AI Coding On Phone

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  Machine learning

  Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed. Advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. Statistics and mathematical optimisation methods compose the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) through unsupervised learning. From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework. == History == The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence. The synonym self-teaching computers was also used during this time period. The earliest machine learning program was introduced in the 1950s, when Samuel invented a computer program that calculated the chance of winning in checkers for each side, but the history of machine learning is rooted in decades of efforts to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book The Organization of Behavior, in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. The Hebbian theory of neuron interaction set the groundwork for how many machine learning algorithms work, with connected artificial neurons changing the strength of their connections based on data. Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including Walter Pitts and Warren McCulloch, who proposed the first mathematical model of neural networks including algorithms that mirror human thought processes. By the early 1960s, an experimental "learning machine" with punched tape memory, called Cybertron, had been developed by Raytheon Company to analyse sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause it to reevaluate incorrect decisions. A representative book on research into machine learning during the 1960s was Nils Nilsson's book "Learning Machines", dealing mostly with machine learning for pattern classification. Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. In 1981, a report was given on using teaching strategies so that an artificial neural network learns to recognise 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal. Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." This definition of the tasks in which machine learning is concerned is fundamentally operational rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question, "Can machines think?", is replaced by asking whether machines can convincingly imitate a human in its responses to human-posed questions. In 2014 Ian Goodfellow and others introduced generative adversarial networks (GANs) which could produce realistic synthetic data. By 2016 AlphaGo had won against top human players in Go using reinforcement learning techniques. == Relationships to other fields == === Artificial intelligence === As a scientific endeavour, machine learning grew out of the quest for artificial intelligence (AI). In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis. However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. By 1980, expert systems had come to dominate AI, and statistics was out of favour. Work on symbolic/knowledge-based learning continued within AI, leading to inductive logic programming (ILP), but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. Neural network research was abandoned by AI and computer science around the same time. This subfield, termed "connectionism", was continued by researchers from other disciplines, including John Hopfield, David Rumelhart, and Geoffrey Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation. Machine learning (ML), reorganised and recognised as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory. === Data compression === === Data mining === Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction based on known properties learned from the training data, data mining focuses on the discovery of previously unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data. Machine learning also has intimate ties to optimization: Many learning problems are formulated as minimisation of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the preassigned labels of a set of examples). === Generalization === Characterizing the generalisation of various learning algorithms is an active topic of current research, especially for deep learning algorithms. === Statistics === Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalisable predictive patterns. Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be. Leo Breiman distinguished two statistical modelling paradigms: the data model and the algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest. Some statisticians have adopted methods from machine learning, producing the field of statistical learning. === Statistical physics === Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyse the weight space of deep neural networks. Statistical physics is thus

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  Mike Vernal

  Mike Vernal (born September 7, 1980) is an American business executive who is a venture capitalist at Conviction. He was previously an investor at Sequoia Capital in Silicon Valley and was one of the top executives at Facebook between 2008 and 2016. Prior to joining Sequoia Capital, he was Vice President of Search, Local, and Developer products at Facebook. == Career == Vernal joined Facebook in 2008. From 2009 to 2013, Vernal managed the Facebook Platform team and is credited with managing the Facebook Platform transition from desktop to mobile. During his time at Facebook, he served as vice president and was considered among the “top executives” who ran the company. In 2016, after eight years at Facebook, Vernal announced his plans to leave the company. In May 2016, he joined Sequoia Capital, a venture-capital firm specializing in technology startups. He is an early investor in Rippling, Clay, Notion and Statsig. In July 2023, The Information reported that Vernal was departing Sequoia. At Conviction, he has led investments in Listen Labs, OpenEvidence and Thinking Machines Lab.

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  DeepSeek

  Hangzhou DeepSeek Artificial Intelligence Basic Technology Research Co., Ltd., doing business as DeepSeek, is a Chinese artificial intelligence (AI) company that develops large language models (LLMs). Based in Hangzhou, Zhejiang, DeepSeek is owned and funded by High-Flyer, a Chinese hedge fund. DeepSeek was founded in July 2023 by Liang Wenfeng, the co-founder of High-Flyer, who also serves as the CEO for both of the companies. The company launched an eponymous chatbot alongside its DeepSeek-R1 model in January 2025. DeepSeek-R1 provided responses comparable to other contemporary large language models, such as OpenAI's GPT-4 and o1. Its training cost was reported to be significantly lower than other LLMs. The company claims that it trained its V3 model for US$6 million—far less than the US$100 million cost for OpenAI's GPT-4 in 2023—and using approximately one-tenth the computing power consumed by Meta's comparable model, Llama 3.1. DeepSeek's success against larger and more established rivals has been described as "upending AI". DeepSeek's models are described as "open-weight", meaning the exact parameters are openly shared, but the training data is not openly licensed. Since the January 2025 debut of DeepSeek-R1, the company has made its new models available under free and open-source software licenses, primarily the MIT License. The company reportedly recruits AI researchers from top Chinese universities and also hires from outside traditional computer science fields to broaden its models' knowledge and capabilities. DeepSeek significantly reduced training expenses for their R1 model by incorporating techniques such as mixture of experts (MoE) layers. The company also trained its models during ongoing trade restrictions on AI chip exports to China, using weaker AI chips intended for export and employing fewer units overall. Observers say this breakthrough sent "shock waves" through the industry which were described as triggering a "Sputnik moment" for the US in the field of artificial intelligence, particularly due to its open-source, cost-effective, and high-performing AI models. This threatened established AI hardware leaders such as Nvidia; Nvidia's share price dropped sharply, losing US$600 billion in market value, the largest single-company decline in U.S. stock market history. == History == === Founding and early years (2016–2023) === In February 2016, High-Flyer was co-founded by AI enthusiast Liang Wenfeng, who had been trading since the 2008 financial crisis while attending Zhejiang University. The company began stock trading using a GPU-dependent deep learning model on 21 October 2016; before then, it had used CPU-based linear models. By the end of 2017, most of its trading was driven by AI. Liang established High-Flyer as a hedge fund focused on developing and using AI trading algorithms, and by 2021 the firm was using AI exclusively, often using Nvidia chips. In 2019, the company began constructing its first computing cluster, Fire-Flyer, at a cost of 200 million yuan; it contained 1,100 GPUs interconnected at 200 Gbit/s and was retired after 1.5 years in operation. By 2021, Liang had started buying large quantities of Nvidia GPUs for an AI project, reportedly obtaining 10,000 Nvidia A100 GPUs before the United States restricted chip sales to China. Computing cluster Fire-Flyer 2 began construction in 2021 with a budget of 1 billion yuan. It was reported that in 2022, Fire-Flyer 2's capacity had been used at over 96%, totaling 56.74 million GPU hours. 27% was used to support scientific computing outside the company. During 2022, Fire-Flyer 2 had 5,000 PCIe A100 GPUs in 625 nodes, each containing 8 GPUs. At the time, it exclusively used PCIe instead of the DGX version of A100, since at the time the models it trained could fit within a single 40 GB GPU VRAM and so there was no need for the higher bandwidth of DGX (i.e., it required only data parallelism but not model parallelism). Later, it incorporated NVLinks and NCCL (Nvidia Collective Communications Library) to train larger models that required model parallelism. On 14 April 2023, High-Flyer announced the launch of an artificial general intelligence (AGI) research lab, stating that the new lab would focus on developing AI tools unrelated to the firm's financial business. Two months later, on 17 July 2023, that lab was spun off into an independent company, DeepSeek, with High-Flyer as its principal investor and backer. Venture capital investors were reluctant to provide funding, as they considered it unlikely that the venture would be able to quickly generate an "exit". === Model releases since 2023 === DeepSeek released its first model, DeepSeek Coder, on 2 November 2023, followed by the DeepSeek-LLM series on 29 November 2023. In January 2024, it released two DeepSeek-MoE models (Base and Chat), and in April 3 DeepSeek-Math models (Base, Instruct, and RL). DeepSeek-V2 was released in May 2024, followed a month later by the DeepSeek-Coder V2 series. In September 2024, DeepSeek V2.5 was introduced and revised in December. On 20 November 2024, the preview of DeepSeek-R1-Lite became available via chat. In December, DeepSeek-V3-Base and DeepSeek-V3 (chat) were released. On 20 January 2025, DeepSeek launched the DeepSeek chatbot—based on the DeepSeek-R1 model—free for iOS and Android. By 27 January, DeepSeek surpassed ChatGPT as the most downloaded freeware app on the iOS App Store in the United States, triggering an 18% drop in Nvidia's share price. On 24 March 2025, DeepSeek released DeepSeek-V3-0324 under the MIT License. On 28 May 2025, DeepSeek released DeepSeek-R1-0528 under the MIT License. The model has been noted for more tightly following official Chinese Communist Party ideology and censorship in its answers to questions than prior models. On 21 August 2025, DeepSeek released DeepSeek V3.1 under the MIT License. This model features a hybrid architecture with thinking and non-thinking modes. It also surpasses prior models like V3 and R1, by over 40% on certain benchmarks like SWE-bench and Terminal-bench. It was updated to V3.1-Terminus on 22 September 2025. V3.2-Exp was released on 29 September 2025. It uses DeepSeek Sparse Attention, a more efficient attention mechanism based on previous research published in February. DeepSeek-V3.2 was released on 1 December 2025, alongside a DeepSeek-V3.2-Speciale variant that focused on reasoning. In February 2026, Anthropic accused DeepSeek of using thousands of fraudulent accounts to generate millions of conversations with Claude to train its own large language models. In April 2026, investors began speaking with DeepSeek for a $300 million funding round, which would bring DeepSeek to a total valuation of $10 billion. On April 24, 2026, DeepSeek released a preview of its V4 series, including the 1.6-trillion parameter DeepSeek-V4-Pro and the 284-billion parameter DeepSeek-V4-Flash, both featuring a 1-million token context window, under the MIT License. DeepSeek's V4 LLM has been adopted by key semiconductor manufacturers and artificial intelligence chipmakers such as Huawei and Cambricon. == Company operation == DeepSeek is headquartered in Hangzhou, Zhejiang, and is owned and funded by High-Flyer. Its co-founder, Liang Wenfeng, serves as CEO. As of May 2024, Liang personally held an 84% stake in DeepSeek through two shell corporations. === Strategy === DeepSeek has stated that it focuses on research and does not have immediate plans for commercialization. This posture also means it can skirt certain provisions of China's AI regulations aimed at consumer-facing technologies. DeepSeek's hiring approach emphasizes skills over lengthy work experience, resulting in many hires fresh out of university. The company likewise recruits individuals without computer science backgrounds to expand the range of expertise incorporated into the models, for instance in poetry or advanced mathematics. According to The New York Times, dozens of DeepSeek researchers have or have previously had affiliations with People's Liberation Army laboratories and the Seven Sons of National Defence. Due to the impact of United States restrictions on chips, DeepSeek refined its algorithms to maximise computational efficiency and thereby leveraged older hardware and reduced energy consumption. DeepSeek also expanded on the African continent as it offers more affordable and less power-hungry AI solutions. The company has bolstered African language models and generated a number of startups, for example in Nairobi. Along with Huawei's storage and cloud computing services, the impact on the tech scene in sub-saharan Africa is considerable. DeepSeek offers local data sovereignty and more flexibility compared to Western AI platforms. == Training framework == High-Flyer/DeepSeek had operated at least two primary computing clusters: Fire-Flyer (萤火一号) and Fire-Flyer 2 (萤火二号). Fire-Flyer 1 was constructed in 2019 and was retired after 1.5 years of operation. Fi

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  Lumpers and splitters

  Lumpers and splitters are opposing factions in any academic discipline that has to place individual examples into rigorously defined categories. The lumper–splitter problem occurs when there is the desire to create classifications and assign examples to them, for example, schools of literature, biological taxa, and so on. A "lumper" is a person who assigns examples broadly, judging that differences are not as important as signature similarities. A "splitter" makes precise definitions, and creates new categories to classify samples that differ in key ways. == Origin of the terms == The earliest known use of these terms was thought to be by Charles Darwin, in a letter to Joseph Dalton Hooker in 1857: "It is good to have hair-splitters & lumpers". But according to research done by the deputy director at NCSE, Glenn Branch, the credit is due to naturalist Edward Newman who wrote in 1845, "The time has arrived for discarding imaginary species, and the duty of doing this is as imperative as the admission of new ones when such are really discovered. The talents described under the respective names of 'hair-splitting' and 'lumping' are unquestionably yielding their power to the mightier power of Truth." They were then introduced more widely by George G. Simpson in his 1945 work The Principles of Classification and a Classification of Mammals. As he put it: splitters make very small units – their critics say that if they can tell two animals apart, they place them in different genera ... and if they cannot tell them apart, they place them in different species. ... Lumpers make large units – their critics say that if a carnivore is neither a dog nor a bear, they call it a cat. A later use can be found in the title of a 1969 paper "On lumpers and splitters ..." by the medical geneticist Victor McKusick. Reference to lumpers and splitters in the humanities appeared in a debate in 1975 between J. H. Hexter and Christopher Hill, in the Times Literary Supplement. It followed from Hexter's detailed review of Hill's book Change and Continuity in Seventeenth Century England, in which Hill developed Max Weber's argument that the rise of capitalism was facilitated by Calvinist Puritanism. Hexter objected to Hill's "mining" of sources to find evidence that supported his theories. Hexter argued that Hill plucked quotations from sources in a way that distorted their meaning. Hexter explained this as a mental habit that he called "lumping". According to him, "lumpers" rejected differences and chose to emphasise similarities. Any evidence that did not fit their arguments was ignored as aberrant. Splitters, by contrast, emphasised differences, and resisted simple schemes. While lumpers consistently tried to create coherent patterns, splitters preferred incoherent complexity. == Usage in various fields == === Biology === The categorisation and naming of a particular species should be regarded as a hypothesis about the evolutionary relationships and distinguishability of that group of organisms. As further information comes to hand, the hypothesis may be confirmed or refuted. Sometimes, especially in the past when communication was more difficult, taxonomists working in isolation have given two distinct names to individual organisms later identified as the same species. When two named species are agreed to be of the same species, the older species name is almost always retained dropping the newer species name honouring a convention known as "priority of nomenclature". This form of lumping is technically called synonymisation. Dividing a taxon into multiple, often new, taxa is called splitting. Taxonomists are often referred to as "lumpers" or "splitters" by their colleagues, depending on their personal approach to recognizing differences or commonalities between organisms. For example, the number of genera used in Pteridophyte Phylogeny Group I (PPG I) has proved controversial. PPG I uses 18 lycophyte and 319 fern genera. The earlier system put forward by Smith et al. (2006) had suggested a range of 274 to 312 genera for ferns alone. By contrast, the system of Christenhusz & Chase (2014) used 5 lycophyte and about 212 fern genera. The number of fern genera was further reduced to 207 in a subsequent publication. Defending PPG I, Schuettpelz et al. (2018) argue that the larger number of genera is a result of "the gradual accumulation of new collections and new data" and hence "a greater appreciation of fern diversity and ... an improved ability to distinguish taxa". They also argue that the number of species per genus in the PPG I system is already higher than in other groups of organisms (about 33 species per genus for ferns as opposed to about 22 species per genus for angiosperms) and that reducing the number of genera as Christenhusz and Chase propose yields the excessive number of about 50 species per genus for ferns. In response, Christenhusz and Chase (2018) argue that the excessive splitting of genera destabilises the usage of names and will lead to greater instability in future, and that the highly split genera have few if any characters that can be used to recognise them, making identification difficult, even to generic level. They further argue that comparing numbers of species per genus in different groups is "fundamentally meaningless". === History === In history, lumpers are those who tend to create broad definitions that cover large periods of time and many disciplines, whereas splitters want to assign names to tight groups of inter-relationships. Lumping tends to create a more and more unwieldy definition, with members having less and less mutually in common. This can lead to definitions which are little more than conventionalities, or groups which join fundamentally different examples. Splitting often leads to "distinctions without difference", ornate and fussy categories, and failure to see underlying similarities. For example, in the arts, "Romantic" can refer specifically to a period of German poetry roughly from 1780 to 1810, but would exclude the later work of Goethe, among other writers. In music it can mean every composer from Hummel through Rachmaninoff, plus many that came after. === Software modelling === Software engineering often proceeds by building models (sometimes known as model-driven architecture). A lumper is keen to generalise, and produces models with a small number of broadly defined objects. A splitter is reluctant to generalise, and produces models with a large number of narrowly defined objects. Conversion between the two styles is not necessarily symmetrical. For example, if error messages in two narrowly defined classes behave in the same way, the classes can be easily combined. But if some messages in a broad class behave differently, every object in the class must be examined before the class can be split. This illustrates the principle that "splits can be lumped more easily than lumps can be split". === Language classification === There is no agreement among historical linguists about what amount of evidence is needed for two languages to be safely classified in the same language family. For this reason, many proposed language families have had lumper–splitter controversies, including Altaic, Pama–Nyungan, Nilo-Saharan, and most of the larger families of the Americas. At a completely different level, the splitting of a mutually intelligible dialect continuum into different languages, or lumping them into one, is also an issue that continually comes up, though the consensus in contemporary linguistics is that there is no completely objective way to settle the question. Splitters regard the comparative method (meaning not comparison in general, but only reconstruction of a common ancestor or protolanguage) as the only valid proof of kinship, and consider genetic relatedness to be the question of interest. American linguists of recent decades tend to be splitters. Lumpers are more willing to admit techniques like mass lexical comparison or lexicostatistics, and mass typological comparison, and to tolerate the uncertainty of whether relationships found by these methods are the result of linguistic divergence (descent from common ancestor) or language convergence (borrowing). Much long-range comparison work has been from Russian linguists belonging to the Moscow School of Comparative Linguistics, most notably Vladislav Illich-Svitych and Sergei Starostin. In the United States, Greenberg and Ruhlen's work has been met with little acceptance from linguists. Earlier American linguists like Morris Swadesh and Edward Sapir also pursued large-scale classifications like Sapir's 1929 scheme for the Americas, accompanied by controversy similar to that today. === Religious studies === Paul F. Bradshaw suggests that the same principles of lumping and splitting apply to the study of early Christian liturgy. Lumpers, who tend to predominate in this field, try to find a single line of successive texts from the apostolic age to the

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  Gödel machine

  A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ⁡ ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.

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  Civitai

  Civitai is an online platform and marketplace for generative artificial intelligence (Gen AI) content, primarily focused on AI-generated images and models, and AI-generated videos. == History == Civitai was founded in 2022 by Justin Maier. By January 2023, the site reached 100,000 registered users and 3 million by November. In November 2023, Civitai secured funding from venture capital firm Andreessen Horowitz. By April 2024, Civitai had 23.2 million monthly accesses. The company is headquartered in Boise, Idaho. == Platform == Civitai allows users to share and download AI models, particularly those used for image generation. The platform supports various AI models, including Stable Diffusion and Flux, and provides a space for users to showcase and monetize their AI-generated content. Users have profile pages and can comment on other users' models and images. The website also features a virtual currency called Buzz that can be used to generate images on Civitai's servers. Buzz can be bought or earned by engaging with the site. The platform is open source. == Controversies == In 2023, 404 Media reported that Civitai began a "Bounties" marketplace where users could commission deepfakes, of real or fake people. Users are rewarded with Buzz for completing Bounties. In December 2023, AI provider OctoML announced it had ended its business relationship with Civitai after concerns were raised users were generating images that “could be categorized as child pornography.”

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  TD-Gammon

  TD-Gammon is a computer backgammon program developed in the 1990s by Gerald Tesauro at IBM's Thomas J. Watson Research Center. Its name comes from the fact that it is an artificial neural net trained by a form of temporal-difference learning, specifically TD-Lambda. It explored strategies that humans had not pursued and led to advances in the theory of correct backgammon play. In 1993, TD-Gammon (version 2.1) was trained with 1.5 million games of self-play, and achieved a level of play just slightly below that of the top human backgammon players of the time. In 1998, during a 100-game series, it was defeated by the world champion by a mere margin of 8 points. Its unconventional assessment of some opening strategies had been accepted and adopted by expert players. TD-gammon is commonly cited as an early success of reinforcement learning and neural networks, and was cited in, for example, papers for deep Q-learning and AlphaGo. == Algorithm for play and learning == During play, TD-Gammon examines on each turn all possible legal moves and all their possible responses (lookahead search), feeds each resulting board position into its evaluation function, and chooses the move that leads to the board position that got the highest score. In this respect, TD-Gammon is no different than almost any other computer board-game program. TD-Gammon's innovation was in how it learned its evaluation function. TD-Gammon's learning algorithm consists of updating the weights in its neural net after each turn to reduce the difference between its evaluation of previous turns' board positions and its evaluation of the present turn's board position—hence "temporal-difference learning". The score of any board position is a set of four numbers reflecting the program's estimate of the likelihood of each possible game result: White wins normally, Black wins normally, White wins a gammon, Black wins a gammon. For the final board position of the game, the algorithm compares with the actual result of the game rather than its own evaluation of the board position. The core of TD-gammon is a neural network with 3 layers. The input layer has two types of neurons. One type codes for the board position. They are non-negative integers ranging from 0 to 15, indicating the number of White or Black checkers at each board location. There are 99 input neurons for each, totaling 198 neurons. Another type codes for hand-crafted features previously used in Neurogammon. These features encoded standard concepts used by human experts, such as "advanced anchor," "blockade strength," "home board strength" and the probability of a "blot" (single checker) being hit. The hidden layer contains hidden neurons. Later versions had more of these. The output layer contains 4 neurons, representing the network's estimate of the probability ("equity") that the current board would lead to. The 4 neurons code for: White normal win, White gammon win, Black normal win, Black gammon win. Backgammon win is so rare that Tesauro opted to not represent it. After each turn, the learning algorithm updates each weight in the neural net according to the following rule: w t + 1 − w t = α ( Y t + 1 − Y t ) ∑ k = 1 t λ t − k ∇ w Y k {\displaystyle w_{t+1}-w_{t}=\alpha (Y_{t+1}-Y_{t})\sum _{k=1}^{t}\lambda ^{t-k}\nabla _{w}Y_{k}} where: It was found that picking small λ {\displaystyle \lambda } offered performance roughly equally good, and large λ {\displaystyle \lambda } degraded performance. Because of this, after 1992, TD-Gammon was trained with λ = 0 {\displaystyle \lambda =0} , degenerating into standard TD-learning. This saved compute by a factor of 2. == Development history == Version 1.0 used simple 1-ply search: every next move is scored by the neural net, and the highest-scoring move is selected. Versions 2.0 and 2.1 used 2-ply search: Make a 1-ply analysis to remove unlikely moves ("forward pruning"). Make a 2-play minimax analysis for only the likely moves. Pick the best move, probability-weighted by each of the opponent's 21 possible dice rolls (weighting non-doubles twice as much as doubles). Versions 3.0 and 3.1 used 3-ply search, using 21 2 = 441 {\displaystyle 21^{2}=441} possible dice rolls instead of 21. The last version, 3.1, was trained specifically for an exhibition match against Malcolm Davis at the 1998 AAAI Hall of Champions. It lost at -8 points, mainly due to one blunder, where TD-Gammon opted to double and got gammoned at -32 points. == Experiments and stages of training == Unlike previous neural-net backgammon programs such as Neurogammon (also written by Tesauro), where an expert trained the program by supplying the "correct" evaluation of each position, TD-Gammon was at first programmed "knowledge-free". In early experimentation, using only a raw board encoding with no human-designed features, TD-Gammon reached a level of play comparable to Neurogammon: that of an intermediate-level human backgammon player. Even though TD-Gammon discovered insightful features on its own, Tesauro wondered if its play could be improved by using hand-designed features like Neurogammon's. Indeed, the self-training TD-Gammon with expert-designed features soon surpassed all previous computer backgammon programs. It stopped improving after about 1,500,000 games (self-play) using a three-layered neural network, with 198 input units encoding expert-designed features, 80 hidden units, and one output unit representing predicted probability of winning. == Advances in backgammon theory == TD-Gammon's exclusive training through self-play (rather than imitation learning) enabled it to explore strategies that humans previously had not considered or had ruled out erroneously. Its success with unorthodox strategies had a significant impact on the backgammon community. Late 1991, Bill Robertie, Paul Magriel, and Malcolm Davis, were invited to play against TD-Gammon (version 1.0). A total of 51 games were played, with TD-Gammon losing at -0.25 ppg. Robertie found TD-Gammon to be at the level of a competent advanced player, and better than any previous backgammon program. Robertie subsequently wrote about the use of TD-Gammon for backgammon study. For example, on the opening play, the conventional wisdom was that given a roll of 2-1, 4-1, or 5-1, White should move a single checker from point 6 to point 5. Known as "slotting", this technique trades the risk of a hit for the opportunity to develop an aggressive position. TD-Gammon found that the more conservative play of splitting 24-23 was superior. Tournament players began experimenting with TD-Gammon's move, and found success. Within a few years, slotting had disappeared from tournament play, replaced by splitting, though in 2006 it made a reappearance for 2-1. Backgammon expert Kit Woolsey found that TD-Gammon's positional judgement, especially its weighing of risk against safety, was superior to his own or any human's. TD-Gammon's excellent positional play was undercut by occasional poor endgame play. The endgame requires a more analytical approach, sometimes with extensive lookahead. TD-Gammon's limitation to two-ply lookahead put a ceiling on what it could achieve in this part of the game. TD-Gammon's strengths and weaknesses were the opposite of symbolic artificial intelligence programs and most computer software in general: it was good at matters that require an intuitive "feel" but bad at systematic analysis. It is also poor at doubling strategies. This is likely due to the fact that the neural network is trained without the doubling cube, with the doubling added by feeding the neural network's cubeless equity estimates into theoretically-based heuristic formulae. This was particularly the case in the 1998 exhibition match, where it played 100 games against Malcolm Davis. A single doubling blunder lost the match. TD-gammon was never commercialized or released to the public in some other form, but it inspired commercial backgammon programs based on neural networks, such as JellyFish (1994) and Snowie (1998).

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  ML.NET

  ML.NET is a free software machine learning library for the C# and F# programming languages. It also supports Python models when used together with NimbusML. The preview release of ML.NET included transforms for feature engineering like n-gram creation, and learners to handle binary classification, multi-class classification, and regression tasks. Additional ML tasks like anomaly detection and recommendation systems have since been added, and other approaches like deep learning will be included in future versions. == Machine learning == ML.NET brings model-based Machine Learning analytic and prediction capabilities to existing .NET developers. The framework is built upon .NET Core and .NET Standard inheriting the ability to run cross-platform on Linux, Windows and macOS. Although the ML.NET framework is new, its origins began in 2002 as a Microsoft Research project named TMSN (text mining search and navigation) for use internally within Microsoft products. It was later renamed to TLC (the learning code) around 2011. ML.NET was derived from the TLC library and has largely surpassed its parent says Dr. James McCaffrey, Microsoft Research. Developers can train a Machine Learning Model or reuse an existing Model by a 3rd party and run it on any environment offline. This means developers do not need to have a background in Data Science to use the framework. Support for the open-source Open Neural Network Exchange (ONNX) Deep Learning model format was introduced from build 0.3 in ML.NET. The release included other notable enhancements such as Factorization Machines, LightGBM, Ensembles, LightLDA transform and OVA. The ML.NET integration of TensorFlow is enabled from the 0.5 release. Support for x86 & x64 applications was added to build 0.7 including enhanced recommendation capabilities with Matrix Factorization. A full roadmap of planned features have been made available on the official GitHub repo. The first stable 1.0 release of the framework was announced at Build (developer conference) 2019. It included the addition of a Model Builder tool and AutoML (Automated Machine Learning) capabilities. Build 1.3.1 introduced a preview of Deep Neural Network training using C# bindings for Tensorflow and a Database loader which enables model training on databases. The 1.4.0 preview added ML.NET scoring on ARM processors and Deep Neural Network training with GPU's for Windows and Linux. === Performance === Microsoft's paper on machine learning with ML.NET demonstrated it is capable of training sentiment analysis models using large datasets while achieving high accuracy. Its results showed 95% accuracy on Amazon's 9GB review dataset. === Model builder === The ML.NET CLI is a Command-line interface which uses ML.NET AutoML to perform model training and pick the best algorithm for the data. The ML.NET Model Builder preview is an extension for Visual Studio that uses ML.NET CLI and ML.NET AutoML to output the best ML.NET Model using a GUI. === Model explainability === AI fairness and explainability has been an area of debate for AI Ethicists in recent years. A major issue for Machine Learning applications is the black box effect where end users and the developers of an application are unsure of how an algorithm came to a decision or whether the dataset contains bias. Build 0.8 included model explainability API's that had been used internally in Microsoft. It added the capability to understand the feature importance of models with the addition of 'Overall Feature Importance' and 'Generalized Additive Models'. When there are several variables that contribute to the overall score, it is possible to see a breakdown of each variable and which features had the most impact on the final score. The official documentation demonstrates that the scoring metrics can be output for debugging purposes. During training & debugging of a model, developers can preview and inspect live filtered data. This is possible using the Visual Studio DataView tools. === Infer.NET === Microsoft Research announced the popular Infer.NET model-based machine learning framework used for research in academic institutions since 2008 has been released open source and is now part of the ML.NET framework. The Infer.NET framework utilises probabilistic programming to describe probabilistic models which has the added advantage of interpretability. The Infer.NET namespace has since been changed to Microsoft.ML.Probabilistic consistent with ML.NET namespaces. === NimbusML Python support === Microsoft acknowledged that the Python programming language is popular with Data Scientists, so it has introduced NimbusML the experimental Python bindings for ML.NET. This enables users to train and use machine learning models in Python. It was made open source similar to Infer.NET. === Machine learning in the browser === ML.NET allows users to export trained models to the Open Neural Network Exchange (ONNX) format. This establishes an opportunity to use models in different environments that don't use ML.NET. It would be possible to run these models in the client side of a browser using ONNX.js, a JavaScript client-side framework for deep learning models created in the Onnx format. === AI School Machine Learning Course === Along with the rollout of the ML.NET preview, Microsoft rolled out free AI tutorials and courses to help developers understand techniques needed to work with the framework.

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  Self-supervised learning

  Self-supervised learning (SSL) is a paradigm in machine learning where a model is trained on a task using the data itself to generate supervisory signals, rather than relying on externally-provided labels. In the context of neural networks, self-supervised learning aims to leverage inherent structures or relationships within the input data to create meaningful training signals. SSL tasks are designed so that solving them requires capturing essential features or relationships in the data. The input data is typically augmented or transformed in a way that creates pairs of related samples, where one sample serves as the input, and the other is used to formulate the supervisory signal. This augmentation can involve introducing noise, cropping, rotation, or other transformations. Self-supervised learning more closely imitates the way humans learn to classify objects. During SSL, the model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels, which help to initialize the model parameters. Next, the actual task is performed with supervised or unsupervised learning. Self-supervised learning has produced promising results in recent years, and has found practical application in fields such as audio processing, and is being used by Facebook and others for speech recognition. == Pseudo-labels == Pseudo-labels are automatically generated labels that a model assigns to unlabeled data based on its own predictions. They are widely used in self-supervised and semi-supervised learning, where ground-truth annotations are limited or unavailable. By treating predicted labels as surrogate ground truth, learning algorithms can make use of large quantities of unlabeled data in the training process. Pseudo-labeling also plays an important role in systems that must adapt to concept drift, where the statistical properties of the data change over time. In these scenarios, the model may detect that an incoming instance deviates from previously learned behavior. The system then generates a classification result for that instance, and this predicted class is used as a pseudo-label for updating or retraining model components that are becoming outdated. This approach enables continuous adaptation in dynamic environments without requiring manual annotation. In many adaptive learning pipelines, pseudo-labels are chosen when the classifier produces sufficiently confident predictions, reducing the risk of propagating errors. These pseudo-labeled instances are then incorporated into training to refresh or evolve the model's understanding of emerging data patterns, particularly when existing components show signs of “aging” due to drift or distributional shifts. This strategy reduces reliance on manual labeling while helping maintain long-term model performance. == Types == === Autoassociative self-supervised learning === Autoassociative self-supervised learning is a specific category of self-supervised learning where a neural network is trained to reproduce or reconstruct its own input data. In other words, the model is tasked with learning a representation of the data that captures its essential features or structure, allowing it to regenerate the original input. The term "autoassociative" comes from the fact that the model is essentially associating the input data with itself. This is often achieved using autoencoders, which are a type of neural network architecture used for representation learning. Autoencoders consist of an encoder network that maps the input data to a lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error). By minimizing this reconstruction error, the autoencoder learns a meaningful representation of the data in its latent space. === Contrastive self-supervised learning === For a binary classification task, training data can be divided into positive examples and negative examples. Positive examples are those that match the target. For example, if training a classifier to identify birds, the positive training data would include images that contain birds. Negative examples would be images that do not. Contrastive self-supervised learning uses both positive and negative examples. The loss function in contrastive learning is used to minimize the distance between positive sample pairs, while maximizing the distance between negative sample pairs. An early example uses a pair of 1-dimensional convolutional neural networks to process a pair of images and maximize their agreement. Contrastive Language-Image Pre-training (CLIP) allows joint pretraining of a text encoder and an image encoder, such that a matching image-text pair have image encoding vector and text encoding vector that span a small angle (having a large cosine similarity). InfoNCE (Noise-Contrastive Estimation) is a method to optimize two models jointly, based on Noise Contrastive Estimation (NCE). Given a set X = { x 1 , … x N } {\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle p\left(x_{t+k}\mid c_{t}\right)} and N − 1 {\displaystyle N-1} negative samples from the 'proposal' distribution p ( x t + k ) {\displaystyle p\left(x_{t+k}\right)} , it minimizes the following loss function: L N = − E X [ log ⁡ f k ( x t + k , c t ) ∑ x j ∈ X f k ( x j , c t ) ] {\displaystyle {\mathcal {L}}_{\mathrm {N} }=-\mathbb {E} _{X}\left[\log {\frac {f_{k}\left(x_{t+k},c_{t}\right)}{\sum _{x_{j}\in X}f_{k}\left(x_{j},c_{t}\right)}}\right]} === Non-contrastive self-supervised learning === Non-contrastive self-supervised learning (NCSSL) uses only positive examples. Counterintuitively, NCSSL converges on a useful local minimum rather than reaching a trivial solution, with zero loss. For the example of binary classification, it would trivially learn to classify each example as positive. Effective NCSSL requires an extra predictor on the online side that does not back-propagate on the target side. === Joint-Embedding and Predictive Architectures === A major class of self-supervised learning moves beyond contrastive pairs, instead maximizing the agreement between views while preventing collapse through statistical constraints. Rooted in Deep Canonical Correlation Analysis (Deep CCA), this approach includes Joint-Embedding Architectures (JEA) like Barlow Twins and VICReg, which enforce covariance constraints to learn invariant representations without negative sampling. Deep Latent Variable Path Modelling (DLVPM) generalizes this to multimodal systems, using path models to enforce correlation and orthogonality across diverse data types. In 2022 Yann LeCun introduced Joint-Embedding Predictive Architectures (JEPA) as a step towards decision making, reasoning, and autonomous human intelligence in machines, including self-improvement through autonomous learning. Founded in representation learning, LeCun included the concept of a “world model” in JEPA which aims to enable machines to replicate human intellect by providing machines with a concept for the world in which they exist. Unlike autoencoders, JEPAs operate entirely in latent space, avoiding pixel-level noise to focus on semantic structure. Rather than just learning invariance, JEPAs learn by predicting masked latent representations from visible context. JEPA has been applied to domains such as image analysis, audio processing, and motion in images and video. == Comparison with other forms of machine learning == SSL belongs to supervised learning methods insofar as the goal is to generate a classified output from the input. At the same time, however, it does not require the explicit use of labeled input-output pairs. Instead, correlations, metadata embedded in the data, or domain knowledge present in the input are implicitly and autonomously extracted from the data. These supervisory signals, extracted from the data, can then be used for training. SSL is similar to unsupervised learning in that it does not require labels in the sample data. Unlike unsupervised learning, however, learning is not done using inherent data structures. Semi-supervised learning combines supervised and unsupervised learning, requiring only a small portion of the learning data be labeled. In transfer learning, a model designed for one task is reused on a different task. Training an autoencoder intrinsically constitutes a self-supervised process, because the output pattern needs to become an optimal reconstruction of the input pattern itself. However, in current jargon, the term 'self-supervised' often refers to tasks based on a pretext-task training setup

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  Thinking Machines Lab

  Thinking Machines Lab Inc. is an American artificial intelligence (AI) startup founded by Mira Murati, the former chief technology officer of OpenAI. The company was founded in February 2025, and by July had completed an early-stage funding round led by Andreessen Horowitz, raising $2 billion at a valuation of $12 billion overall from investors such as Nvidia, AMD, Cisco, and Jane Street. The company is based in San Francisco and structured as a public benefit corporation. == History == By its launch in February 2025, Thinking Machines Lab was reported to have hired about 30 researchers and engineers from competitors including OpenAI, Meta AI, and Mistral AI. Its founding team members include Barret Zoph, former OpenAI VP of Research (Post-Training), Lilian Weng, former OpenAI VP, and OpenAI cofounder John Schulman, who joined after a brief stint at the lab's competitor Anthropic. In January 2026, it was reported that Barret Zoph and Luke Metz, departed the startup to return to OpenAI. Other former OpenAI employees who have been hired include Jonathan Lachman and Andrew Tulloch (although Tulloch departed after getting recruited for Meta Superintelligence Labs). Thinking Machines Lab's advisers include Bob McGrew, previously OpenAI's chief research officer, and Alec Radford, who was a lead researcher for OpenAI. On October 1, 2025, it announced Tinker, an API for fine-tuning language models. Users would submit jobs through the API for fine-tuning one of the various open-weight models supported. The Lab would run the jobs on its internal clusters and training infrastructure. == Business structure == Thinking Machines Lab grants Mira Murati a deciding vote on board matters, weighted to provide her with a majority decision-making capability. Additionally, founding shareholders possess votes weighted 100 times greater than those of regular shareholders. In July 2025, Andreessen Horowitz was reported to have led the company's initial funding round, raising "about $2 billion at a valuation of $12 billion". The government of Albania (Murati's country of origin) was also included in this round, making a $10 million investment which required an amendment to the country's 2025 budget. == Partnership == In March 2026, Thinking Machines Lab announced a strategic partnership with NVIDIA involving an undisclosed investment and a multi-year agreement to deploy one gigawatt of Vera Rubin computing capacity.

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  Reification (knowledge representation)

  Reification in knowledge representation is the process of turning a predicate or statement into an addressable object. Reification allows the representation of assertions so that they can be referred to or qualified by other assertions, i.e., meta-knowledge. The message "John is six feet tall" is an assertion involving truth that commits the speaker to its factuality, whereas the reified statement "Mary reports that John is six feet tall" defers such commitment to Mary. In this way, the statements can be incompatible without creating contradictions in reasoning. For example, the statements "John is six feet tall" and "John is five feet tall" are mutually exclusive (and thus incompatible), but the statements "Mary reports that John is six feet tall" and "Paul reports that John is five feet tall" are not incompatible, as they are both governed by a conclusive rationale that either Mary or Paul is (or both are), in fact, incorrect. In linguistics, reporting, telling, and saying are recognized as verbal processes that project a wording (or locution). If a person says that "Paul told x" and "Mary told y", this person stated only that the telling took place. In this case, the person who made these two statements did not represent a person inconsistently. In addition, if two people are talking to each other, let's say Paul and Mary, and Paul tells Mary "John is five feet tall" and Mary rejects Paul's statement by saying "No, he is actually six feet tall", the socially constructed model of John does not become inconsistent. The reason for that is that statements are to be understood as an attempt to convince the addressee of something (Austin's How to do things with words), alternatively as a request to add some attribute to the model of Paul. The response to a statement can be an acknowledgement, in which case the model is changed, or it can be a statement rejection, in which case the model does not get changed. Finally, the example above for which John is said to be "five feet tall" or "six feet tall" is only incompatible because John can only be a single number of feet tall. If the attribute were a possession as in "he has a dog" or "he also has a cat", a model inconsistency would not happen. In other words, the issue of model inconsistency has to do with our model of the domain element (John) and not with the ascription of different range elements (measurements such as "five feet tall" or "six feet tall").

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  Eimear Kenny

  Eimear E. Kenny is a researcher in population genetics and translation genomics, and is the Founding Director of the Institute for Genomic Health, and Endowed Chair and Professor of Genomic Health at the Icahn School of Medicine at Mount Sinai. She is known for novel approaches in computational genomics, advancing the study of human genetic variation and its connection to disease risk and diagnosis. Her research has laid the foundation for integrating artificial intelligence (AI) and genomics into precision medicine and routine clinical care. By combining genomics, computer science, and medicine, her work leverages genomic sequencing technologies and machine learning algorithms to uncover insights that improve patient care, accelerate genomic data analysis, and enable the future of AI-driven healthcare. She has led multiple genomics-based clinical trials, applying computational biology and AI in clinical settings to advance genomic medicine and precision healthcare. == Research == A recipient of the Early-Career Award from the American Society of Human Genetics (USA), Kenny, as of 2024, leads a team in genetics, computer science, and medicine, focusing on genetic ancestry, large-scale genomics, clinical trials, and genomic medicine at the Institute for Genomic Health. The lab works to advance understanding of genetic ancestry and its impact on health in order to inform better clinical medicine models. She is recognized for her work to leverage biobanks for translational genomics and her development of new genetic tests an strategies for health care management. In one study, she and her colleagues investigated genetic disorders that might be under-diagnosed due to insufficient data, and found a variant in a collagen gene associated with Steel syndrome. This syndrome caused short stature and bone and joint issues and was thought to be rare. However, the study revealed it is common in individuals with Puerto Rican ancestry. Three of Kenny's genomic medicine clinical trials assessed how to bring new technology, such as digital apps, or information, such as polygenic risk scores, into routine clinical care. In the 2010s, Kenny was instrumental in several large-scale sequencing studies, including the 1000 Genomes Project, the Exome Sequencing Project, the Genome Sequencing Project, and the Trans-Omics for Precision Medicine. In 2012, she led work that discovered the variant responsible for blond hair in Melanesia, work that was featured in the Smithsonian NHGRI Human Genome Exhibit in Washington, D.C. In 2017, her group was one of the first to demonstrate that polygenic risk scores derived in predominantly European populations have reduced accuracy when applied in populations now widely acknowledged as a major challenge in the field of genomic risk prediction. As of 2024, she is Principal Investigator in many NIH-funded international consortium focused on computational genomics and genomic medicine, including Electronic Medical Records and Genomics, Polygenic Risk Methods in Diverse Populations, and the Human Pangenome Reference Consortium. In 2023, Kenny played a key role in a groundbreaking advancement in genomics research by helping to map a diverse human pangenome—a major shift from reliance on a single reference genome. Unlike the earlier genetic map, based on one man of mixed European and African ancestry in Buffalo, this new pangenome project captures far greater human genetic diversity. As reported by The Washington Post, Kenny's work demonstrates how a more inclusive human genome can drive discoveries in rare genetic diseases, improve genomic medicine, and accelerate the future of precision healthcare. Kenny was co-developer and current license holder for Random Forest adMIXture (RFMix), a patented software for inferring continental and sub-continental ancestry at genomic loci. == Education and career == Kenny graduated from Trinity College Dublin with a BA in Biochemistry in 1999 and did a masters in Bioinformatics at Leeds University. She received her PhD in Computational Genomics at Rockefeller University, and did her post-doctoral work in the lab of Dr. Carlos D. Bustamante at Stanford University. === Academic appointments === As of 2024, at Mount Sinai, she serves as the Endowed Chair and Professor of Genomic Health, Professor at the Department of Medicine and Professor at the Department of Genetics and Genomic Sciences. Since 2018 she has served as the Founding Director of the Institute for Genomic Health, and since 2022, she also serves as the Founding Director of the Center for Translational Genomics. She is also the Director of Translational Research, Division for Genomic Medicine. Former appointments include Assistant Professor at the Department of Genetics and Genomic Sciences and Member at The Charles Bronfman Institute of Personalized Medicine, both at Mount Sinai. She was also Bioinformatics Programmer at the California Institute of Technology, and research assistant at the Massachusetts Institute of Technology. == Publications == As of 2024, Kenny is an advisor to Cell Genomics. Google Scholar reports 50,623 citations, an h-index of 66 and an i10-index of 130. The five most-cited articles she contributed to are: Auton, A; Brooks, LD; Durbin, RM; Garrison, EP; Kang, HM; Korbel, JO; Marchini, JL; McCarthy, S; McVean, GA; Abecasis, GR (2015). "A global reference for human genetic variation". Nature. 526 (7571): 68–74. Bibcode:2015Natur.526...68T. doi:10.1038/nature15393. PMC 4750478. PMID 26432245.. Cited by 14847 Abecasis, GR; Auton, A; Brooks, LD; DePristo, MA; Durbin, RM; Handsaker, RE; Kang, HM; Marth, GT; McVean, GA (2012). "An integrated map of genetic variation from 1,092 human genomes". Nature. 491 (7422): 56–65. Bibcode:2012Natur.491...56T. doi:10.1038/nature11632. PMC 3498066. PMID 23128226.. Cited by 8287 Jacob A. Tennessen et al. Evolution and Functional Impact of Rare Coding Variation from Deep Sequencing of Human Exomes.Science337,64–69(2012).DOI:10.1126/science.1219240 Cited by 1886 Taliun, D.; Harris, D.N.; Kessler, M.D.; et al. (2021). "Sequencing of 53,831 diverse genomes from the NHLBI TOPMed Program". Nature. 590 (7845): 290–299. Bibcode:2021Natur.590..290T. doi:10.1038/s41586-021-03205-y. PMC 7875770. PMID 33568819.. Cited by 1369 Vilhjálmsson, BJ; et al. (2015). "Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores". Am J Hum Genet. 97 (4): 576–92. doi:10.1016/j.ajhg.2015.09.001. PMC 4596916. PMID 26430803.. Cited by 1327

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  List of software palettes

  This is a list of software palettes used by computers. Systems that use a 4-bit or 8-bit pixel depth can display up to 16 or 256 colors simultaneously. Many personal computers in the early 1990s displayed at most 256 different colors, freely selected by software (either by the user or by a program) from their wider hardware's RGB color palette. Usual selections of colors in limited subsets (generally 16 or 256) of the full palette includes some RGB level arrangements commonly used with the 8-bit palettes as master palettes or universal palettes (i.e., palettes for multipurpose uses). These are some representative software palettes, but any selection can be made in such of systems. For specific hardware color palettes, see the list of monochrome and RGB palettes, list of 8-bit computer hardware graphics, the list of 16-bit computer hardware graphics and the list of video game console palettes articles. Each palette is represented by an array of color patches. A one-pixel size version appears below each palette, to make it easy to compare palette sizes. For each unique palette, an image color test chart and sample image (truecolor original follows) rendered with that palette (without dithering) are given. The test chart shows the full 8-bit, 256 levels of the red, green, and blue (RGB) primary colors and cyan, magenta, and yellow complementary colors, along with a full 8-bit, 256 levels grayscale. Gradients of RGB intermediate colors (orange, lime green, sea green, sky blue, violet and fuchsia), and a full hue spectrum are also present. Color charts are not gamma corrected. These elements illustrate the color depth and distribution of the colors of any given palette, and the sample image indicates how the color selection of such palettes could represent real-life images. == System specifics == These are selections of colors officially employed as system palettes in some popular operating systems for personal computers that support 8-bit displays. === Microsoft Windows and IBM OS/2 default 16-color palette === Used by these platforms as a roughly backward compatible palette for the CGA, EGA and VGA text modes, but with colors arranged in a different order. Also, is the default palette for 16 color icons. The corresponding indices into this palette are: === Microsoft Windows default 20-color palette === In 256-color mode, there are four additional standard Windows colors, twenty system reserved colors in total; thus the system leaves 236 palette indexes free for applications to use. The system color entries inside a 256-color palette table are the first ten plus the last ten. In any case, the additional system colors do not seem to add a sharp color richness: they are only some intermediate shades of grayish colors. Since Windows 95, these additional colors can be changed by the system when a color scheme needs custom colors, reducing their utility as static, unchanging palette entries. The complete 20-color Windows system palette is: === Apple Macintosh default 16-color palette === When Apple Computer introduced the Macintosh II in 1987, this 16-color palette was included in System 4.1. === RISC OS default palette === Acorn RISC OS 2.x and 3.x provided this 16-color palette: === Solaris default 16-color palette === Solaris OS used this color palette: == RGB arrangements == These are selections of colors based in evenly ordered RGB levels which provide complete RGB combinations, mainly used as master palettes to display any kind of image within the limitations of the 8-bit pixel depth. === 6 level RGB === Having six levels for every primary, with 6³ = 216 combinations. The index can be addressed by (36×R)+(6×G)+B, with all R, G and B values in a range from 0 to 5. Intended as homogeneous RGB cube, it gives six true grays. Also, there is room for another sorts of 40 colors, so operating systems or programs can add extra colors. Systems that use this software palette are: Web-safe colors Apple Macintosh 256 color default palette. It also contains four gradients of ten shades each for gray, red, green and blue. === 6-7-6 levels RGB === This palette is constructed with six levels for red and blue primaries and seven levels for the green primary, giving 6×7×6 = 252 combinations. The index can be addressed by (42×R)+(6×G)+B, with R and B values in a range from 0 to 5 and G in a range from 0 to 6. The same case as the former, but with an added level of green due to the greater sensibility of the normal human eye to this frequency. It does not provide true grays, but remaining indexes can be filled with four intermediate grays. In any case, there is little room for any other color. === 6-8-5 levels RGB === This palette is constructed with six levels for red, eight levels for green and five levels for the blue primaries, giving 6×8×5 = 240 combinations. The index can be addressed by (40×R)+(5×G)+B, with R ranging from 0 to 5, G from 0 to 7 and B from 0 to 4. Levels are chosen in function of sensibility of the normal human eye to every primary color. Also, it does not provide true grays. Remaining indexes can be filled with sixteen intermediate grays or other fixed colors. In fact, this is the best balanced RGB master software palette, in a compromise between the RGB arrangement based in the human eye's sensibility and a sufficient remaining palette entries for another purposes. === 8-8-4 levels RGB === The 8-8-4 level RGB use eight levels for each of the red and green color components (3+3 high order bits), and four levels (2 low order bits) for the blue component, due to the lesser sensitivity of the normal human eye to this primary color. This results in an 8×8×4 = 256-color palette as follows: This RGB software palette occupies the full 8-bit range of possible palette entries, so there is no room for other fixed colors. Software using this palette must draw their user interface elements with the same colors used to show pictures. Also again, it does not provide true grays. == Other common uses of software palettes == === Grayscale palettes === Simple palette made doing every triplet RGB primaries having equal values as a continuous gradient from black to white through the full available palette entries. Here is the 8-bit, 256 levels palette: Used to display pure grayscale TIFF or JPEG images, for example. === Color gradient palettes === Palettes made of a continuous color gradient from darkest to lightest arbitrary hues. The pixel data is treated as if it were grayscale, but the color table plays with RGB color combinations, not only gray. The relationship between the original luminance and the mapped one can vary, but the lighting scale is preserved along all the palette entries. One very common case of such palettes is the sepia tone palette, which gives an image an old fashioned and aged look (left). Another gradient example, based on blue hues, is presented here (right), but any hue or mixing of hues can be used. Many cell phones with built-in cameras have options to take colorized photos using this technique. === Adaptive palettes === Those whose whole number of available indexes are filled with RGB combinations selected from the statistical order of appearance (usually balanced) of a concrete full true color original image. There exist many algorithms to pick the colors through color quantization; one well known is the Heckbert's median-cut algorithm. Here is the 8-bit, 256 color palette used with the color test chart and the image sample above: Adaptive palettes only work well with a unique image. Trying to display different images with adaptive palettes over an 8-bit display usually results in only one image with correct colors, because the images have different palettes and only one can be displayed at a time. Here is an example of what happens when an indexed color image is displayed with any color palette that is not its own adaptive palette: === False color palettes === Arbitrary gradient color scales, usually 256 shades, with no relationship with real colors of a given image. They are employed to artificially colorize a grayscale image to reveal details and/or to map the pixel level values to amounts of some physical magnitude (potential, temperature, altitude, etc.) Note, in the example above, that new details can be seen as blue over magenta in the background's dark areas of the original photograph. Here is the 8-bit, 256 color gradient palette used with the color test chart and the image sample above: There exist many false color palettes, some of them standardized, used mainly in scientific applications: astronomy and radioastronomy, satellite land imaging, thermography, study of materials, tomography and magnetic resonance imaging in medicine, etc.

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  BabelNet

  BabelNet is a multilingual lexical-semantic knowledge graph, ontology and encyclopedic dictionary developed at the NLP group of the Sapienza University of Rome under the supervision of Roberto Navigli. BabelNet was automatically created by linking Wikipedia to the most popular computational lexicon of the English language, WordNet. The integration is done using an automatic mapping and by filling in lexical gaps in resource-poor languages by using statistical machine translation. The result is an encyclopedic dictionary that provides concepts and named entities lexicalized in many languages and connected with large amounts of semantic relations. Additional lexicalizations and definitions are added by linking to free-license wordnets, OmegaWiki, the English Wiktionary, Wikidata, FrameNet, VerbNet and others. Similarly to WordNet, BabelNet groups words in different languages into sets of synonyms, called Babel synsets. For each Babel synset, BabelNet provides short definitions (called glosses) in many languages harvested from both WordNet and Wikipedia. == Statistics of BabelNet == As of December 2023, BabelNet (version 5.3) covers 600 languages. It contains almost 23 million synsets and around 1.7 billion word senses (regardless of their language). Each Babel synset contains 2 synonyms per language, i.e., word senses, on average. The semantic network includes all the lexico-semantic relations from WordNet (hypernymy and hyponymy, meronymy and holonymy, antonymy and synonymy, etc., totaling around 364,000 relation edges) as well as an underspecified relatedness relation from Wikipedia (totaling around 1.9 billion edges). Version 5.3 also associates around 61 million images with Babel synsets and provides a Lemon RDF encoding of the resource, available via a SPARQL endpoint. 2.67 million synsets are assigned domain labels. == Applications == BabelNet has been shown to enable multilingual natural language processing applications. The lexicalized knowledge available in BabelNet has been shown to obtain state-of-the-art results in: Semantic relatedness, Multilingual word-sense disambiguation and entity linking, with the Babelfy system, Video games with a purpose. == Prizes and acknowledgments == BabelNet received the META prize 2015 for "groundbreaking work in overcoming language barriers through a multilingual lexicalised semantic network and ontology making use of heterogeneous data sources". The Artificial Intelligence Journal paper that describes BabelNet won the Prominent Paper Award in 2017. BabelNet featured prominently in a Time magazine article about the new age of innovative and up-to-date lexical knowledge resources available on the Web.

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  Infomax

  Infomax', or the principle of maximum information preservation, is an optimization principle for artificial neural networks and other information processing systems. It prescribes that a function that maps a set of input values x {\displaystyle x} to a set of output values z ( x ) {\displaystyle z(x)} should be chosen or learned so as to maximize the average Shannon mutual information between x {\displaystyle x} and z ( x ) {\displaystyle z(x)} , subject to a set of specified constraints and/or noise processes. Infomax algorithms are learning algorithms that perform this optimization process. The principle was described by Linsker in 1988. The objective function is called the InfoMax objective. As the InfoMax objective is difficult to compute exactly, a related notion uses two models giving two outputs z 1 ( x ) , z 2 ( x ) {\displaystyle z_{1}(x),z_{2}(x)} , and maximizes the mutual information between these. This contrastive InfoMax objective is a lower bound to the InfoMax objective. Infomax, in its zero-noise limit, is related to the principle of redundancy reduction proposed for biological sensory processing by Horace Barlow in 1961, and applied quantitatively to retinal processing by Atick and Redlich. == Applications == (Becker and Hinton, 1992) showed that the contrastive InfoMax objective allows a neural network to learn to identify surfaces in random dot stereograms (in one dimension). One of the applications of infomax has been to an independent component analysis algorithm that finds independent signals by maximizing entropy. Infomax-based ICA was described by (Bell and Sejnowski, 1995), and (Nadal and Parga, 1995).

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