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  Dental AI

  Dental artificial intelligence (Dental AI) refers to the application of artificial intelligence (AI) and machine-learning methods to oral healthcare data. These systems can be used to find patterns or make predictions that can aid in diagnosis, treatment, patient communication, or practice management. == History and development == Research into AI for dentistry dates to the 1990s and 2000s, alongside early CAD/CAM and image-analysis work in dental radiology. Recent developments in deep learning, especially those involving computer vision, such as convolutional neural networks, trained on large image datasets, led to a rapid improvement in performance, as well as a move from prototype technology to productization suitable for use in dental chairs. Dental schools and continuing education programs started incorporating AI content in the 2020s. == Definition and core technologies == The dental AI software accomplishes this task by using various dental images and patient data. Dental images and data used by the dental AI software include bitewing and periapical X-rays, complete mouth X-rays, detailed 3D images, intraoral images, and the patient’s medical history. The dental AI software utilizes several core technologies in accomplishing its task of assisting the dentist. First, the dental AI software utilizes machine learning and deep learning using programs that can learn from examples. Such programs are referred to as convolutional neural network (CNN) and can detect cavities and identify bone changes related to gum disease. The dental AI software utilizes computer vision, which enables the AI software to identify and quantify important features in images and data, whether they are 2D images or 3D images. Natural language processing (NLP) is used for the AI software to understand written text and can automatically generate dental notes and communicate with the patient. Furthermore, the dental AI software utilizes predictive analytics to identify patients that are more prone to dental complications and can suggest the best intervals for checkups or future dental procedures. == Applications in dentistry == Reported clinical and operational applications include diagnostic assistance for caries and periodontal disease, treatment planning assistance, patient education overlays, quality assurance, curriculum assistance for dental education, and claims documentation. Systematic reviews continue to find image-based applications such as caries detection with some variability in study design and a need for prospective validation. == Academic research and clinical validation == Several peer-reviewed studies have measured the effectiveness of AI for applications such as interproximal caries detection and periodontal bone level assessment, showing improvements over unaided readings with a focus on bias within the dataset. The Dental AI Council found variability among clinicians for diagnosis and treatment planning, suggesting the use of a standard tool as an assist. == Industry adoption == Multiple vendors offer FDA-cleared chairside AI for dental imaging: Pearl — Received U.S. FDA 510(k) clearance for its real-time radiologic aid (“Second Opinion”) in 2022 (2D), with subsequent clearances including pediatric and CBCT (“Second Opinion 3D”). TIME gave “Second Opinion” a special mention on its Best Inventions of 2022 list. Overjet — FDA-cleared for bone-level quantification and detection/outline of caries and calculus (e.g., K210187), with additional clearances expanding capabilities. VideaHealth — Received an FDA 510(k) covering 30+ detections across common dental findings (K232384), including indications for patients ages 3 and up; trade coverage has described elements of this as the first pediatric dental-AI clearance. == Regulations == In the U.S., AI-enabled dental imaging software is generally reviewed via the FDA’s 510(k) pathway. The FDA maintains a public AI-Enabled Medical Devices List, which includes numerous medical-imaging AI tools (including dental). Specific dental clearances include Overjet (K210187), VideaHealth (K232384), and Pearl entries such as “Second Opinion 3D” (K243989).

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  Representation collapse

  Representation collapse is a phenomenon in machine learning and representation learning where a model maps different inputs to the same or very similar embeddings, which means it loses important information about how the data is spread out. It is frequently encountered in self-supervised learning, especially within contrastive and non-contrastive frameworks, when training objectives or model architectures do not maintain variance across representations. Collapse results in degenerate solutions characterized by uninformative learned features, significantly impairing downstream task performance. Various techniques have been proposed to mitigate representation collapse, including the use of negative samples, architectural asymmetry, stop-gradient operations, variance regularization, and redundancy reduction objectives, as seen in methods such as SimCLR, BYOL, and VICReg. Comprehending and averting representation collapse is regarded as a fundamental challenge in the advancement of stable and efficient self-supervised learning systems.

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  2024–present global memory supply shortage

  A global computer memory supply shortage started in 2024 due to supply constraints and rapid price escalation in the semiconductor memory market, particularly affecting DRAM and NAND flash memory. This shortage is sometimes labelled by tech media outlets as "RAMmageddon" or the "RAMpocalypse". Unlike the 2020–2023 global chip shortage, which stemmed primarily from pandemic-related supply chain disruptions from COVID-19, this shortage is driven by a structural reallocation of manufacturing capacity toward high-margin products for artificial intelligence infrastructure, creating scarcity of computer memory in consumer and enterprise PC markets. According to a 2026 Kearney's PERLab analysis, the shortage is expected to last at least until 2030, with CEOs agreeing with the timelines. == Background == Following a severe market downturn in 2022–2023, major memory manufacturers—Samsung Electronics, SK Hynix, and Micron Technology—implemented strategic production cuts to stabilize pricing. By mid-2024, the rapid expansion of generative AI services triggered unprecedented demand for specialized memory products, particularly High Bandwidth Memory (HBM) used in AI accelerators and data center GPUs. Specialized components of semiconductor technology are also experiencing supply constraints due to high demand in AI application. For example, glass cloth, a high-performance glass fiber substrate used for power efficient high speed data transfer and a crucial component of semiconductor manufacturing, is experiencing a supply crisis. Nitto Boseki, a Japanese firm having overwhelming monopoly in its production, is not able to meet increased demands, making chip-makers such as Qualcomm, Apple, Nvidia and AMD compete for securing supply. There are also reports of smaller electronics companies struggling to find suppliers for components such as NAND flash. Memory suppliers are adapting to increased demands and market unpredictability by requiring prepayment or shorter time-frame of payment, which makes it more difficult for smaller firms to acquire capital to survive. By 2026, due to steadily increased demand on resources, CPUs are also experiencing shortage issues due to low fabrication capacity, prioritisation of server CPUs, and increased demand, with CPU prices also being forecast to increase by as much as 15%. The demand on memory has also increased strain on other electronic components such as hard disk devices, with reports such as Western Digital's hard disk supply for 2026 being booked for enterprise applications before February 2026. A 2024 McKinsey analysis projected that global demand for AI-ready data center capacity would grow at approximately 33% annually through 2030, with AI workloads consuming roughly 70% of total data center capacity by the decade's end. In addition, according to Kearney's State of Semiconductor 2025 Report, executives were already expecting a shortage in the <8nm wafer size with memory chips being mentioned as an acute source of concern. Multiple companies mentioned being prepared for it through long-term agreements with RAM suppliers or amassing additional inventory. On 24 March 2026, Google announced TurboQuant, a memory compression technology focused on large language models (LLM) and vector search engines, which it claimed achieves 6x lower memory consumption in tested local LLMs and 8x performance enhancement in tests running on H100 accelerators. The technology is also a drop in enhancement for existing inference pipeline. Amid speculation about memory demand trends, memory manufacturers, SanDisk, Micron, Western Digital and Seagate, among other companies involved in memory manufacture experienced stock price declines. Prices of memory kits also reduced in the following months, although still at inflated prices. == Causes == === HBM production displacement === HBM manufacturing requires significantly more wafer capacity per bit than standard DRAM modules. Industry sources reported that as manufacturers allocated increasing wafer capacity to HBM production to meet contracts with AI infrastructure providers, the supply of conventional DDR4 and DDR5 modules for consumer PCs and smartphones contracted sharply. By September 2025, Samsung Electronics had reportedly expanded its 1c DRAM capacity to target 60,000 wafers per month specifically for HBM4 production, further diverting resources from consumer memory lines. === Geopolitical and trade barriers === The supply chain was further constrained by escalating trade tensions between the United States and China. Throughout 2025, fears of U.S. regulatory backlash and new tariff structures led major manufacturers like Samsung and SK Hynix to halt sales of older semiconductor manufacturing equipment to Chinese entities, effectively capping production capacity in the region. Additionally, proposed tariff policies by the U.S. administration in late 2025 prompted supply chain realignments, with Apple reportedly accelerating plans to source all U.S.-bound iPhones from India to avoid potential levies. === NAND flash capacity constraints === In the NAND flash segment, manufacturers prioritized higher-margin enterprise SSDs for data center applications while phasing out older process nodes more rapidly than anticipated. In November 2025, contract prices for NAND wafers increased by more than 60% month-over-month for certain product categories, with 512GB TLC experiencing the steepest rise as legacy manufacturing capacity was retired. == Impact on industry and consumers == === Manufacturer responses === Major PC manufacturers responded to component cost increases with significant price adjustments and supply chain strategies. Dell Technologies Chief Operating Officer Jeff Clarke stated during a November 2025 analyst call that the company had "never witnessed costs escalating at the current pace," describing tighter availability across DRAM, hard drives, and NAND flash memory. Analysts at Morgan Stanley downgraded Dell Technologies stock from "Overweight" to "Underweight" in late 2025, citing the company's heavy exposure to rising server memory costs. The firm warned that skyrocketing memory prices could significantly erode margins for server and PC OEMs. Conversely, Apple Inc. was reportedly less affected than its competitors, having secured long-term supply agreements for DRAM through the first quarter of 2026. Lenovo Chief Financial Officer Winston Cheng described the cost surge as "unprecedented" and disclosed that the company's memory inventories were approximately 50% above normal levels in anticipation of further price increases. === Consumer electronics sector === The shortage particularly affected smartphone manufacturers and other consumer electronics producers. DRAM prices reportedly rose by 172% throughout 2025, leading manufacturers like Samsung to halt new orders for DDR5 modules to reassess pricing structures and Micron to exit its 'Crucial' brand of consumer products. In Tokyo's Akihabara electronics district, retailers began limiting purchases of memory products to prevent hoarding, with prices for popular DDR5 memory modules more than doubling in some cases. Despite the broad trend of rising hardware costs, some companies engaged in aggressive pricing strategies to maintain market share; for example, Sony reduced the price of the PlayStation 5 by $100 for Black Friday 2025, potentially absorbing increased component costs to stimulate software ecosystem growth. Due to memory prices more than doubling in a single quarter, HP revealed in its Q1 2026 earnings call that memory costs account for 35% of PC build materials up from 15-18% previous quarter. Despite showing strong Q1 2026 earning driven by Windows 11 upgrade cycle and AI PC adoption, HP warned investors of low operating margins and up to double digit percentage decline for coming quarter. Trendforce, an IT analytics company, updated its forecast from 1.7% year-over-year growth in PC market to 2.6% year-over-year decline for 2026, amid backdrop of steadily increasing prices and supply crisis. Research and analytics firms, Gartner and IDC expect worldwide PC market to decline 10-11% and smartphone market to decline 8-9% in 2026. Gartner also projects that rising memory prices will make low-margin entry level laptops under 500 USD financially unviable in two years. The RAM shortage has delayed the release of Valve's second Steam Machine due to increased memory prices. The device was originally set to launch in early 2026. === AI infrastructure competition === Technology companies including Google, Amazon, Microsoft, and Meta Platforms placed open-ended orders with memory suppliers, indicating they would accept as much supply as available regardless of cost, according to Reuters sources. The limited supply of AI chips has been cited as a reason for the slow down in compute growth. In October 2025, OpenAI formally announced a strategic partnership using letters of intent with Samsung Electronics and SK Hynix

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  Learning to rank

  Learning to rank (LTR) or machine-learned ranking (MLR) is the application of machine learning, often supervised, semi-supervised or reinforcement learning, in the construction of ranking models for information retrieval and recommender systems. Training data may, for example, consist of lists of items with some partial order specified between items in each list. This order is typically induced by giving a numerical or ordinal score or a binary judgment (e.g. "relevant" or "not relevant") for each item. The goal of constructing the ranking model is to rank new, unseen lists in a similar way to rankings in the training data. == Applications == === In information retrieval === Ranking is a central part of many information retrieval problems, such as document retrieval, collaborative filtering, sentiment analysis, and online advertising. A possible architecture of a machine-learned search engine is shown in the accompanying figure. Training data consists of queries and documents matching them together with the relevance degree of each match. It may be prepared manually by human assessors (or raters, as Google calls them), who check results for some queries and determine relevance of each result. It is not feasible to check the relevance of all documents, and so typically a technique called pooling is used — only the top few documents, retrieved by some existing ranking models are checked. This technique may introduce selection bias. Alternatively, training data may be derived automatically by analyzing clickthrough logs (i.e. search results which got clicks from users), query chains, or such search engines' features as Google's (since-replaced) SearchWiki. Clickthrough logs can be biased by the tendency of users to click on the top search results on the assumption that they are already well-ranked. Training data is used by a learning algorithm to produce a ranking model which computes the relevance of documents for actual queries. Typically, users expect a search query to complete in a short time (such as a few hundred milliseconds for web search), which makes it impossible to evaluate a complex ranking model on each document in the corpus, and so a two-phase scheme is used. First, a small number of potentially relevant documents are identified using simpler retrieval models which permit fast query evaluation, such as the vector space model, Boolean model, weighted AND, or BM25. This phase is called top- k {\displaystyle k} document retrieval and many heuristics were proposed in the literature to accelerate it, such as using a document's static quality score and tiered indexes. In the second phase, a more accurate but computationally expensive machine-learned model is used to re-rank these documents. === In other areas === Learning to rank algorithms have been applied in areas other than information retrieval: In machine translation for ranking a set of hypothesized translations; In computational biology for ranking candidate 3-D structures in protein structure prediction problems; In recommender systems for identifying a ranked list of related news articles to recommend to a user after he or she has read a current news article. == Feature vectors == For the convenience of MLR algorithms, query-document pairs are usually represented by numerical vectors, which are called feature vectors. Such an approach is sometimes called bag of features and is analogous to the bag of words model and vector space model used in information retrieval for representation of documents. Components of such vectors are called features, factors or ranking signals. They may be divided into three groups (features from document retrieval are shown as examples): Query-independent or static features — those features, which depend only on the document, but not on the query. For example, PageRank or document's length. Such features can be precomputed in off-line mode during indexing. They may be used to compute document's static quality score (or static rank), which is often used to speed up search query evaluation. Query-dependent or dynamic features — those features, which depend both on the contents of the document and the query, such as TF-IDF score or other non-machine-learned ranking functions. Query-level features or query features, which depend only on the query. For example, the number of words in a query. Some examples of features, which were used in the well-known LETOR dataset: TF, TF-IDF, BM25, and language modeling scores of document's zones (title, body, anchors text, URL) for a given query; Lengths and IDF sums of document's zones; Document's PageRank, HITS ranks and their variants. Selecting and designing good features is an important area in machine learning, which is called feature engineering. == Evaluation measures == There are several measures (metrics) which are commonly used to judge how well an algorithm is doing on training data and to compare the performance of different MLR algorithms. Often a learning-to-rank problem is reformulated as an optimization problem with respect to one of these metrics. Examples of ranking quality measures: Mean average precision (MAP); DCG and NDCG; Precision@n, NDCG@n, where "@n" denotes that the metrics are evaluated only on top n documents; Mean reciprocal rank; Kendall's tau; Spearman's rho. DCG and its normalized variant NDCG are usually preferred in academic research when multiple levels of relevance are used. Other metrics such as MAP, MRR and precision, are defined only for binary judgments. Recently, there have been proposed several new evaluation metrics which claim to model user's satisfaction with search results better than the DCG metric: Expected reciprocal rank (ERR); Yandex's pfound. Both of these metrics are based on the assumption that the user is more likely to stop looking at search results after examining a more relevant document, than after a less relevant document. == Approaches == Learning to Rank approaches are often categorized using one of three approaches: pointwise (where individual documents are ranked), pairwise (where pairs of documents are ranked into a relative order), and listwise (where an entire list of documents are ordered). Tie-Yan Liu of Microsoft Research Asia has analyzed existing algorithms for learning to rank problems in his book Learning to Rank for Information Retrieval. He categorized them into three groups by their input spaces, output spaces, hypothesis spaces (the core function of the model) and loss functions: the pointwise, pairwise, and listwise approach. In practice, listwise approaches often outperform pairwise approaches and pointwise approaches. This statement was further supported by a large scale experiment on the performance of different learning-to-rank methods on a large collection of benchmark data sets. In this section, without further notice, x {\displaystyle x} denotes an object to be evaluated, for example, a document or an image, f ( x ) {\displaystyle f(x)} denotes a single-value hypothesis, h ( ⋅ ) {\displaystyle h(\cdot )} denotes a bi-variate or multi-variate function and L ( ⋅ ) {\displaystyle L(\cdot )} denotes the loss function. === Pointwise approach === In this case, it is assumed that each query-document pair in the training data has a numerical or ordinal score. Then the learning-to-rank problem can be approximated by a regression problem — given a single query-document pair, predict its score. Formally speaking, the pointwise approach aims at learning a function f ( x ) {\displaystyle f(x)} predicting the real-value or ordinal score of a document x {\displaystyle x} using the loss function L ( f ; x j , y j ) {\displaystyle L(f;x_{j},y_{j})} . A number of existing supervised machine learning algorithms can be readily used for this purpose. Ordinal regression and classification algorithms can also be used in pointwise approach when they are used to predict the score of a single query-document pair, and it takes a small, finite number of values. === Pairwise approach === In this case, the learning-to-rank problem is approximated by a classification problem — learning a binary classifier h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} that can tell which document is better in a given pair of documents. The classifier shall take two documents as its input and the goal is to minimize a loss function L ( h ; x u , x v , y u , v ) {\displaystyle L(h;x_{u},x_{v},y_{u,v})} . The loss function typically reflects the number and magnitude of inversions in the induced ranking. In many cases, the binary classifier h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} is implemented with a scoring function f ( x ) {\displaystyle f(x)} . As an example, RankNet adapts a probability model and defines h ( x u , x v ) {\displaystyle h(x_{u},x_{v})} as the estimated probability of the document x u {\displaystyle x_{u}} has higher quality than x v {\displaystyle x_{v}} : P u , v ( f ) = CDF ( f ( x u ) − f ( x v ) ) , {\displaystyle P_{u,v}(f)={\text{CDF}

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  Just This Once

  Just This Once is a 1993 romance novel written in the style of Jacqueline Susann by a Macintosh IIcx computer named "Hal" in collaboration with its programmer, Scott French. French reportedly spent $40,000 and 8 years developing an artificial intelligence program to analyze Susann's works and attempt to create a novel that Susann might have written. A legal dispute between the estate of Jacqueline Susann and the publisher resulted in a settlement to split the profits, and the book was referenced in several legal journal articles about copyright laws. The book had two small print runs totaling 35,000 copies, receiving mixed reviews. == Creation == The novel's creation spanned the fields of artificial intelligence, expert systems, and natural language processing. Scott French first scanned and analyzed portions of two books by Jacqueline Susann, Valley of the Dolls and Once Is Not Enough, to determine constituents of Susann's writing style, which French stated was the most difficult task. This analysis extracted several hundred components including frequency and type of sexual acts and sentence structure. "Once you're there, the writer's style emerges, part of her actual personality comes out, and the computer can be programmed to make a story." French also created several thousand rules to govern tone, plotting, scenes, and characters. The text generated by Hal, the computer, was intended to mimic what Susann might have written, although the output required significant editing. French credits Hal's work with "almost 100% of the plot, 100% of the theme and style." French estimates that he wrote 10% of the prose, the computer Hal wrote about 25% of the prose, and the remaining two-thirds was more of a collaboration between the two. A typical scenario to write a scene would involve Hal asking questions that French would answer (for example, Hal might ask about the "cattiness factor" involved in a meeting between two key female characters, and French would reply with a range of 1 to 10), and the computer would then generate a few sentences to which French would make minor edits. The process would repeat for the next few sentences until the scene was written. == Legal issues == Jacqueline Susann's publisher was skeptical of the legality of Just This Once, although French doubted that an author's thought processes could be copyrighted. Susann's estate reportedly threatened to sue Scott French but the parties settled out of court; the settlement involved splitting profits between the parties but the terms of the settlement were not disclosed. The publication of Just This Once raised questions in the legal profession concerning how copyright law applies to computer-generated works derived from an analysis of other copyrighted works, and whether the generation of such works infringes on copyright. The publications on this topic suggested that the copyright laws of the time were ill-equipped to deal with computer-generated creative works. == Reception == The book's publisher Steven Shragis of Carol Group said of the novel, "I'm not going to say this is a great literary work, but it's every bit as good as anything out in this field, and better than an awful lot." The novel received some positive early reviews. In USA Today, novelist Thomas Gifford compared Just This Once to another novel in the same genre, American Star by Jackie Collins. Gifford concluded: "If you do like this stuff, you'd be much, much better off with the one written by the computer." The Dead Jackie Susann Quarterly declared that Susann "would be proud. Lots of money, sleaze, disease, death, oral sex, tragedy and the good girl gone bad." Other reviews were mixed. Publishers Weekly wrote, "If the books of Jacqueline Susann and Harold Robbins seem formulaic, this debut novel of sin and success in Las Vegas outdoes them all. And that, in a way, is the point.... All novelty rests in the conceit of computer authorship, not in the story itself." Library Journal stated "French invested eight years and $50,000 in a scheme to use artificial intelligence to fulfill his authentic, if dubious, desire to generate a trashy novel a la Jacqueline Susann. Shallow, beautiful-people characters are flatly conceived and randomly accessed in a formulaic plot ... a sexy, boring morality tale. Of possible interest to computer buffs for its use of Expert Systems and the virtual promise of more worthy possibilities; others should read Susann." Kirkus Reviews wrote: "The deal here is that author French is not the author, he's just the midwife, having allegedly programmed his computer to write about our times just the way Susann would... almost perfectly capturing glamorous Jackie's turgid but E-Z reading prose style and ultrareliable mix of sex, glitz, dope 'n' despair.... One wonders, though, if French's tale spinning PC will do as well on the talkshows as Jackie did. The computer weenies have been trying to tell us for years, garbage in-garbage out."

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  Hierarchical control system

  A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. == Overview == A human-built system with complex behavior is often organized as a hierarchy. For example, a command hierarchy has among its notable features the organizational chart of superiors, subordinates, and lines of organizational communication. Hierarchical control systems are organized similarly to divide the decision making responsibility. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas sensations and command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a hierarchical control system are related to its layers. Each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer. The lower layers have local tasks, goals, and sensations, and their activities are planned and coordinated by higher layers which do not generally override their decisions. The layers form a hybrid intelligent system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning. A hierarchical task network is a good fit for planning in a hierarchical control system. Besides artificial systems, an animal's control systems are proposed to be organized as a hierarchy. In perceptual control theory, which postulates that an organism's behavior is a means of controlling its perceptions, the organism's control systems are suggested to be organized in a hierarchical pattern as their perceptions are constructed so. == Control system structure == The accompanying diagram is a general hierarchical model which shows functional manufacturing levels using computerised control of an industrial control system. Referring to the diagram; Level 0 contains the field devices such as flow and temperature sensors, and final control elements, such as control valves Level 1 contains the industrialised Input/Output (I/O) modules, and their associated distributed electronic processors. Level 2 contains the supervisory computers, which collate information from processor nodes on the system, and provide the operator control screens. Level 3 is the production control level, which does not directly control the process, but is concerned with monitoring production and monitoring targets Level 4 is the production scheduling level. == Applications == === Manufacturing, robotics and vehicles === Among the robotic paradigms is the hierarchical paradigm in which a robot operates in a top-down fashion, heavy on planning, especially motion planning. Computer-aided production engineering has been a research focus at NIST since the 1980s. Its Automated Manufacturing Research Facility was used to develop a five layer production control model. In the early 1990s DARPA sponsored research to develop distributed (i.e. networked) intelligent control systems for applications such as military command and control systems. NIST built on earlier research to develop its Real-Time Control System (RCS) and Real-time Control System Software which is a generic hierarchical control system that has been used to operate a manufacturing cell, a robot crane, and an automated vehicle. In November 2007, DARPA held the Urban Challenge. The winning entry, Tartan Racing employed a hierarchical control system, with layered mission planning, motion planning, behavior generation, perception, world modelling, and mechatronics. === Artificial intelligence === Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a particular goal of the software agent (i.e. system as a whole), and higher layers are increasingly more abstract. Each layer's goal subsumes that of the underlying layers, e.g. the decision to move forward by the eat-food layer takes into account the decision of the lowest obstacle-avoidance layer. Behavior need not be planned by a superior layer, rather behaviors may be triggered by sensory inputs and so are only active under circumstances where they might be appropriate. Reinforcement learning has been used to acquire behavior in a hierarchical control system in which each node can learn to improve its behavior with experience. James Albus, while at NIST, developed a theory for intelligent system design named the Reference Model Architecture (RMA), which is a hierarchical control system inspired by RCS. Albus defines each node to contain these components. Behavior generation is responsible for executing tasks received from the superior, parent node. It also plans for, and issues tasks to, the subordinate nodes. Sensory perception is responsible for receiving sensations from the subordinate nodes, then grouping, filtering, and otherwise processing them into higher level abstractions that update the local state and which form sensations that are sent to the superior node. Value judgment is responsible for evaluating the updated situation and evaluating alternative plans. World Model is the local state that provides a model for the controlled system, controlled process, or environment at the abstraction level of the subordinate nodes. At its lowest levels, the RMA can be implemented as a subsumption architecture, in which the world model is mapped directly to the controlled process or real world, avoiding the need for a mathematical abstraction, and in which time-constrained reactive planning can be implemented as a finite-state machine. Higher levels of the RMA however, may have sophisticated mathematical world models and behavior implemented by automated planning and scheduling. Planning is required when certain behaviors cannot be triggered by current sensations, but rather by predicted or anticipated sensations, especially those that come about as result of the node's actions.

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  Symbolic artificial intelligence

  In artificial intelligence, symbolic artificial intelligence (also known as classical artificial intelligence or logic-based artificial intelligence) is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic, and search. Symbolic AI used tools such as logic programming, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to important ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems. Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. Researchers in the 1960s and the 1970s were convinced that symbolic approaches would eventually succeed in creating a machine with artificial general intelligence and considered this the ultimate goal of their field. An early boom, with early successes such as the Logic Theorist and Samuel's Checkers Playing Program, led to unrealistic expectations and promises and was followed by the first AI Winter as funding dried up. A second boom (1969–1986) occurred with the rise of expert systems, their promise of capturing corporate expertise, and an enthusiastic corporate embrace. That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. Problems with difficulties in knowledge acquisition, maintaining large knowledge bases, and brittleness in handling out-of-domain problems arose. Another, second, AI Winter (1988–2011) followed. Subsequently, AI researchers focused on addressing underlying problems in handling uncertainty and in knowledge acquisition. Uncertainty was addressed with formal methods such as hidden Markov models, Bayesian reasoning, and statistical relational learning. Symbolic machine learning addressed the knowledge acquisition problem with contributions including Version Space, Valiant's PAC learning, Quinlan's ID3 decision-tree learning, case-based learning, and inductive logic programming to learn relations. Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt's perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, and work in convolutional neural networks by LeCun et al. in 1989. However, neural networks were not viewed as successful until about 2012: "Until Big Data became commonplace, the general consensus in the Al community was that the so-called neural-network approach was hopeless. Systems just didn't work that well, compared to other methods. ... A revolution came in 2012, when a number of people, including a team of researchers working with Hinton, worked out a way to use the power of GPUs to enormously increase the power of neural networks." Over the next several years, deep learning had spectacular success in handling vision, speech recognition, speech synthesis, image generation, and machine translation, though symbolic approaches continue to be useful in a few domains such as computer algebra systems and proof assistants. == History == A short history of symbolic AI to the present day follows below. Time periods and titles are drawn from Henry Kautz's 2020 AAAI Robert S. Engelmore Memorial Lecture and the longer Wikipedia article on the History of AI, with dates and titles differing slightly for increased clarity. === The first AI summer: irrational exuberance, 1948–1966 === Success at early attempts in AI occurred in three main areas: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section summarizes Kautz's reprise of early AI history. ==== Approaches inspired by human or animal cognition or behavior ==== Cybernetic approaches attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural net, was built as early as 1948. This work can be seen as an early precursor to later work in neural networks, reinforcement learning, and situated robotics. An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955–56, as it was able to prove 38 elementary theorems from Whitehead and Russell's Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved problems represented with formal operators via state-space search using means-ends analysis. During the 1960s, symbolic approaches achieved great success at simulating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research. Earlier approaches based on cybernetics or artificial neural networks were abandoned or pushed into the background. Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research and management science. Their research team used the results of psychological experiments to develop programs that simulated the techniques that people used to solve problems. This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. ==== Heuristic search ==== In addition to the highly specialized domain-specific kinds of knowledge that we will see later used in expert systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, rules of thumb that guide a search in promising directions: "How can non-enumerative search be practical when the underlying problem is exponentially hard? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions." Another important advance was to find a way to apply these heuristics that guarantees a solution will be found, if there is one, not withstanding the occasional fallibility of heuristics: "The A algorithm provided a general frame for complete and optimal heuristically guided search. A is used as a subroutine within practically every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the cost of worst-case exponential time. ==== Early work on knowledge representation and reasoning ==== Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner. ===== Modeling formal reasoning with logic: the "neats" ===== Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the exact mechanisms of human thought, but could instead try to find the essence of abstract reasoning and problem-solving with logic, regardless of whether people used the same algorithms. His laboratory at Stanford (SAIL) focused on using formal logic to solve a wide variety of problems, including knowledge representation, planning and learning. Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the development of the programming language Prolog and the science of logic programming. ===== Modeling implicit common-sense knowledge with frames and scripts: the "scruffies" ===== Researchers at MIT (such as Marvin Minsky and Seymour Papert) found that solving difficult problems in vision and natural language processing required ad hoc solutions—they argued that no simple and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank described their "anti-logic" approaches as "scruffy" (as opposed to the "neat" paradigms at CMU and Stanford). Commonsense knowledge bases (such as Doug Lenat's Cyc) are an example of "scruffy" AI, since they must be built by hand, one complicated concept at a time. === The first AI winter: crushed dreams, 1967–1977 === The first AI winter was a shock: During the first AI summer, many people thought that machine intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for inte

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  Deadbot

  A deadbot, deathbot, or griefbot is a digital avatar, created with artificial intelligence, which resembles a person who is dead. Griefbots employ natural language processing and machine-learning techniques to approximate the style and personality of a deceased person. They may appear as chatbots, voice assistants, or animated avatars, and are often trained on an individual's digital remains. == History == Among the earliest researchers, Muhammad Aurangzeb Ahmad of the University of Washington, developed the Grandpa Bot project, a conversational simulation of his late father designed for his children to interact with. Other efforts include journalist James Vlahos's Dadbot, which evolved into the commercial platform HereAfter AI. Hossein Rahnama's Augmented Eternity research at MIT Media Lab and Toronto Metropolitan University, and game designer Jason Rohrer's "Project December", have enabled users to converse with language-model representations of loved ones. Early commercial projects such as Eternime, founded by Marius Ursache, also popularized the notion of interactive digital immortality. == Cultural and societal impact == Scholars have proposed frameworks and critiques addressing the ethics of these technologies. Tomasz Hollanek and Katarzyna Nowaczyk-Basińska developed a design-ethics taxonomy distinguishing the data donor, data recipient, and interactant. Edina Harbinja and Lilian Edwards formalized the concept of post-mortem privacy, and Carl J. Öhman at the Oxford Internet Institute studied the management of large-scale digital remains. Cultural acceptance varies: while some view them as expressions of remembrance, others regard them as unsettling or ethically problematic. Concerns have been raised about deadbots' potential for creating psychological harm. Griefbots are considered part of the phenomenon of artificial intimacy.

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  Scan line

  A scan line (also scanline) is one line, or row, in a raster scanning pattern, such as a line of video on a cathode-ray tube (CRT) display of a television set or computer monitor. On CRT screens the horizontal scan lines are visually discernible, even when viewed from a distance, as alternating colored lines and black lines, especially when a progressive scan signal with below maximum vertical resolution is displayed. This is sometimes used today as a visual effect in computer graphics. The term is used, by analogy, for a single row of pixels in a raster graphics image. Scan lines are important in representations of image data, because many image file formats have special rules for data at the end of a scan line. For example, there may be a rule that each scan line starts on a particular boundary (such as a byte or word; see for example BMP file format). This means that even otherwise compatible raster data may need to be analyzed at the level of scan lines in order to convert between formats.

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  Confusion matrix

  In machine learning, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one. In unsupervised learning it is usually called a matching matrix. The term is used specifically in the problem of statistical classification. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The diagonal of the matrix therefore represents all instances that are correctly predicted. The name stems from the fact that it makes it easy to identify whether the system is confusing two classes (i.e., commonly mislabeling one class as another). The confusion matrix has its origins in human perceptual studies of auditory stimuli. It was adapted for machine learning studies and used by Frank Rosenblatt, among other early researchers, to compare human and machine classifications of visual (and later auditory) stimuli. It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table). == Example == Given a sample of 12 individuals, 8 that have been diagnosed with cancer and 4 that are cancer-free, where individuals with cancer belong to class 1 (positive) and non-cancer individuals belong to class 0 (negative), we can display that data as follows: Assume that we have a classifier that distinguishes between individuals with and without cancer in some way, we can take the 12 individuals and run them through the classifier. The classifier then makes 9 accurate predictions and misses 3: 2 individuals with cancer wrongly predicted as being cancer-free (sample 1 and 2), and 1 person without cancer that is wrongly predicted to have cancer (sample 9). Notice, that if we compare the actual classification set to the predicted classification set, there are 4 different outcomes that could result in any particular column: The actual classification is positive and the predicted classification is positive (1,1). This is called a true positive result because the positive sample was correctly identified by the classifier. The actual classification is positive and the predicted classification is negative (1,0). This is called a false negative result because the positive sample is incorrectly identified by the classifier as being negative. The actual classification is negative and the predicted classification is positive (0,1). This is called a false positive result because the negative sample is incorrectly identified by the classifier as being positive. The actual classification is negative and the predicted classification is negative (0,0). This is called a true negative result because the negative sample gets correctly identified by the classifier. We can then perform the comparison between actual and predicted classifications and add this information to the table, making correct results appear in green so they are more easily identifiable. The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications. The four outcomes can be formulated in a 2×2 confusion matrix, as follows: The color convention of the three data tables above were picked to match this confusion matrix, in order to easily differentiate the data. Now, we can simply total up each type of result, substitute into the template, and create a confusion matrix that will concisely summarize the results of testing the classifier: In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will represent them. By summing up the 2 rows of the confusion matrix, one can also deduce the total number of positive (P) and negative (N) samples in the original dataset, i.e. P = T P + F N {\displaystyle P=TP+FN} and N = F P + T N {\displaystyle N=FP+TN} . == Table of confusion == In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer). According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their significance and use. Some researchers have argued that the confusion matrix, and the metrics derived from it, do not truly reflect a model's knowledge. In particular, the confusion matrix cannot show whether correct predictions were reached through sound reasoning or merely by chance (a problem known in philosophy as epistemic luck). It also does not capture situations where the facts used to make a prediction later change or turn out to be wrong (defeasibility). This means that while the confusion matrix is a useful tool for measuring classification performance, it may give an incomplete picture of a model’s true reliability. == Confusion matrices with more than two categories == Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, with zero values omitted for clarity. == Confusion matrices in multi-label and soft-label classification == Confusion matrices are not limited to single-label classification (where only one class is present) or hard-label settings (where classes are either fully present, 1, or absent, 0). They can also be extended to Multi-label classification (where multiple classes can be predicted at once) and soft-label classification (where classes can be partially present). One such extension is the Transport-based Confusion Matrix (TCM), which builds on the theory of optimal transport and the principle of maximum entropy. TCM applies to single-label, multi-label, and soft-label settings. It retains the familiar structure of the standard confusion matrix: a square matrix sized by the number of classes, with diagonal entries indicating correct predictions and off-diagonal entries indicating confusion. In the single-label case, TCM is identical to the standard confusion matrix. TCM follows the same reasoning as the standard confusion matrix: if class A is overestimated (its predicted value is greater than its label value) and class B is underestimated (its predicted value is less than its label value), A is considered confused with B, and the entry (B, A) is increased. If a class is both predicted and present, it is correctly identified, and the diagonal entry (A, A) increases. Optimal transport and maximum entropy are used to determine the extent to which these entries are updated. TCM enables clearer comparison between predictions and labels in complex classification tasks, while maintaining a consistent matrix format across settings.

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  Concurrent MetateM

  Concurrent MetateM is a multi-agent language in which each agent is programmed using a set of (augmented) temporal logic specifications of the behaviour it should exhibit. These specifications are executed directly to generate the behaviour of the agent. As a result, there is no risk of invalidating the logic as with systems where logical specification must first be translated to a lower-level implementation. The root of the MetateM concept is Gabbay's separation theorem; any arbitrary temporal logic formula can be rewritten in a logically equivalent past → future form. Execution proceeds by a process of continually matching rules against a history, and firing those rules when antecedents are satisfied. Any instantiated future-time consequents become commitments which must subsequently be satisfied, iteratively generating a model for the formula made up of the program rules. == Temporal Connectives == The Temporal Connectives of Concurrent MetateM can divided into two categories, as follows: Strict past time connectives: '●' (weak last), '◎' (strong last), '◆' (was), '■' (heretofore), 'S' (since), and 'Z' (zince, or weak since). Present and future time connectives: '◯' (next), '◇' (sometime), '□' (always), 'U' (until), and 'W' (unless). The connectives {◎,●,◆,■,◯,◇,□} are unary; the remainder are binary. === Strict past time connectives === ==== Weak last ==== ●ρ is satisfied now if ρ was true in the previous time. If ●ρ is interpreted at the beginning of time, it is satisfied despite there being no actual previous time. Hence "weak" last. ==== Strong last ==== ◎ρ is satisfied now if ρ was true in the previous time. If ◎ρ is interpreted at the beginning of time, it is not satisfied because there is no actual previous time. Hence "strong" last. ==== Was ==== ◆ρ is satisfied now if ρ was true in any previous moment in time. ==== Heretofore ==== ■ρ is satisfied now if ρ was true in every previous moment in time. ==== Since ==== ρSψ is satisfied now if ψ is true at any previous moment and ρ is true at every moment after that moment. ==== Zince, or weak since ==== ρZψ is satisfied now if (ψ is true at any previous moment and ρ is true at every moment after that moment) OR ψ has not happened in the past. === Present and future time connectives === ==== Next ==== ◯ρ is satisfied now if ρ is true in the next moment in time. ==== Sometime ==== ◇ρ is satisfied now if ρ is true now or in any future moment in time. ==== Always ==== □ρ is satisfied now if ρ is true now and in every future moment in time. ==== Until ==== ρUψ is satisfied now if ψ is true at any future moment and ρ is true at every moment prior. ==== Unless ==== ρWψ is satisfied now if (ψ is true at any future moment and ρ is true at every moment prior) OR ψ does not happen in the future.

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  Explanation-based learning

  Explanation-based learning (EBL) is a form of machine learning that exploits a very strong, or even perfect, domain theory (i.e. a formal theory of an application domain akin to a domain model in ontology engineering, not to be confused with Scott's domain theory) in order to make generalizations or form concepts from training examples. It is also linked with Encoding (memory) to help with Learning. == Details == An example of EBL using a perfect domain theory is a program that learns to play chess through example. A specific chess position that contains an important feature such as "Forced loss of black queen in two moves" includes many irrelevant features, such as the specific scattering of pawns on the board. EBL can take a single training example and determine what are the relevant features in order to form a generalization. A domain theory is perfect or complete if it contains, in principle, all information needed to decide any question about the domain. For example, the domain theory for chess is simply the rules of chess. Knowing the rules, in principle, it is possible to deduce the best move in any situation. However, actually making such a deduction is impossible in practice due to combinatoric explosion. EBL uses training examples to make searching for deductive consequences of a domain theory efficient in practice. In essence, an EBL system works by finding a way to deduce each training example from the system's existing database of domain theory. Having a short proof of the training example extends the domain-theory database, enabling the EBL system to find and classify future examples that are similar to the training example very quickly. The main drawback of the method—the cost of applying the learned proof macros, as these become numerous—was analyzed by Minton. === Basic formulation === EBL software takes four inputs: a hypothesis space (the set of all possible conclusions) a domain theory (axioms about a domain of interest) training examples (specific facts that rule out some possible hypothesis) operationality criteria (criteria for determining which features in the domain are efficiently recognizable, e.g. which features are directly detectable using sensors) == Application == An especially good application domain for an EBL is natural language processing (NLP). Here a rich domain theory, i.e., a natural language grammar—although neither perfect nor complete, is tuned to a particular application or particular language usage, using a treebank (training examples). Rayner pioneered this work. The first successful industrial application was to a commercial NL interface to relational databases. The method has been successfully applied to several large-scale natural language parsing systems, where the utility problem was solved by omitting the original grammar (domain theory) and using specialized LR-parsing techniques, resulting in huge speed-ups, at a cost in coverage, but with a gain in disambiguation. EBL-like techniques have also been applied to surface generation, the converse of parsing. When applying EBL to NLP, the operationality criteria can be hand-crafted, or can be inferred from the treebank using either the entropy of its or-nodes or a target coverage/disambiguation trade-off (= recall/precision trade-off = f-score). EBL can also be used to compile grammar-based language models for speech recognition, from general unification grammars. Note how the utility problem, first exposed by Minton, was solved by discarding the original grammar/domain theory, and that the quoted articles tend to contain the phrase grammar specialization—quite the opposite of the original term explanation-based generalization. Perhaps the best name for this technique would be data-driven search space reduction. Other people who worked on EBL for NLP include Guenther Neumann, Aravind Joshi, Srinivas Bangalore, and Khalil Sima'an.

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  BulSemCor

  The Bulgarian Sense-annotated Corpus (BulSemCor) (Bulgarian: Български семантично анотиран корпус (БулСемКор)) is a structured corpus of Bulgarian texts in which each lexical item is assigned a sense tag. BulSemCor was created by the Department of Computational Linguistics at the Institute for Bulgarian Language of the Bulgarian Academy of Sciences. == Structure == BulSemCor was created as part of a nationally funded project titled "BulNet – A lexico-semantic network for the Bulgarian Language" (2005–2010). It follows the general methodology of SemCor combined with some specific principles. The corpus for annotation consists of 101,791 tokens covering an excerpt from the Bulgarian "Brown" Corpus modelled on the Brown Corpus.Francis Kucera An important feature of BulSemCor is that the samples are selected using heuristics that provide optimal coverage of ambiguous lexis. BulSemCor is manually sense-annotated according to the Bulgarian WordNet. Its size is comparable to that of other contemporary semantically annotated corpora or pool of acceptable linguistic components. The semantic annotation consists in associating each lexical item in the corpus with exactly one synonym set (synset) in the Bulgarian WordNet that best describes its sense in the particular context. The selection of the best match among the suggested candidates is based on a set of procedures, such as the other synset members, the synset gloss (explanatory definition) and the position of a given candidate in the WordNet structure. == Scale == The number of annotated tokens is 99,480 (the difference in the number of tokens compared to the initial corpus is due to the fact that some of them are not linguistic items). The simple word count is 86,842 and multiword expressions (MWE) are 5,797 (12,638 tokens). == Specific features == All words in BulSemCor are assigned a sense, while according to established practice only simple content words or content word classes (typically nouns and verbs) are annotated. Since 2000 the development of language resources, has broadened to include annotation of function words and multiword expressions covering particular senses or types of words and expressions. In this respect, BulSemCor's annotation is more exhaustive and hence provides greater opportunities for linguistic observations and non-linear programming (NLP) applications. Annotated items inherit the linguistic information associated with the corresponding synset, which along with morphological and semantic tags may include annotation on one or more of the following additional levels: Partial information about the syntactic structure of MWE types – particularly, information about syntactic heads and their dependents; Information about the category of the named entities – names, locations, organisations, dates, numbers, etc.; Information about the taxonomic category of adverbs, such as time, place, manner, degree, quantity, etc.; Information about the type of the syntactic relationships – coordination or subordination – expressed by conjunctions; Information about the original part-of-speech of substantivised words (non-nouns that act as nouns in a particular context); Stylistic/register, grammatical and other information about synsets or individual synset members;

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  Double descent

  Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.

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  Alexander Y. Tetelbaum

  Alexander Y. Tetelbaum (born August 16, 1948) is a Ukrainian American computer scientist, inventor, and academic who has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the late 1960s; and holds 46 U.S. patents in EDA and related fields. Tetelbaum is the founding president of International Solomon University, the first Jewish university in Ukraine, established during a period of renewed efforts to address antisemitism in Ukraine. == Early life and education == He graduated from a Kyiv mathematical high school with a silver medal in 1966. Tetelbaum enrolled at the Kyiv Polytechnic Institute (KPI), now National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" in 1966, graduating in 1972 with an MS in Electronics with honors. He earned his PhD in Electrical and Computer Engineering from KPI in 1975, with a dissertation on electronic design automation, and his Doctor of Engineering Science in 1986. == Academic career == Tetelbaum began his academic career at KPI in 1973 as a junior scientist, becoming a professor in the Computer and Electrical Engineering Department in 1980. Later, he founded and served as president of International Solomon University in Kyiv from 1991 to 1996, the first Jewish university in Ukraine. The university became a major academic center for computer science and Jewish studies in the post-Soviet era. He was a visiting and adjunct professor at Michigan State University from 1993 to 1996. == Professional career == Tetelbaum worked as an engineer at the Kiev Institute of Cybernetics from 1972 to 1973, and later, he led the Design Automation Lab at Kyiv Polytechnic Institute from 1975 to 1987. In the United States, he served as EDA manager at Silicon Graphics Corporation from 1996 to 1998 and principal engineer at LSI Corporation from 1998 to 2012. He founded and served as CEO of Abelite Design Automation, Inc., from 2012 to 2022. == Contributions in computer science == Tetelbaum has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the 1960s. His early work included methods for EDA, particularly physical design automation and mathematical optimization; and he developed force-directed placement and topological routing methods. Tetelbaum generalized Rent's rule for hierarchical systems and large blocks, proposing a graph-based framework that extends applicability to arbitrary partition sizes with improved accuracy. Additional IEEE and related conference contributions from the mid-1990s include: "Path Search for Complicated Function", 1995 IEEE International Symposium on Circuits and Systems "A Performance-driven Placement Approach of Standard Cells" (International Conference on Intelligent Systems, 1995) "Framework of a New Methodology for Behavioral to Physical Design Linkage" (38th Midwest Symposium on Circuits and Systems, 1996) Statistical timing design and variations Test Methodologies These and other works and patents contributed to timing-driven placement, crosstalk reduction, clock tree synthesis, and interconnect optimization in VLSI design. == Patents == Tetelbaum holds 46 U.S. patents in EDA and related fields. Notable examples include: For the full list of patents, see Justia Patents or Google Patents. == Publications == === Early publications in the Soviet Union === Before the appearance of American books on electronic design automation (EDA), Tetelbaum published several scientific books and monographs on the subject in Russian/Ukrainian. Electronic Design Automation, Kiev: Znanie Publisher, 1975. Planar Design of Electronic Circuits, Kiev: Znanie Publisher, 1977. Formal Design of Computer Systems, Moscow: Sovetskoe Radio, 1979. CAD of Electronic Equipment: Topological Approach, Kiev: Vyssha Shkola, 1980; 2nd ed. 1981. Automated Design of Electronic Circuits (1981) CAD of VLSI Circuits, Kiev: Vyssha Shkola, 1983. Topological Algorithms of Multilayer Printed Circuit Boards Routing, Moscow: Radio i Svyaz, 1983. CAD of VLSI Circuits on Master Slice Chips, Moscow: Radio i Svyaz, 1988. Increasing the Effectiveness of CAD Systems, Kiev: UMKVO, 1991. === Scientific Monographs (English) === Minimum Number of Timing Signoff Corners (2022) Interviewing AI (2026) The AI Debate (2026) New Nostradamus Predictions: 2026: The Next Decade & Beyond (2035–2050+) (2026) For a consolidated record of Tetelbaum's publications, see Alexander Y. Tetelbaum, Wikidata Q4720205. === Other publications === Tetelbaum also published educational books on problem-solving methods: Yes-No Puzzles-Games Puzzle Games for Kids Solving Non-Standard Problems Solving Non-Standard Very Hard Problems Additionally, Tetelbaum published three thrillers: Omerta Operations Executive Director Eruption Yacht Finally, he published his memoir and an entertaining book: Unfinished Equations Artificially Intelligent Humor

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