AI Assistant Grok

AI Assistant Grok — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Neural processing unit

A neural processing unit (NPU), also known as an AI accelerator or deep learning processor, is a class of specialized hardware accelerator or computer system designed to accelerate artificial intelligence and machine learning applications, including artificial neural networks and computer vision. == Use == Their purpose is either to efficiently execute already trained AI models (inference) or to train AI models. NPUs can be more efficient in terms of speed or power consumption. NPU applications include algorithms for robotics, Internet of things, and data-intensive or sensor-driven tasks. They are often manycore or spatial designs and focus on low-precision arithmetic, novel dataflow architectures, or in-memory computing capability. As of 2024, a widely used datacenter-grade AI integrated circuit chip, the Nvidia H100 GPU, contains tens of billions of MOSFETs. === Consumer devices === AI accelerators are used in Apple silicon, Qualcomm, Samsung, Huawei, and Google Tensor smartphone processors. Vision processing units are accelerators specialized for machine vision algorithms such as CNN (convolutional neural networks) and SIFT (scale-invariant feature transform). They are used in devices that need to keep track of objects visually such as AR headsets and drones. It is more recently (circa 2017) added to processors from Apple and (circa 2022) to processors from Intel and AMD. All models of Intel Meteor Lake processors have a built-in versatile processor unit (VPU) for accelerating inference for computer vision and deep learning. On consumer devices, the NPU is intended to be small, power-efficient, but reasonably fast when used to run small models. To do this they are designed to support low-bitwidth operations using data types such as INT4, INT8, FP8, and FP16. A common metric is trillions of operations per second (TOPS). Although TOPS does not explicitly specify the kind of operations, it is typically INT8 additions and multiplications. === Datacenters === Accelerators are used in cloud computing servers: e.g., tensor processing units (TPU) for Google Cloud Platform, and Trainium and Inferentia chips for Amazon Web Services. Many vendor-specific terms exist for devices in this category, and it is an emerging technology without a dominant design. Since the late 2010s, graphics processing units designed by companies such as Nvidia and AMD often include AI-specific hardware in the form of dedicated functional units for low-precision matrix-multiplication operations. These GPUs are commonly used as AI accelerators, both for training and inference. === Scientific computation === Although NPUs are tailored for low-precision (e.g., FP16, INT8) matrix multiplication operations, they can be used to emulate higher-precision matrix multiplications in scientific computing. As modern GPUs place much focus on making the NPU part fast, using emulated FP64 (Ozaki scheme) on NPUs can potentially outperform native FP64. This has been demonstrated using FP16-emulated FP64 on NVIDIA TITAN RTX and using INT8-emulated FP64 on NVIDIA consumer GPUs and the A100 GPU. Consumer GPUs especially benefited as they have limited FP64 hardware capacity, showing a 6× speedup. Since CUDA Toolkit 13.0 Update 2, cuBLAS automatically uses INT8-emulated FP64 matrix multiplication of the equivalent precision if it is faster than native. This is in addition to the FP16-emulated FP32 feature introduced in version 12.9. == Programming == An operating system or a higher-level library may provide application programming interfaces such as TensorFlow with LiteRT Next (Android), CoreML (iOS, macOS) or DirectML (Windows). Formats such as ONNX are used to represent trained neural networks. Consumer CPU-integrated NPUs are accessible through vendor-specific APIs. AMD (Ryzen AI), Intel (OpenVINO), Apple silicon (CoreML), and Qualcomm (SNPE) each have their own APIs, which can be built upon by a higher-level library. GPUs generally use existing GPGPU pipelines such as CUDA and OpenCL adapted for lower precisions and specialized matrix-multiplication operations. Vulkan is also being used. Custom-built systems such as the Google TPU use private interfaces. There are a large number of separate underlying acceleration APIs and compilers/runtimes in use in the AI field, causing a great increase in software development effort due to the many combinations involved. As of 2025, the open standard organization Khronos Group is pursuing standardization of AI-related interfaces to reduce the amount of work needed. Khronos is working on three separate fronts: expansion of data types and intrinsic operations in OpenCL and Vulkan, inclusion of compute graphs in SPIR-V, and a NNEF/SkriptND file format for describing a neural network.
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Character computing

Character computing is a trans-disciplinary field of research at the intersection of computer science and psychology. It is any computing that incorporates the human character within its context. Character is defined as all features or characteristics defining an individual and guiding their behavior in a specific situation. It consists of stable trait markers (e.g., personality, background, history, socio-economic embeddings, culture,...) and variable state markers (emotions, health, cognitive state, ...). Character computing aims at providing a holistic psychologically driven model of human behavior. It models and predicts behavior based on the relationships between a situation and character. Three main research modules fall under the umbrella of character computing: character sensing and profiling, character-aware adaptive systems, and artificial characters. == Overview == Character computing can be viewed as an extension of the well-established field of affective computing. Based on the foundations of the different psychology branches, it advocates defining behavior as a compound attribute that is not driven by either personality, emotions, situation or cognition alone. It rather defines behavior as a function of everything that makes up an individual i.e., their character and the situation they are in. Affective computing aims at allowing machines to understand and translate the non-verbal cues of individuals into affect. Accordingly, character computing aims at understanding the character attributes of an individual and the situation to translate it to predicted behavior, and vice versa. ''In practical terms, depending on the application context, character computing is a branch of research that deals with the design of systems and interfaces that can observe, sense, predict, adapt to, affect, understand, or simulate the following: character based on behavior and situation, behavior based on character and situation, or situation based on character and behavior.'' The Character-Behavior-Situation (CBS) triad is at the core of character computing and defines each of the three edges based on the other two. Character computing relies on simultaneous development from a computational and psychological perspective and is intended to be used by researchers in both fields. Its main concept is aligning the computational model of character computing with empirical results from in-lab and in-the-wild psychology experiments. The model is to be continuously built and validated through the emergence of new data. Similar to affective and personality computing, the model is to be used as a base for different applications towards improving user experience. == History == Character computing as such was first coined in its first workshop in 2017. Since then it has had 3 international workshops and numerous publications. Despite its young age, it has already drawn some interest in the research community, leading to the publication of the first book under the same title in early 2020 published by Springer Nature. Research that can be categorized under the field dates much older than 2017. The notion of combining several factors towards the explanation of behavior or traits and states has long been investigated in both Psychology and Computer Science, for example. == Character == The word character originates from the Greek word meaning “stamping tool”, referring to distinctive features and traits. Over the years it has been given many different connotations, like the moral character in philosophy, the temperament in psychology, a person in literature or an avatar in various virtual worlds, including video games. According to character computing character is a unification of all the previous definitions, by referring back to the original meaning of the word. Character is defined as the holistic concept representing all interacting trait and state markers that distinguish an individual. Traits are characteristics that mainly remain stable over time. Traits include personality, affect, socio-demographics, and general health. States are characteristics that vary in short periods of time. They include emotions, well-being, health, cognitive state. Each characteristic has many representation methods and psychological models. The different models can be combined or one model can be preset for each characteristic. This depends on the use-case and the design choices. == Areas == Research into character computing can be divided into three areas, which complement each other but can each be investigated separately. The first area is sensing and predicting character states and traits or ensuing behavior. The second area is adapting applications to certain character states or traits and the behavior they predict. It also deals with trying to change or monitor such behavior. The final area deals with creating artificial agents e.g., chatbots or virtual reality avatars that exhibit certain characteristics. The three areas are investigated separately and build on existing findings in the literature. The results of each of the three areas can also be used as a stepping stone for the next area. Each of the three areas has already been investigated on its own in different research fields with focus on different subsets of character. For example, affective computing and personality computing both cover different areas with a focus on some character components without the others to account for human behavior. == The Character-Behavior-Situation triad == Character computing is based on a holistic psychologically driven model of human behavior. Human behavior is modeled and predicted based on the relationships between a situation and a human's character. To further define character in a more formal or holistic manner, we represent it in light of the Character–Behavior–Situation triad. This highlights that character not only determines who we are but how we are, i.e., how we behave. The triad investigated in Personality Psychology is extended through character computing to the Character–Behavior–Situation triad. Any member of the CBS triad is a function of the two other members, e.g., given the situation and personality, the behavior can be predicted. Each of the components in the triad can be further decomposed into smaller units and features that may best represent the human's behavior or character in a particular situation. Character is thus behind a person's behavior in any given situation. While this is a causality relation, the correlation between the three components is often more easily used to predict the components that are most difficult to measure from those measured more easily. There are infinitely many components to include in the representation of any of C, B, and S. The challenge is always to choose the smallest subset needed for prediction of a person's behavior in a particular situation.
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Inauthentic text

An inauthentic text is a computer-generated expository document meant to appear as genuine, but which is actually meaningless. Frequently they are created in order to be intermixed with genuine documents and thus manipulate the results of search engines, as with Spam blogs. They are also carried along in email in order to fool spam filters by giving the spam the superficial characteristics of legitimate text. Sometimes nonsensical documents are created with computer assistance for humorous effect, as with Dissociated press or Flarf poetry. They have also been used to challenge the veracity of a publication—MIT students submitted papers generated by a computer program called SCIgen to a conference, where they were initially accepted. This led the students to claim that the bar for submissions was too low. With the amount of computer generated text outpacing the ability of people to humans to curate it, there needs some means of distinguishing between the two. Yet automated approaches to determining absolutely whether a text is authentic or not face intrinsic challenges of semantics. Noam Chomsky coined the phrase "Colorless green ideas sleep furiously" giving an example of grammatically correct, but semantically incoherent sentence; some will point out that in certain contexts one could give this sentence (or any phrase) meaning. The first group to use the expression in this regard can be found below from Indiana University. Their work explains in detail an attempt to detect inauthentic texts and identify pernicious problems of inauthentic texts in cyberspace. The site has a means of submitting text that assesses, based on supervised learning, whether a corpus is inauthentic or not. Many users have submitted incorrect types of data and have correspondingly commented on the scores. This application is meant for a specific kind of data; therefore, submitting, say, an email, will not return a meaningful score.
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Halite AI Programming Competition

Halite is an open-source computer programming contest developed by the hedge fund/tech firm Two Sigma in partnership with a team at Cornell Tech. Programmers can see the game environment and learn everything they need to know about the game. Participants are asked to build bots in whichever language they choose to compete on a two-dimensional virtual battle field. == History == Benjamin Spector and Michael Truell created the first Halite competition in 2016, before partnering with Two Sigma later that year. === Halite I === Halite I asked participants to conquer territory on a grid. It launched in November 2016 and ended in February 2017. Halite I attracted about 1,500 players. === Halite II === Halite II was similar to Halite I, but with a space-war theme. It ran from October 2017 until January 2018. The second installment of the competition attracted about 6,000 individual players from more than 100 countries. Among the participants were professors, physicists and NASA engineers, as well as high school and university students. === Halite III === Halite III launched in mid-October 2018. It ran from October 2018 to January 2019, with an ocean themed playing field. Players were asked to collect and manage Halite, an energy resource. By the end of the competition, Halite III included more than 4000 players and 460 organizations. === Halite IV === Halite IV was hosted by Kaggle, and launched in mid-June 2020.
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Josh (app)

Josh (stylized as JOSH) was a video-sharing social networking service but it has since evolved into a live call and chat application owned by VerSe Innovation – an Indian technology company based in Bangalore, India. Josh was an Indian short video app that was launched in immediately after the Indian Government banned TikTok and other Chinese apps in June 2020. The founders of the platform have promoted the app as the “Instagram for Bharat” referring to their focus on the Indian audience that speaks its own regional and state languages. Josh was among the top 10 most downloaded apps social and entertainment apps in India of 2021 and had 150 million monthly active users as per April 2022. The word 'Josh' translates to fervour or passion. The app was launched under the aegis of the Atmanirbhar Bharat campaign and to compete with the duopoly of Google and Facebook in India. Josh's parent company VerSe Innovations Pvt. Ltd. owns another startup Dailyhunt, which a content and news aggregator application. Both Dailyhunt and Josh are a part of the VerSe's focus on the "next billion" regional language users of India. Founders Virendra Gupta and Umang Bedi conceptualised Josh as a short-video platform that made content creation accessible to vernacular language users, essentially the non-English speaking audience in India. == Features == Josh is currently available in 12 Indian languages and allows users to upload, share, remix bite-sized videos of up to 120 seconds. There are various categories across the video section including viral, trending, glamour, dance, devotion, yoga and cooking among others. Similar to Instagram and TikTok, it has a video feed which is curated for individuals on the basis of their app behaviour. The app hosts many daily, weekly and monthly social media challenges. == Funding == In December 2020, within 3 months of its launch, Josh's parent app VerSe Innovation raised more than $100 million from investors including Alphabet Inc's Google and Microsoft. In February 2021, VerSe Innovation raised $100 million in Series H funding from Qatar Investment Authority, the sovereign wealth fund of the State of Qatar, and Glade Brook Capital Partners. In August 2021, VerSe raised over $450 million in its Series I financing round with a valuation of $1 billion. Investors included Canada Pension Plan Investment Board (CPPIB), Siguler Guff, Baillie Gifford, Carlyle Asia Partners Growth II affiliates, and others. The startup announced its plan to expand overseas and broaden its ecommerce play for both Dailyhunt and Josh. In April 2022, VerSe announced that it has raised $805 million in funding from investors at a valuation of nearly $5 billion. ByteDance Offloads Stake In Josh Parent VerSe, Exits At 56% Discount == Partnerships == In February 2021, Saregama and Josh signed a music licensing deal, wherein Josh expanded its musical library with 1.3 lakh songs from Saregama in 25 different languages. To improve their user experience, Josh partnered with computer vision company D-ID in August 2021. The company helped Josh introduce photo-to-video features, live portrait technology, animate their photos etc. In order to solidify their efforts in enhancing Josh, VerSe acquired Indian social networking platform GolBol in October 2021. The move came as an effort by the startup to strengthen their discovery initiatives on the platform and classify content at scale and understand the core behaviour of Indian regional audiences. Josh has also announced its plans to include live commerce as a potential revenue stream through its partnership with multiple large e-commerce players. == Notable campaigns == Say No To Dowry – In association with Josh, the Kerala Police partook in the #SayNo2Dowry online social media campaign that was started to highlight and stop the social evil in the state. Salute India – Josh entered the Guinness World Records by creating the largest online video album of people saluting (29,529). It organised an online campaign #SaluteIndia on the app during the 75th Independence Day of India during 10–15 August 2021.
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Artificial intelligence

Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in engineering, mathematics and computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines, chatbots, virtual assistants, autonomous vehicles, and play and analysis in strategy games (e.g., chess and Go). Since the 2020s, generative AI has become widely available to generate images, audio, and videos from text prompts. The traditional goals of AI research include learning, reasoning, knowledge representation, planning, natural language processing, and perception, as well as support for robotics. To reach these goals, AI researchers have used techniques including state space search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics. AI also draws upon psychology, linguistics, philosophy, neuroscience, and other fields. Some companies, such as OpenAI, Google DeepMind and Meta, aim to create artificial general intelligence (AGI) – AI that can complete virtually any cognitive task at least as well as a human. Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest increased substantially after 2012, when graphics processing units began being used to accelerate neural networks, and deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture. In the 2020s, an AI boom has coincided with advances in generative AI, which allowed for the creation and modification of media. In addition to AI safety and unintended consequences and harms from the use of AI, ethical concerns, AI's long-term effects, and potential existential risks have prompted discussions of AI regulation. == Goals == The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research. === Reasoning and problem-solving === Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions. By the late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics. Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments. Accurate and efficient reasoning is an unsolved problem. === Knowledge representation === Knowledge representation and knowledge engineering allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas. A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; situations, events, states, and time; causes and effects; knowledge about knowledge (what we know about what other people know); default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing); and many other aspects and domains of knowledge. Among the most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous); and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition, the problem of obtaining knowledge for AI applications. === Planning and decision-making === An "agent" is any entity (artificial or not) that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning, the agent has a specific goal. In automated decision-making, the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called the "utility") that measures how much the agent prefers it. For each possible action, it can calculate the "expected utility": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility. In classical planning, the agent knows exactly what the effect of any action will be. In most real-world problems, however, the agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. Alongside thorough testing and improvement based on previous decisions, having an explanation for why the agent took certain decisions is a way to build trust, especially when the decisions have to be relied upon. In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or experimental actions. The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be. A Markov decision process has a transition model that describes the probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration), be heuristic, or it can be learned. Game theory describes the rational behavior of multiple interacting agents and is used in AI programs that make decisions that involve other agents. === Learning === Machine learning is the study of programs that can improve their performance on a given task automatically. It has been a part of AI from the beginning. There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance. Supervised learning requires labeling the training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input). In reinforcement learning, the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good". Transfer learning is when the knowledge gained from one problem is applied to a new problem. Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning. Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization. === Natural language processing === Natural language processing (NLP) allows programs to read, write and communicate in human languages. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval and question answering. Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation unless
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Tensor (machine learning)

In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .
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Grokking (machine learning)

In machine learning, grokking, or delayed generalization, is a phenomenon observed in some settings where a model abruptly transitions from overfitting (performing well only on training data) to generalizing (performing well on both training and test data), after many training iterations with little or no improvement on the held-out data. This contrasts with what is typically observed in machine learning, where generalization occurs gradually alongside improved performance on training data. == Origin == Grokking was introduced by OpenAI researcher Alethea Power and colleagues in the January 2022 paper "Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets". It is derived from the word grok coined by Robert Heinlein in his novel Stranger in a Strange Land. In ML research, "grokking" is not used as a synonym for "generalization"; rather, it names a sometimes-observed delayed‑generalization training phenomenon in which training and held‑out performance do not improve in tandem, and in which held‑out performance rises abruptly later. Authors also analyze the "grokking time", the epoch or step at which this transition occurs in those scenarios. == Interpretations == Grokking can be understood as a phase transition during the training process. In particular, recent work has shown that grokking may be due to a complexity phase transition in the model during training. While grokking has been thought of as largely a phenomenon of relatively shallow models, grokking has been observed in deep neural networks and non-neural models and is the subject of active research. One potential explanation is that the weight decay (a component of the loss function that penalizes higher values of the neural network parameters, also called regularization) slightly favors the general solution that involves lower weight values, but that is also harder to find. According to Neel Nanda, the process of learning the general solution may be gradual, even though the transition to the general solution occurs more suddenly later. Recent theories have hypothesized that grokking occurs when neural networks transition from a "lazy training" regime where the weights do not deviate far from initialization, to a "rich" regime where weights abruptly begin to move in task-relevant directions. Follow-up empirical and theoretical work has accumulated evidence in support of this perspective, and it offers a unifying view of earlier work as the transition from lazy to rich training dynamics is known to arise from properties of adaptive optimizers, weight decay, initial parameter weight norm, and more. This perspective is complementary to a unifying "pattern learning speeds" framework that links grokking and double descent; within this view, delayed generalization can arise across training time ("epoch‑wise") or across model size ("model‑wise"), and the authors report "model‑wise grokking".
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Clesh

Clesh (clip load edit share) is a cloud-based video editing platform, created by Forbidden Technologies plc, designed for the consumers, prosumers, and online communities to integrate user-generated content. The core technology is based on FORscene which is geared towards professionals working for example in broadcasting, news media, post production. Video, audio, and graphical content is uploaded to Clesh via a standard web browser, a mobile device such as a phone / tablet, or desktop software for DV capture over FireWire. The hosted material can then be reviewed, searched, edited, and published online by anyone with a standard web browser or compatible mobile device. Clesh supports storyboard shot selection, frame-accurate editing, transitions and various other functions such as; pan, zoom, colour and light correction, and audio levels. Content can be published in formats for example; Podcast, Mpeg2, HTML video or in a proprietary Java format. Cloud-based software provides greater scope for sharing information and collaborating compared to LAN or desktop based systems. Users of cloud-based software rely on the cloud's owner for adequate security, performance and resilience. Clesh does not assert any rights over uploaded content in contrast to other platforms (such as YouTube). All rights to any content uploaded to Clesh remain with the Author. == Features == Some of the services available to Clesh users: Access via Java enabled desktops or Android smartphones or tablets Real-time video rendering including effects and transitions Multiple audio tracks Secured log-on Frame accurate timeline for fine cut editing Logging / meta-data annotation assigns text to portions of video (usable by Clesh and web search engines) Storyboard assembles rough cuts using drag-and-drop Import, host, organise and search for media (DV tape and various video, audio, and still image formats) Publish content to in formats such as podcast, MPEG-2, web (Java Applet), Flash, Ogg, HTML and JPEG Chatrooms to talk to other Clesh users Showreel (a gallery for publishing material visible to internet users) Moderation for approval of material prior to distribution downstream Re-branding and integration support for white-label deployment == Technology == Clesh is based on the same technology as FORscene. An array of servers on the internet backbone provide the cloud computing platform to host Clesh. As a white-label solution Clesh would be branded and hosted per the client requirement. == User interface == End-users access Clesh on clients such as standard Java-enabled Web Browsers and / or Android enabled mobile devices such as tablets and smartphones. == History == Clesh was launched January 2006 and subject to several upgrades during the year to extend functionality including; storyboard, podcasting, moderation, chat and a showreel. During 2007 consumers are offered Clesh via a subscription model. Upgrades include Web Start and graphics upload. Mr Paparazzi selects Clesh as the platform to host its video offering and TrueTube does the same in 2008 by choosing to use Clesh to manage its video portal. Several further upgrades are applied and include; better audio quality, image enhancement controls, transitions, fades, titles, and additional publishing options such as JPEG. In 2010 a version of Clesh is demonstrated on an Android OS tablet device (Samsung Galaxy S Tab), and several upgrades are applied including; HTML publishing, pan, zoom, and overlays.
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Artificial intelligence in education

Artificial intelligence in education (often abbreviated as AIEd) is a subfield of educational technology that studies how to use artificial intelligence to create learning environments. Considerations in the field include data-driven decision-making, AI ethics, data privacy and AI literacy. Concerns include the potential for cheating, over-reliance, equity of access, reduced critical thinking, and the perpetuation of misinformation and bias. == History == Efforts to integrate AI into educational contexts have often followed technological advancement in the history of artificial intelligence. In the 1960s, educators and researchers began developing computer-based instruction systems, such as PLATO, developed by the University of Illinois. In the 1970s and 1980s, intelligent tutoring systems (ITS) were being adapted for classroom instruction. The International Artificial Intelligence in Education Society was founded in 1993. Coinciding with the AI boom of the 2020s, the use of large language models in the global north has been promoted and funded by venture capital and big tech. Companies creating AI services have targeted students and educational institutions as customers. Similarly, pre-AI boom educational companies have expanded their use of AI technologies. These commercial incentives for AIEd use may be related to a potential AI bubble. In the U.S., bipartisan support of AI development in K-12 education has been expressed, but specific implementations and best practices remain contentious. == Theory == AIEd applies theory from education studies, machine learning, and related fields. A 2019 review of the previous decade of studies found that most research prioritized technological design over pedagogical integration. Ouyang and Jiao (2021) propose three paradigms for AI in education, which follow roughly from least to most learner-centered and from requiring least to most technical complexity from the AI systems: AI-directed, learner-as-recipient: AIEd systems present a pre-set curriculum based on statistical patterns that do not adjust to learner's feedback. AI-supported, learner-as-collaborator: Systems that incorporate responsiveness to learner's feedback through, for example, natural language processing, wherein AI can support knowledge construction. AI-empowered, learner-as-leader: This model seeks to position AI as a supplement to human intelligence wherein learners take agency and AI provides consistent and actionable feedback. Some scholars place AI in education within a socio-technical framework. This positions AI alongside other emerging educational technologies, such as computing, the internet, and social media. The framework of Tsao, Heinrichs and Camit (2025) draws on new materialism and posthumanism, specifically Donna Haraway's concept of sympoiesis (making-with). This perspective views learning as an entanglement of human and non-human actors (students, teachers, and AI algorithms), where knowledge is co-composed in contact zones between human context and algorithmic prediction. AI agents have been trained on biased datasets, and thus continue to perpetuate societal biases. Since LLMs were created to produce human-like text, algorithmic bias can be introduced and reproduced. AI's data processing and monitoring reinforce neoliberal approaches to education rather than addressing inequalities. == Applications == Uses of generative AI chatbots in education have included assessment and feedback, machine translations, proof-reading exam question generation and copy editing, or as virtual assistants. Emotional AI in education is the study and development of systems that can detect learners' emotions or provide emotional support in learning. == Usage == === Schools and educators === Following the release of ChatGPT in November 2022, some schools and large school districts blocked access to the site and issued warnings that the use of such tools would be seen as cheating. Governmental and non-governmental organizations such as UNESCO, Article 4 of the European Union's AI Act, and the U.S. Department of Education have published reports advocating for specific AIEd approaches. National higher-education bodies have also published guidance on generative AI, including Ireland's Higher Education Authority, which issued a policy framework for higher education teaching and learning in December 2025. In 2024, UNESCO released updated global guidance for generative AI in education, emphasizing ethical use, teacher training, and data protection to ensure responsible integration of AI tools in learning environments. According to Taso (2025), policy implementation in higher education is interpreted and enacted differently by various organizations. These decentralized policies can lead to inconsistent enforcement and confusion among students regarding what constitutes acceptable use, with the burden of ethical navigation falling on individual teachers and students. AI integration in classrooms has created new forms of invisible labour for educators, who must navigate ambiguous policies, redesign assessments to be AI-resilient, and adjudicate potential academic integrity violations. The use of AI detection tools has also been criticised for creating an adversarial relationship between students and institutions, where students may be falsely accused of misconduct based on probabilistic software. AIEd advocates say that efforts should be made towards increasing global accessibility and training educators to serve underprivileged areas. === Students === Reliance on generative AI has been linked with reduced academic self-esteem and performance, and heightened learned helplessness. Algorithm errors and hallucinations are common flaws in AI agents, making them less trustworthy and reliable. According to a 2025 survey from Inside Higher Ed, 85% of higher education students use generative AI technology in some way, with 25% using AI to complete assignments for them. The most common reason cited for using AI to cheat was pressure to get high grades. 97% of students wanted some form of action from schools on the threat to academic integrity caused by AI, with the most popular options being clearer policies and more education about ethical uses of AI. In September 2025, The Atlantic published an op-ed from a high school senior arguing that the normalization of AI cheating was eroding critical thinking, academic integrity, creativity, and the shared student experience.
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Behavior informatics

Behavior informatics (BI) is the informatics of behaviors so as to obtain behavior intelligence and behavior insights. BI is a research method combining science and technology, specifically in the area of engineering. The purpose of BI includes analysis of current behaviors as well as the inference of future possible behaviors. This occurs through pattern recognition. Different from applied behavior analysis from the psychological perspective, BI builds computational theories, systems and tools to qualitatively and quantitatively model, represent, analyze, and manage behaviors of individuals, groups and/or organizations. BI is built on classic study of behavioral science, including behavior modeling, applied behavior analysis, behavior analysis, behavioral economics, and organizational behavior. Typical BI tasks consist of individual and group behavior formation, representation, computational modeling, analysis, learning, simulation, and understanding of behavior impact, utility, non-occurring behaviors, etc. for behavior intervention and management. The Behavior Informatics approach to data utilizes cognitive as well as behavioral data. By combining the data, BI has the potential to effectively illustrate the big picture when it comes to behavioral decisions and patterns. One of the goals of BI is also to be able to study human behavior while eliminating issues like self-report bias. This creates more reliable and valid information for research studies. == Behavior == From an Informatics perspective, a behavior consists of three key elements: actors (behavioral subjects and objects), operations (actions, activities) and interactions (relationships), and their properties. A behavior can be represented as a behavior vector, all behaviors of an actor or an actor group can be represented as behavior sequences and multi-dimensional behavior matrix. The following table explains some of the elements of behavior. Behavior Informatics takes into account behavior when analyzing business patterns and intelligence. The inclusion of behavior in these analyses provides prominent information on social and driving factors of patterns. == Applications == Behavior Informatics is being used in a variety of settings, including but not limited to health care management, telecommunications, marketing, and security. Behavior Informatics provides a manner in which to analyze and organize the many aspects that go into a person's health care needs and decisions. When it comes to business models, behavior informatics may be utilized for a similar role. Organizations implement behavior informatics to enhance business structure and regime, where it helps moderate ideal business decisions and situations.
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Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and image segmentation in computer vision. == Description == CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations X {\displaystyle {\boldsymbol {X}}} and random variables Y {\displaystyle {\boldsymbol {Y}}} as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph such that Y = ( Y v ) v ∈ V {\displaystyle {\boldsymbol {Y}}=({\boldsymbol {Y}}_{v})_{v\in V}} , so that Y {\displaystyle {\boldsymbol {Y}}} is indexed by the vertices of G {\displaystyle G} . Then ( X , Y ) {\displaystyle ({\boldsymbol {X}},{\boldsymbol {Y}})} is a conditional random field when each random variable Y v {\displaystyle {\boldsymbol {Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G and not its past states: P ( Y v | X , { Y w : w ≠ v } ) = P ( Y v | X , { Y w : w ∼ v } ) {\displaystyle P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\neq v\})=P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\sim v\})} , where w ∼ v {\displaystyle {\mathit {w}}\sim v} means that w {\displaystyle w} and v {\displaystyle v} are neighbors in G {\displaystyle G} . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {\displaystyle {\boldsymbol {X}}} and Y {\displaystyle {\boldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {\displaystyle p({\boldsymbol {Y}}|{\boldsymbol {X}})} is then modeled. === Inference === For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold. However, there exist special cases for which exact inference is feasible: If the graph is a chain or a tree, message passing algorithms yield exact solutions. The algorithms used in these cases are analogous to the forward-backward and Viterbi algorithm for the case of HMMs. If the CRF only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief propagation Alpha expansion Mean field inference Linear programming relaxations === Parameter learning === Learning the parameters θ {\displaystyle \theta } is usually done by maximum likelihood learning for p ( Y i | X i ; θ ) {\displaystyle p(Y_{i}|X_{i};\theta )} . If all nodes have exponential family distributions and all nodes are observed during training, this optimization is convex. It can be solved for example using gradient descent algorithms, or Quasi-Newton methods such as the L-BFGS algorithm. On the other hand, if some variables are unobserved, the inference problem has to be solved for these variables. Exact inference is intractable in general graphs, so approximations have to be used. === Examples === In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\displaystyle X} represents a sequence of observations and Y {\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i − 1 {\displaystyle Y_{i-1}} and Y i {\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\displaystyle Y_{i}} as "labels" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\displaystyle Y_{i}} and feature functions from some corpus of training data. decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} . The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} . Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation. == Variants == === Higher-order CRFs and semi-Markov CRFs === CRFs can be extended into higher order models by making each Y i {\displaystyle Y_{i}} dependent on a fixed number k {\displaystyle k} of previous variables Y i − k , . . . , Y i − 1 {\displaystyle Y_{i-k},...,Y_{i-1}} . In conventional formulations of higher order CRFs, training and inference are only practical for small values of k {\displaystyle k} (such as k ≤ 5), since their computational cost increases exponentially with k {\displaystyle k} . However, another recent advance has managed to ameliorate these issues by leveraging concepts and tools from the field of Bayesian nonparametrics. Specifically, the CRF-infinity approach constitutes a CRF-type model that is capable of learning infinitely-long temporal dynamics in a scalable fashion. This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence Y {\displaystyle Y} . This provides much of the power of higher-order CRFs to model long-range dependencies of the Y i {\displaystyle Y_{i}} , at a reasonable computational cost. Finally, large-margin models for structured prediction, such as the structured Support Vector Machine can be seen as an alternative training procedure to CRFs. === Latent-dynamic conditional random field === Latent-dynamic conditional random fields (LDCRF) or discriminative probabilistic latent variable models (DPLVM) are a type of CRFs for sequence tagging tasks. They are latent variable models that are trained discriminatively. In an LDCRF, like in any sequence tagging task, given a sequence of observations x = x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the main problem the model must solve is how to assign a sequence of labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set
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Manifold regularization

In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm
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Instance (computer science)

In computer science, an instance or token (from metalogic and metamathematics) is a specific occurrence of a software element that is based on a type definition. When created, an occurrence is said to have been instantiated, and both the creation process and the result of creation are called instantiation. == Examples == Chat AI instance In chat-based AI systems, an assistant can be invoked across many independent conversation sessions (often called a thread), each with its own message history. A specific execution of the assistant over that session may be represented as a run (an execution on a thread). Class instance In object-oriented programming, an object created from a class type. Each instance of a class shares the class-defined structure and behavior but has its own identity and state. Procedural instance In some contexts (including Simula), each procedure call can be viewed as an instance of that procedure—an activation with its own parameters and local variables. Computer instance In cloud computing and virtualization, an instance commonly refers to a provisioned virtual machine or virtual server with an allocated combination of compute, memory, network, and storage resources. Polygonal model In computer graphics, a model may be instanced so it can be drawn multiple times with different transforms and parameters, improving performance by reusing shared geometry data. Program instance In a POSIX-oriented operating system, a running process is an instance of a program. It can be instantiated via system calls such as fork() and exec(). Each executing process is an instance of a program it has been instantiated from.
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H2O (software)

H2O is an open-source, in-memory, distributed machine learning and predictive analytics platform developed by the company H2O.ai (previously 0xdata). The software uses a distributed architecture for parallel processing on standard hardware. It supports algorithms for large-scale data analysis and model deployment. H2O is primarily used by data scientists and developers for statistical modeling and data-driven decision-making. The platform is designed to handle in-memory computations across a distributed computing environment. It offers implementations for numerous statistical and machine learning algorithms, which are accessible through various programming interfaces. The software is released under the Apache License 2.0. == Functionality and features == H2O provides a suite of supervised and unsupervised machine learning algorithms. Its core functions include: Supervised learning: algorithms in the field of statistics, data mining and machine learning such as generalized linear models, random forests, gradient boosting and deep learning are implemented for classification and regression tasks. Unsupervised learning: including K-Means clustering and principal component analysis. Automated machine learning: a features designed to automate the processes of model selection, tuning, and ensemble creation. The software can ingest data from various sources, including the Hadoop Distributed File System, Amazon S3, SQL databases, as well as local file systems. It operates natively on Apache Spark clusters through Sparkling Water. Proponents claim that improved performance is achieved compared to other analysis tools. The software is distributed free of charge, under a business model based on the development of individual applications and support. == Architecture == H2O is primarily written in Java. It uses a distributed architecture that allows the platform to cluster nodes for parallel processing and in-memory storage of data and models. Users interact with the H2O platform through several primary interfaces: Programming language interfaces: APIs are provided for the R and Python programming languages, and various Apache offerings (Apache Hadoop and Spark, as well as Maven). H2O Flow: a graphical web-based interactive computational environment that functions as a notebook interface for data exploration, model building, and scripting. REST-API: allows for integration with other applications and frameworks such as Microsoft Excel or RStudio. With the H2O Machine Learning Integration Nodes, KNIME offers algorithmic workflows. While the algorithm executes, approximate results are displayed, so that users can track the progress and intervene if needed. == History, influences, and extensions == The software project was initiated by the company 0xdata, which later changed its name to H2O.ai. The three Stanford professors Stephen P. Boyd, Robert Tibshirani and Trevor Hastie form a panel that advises H2O on scientific issues. Since its inception, H2O provides open-source machine learning libraries for enterprise use. The core H2O platform is often complemented by offerings from H2O.ai, such as H2O Driverless AI. == Reception == H2O is referenced in peer-reviewed literature regarding automated machine learning (AutoML). The platform has been categorized as a "Leader" and a "Strong Performer" in industry reports by Forrester Research. H2O (the open-source platform) and the associated commercial platform Driverless AI have been recurring winners of InfoWorld's most prestigious awards, including both the Best of Open Source Software ("Bossies") and the Technology of the Year awards.
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