confidence scores (from 10-25ms audio frame logit aggregation) closely correlated with genuine listener intelligibility. Others have been able to assess intelligibility using Levenshtein or dynamic time warping distance measures from Wav2Vec2 representation of good speech. Further work through 2025 has focused specifically on measuring intelligibility. A 2025 study of 42 pronunciation and speech coaching apps (32 mobile and 10 web) found that none offered intelligibility assessment. Instead, most provided only segmental and accent-focused scoring. About two-thirds of the apps provided some form of specific pronunciation feedback, usually with phonetic transcriptions, but accompanied by visual cues (such as animations of the vocal tract or the lips and tongue from the front) in only about 5% of the apps. Less than a third provided feedback on learner perception of exemplar speech. == Evaluation == Although there are as yet no industry-standard benchmarks for evaluating pronunciation assessment accuracy, researchers occasionally release evaluation speech corpuses for others to use for improving assessment quality. Such evaluation databases often emphasize formally unaccented pronunciation to the exclusion of genuine intelligibility evident from blinded listener transcriptions. As of mid-2025, state of the art approaches for automatically transcribing phonemes typically achieve an error rate of about 10% from known good speech. The International Speech Communication Association (ISCA) 2025 Workshop on Speech and Language Technology in Education (SLaTE) administered a Speak & Improve Challenge: Spoken Language Assessment and Feedback, introducing benchmarks for evaluating pronunciation assessment and remediation systems across languages, accents, and learner populations. The challenge emphasized cross-lingual generalization and alignment with human intelligibility judgments, for more robust and interpretable assessment systems. Ethical issues in pronunciation assessment are present in both human and automatic methods. Authentic validity, fairness, and mitigating bias in evaluation are all crucial. Diverse speech data should be included in automatic pronunciation assessment models. Combining human judgments, especially blinded transcriptions from a wide diversity of listeners, with automated feedback can improve accuracy and fairness. Second language learners benefit substantially from their use of widely available speech recognition systems for dictation, virtual assistants, and AI chatbots. In such systems, users naturally try to correct their own errors evident in speech recognition results that they notice. Such use improves their grammar and vocabulary development along with their pronunciation skills. The extent to which explicit pronunciation assessment and remediation approaches improve on such self-directed interactions remains an open question. Similarly, automatic dictation results have been shown to reflect intelligibility about as well as human scorers. == Recent developments == During 2021–22, a smartphone-based CAPT system was used to sense articulation through both audible and inaudible signals, providing feedback at the phoneme level. Some promising areas for improvement which were being developed in 2024 include articulatory feature extraction and transfer learning to suppress unnecessary corrections. Other interesting advances under development include "augmented reality" interfaces for mobile devices using optical character recognition to provide pronunciation training on text found in user environments. In 2024, audio multimodal large language models were first described as assessing pronunciation. That work has been carried forward by other researchers in 2025 who report positive results. Subsequently, researchers demonstrated pronunciation scoring by providing a language model with textual descriptions of speech, including the speech-to-text transcript, phoneme sequences, pauses, and phoneme sequence matching; this approach can achieve performance similar to multimodal LLMs that analyze raw audio while avoiding their higher computational cost. In 2025, the Duolingo English Test authors published a description of their pronunciation assessment method, purportedly built to measure intelligibility rather than accent imitation. While achieving a correlation of 0.82 with expert human ratings, very close to inter-rater agreement and outperforming alternative methods, the method is nonetheless based on experts' scores along the six-point CEFR common reference levels scale, instead of actual blinded listener transcriptions. Further promising work in 2025 includes assessment feedback aligning learner speech to synthetic utterances using interpretable features, identifying continuous spans of words for remediation feedback; synthesizing corrected speech matching learners' self-perceived voices, which they prefer and imitate more accurately as corrections; and streaming such interactions. On January 21, 2026, Educational Testing Service's TOEFL iBT high-stakes English language test, required by US university admissions and employers from English as a foreign language applicants more often than all other internet-based tests combined, changed its speaking assessments. While official rubrics claim that the new scoring will be based primarily on intelligibility, the new test's technical description indicates that it ju

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  Natural-language user interface

  Natural-language user interface (LUI or NLUI) is a type of computer human interface where linguistic phenomena such as verbs, phrases and clauses act as UI controls for creating, selecting and modifying data in software applications. Chatbots are a common implementation of natural-language interfaces, enabling users to interact with software through conversational text or speech. In interface design, natural-language interfaces are sought after for their speed and ease of use, but most suffer the challenges to understanding wide varieties of ambiguous input. Natural-language interfaces are an active area of study in the field of natural-language processing and computational linguistics. An intuitive general natural-language interface is one of the active goals of the Semantic Web. Text interfaces are "natural" to varying degrees. Many formal (un-natural) programming languages incorporate idioms of natural human language. Likewise, a traditional keyword search engine could be described as a "shallow" natural-language user interface. == Overview == A natural-language search engine would in theory find targeted answers to user questions (as opposed to keyword search). For example, when confronted with a question of the form 'which U.S. state has the highest income tax?', conventional search engines ignore the question and instead search on the keywords 'state', 'income' and 'tax'. Natural-language search, on the other hand, attempts to use natural-language processing to understand the nature of the question and then to search and return a subset of the web that contains the answer to the question. If it works, results would have a higher relevance than results from a keyword search engine, due to the question being included. == History == Prototype Nl interfaces had already appeared in the late sixties and early seventies. SHRDLU, a natural-language interface that manipulates blocks in a virtual "blocks world" Lunar, a natural-language interface to a database containing chemical analyses of Apollo 11 Moon rocks by William A. Woods. Chat-80 transformed English questions into Prolog expressions, which were evaluated against the Prolog database. The code of Chat-80 was circulated widely, and formed the basis of several other experimental Nl interfaces. An online demo is available on the LPA website. ELIZA, written at MIT by Joseph Weizenbaum between 1964 and 1966, mimicked a psychotherapist and was operated by processing users' responses to scripts. Using almost no information about human thought or emotion, the DOCTOR script sometimes provided a startlingly human-like interaction. An online demo is available on the LPA website. Janus is also one of the few systems to support temporal questions. Intellect from Trinzic (formed by the merger of AICorp and Aion). BBN's Parlance built on experience from the development of the Rus and Irus systems. IBM Languageaccess Q&A from Symantec. Datatalker from Natural Language Inc. Loqui from BIM Systems. English Wizard from Linguistic Technology Corporation. == Challenges == Natural-language interfaces have in the past led users to anthropomorphize the computer, or at least to attribute more intelligence to machines than is warranted. On the part of the user, this has led to unrealistic expectations of the capabilities of the system. Such expectations will make it difficult to learn the restrictions of the system if users attribute too much capability to it, and will ultimately lead to disappointment when the system fails to perform as expected as was the case in the AI winter of the 1970s and 80s. A 1995 paper titled 'Natural Language Interfaces to Databases – An Introduction', describes some challenges: Modifier attachment The request "List all employees in the company with a driving licence" is ambiguous unless you know that companies can't have driving licences. Conjunction and disjunction "List all applicants who live in California and Arizona" is ambiguous unless you know that a person can't live in two places at once. Anaphora resolution resolve what a user means by 'he', 'she' or 'it', in a self-referential query. Other goals to consider more generally are the speed and efficiency of the interface, in all algorithms these two points are the main point that will determine if some methods are better than others and therefore have greater success in the market. In addition, localisation across multiple language sites requires extra consideration - this is based on differing sentence structure and language syntax variations between most languages. Finally, regarding the methods used, the main problem to be solved is creating a general algorithm that can recognize the entire spectrum of different voices, while disregarding nationality, gender or age. The significant differences between the extracted features - even from speakers who says the same word or phrase - must be successfully overcome. == Uses and applications == The natural-language interface gives rise to technology used for many different applications. Some of the main uses are: Dictation, is the most common use for automated speech recognition (ASR) systems today. This includes medical transcriptions, legal and business dictation, and general word processing. In some cases special vocabularies are used to increase the accuracy of the system. Command and control, ASR systems that are designed to perform functions and actions on the system are defined as command and control systems. Utterances like "Open Netscape" and "Start a new xterm" will do just that. Telephony, some PBX/Voice Mail systems allow callers to speak commands instead of pressing buttons to send specific tones. Wearables, because inputs are limited for wearable devices, speaking is a natural possibility. Medical, disabilities, many people have difficulty typing due to physical limitations such as repetitive strain injuries (RSI), muscular dystrophy, and many others. For example, people with difficulty hearing could use a system connected to their telephone to convert a caller's speech to text. Embedded applications, some new cellular phones include C&C speech recognition that allow utterances such as "call home". This may be a major factor in the future of automatic speech recognition and Linux. Below are named and defined some of the applications that use natural-language recognition, and so have integrated utilities listed above. === Ubiquity === Ubiquity, an add-on for Mozilla Firefox, is a collection of quick and easy natural-language-derived commands that act as mashups of web services, thus allowing users to get information and relate it to current and other webpages. === Wolfram Alpha === Wolfram Alpha is an online service that answers factual queries directly by computing the answer from structured data, rather than providing a list of documents or web pages that might contain the answer as a search engine would. It was announced in March 2009 by Stephen Wolfram, and was released to the public on May 15, 2009. === Siri === Siri is an intelligent personal assistant application integrated with operating system iOS. The application uses natural language processing to answer questions and make recommendations. Siri's marketing claims include that it adapts to a user's individual preferences over time and personalizes results, and performs tasks such as making dinner reservations while trying to catch a cab. === Others === Ask.com – The original idea behind Ask Jeeves (Ask.com) was traditional keyword searching with an ability to get answers to questions posed in everyday, natural language. The current Ask.com still supports this, with added support for math, dictionary, and conversion questions. Braina – Braina is a natural language interface for Windows OS that allows to type or speak English language sentences to perform a certain action or find information. GNOME Do – Allows for quick finding miscellaneous artifacts of GNOME environment (applications, Evolution and Pidgin contacts, Firefox bookmarks, Rhythmbox artists and albums, and so on) and execute the basic actions on them (launch, open, email, chat, play, etc.). hakia – hakia was an Internet search engine. The company invented an alternative new infrastructure to indexing that used SemanticRank algorithm, a solution mix from the disciplines of ontological semantics, fuzzy logic, computational linguistics, and mathematics. hakia closed in 2014. Lexxe – Lexxe was an Internet search engine that used natural-language processing for queries (semantic search). Searches could be made with keywords, phrases, and questions, such as "How old is Wikipedia?" Lexxe closed its search engine services in 2015. Pikimal – Pikimal used natural-language tied to user preference to make search recommendations by template. Pikimal closed in 2015. Powerset – On May 11, 2008, the company unveiled a tool for searching a fixed subset of Wikipedia using conversational phrases rather than keywords. On July 1, 2008, it was purchased by

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  OrCam device

  OrCam devices such as OrCam MyEye are portable, artificial vision devices that allow visually impaired people to understand text and identify objects through audio feedback, describing what they are unable to see. Reuters described an important part of how it works as "a wireless smartcamera" which, when attached outside eyeglass frames, can read and verbalize text, and also supermarket barcodes. This information is converted to spoken words and entered "into the user’s ear." Face-recognition is also part of OrCam's feature set. == Devices == OrCam Technologies Ltd has created three devices; OrCam MyEye 2.0, OrCam MyEye 1, and OrCam MyReader. OrCam My Eye 2.0: OrCam debuted the second-generation model, the OrCam MyEye 2.0 in December 2017. About the size of a finger, the MyEye 2.0 is battery-powered, and has been compressed into a self-contained device. The device snaps onto any eyeglass frame magnetically. Orcam 2.0 is small and light (22.5 grams/0.8 ounces) with functionality to restore independence to the visually impaired. It comes in two versions. The basic model can read text, and a more advanced one adds features such as face recognition and barcode reading. As of July 2023, the retail cost is between $4000 and $6000 (USD). == Clinical Studies == JAMA Ophthalmology: In 2016 JAMA Ophthalmology conducted a study involving 12 legally blind participants to evaluate the usefulness of a portable artificial vision device (OrCam) for patients with low vision. The results showed that the OrCam device improved the patient's ability to perform tasks simulating those of daily living, such as reading a message on an electronic device, a newspaper article or a menu. Wills Eye: Wills Eye was a clinical study designed to measure the impact of the OrCam device on the quality of life of patients with End-stage Glaucoma. The conclusion was that OrCam, a novel artificial vision device using a mini-camera mounted on eyeglasses, allowed legally blind patients with end-stage glaucoma to read independently, subsequently improving their quality of life. == Employee testing == The New York Times described how a pre-release OrCam device was used by a Coloboma-impaired employee of the device's developer in 2013 for grocery shopping. It was the small size of the prototype rather than the functionality that gave her added mobility in an Israeli store's aisles. Added life-enhancement was described: "to both recognize and speak .. bus numbers .. traffic lights." == Social aspects == In contrast to an early version of Google Glass, which "failed ... because .. Glass wearers were ..mocked", early OrCam devices used designs that "clip unobtrusively on your shirt or perhaps your belt." In addition, it does not record sounds or images, what was called "the privacy puzzle that stumped Google. One 2018 technology reviewer wrote that he wished it had a headphone jack "so it would be less disruptive in places where others are working." An attempt was made to use bone conduction. == USA introduction == In 2018 a team headed by New York Assemblyman Dov Hikind introduced use of OrCam devices to ten individuals screened for what he termed "new Israeli technology that really makes a difference to the blind." Although not the first USA success, it was more focused than a publicly funded project that was authorized in 2016 by a California government agency. Also in 2016 the Chicago Lighthouse for the Blind demonstrated its use. == Technology == In the area of hardware, miniaturization has been quite important, but one major area, software, was mentioned by Assemblyman Hikind, and reported by The Times of Israel is the "AI-driven algorithms" that "reports .. how many people are in a room. In addition to reading printed text, it can also aid in "seeing" what is on a television or computer screen. Although OrCam can't help with handwritten information, it can reuse information, the basis of recognizing "US currency, and even faces." === Features === While early language support was for English, French, German, Hebrew and Spanish, others now available include Danish, Dutch, Finnish, Italian, Norwegian, Portuguese and Swedish. == History == OrCam Technologies Ltd was founded in 2010 by Professor Amnon Shashua and Ziv Aviram. Before co-founding OrCam, the two in 1999 co-founded Mobileye, an Israeli company that develops vision-based advanced driver-assistance systems (ADAS) providing warnings for collision prevention and mitigation, which was acquired by Intel for $15.3 billion in 2017. OrCam launched OrCam MyEye in 2013 after years of development and testing, and began selling it commercially in 2015. In its early years, the company raised $22 million, $6 million of which came from Intel Capital. By 2014, Intel, which was also investing in Google Glass, had invested $15 million in Orcam. In March 2017, OrCam had raised $41 million in capital, making it worth $600 million. === Marketing === One outcome of initial marketing in the USA was that they "reached a deal with the California Department of Rehabilitation, ...qualifying blind and visually impaired state residents." == OrCam Technologies Ltd == OrCam Technologies Ltd. is the Israeli-based company producing these OrCam devices, which are wearable artificial intelligence space. The company develops and manufactures assistive technology devices for individuals who are visually impaired, partially sighted, blind, print disabilities, or have other disabilities. OrCam headquarters is located in Jerusalem, operating under the company name OrCam Technologies Ltd. OrCam has over 150 employees, is headquartered in Jerusalem, and has offices in New York, Toronto, and London. == Awards == 2018 Last Gadget Standing Winner 2018 CES Innovation Awards Honoree in Accessible Tech 2017 NAIDEX Innovation Award 2016 Louise Braille Corporate Recognition Award 2016 Silmo-d-Or Award

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  Winner-take-all in action selection

  Winner-take-all is a computer science concept that has been widely applied in behavior-based robotics as a method of action selection for intelligent agents. Winner-take-all systems work by connecting modules (task-designated areas) in such a way that when one action is performed it stops all other actions from being performed, so only one action is occurring at a time. The name comes from the idea that the "winner" action takes all of the motor system's power. == History == In the 1980s and 1990s, many roboticists and cognitive scientists were attempting to find speedier and more efficient alternatives to the traditional world modeling method of action selection. In 1982, Jerome A. Feldman and D.H. Ballard published the "Connectionist Models and Their Properties", referencing and explaining winner-take-all as a method of action selection. Feldman's architecture functioned on the simple rule that in a network of interconnected action modules, each module will set its own output to zero if it reads a higher input than its own in any other module. In 1986, Rodney Brooks introduced behavior-based artificial intelligence. Winner-take-all architectures for action selection soon became a common feature of behavior-based robots, because selection occurred at the level of the action modules (bottom-up) rather than at a separate cognitive level (top-down), producing a tight coupling of stimulus and reaction. == Types of winner-take-all architectures == === Hierarchy === In the hierarchical architecture, actions or behaviors are programmed in a high-to-low priority list, with inhibitory connections between all the action modules. The agent performs low-priority behaviors until a higher-priority behavior is stimulated, at which point the higher behavior inhibits all other behaviors and takes over the motor system completely. Prioritized behaviors are usually key to the immediate survival of the agent, while behaviors of lower priority are less time-sensitive. For example, "run away from predator" would be ranked above "sleep." While this architecture allows for clear programming of goals, many roboticists have moved away from the hierarchy because of its inflexibility. === Heterarchy and fully distributed === In the heterarchy and fully distributed architecture, each behavior has a set of pre-conditions to be met before it can be performed, and a set of post-conditions that will be true after the action has been performed. These pre- and post-conditions determine the order in which behaviors must be performed and are used to causally connect action modules. This enables each module to receive input from other modules as well as from the sensors, so modules can recruit each other. For example, if the agent's goal were to reduce thirst, the behavior "drink" would require the pre-condition of having water available, so the module would activate the module in charge of "find water". The activations organize the behaviors into a sequence, even though only one action is performed at a time. The distribution of larger behaviors across modules makes this system flexible and robust to noise. Some critics of this model hold that any existing set of division rules for the predecessor and conflictor connections between modules produce sub-par action selection. In addition, the feedback loop used in the model can in some circumstances lead to improper action selection. === Arbiter and centrally coordinated === In the arbiter and centrally coordinated architecture, the action modules are not connected to each other but to a central arbiter. When behaviors are triggered, they begin "voting" by sending signals to the arbiter, and the behavior with the highest number of votes is selected. In these systems, bias is created through the "voting weight", or how often a module is allowed to vote. Some arbiter systems take a different spin on this type of winner-take-all by using a "compromise" feature in the arbiter. Each module is able to vote for or against each smaller action in a set of actions, and the arbiter selects the action with the most votes, meaning that it benefits the most behavior modules. This can be seen as violating the general rule against creating representations of the world in behavior-based AI, established by Brooks. By performing command fusion, the system is creating a larger composite pool of knowledge than is obtained from the sensors alone, forming a composite inner representation of the environment. Defenders of these systems argue that forbidding world-modeling puts unnecessary constraints on behavior-based robotics, and that agents benefits from forming representations and can still remain reactive.

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  Vector database

  A vector database, vector store or vector search engine is a database that stores and retrieves embeddings of data in vector space. Vector databases typically implement approximate nearest neighbor algorithms so users can search for records semantically similar to a given input, unlike traditional databases which primarily look up records by exact match. Use-cases for vector databases include similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation (RAG). Vector embeddings are mathematical representations of data in a high-dimensional space. In this space, each dimension corresponds to a feature of the data, with the number of dimensions ranging from a few hundred to tens of thousands, depending on the complexity of the data being represented. Each data item is represented by one vector in this space. Words, phrases, or entire documents, as well as images, audio, and other types of data, can all be vectorized. These feature vectors may be computed from the raw data using machine learning methods such as feature extraction algorithms, word embeddings or deep learning networks. The goal is that semantically similar data items receive feature vectors close to each other. Vector retrieval can be combined with metadata filtering or lexical search to support filtered and hybrid retrieval workflows. == Techniques == Common techniques for similarity search on high-dimensional vectors include: Hierarchical Navigable Small World (HNSW) graphs Locality-sensitive hashing (LSH) and sketching Product quantization (PQ) Inverted files These techniques may also be combined in vector search systems. In recent benchmarks, HNSW-based implementations have been among the best performers. Conferences such as the International Conference on Similarity Search and Applications (SISAP) and the Conference on Neural Information Processing Systems (NeurIPS) have hosted competitions on vector search in large databases. == Applications == Vector databases are used in a wide range of machine learning applications including similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation. === Retrieval-augmented generation === An especially common use-case for vector databases is in retrieval-augmented generation (RAG), a method to improve domain-specific responses of large language models. The retrieval component of a RAG can be any search system, but is most often implemented as a vector database. Text documents describing the domain of interest are collected, and for each document or document section, a feature vector (known as an "embedding") is computed, typically using a deep learning network, and stored in a vector database along with a link to the document. Given a user prompt, the feature vector of the prompt is computed, and the database is queried to retrieve the most relevant documents. These are then automatically added into the context window of the large language model, and the large language model proceeds to create a response to the prompt given this context. == Implementations ==

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  Knowledge assessment methodology

  The knowledge assessment methodology (KAM) is "an interactive benchmarking tool created by the World Bank's Knowledge for Development Program to help countries identify the challenges and opportunities they face in making the transition to the knowledge-based economy." KAM does so by providing information on knowledge economy indicators for 146 countries. Its products include the Knowledge Economy Index and the Knowledge Index.

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  Inverse depth parametrization

  In computer vision, the inverse depth parametrization is a parametrization used in methods for 3D reconstruction from multiple images such as simultaneous localization and mapping (SLAM). Given a point p {\displaystyle \mathbf {p} } in 3D space observed by a monocular pinhole camera from multiple views, the inverse depth parametrization of the point's position is a 6D vector that encodes the optical centre of the camera c 0 {\displaystyle \mathbf {c} _{0}} when in first observed the point, and the position of the point along the ray passing through p {\displaystyle \mathbf {p} } and c 0 {\displaystyle \mathbf {c} _{0}} . Inverse depth parametrization generally improves numerical stability and allows to represent points with zero parallax. Moreover, the error associated to the observation of the point's position can be modelled with a Gaussian distribution when expressed in inverse depth. This is an important property required to apply methods, such as Kalman filters, that assume normality of the measurement error distribution. The major drawback is the larger memory consumption, since the dimensionality of the point's representation is doubled. == Definition == Given 3D point p = ( x , y , z ) {\displaystyle \mathbf {p} =(x,y,z)} with world coordinates in a reference frame ( e 1 , e 2 , e 3 ) {\displaystyle (e_{1},e_{2},e_{3})} , observed from different views, the inverse depth parametrization y {\displaystyle \mathbf {y} } of p {\displaystyle \mathbf {p} } is given by: y = ( x 0 , y 0 , z 0 , θ , ϕ , ρ ) {\displaystyle \mathbf {y} =(x_{0},y_{0},z_{0},\theta ,\phi ,\rho )} where the first five components encode the camera pose in the first observation of the point, being c 0 = ( x 0 , y 0 , z 0 ) {\displaystyle \mathbf {c_{0}} =(x_{0},y_{0},z_{0})} the optical centre, ϕ {\displaystyle \phi } the azimuth, θ {\displaystyle \theta } the elevation angle, and ρ = 1 ‖ p − c 0 ‖ {\displaystyle \rho ={\frac {1}{\left\Vert \mathbf {p} -\mathbf {c} _{0}\right\Vert }}} the inverse depth of p {\displaystyle p} at the first observation.

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  Mathematical morphology

  Mathematical morphology (MM) is a theory and technique for analyzing and processing geometrical structures. It's based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures. Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete spaces. MM is also the foundation of morphological image processing, which consists of a set of operators that transform images according to the above characterizations. The basic morphological operators are erosion, dilation, opening and closing. MM was originally developed for binary images, and was later extended to grayscale functions and images. The subsequent generalization to complete lattices is widely accepted today as MM's theoretical foundation. == History == Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France. Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and topology. In 1968, the Centre de Morphologie Mathématique was founded by the École des Mines de Paris in Fontainebleau, France, led by Matheron and Serra. During the rest of the 1960s and most of the 1970s, MM dealt essentially with binary images, treated as sets, and generated a large number of binary operators and techniques: Hit-or-miss transform, dilation, erosion, opening, closing, granulometry, thinning, skeletonization, ultimate erosion, conditional bisector, and others. A random approach was also developed, based on novel image models. Most of the work in that period was developed in Fontainebleau. From the mid-1970s to mid-1980s, MM was generalized to grayscale functions and images as well. Besides extending the main concepts (such as dilation, erosion, etc.) to functions, this generalization yielded new operators, such as morphological gradients, top-hat transform and the Watershed (MM's main segmentation approach). In the 1980s and 1990s, MM gained a wider recognition, as research centers in several countries began to adopt and investigate the method. MM started to be applied to a large number of imaging problems and applications, especially in the field of non-linear filtering of noisy images. In 1986, Serra further generalized MM, this time to a theoretical framework based on complete lattices. This generalization brought flexibility to the theory, enabling its application to a much larger number of structures, including color images, video, graphs, meshes, etc. At the same time, Matheron and Serra also formulated a theory for morphological filtering, based on the new lattice framework. The 1990s and 2000s also saw further theoretical advancements, including the concepts of connections and levelings. In 1993, the first International Symposium on Mathematical Morphology (ISMM) took place in Barcelona, Spain. Since then, ISMMs are organized every 2–3 years: Fontainebleau, France (1994); Atlanta, USA (1996); Amsterdam, Netherlands (1998); Palo Alto, CA, USA (2000); Sydney, Australia (2002); Paris, France (2005); Rio de Janeiro, Brazil (2007); Groningen, Netherlands (2009); Intra (Verbania), Italy (2011); Uppsala, Sweden (2013); Reykjavík, Iceland (2015); Fontainebleau, France (2017); and Saarbrücken, Germany (2019). =

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  Transduction (machine learning)

  In logic, statistical inference, and supervised learning, transduction or transductive inference is reasoning from observed, specific (training) cases to specific (test) cases. In contrast, induction is reasoning from observed training cases to general rules, which are then applied to the test cases. The distinction is most interesting in cases where the predictions of the transductive model are not achievable by any inductive model. Note that this is caused by transductive inference on different test sets producing mutually inconsistent predictions. Transduction was introduced in a computer science context by Vladimir Vapnik in the 1990s, motivated by his view that transduction is preferable to induction since, according to him, induction requires solving a more general problem (inferring a function) before solving a more specific problem (computing outputs for new cases): "When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need but not a more general one.". An example of learning which is not inductive would be in the case of binary classification, where the inputs tend to cluster in two groups. A large set of test inputs may help in finding the clusters, thus providing useful information about the classification labels. The same predictions would not be obtainable from a model which induces a function based only on the training cases. Some people may call this an example of the closely related semi-supervised learning, since Vapnik's motivation is quite different. The most well-known example of a case-bases learning algorithm is the k-nearest neighbor algorithm, which is related to transductive learning algorithms. Another example of an algorithm in this category is the Transductive Support Vector Machine (TSVM). A third possible motivation of transduction arises through the need to approximate. If exact inference is computationally prohibitive, one may at least try to make sure that the approximations are good at the test inputs. In this case, the test inputs could come from an arbitrary distribution (not necessarily related to the distribution of the training inputs), which wouldn't be allowed in semi-supervised learning. An example of an algorithm falling in this category is the Bayesian Committee Machine (BCM). == Historical context == The mode of inference from particulars to particulars, which Vapnik came to call transduction, was already distinguished from the mode of inference from particulars to generalizations in part III of the Cambridge philosopher and logician W.E. Johnson's 1924 textbook, Logic. In Johnson's work, the former mode was called 'eduction' and the latter was called 'induction'. Bruno de Finetti developed a purely subjective form of Bayesianism in which claims about objective chances could be translated into empirically respectable claims about subjective credences with respect to observables through exchangeability properties. An early statement of this view can be found in his 1937 La Prévision: ses Lois Logiques, ses Sources Subjectives and a mature statement in his 1970 Theory of Probability. Within de Finetti's subjective Bayesian framework, all inductive inference is ultimately inference from particulars to particulars. == Example problem == The following example problem contrasts some of the unique properties of transduction against induction. A collection of points is given, such that some of the points are labeled (A, B, or C), but most of the points are unlabeled (?). The goal is to predict appropriate labels for all of the unlabeled points. The inductive approach to solving this problem is to use the labeled points to train a supervised learning algorithm, and then have it predict labels for all of the unlabeled points. With this problem, however, the supervised learning algorithm will only have five labeled points to use as a basis for building a predictive model. It will certainly struggle to build a model that captures the structure of this data. For example, if a nearest-neighbor algorithm is used, then the points near the middle will be labeled "A" or "C", even though it is apparent that they belong to the same cluster as the point labeled "B", compared to semi-supervised learning. Transduction has the advantage of being able to consider all of the points, not just the labeled points, while performing the labeling task. In this case, transductive algorithms would label the unlabeled points according to the clusters to which they naturally belong. The points in the middle, therefore, would most likely be labeled "B", because they are packed very close to that cluster. An advantage of transduction is that it may be able to make better predictions with fewer labeled points, because it uses the natural breaks found in the unlabeled points. One disadvantage of transduction is that it builds no predictive model. If a previously unknown point is added to the set, the entire transductive algorithm would need to be repeated with all of the points in order to predict a label. This can be computationally expensive if the data is made available incrementally in a stream. Further, this might cause the predictions of some of the old points to change (which may be good or bad, depending on the application). A supervised learning algorithm, on the other hand, can label new points instantly, with very little computational cost. == Transduction algorithms == Transduction algorithms can be broadly divided into two categories: those that seek to assign discrete labels to unlabeled points, and those that seek to regress continuous labels for unlabeled points. Algorithms that seek to predict discrete labels tend to be derived by adding partial supervision to a clustering algorithm. Two classes of algorithms can be used: flat clustering and hierarchical clustering. The latter can be further subdivided into two categories: those that cluster by partitioning, and those that cluster by agglomerating. Algorithms that seek to predict continuous labels tend to be derived by adding partial supervision to a manifold learning algorithm. === Partitioning transduction === Partitioning transduction can be thought of as top-down transduction. It is a semi-supervised extension of partition-based clustering. It is typically performed as follows: Consider the set of all points to be one large partition. While any partition P contains two points with conflicting labels: Partition P into smaller partitions. For each partition P: Assign the same label to all of the points in P. Of course, any reasonable partitioning technique could be used with this algorithm. Max flow min cut partitioning schemes are very popular for this purpose. === Agglomerative transduction === Agglomerative transduction can be thought of as bottom-up transduction. It is a semi-supervised extension of agglomerative clustering. It is typically performed as follows: Compute the pair-wise distances, D, between all the points. Sort D in ascending order. Consider each point to be a cluster of size 1. For each pair of points {a,b} in D: If (a is unlabeled) or (b is unlabeled) or (a and b have the same label) Merge the two clusters that contain a and b. Label all points in the merged cluster with the same label. === Continuous Label Transduction === These methods seek to regress continuous labels, often via manifold learning techniques. The idea is to learn a low-dimensional representation of the data and infer values smoothly across the manifold. == Applications and related concepts == Transduction is closely related to: Semi-supervised learning – uses both labeled and unlabeled data but typically induces a model. Case-based reasoning – such as the k-nearest neighbor (k-NN) algorithm, often considered a transductive method. Transductive Support Vector Machines (TSVM) – extend standard SVMs to incorporate unlabeled test data during training. Bayesian Committee Machine (BCM) – an approximation method that makes transductive predictions when exact inference is too costly.

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  Semantic analytics

  Semantic analytics, also termed semantic relatedness, is the use of ontologies to analyze content in web resources. This field of research combines text analytics and Semantic Web technologies like RDF. Semantic analytics measures the relatedness of different ontological concepts. Some academic research groups that have active project in this area include Kno.e.sis Center at Wright State University among others. == History == An important milestone in the beginning of semantic analytics occurred in 1996, although the historical progression of these algorithms is largely subjective. In his seminal study publication, Philip Resnik established that computers have the capacity to emulate human judgement. Spanning the publications of multiple journals, improvements to the accuracy of general semantic analytic computations all claimed to revolutionize the field. However, the lack of a standard terminology throughout the late 1990s was the cause of much miscommunication. This prompted Budanitsky & Hirst to standardize the subject in 2006 with a summary that also set a framework for modern spelling and grammar analysis. In the early days of semantic analytics, obtaining a large enough reliable knowledge bases was difficult. In 2006, Strube & Ponzetto demonstrated that Wikipedia could be used in semantic analytic calculations. The usage of a large knowledge base like Wikipedia allows for an increase in both the accuracy and applicability of semantic analytics. == Methods == Given the subjective nature of the field, different methods used in semantic analytics depend on the domain of application. No singular methods is considered correct, however one of the most generally effective and applicable method is explicit semantic analysis (ESA). ESA was developed by Evgeniy Gabrilovich and Shaul Markovitch in the late 2000s. It uses machine learning techniques to create a semantic interpreter, which extracts text fragments from articles into a sorted list. The fragments are sorted by how related they are to the surrounding text. Latent semantic analysis (LSA) is another common method that does not use ontologies, only considering the text in the input space. == Applications == Entity linking Ontology building / knowledge base population Search and query tasks Natural language processing Spoken dialog systems (e.g., Amazon Alexa, Google Assistant, Microsoft's Cortana) Artificial intelligence Knowledge management The application of semantic analysis methods generally streamlines organizational processes of any knowledge management system. Academic libraries often use a domain-specific application to create a more efficient organizational system. By classifying scientific publications using semantics and Wikipedia, researchers are helping people find resources faster. Search engines like Semantic Scholar provide organized access to millions of articles.

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  LMArena

  Arena (formerly LMArena and Chatbot Arena) is a public, web-based platform that evaluates large language models (LLMs). Users enter prompts for two anonymous models to respond to and vote on the model that gave the better response, after which the models' identities are revealed. Users can also choose models to test themselves via the "Direct" selection. Companies which have supplied the company with their large language models include OpenAI, Google DeepMind, and Anthropic. The website has been used for preview releases of upcoming models. Chinese company DeepSeek tested its prototype models in the Arena months before its R1 model gained attention in Western media. Other notable pre-release models include OpenAI's GPT-5 under the codename "summit" and Google DeepMind's Gemini 2.5 Flash Image (an image-generation and editing model) under the codename "Nano Banana". Research has identified specific limitations in Arena's methodology. == History == Chatbot Arena was released on April 24, 2023. In June 2024, Chatbot Arena added image support. In September 2024, Chatbot Arena moved to its own dedicated domain name, lmarena.ai (or LMArena). In April 2025, Meta released Llama 4. Llama 4 Maverick beat GPT-4o and Gemini 2.0 Flash on LMArena, but the version of Maverick on LMArena unfairly differed from the publicly available version. LMArena updated their policies in response. In April 2025, LMArena incorporated as an independent company. That May, LMArena raised $100 million in a seed funding round, valuing the company at $600 million. Participants in the seed funding round included Andreessen Horowitz, UC Investments, Lightspeed Venture Partners, Felicis Ventures, and Kleiner Perkins. On January 6, 2026, LMArena announced the closing of a $150 million Series A funding round, bringing the company’s post-money valuation to approximately $1.7 billion. The round was led by Felicis and UC Investments (University of California), with participation from Andreessen Horowitz, The House Fund, LDVP, Kleiner Perkins, Lightspeed Venture Partners, and Laude Ventures. In January 2026, LMArena added video support. On January 28, 2026, LMArena rebranded to "Arena".

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  Desktop video

  Desktop video refers to a phenomenon lasting from the mid-1980s to the early 1990s when the graphics capabilities of personal computers such as the Amiga, Macintosh II, and specially-upgraded IBM PC compatibles had advanced to the point where individuals and local broadcasters could use them for analog non-linear editing and vision mixing in video production. Despite the use of computers, desktop video should not be confused with digital video since the video data remained analog, and it uses items like a VCR and a camcorder to record the video. Full-screen, full-motion video's vast storage requirements meant that the promise of digital encoding would not be realized on desktop computers for at least another decade. == Description == There were multiple models of genlock cards available to synchronize the content; the Newtek Video Toaster was commonly used in Amiga in countries that used NTSC (PAL-M in Brazil), while PCs had Truevision and Matrox Illuminator cards and Mac systems had the SuperMac Video Spigot and Radius VideoVision cards. Apple later introduced the Macintosh Quadra 840AV and Centris 660AV systems to specifically address this market. Desktop video was a parallel development to desktop publishing and enabled many small production houses and local TV stations to produce their own original content for the first time. Along with the advent of public-access cable channels, desktop video meant that television advertising became affordable for local businesses such as retailers, restaurants, real estate agents, contractors and auto dealers. As with the phrase desktop publishing, use of the term died out as the technologies to which it referred become the norm for any kind of video production.

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  Uniform convergence in probability

  Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family uniformly converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. Specifically, the Glivenko-Cantelli theorem and the homonymous classes of functions are fundamentally related to uniform convergence. The law of large numbers says that, for each single event A {\displaystyle A} , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class S {\displaystyle S} from one and the same sample. Moreover, it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events S {\displaystyle S} . The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds. == Definitions == For a class of predicates H {\displaystyle H} defined on a set X {\displaystyle X} and a set of samples x = ( x 1 , x 2 , … , x m ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{m})} , where x i ∈ X {\displaystyle x_{i}\in X} , the empirical frequency of h ∈ H {\displaystyle h\in H} on x {\displaystyle x} is Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | . {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|.} The theoretical probability of h ∈ H {\displaystyle h\in H} is defined as Q P ( h ) = P { y ∈ X : h ( y ) = 1 } . {\displaystyle Q_{P}(h)=P\{y\in X:h(y)=1\}.} The Uniform Convergence Theorem states, roughly, that if H {\displaystyle H} is "simple" and we draw samples independently (with replacement) from X {\displaystyle X} according to any distribution P {\displaystyle P} , then with high probability, the empirical frequency will be close to its expected value, which is the theoretical probability. Here "simple" means that the Vapnik–Chervonenkis dimension of the class H {\displaystyle H} is small relative to the size of the sample. In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole. The Uniform Convergence Theorem was first proved by Vapnik and Chervonenkis using the concept of growth function. == Uniform Convergence Theorem == The statement of the Uniform Convergence Theorem is as follows: If H {\displaystyle H} is a set of { 0 , 1 } {\displaystyle \{0,1\}} -valued functions defined on a set X {\displaystyle X} and P {\displaystyle P} is a probability distribution on X {\displaystyle X} then for ε > 0 {\displaystyle \varepsilon >0} and m {\displaystyle m} a positive integer, we have: P m { | Q P ( h ) − Q x ^ ( h ) | ≥ ε for some h ∈ H } ≤ 4 Π H ( 2 m ) e − ε 2 m / 8 . {\displaystyle P^{m}\{|Q_{P}(h)-{\widehat {Q_{x}}}(h)|\geq \varepsilon {\text{ for some }}h\in H\}\leq 4\Pi _{H}(2m)e^{-\varepsilon ^{2}m/8}.} In the above, for any x ∈ X m , {\displaystyle x\in X^{m},} Q P ( h ) = P { ( y ∈ X : h ( y ) = 1 } , {\displaystyle Q_{P}(h)=P\{(y\in X:h(y)=1\},} Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|} and | x | = m . {\displaystyle |x|=m.} P m {\displaystyle P^{m}} indicates that the probability is taken over x {\displaystyle x} consisting of m {\displaystyle m} i.i.d. draws from the distribution P . {\displaystyle P.} Finally, the growth function Π H {\displaystyle \Pi _{H}} is defined in the following way, for any { 0 , 1 } {\displaystyle \{0,1\}} -valued functions H {\displaystyle H} over X {\displaystyle X} and for any natural number m {\displaystyle m} : Π H ( m ) = max | { h ∩ D : D ⊆ X , | D | = m , h ∈ H } | . {\displaystyle \Pi _{H}(m)=\max |\{h\cap D:D\subseteq X,|D|=m,h\in H\}|.} From the point of view of Learning Theory one can consider H {\displaystyle H} to be the Concept/Hypothesis class defined over the instance set X {\displaystyle X} . Crucially, the Sauer–Shelah lemma implies that Π H ( m ) ≤ m d {\displaystyle \Pi _{H}(m)\leq m^{d}} , where d {\displaystyle d} is the VC dimension of H {\displaystyle H} . == Proof of the Uniform Convergence Theorem == and are the sources of the proof below. Before we get into the details of the proof of the Uniform Convergence Theorem we will present a high level overview of the proof. Symmetrization: We transform the problem of analyzing | Q P ( h ) − Q ^ x ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon } into the problem of analyzing | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} , where r {\displaystyle r} and s {\displaystyle s} are i.i.d samples of size m {\displaystyle m} drawn according to the distribution P {\displaystyle P} . One can view r {\displaystyle r} as the original randomly drawn sample of length m {\displaystyle m} , while s {\displaystyle s} may be thought as the testing sample which is used to estimate Q P ( h ) {\displaystyle Q_{P}(h)} . Permutation: Since r {\displaystyle r} and s {\displaystyle s} are picked identically and independently, so swapping elements between them will not change the probability distribution on r {\displaystyle r} and s {\displaystyle s} . So, we will try to bound the probability of | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} for some h ∈ H {\displaystyle h\in H} by considering the effect of a specific collection of permutations of the joint sample x = r | | s {\displaystyle x=r||s} . Specifically, we consider permutations σ ( x ) {\displaystyle \sigma (x)} which swap x i {\displaystyle x_{i}} and x m + i {\displaystyle x_{m+i}} in some subset of 1 , 2 , . . . , m {\displaystyle {1,2,...,m}} . The symbol r | | s {\displaystyle r||s} means the concatenation of r {\displaystyle r} and s {\displaystyle s} . Reduction to a finite class: We can now restrict the function class H {\displaystyle H} to a fixed joint sample and hence, if H {\displaystyle H} has finite VC Dimension, it reduces to the problem to one involving a finite function class. We present the technical details of the proof. It should be stressed that this proof glosses over details like the measurability of the events V {\displaystyle V} and R {\displaystyle R} ; measurability is granted in the case of H {\displaystyle H} being finite or countable, but this is not normally the case in standard applications of the theorem (e.g. for statistical learning theory or to prove the Glivenko-Cantelli theorem). To get measurability, one needs to use a notion of separability of the underlying space, possibly related to H {\displaystyle H} . === Symmetrization === Lemma: Let V = { x ∈ X m : | Q P ( h ) − Q ^ x ( h ) | ≥ ε for some h ∈ H } {\displaystyle V=\{x\in X^{m}:|Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon {\text{ for some }}h\in H\}} and R = { ( r , s ) ∈ X m × X m : | Q r ^ ( h ) − Q ^ s ( h ) | ≥ ε / 2 for some h ∈ H } . {\displaystyle R=\{(r,s)\in X^{m}\times X^{m}:|{\widehat {Q_{r}}}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2{\text{ for some }}h\in H\}.} Then for m ≥ 2 ε 2 {\displaystyle m\geq {\frac {2}{\varepsilon ^{2}}}} , P m ( V ) ≤ 2 P 2 m ( R ) {\displaystyle P^{m}(V)\leq 2P^{2m}(R)} . Proof: By the triangle inequality, if | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2} then | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} . Therefore, P 2 m ( R ) ≥ P 2 m { ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } = ∫ V P m { s : ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } d P m ( r ) = A {\displaystyle {\begin{aligned}&P^{2m}(R)\\[5pt]\geq {}&P^{2m}\{\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\\[5pt]={}&\int _{V}P^{m}\{s:\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\,dP^{m}(r)\\[5pt]={}&A\end{aligned}}} since r {\displaystyle r} and s {\displaystyle s} are independent. Now for r ∈ V {\displaystyle r\in V} fix an h ∈ H {\displaystyle h\in H} such that | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } . For this h {\displaystyle h} , we shall

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  Stixel

  In computer vision, a stixel (portmanteau of "stick" and "pixel") is a superpixel representation of depth information in an image, in the form of a vertical stick that approximates the closest obstacles within a certain vertical slice of the scene. Introduced in 2009, stixels have applications in robotic navigation and advanced driver-assistance systems, where they can be used to define a representation of robotic environments and traffic scenes with a medium level of abstraction. == Definition == One of the problems of scene understanding in computer vision is to determine horizontal freespace around the camera, where the agent can move, and the vertical obstacles delimiting it. An image can be paired with depth information (produced e.g. from stereo disparity, lidar, or monocular depth estimation), allowing a dense tridimensional reconstruction of the observed scene. One drawback of dense reconstruction is the large amount of data involved, since each pixel in the image is mapped to an element of a point cloud. Vision problems characterised by planar freespace delimited by mostly vertical obstacles, such as traffic scenes or robotic navigation, can benefit from a condensed representation that allows to save memory and processing time. Stixels are thin vertical rectangles representing a slice of a vertical surface belonging to the closest obstacle in the observed scene. They allow to dramatically reduce the amount of information needed to represent a scene in such problems. A stixel is characterised by three parameters: vertical coordinate of the bottom, height of the stick, and depth. Stixels have fixed width, with each stixel spanning over a certain number of image columns, allowing downsampling of the horizontal image resolution. In the original formulation, each column of the image would contain at most one stixel, and later extensions were developed to allow multiple stixels on each column, allowing to represent multiple objects at different distances. == Stixel estimation == The input to stixel estimation is a dense depth map, that can be computed from stereo disparity or other means. The original approach computes an occupancy grid that can be segmented to estimate the freespace, with dynamic programming providing an efficient method to find an optimal segmentation. Alternative approaches can be used instead of occupancy grid mapping, such as manifold-based methods. The freespace boundary provides the base points of the obstacles at closest longitudinal distance, however multiple objects at different distances might appear in each column of the image. To fully define the obstacles, their height should be estimated, and this is accomplished by segmenting the depth of the object from the depth of the background. A membership function over the pixels can be defined based on the depth value, where the membership represents the confidence of a pixel belonging to the closest vertical obstacle or to the background, and a cut separating the obstacles from the background can again be computed effectively with dynamic programming. Once both the freespace and the obstacle height are known, the stixels can be estimated by fusing the information over the columns spanned by each stixel, and finally a refined depth of the stixel can be estimated via model fitting over the depth of the pixels covered by the stixel, possibly paired with confidence information (e.g. disparity confidence produced by methods such as semi-global matching).

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