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Throughout this pretraining, GPT models accumulate knowledge about the world and can then generate human-like text by repeatedly predicting the next token
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https://en.wikipedia.org/wiki/AI
[16] These models can produce incorrect outputs or "hallucinations," unlike symbolic reasoning systems
https://en.wikipedia.org/wiki/Tragedy_of_the_commons
Each man is locked into a system that compels him to increase his herd without limit – in a world that is limited
https://en.wikipedia.org/wiki/The_Buddha
n | pli = Siddhattha Gotama }}"},"birth_name":{"wt":"Siddhartha Gautama"},"birth_date":{"wt":"{{circa|563 or 480 BCE}}"},"death_date":{"wt":"{{circa|483 or 400 BCE}} (aged 80){{sfnp|Cousins|1996|pp=57–63}}{{sfnp|Norman|1997|p=33}}{{sfnp|Prebish|2008}}{{efn|name=\"dating\"}}"},"birth_place":{"wt":
https://en.wikipedia.org/wiki/Artificial_intelligence
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https://en.wikipedia.org/wiki/Information_retrieval
The information need can be specified in the form of a search query
https://en.wikipedia.org/wiki/Financial_economics
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https://en.wikipedia.org/wiki/Dromedary
The domesticated dromedary is kept in the semiarid to arid regions of the Old World, mainly in Africa, the Arabian Peninsula and the Thar desert in Pakistan and India
https://en.wikipedia.org/wiki/Camel
org|access-date=2021-12-17|archive-date=2021-12-12|archive-url=https://web
https://en.wikipedia.org/wiki/Wild_boar
en |access-date=16 November 2021}}</ref>"},"taxon":{"wt":"Sus scrofa"},"authority":{"wt":"[[Carl Linnaeus|Linnaeus]], [[10th edition of Systema Naturae|1758]]"},"range_map":{"wt":"Sus scrofa range map
https://en.wikipedia.org/wiki/Markov_chain
Markov chains have many applications as statistical models of real-world processes
https://en.wikipedia.org/wiki/Nonviolence
The reasons for it may be strategic or pragmatic;[1] failure to distinguish between the two can lead to distortion in the concept's meaning and effectiveness, which can subsequently result in confusion
https://en.wikipedia.org/wiki/Game_theory
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https://en.wikipedia.org/wiki/Historicity_of_the_Bible
In fact, though, 'maximalist' has been widely defined as someone who accepts the biblical text unless it can be proven wrong
https://en.wikipedia.org/wiki/Nicolaus_Copernicus
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https://en.wikipedia.org/wiki/Dinosaurs
org/content/379/1/353 |journal=Geological Society, London, Special Publications |language=en |volume=379 |issue=1 |pages=353–392 |doi=10
https://en.wikipedia.org/wiki/Operator_algebra
From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator
https://en.wikipedia.org/wiki/Module_homomorphism
}
The preimage of the zero element under f is called the kernel of f
https://en.wikipedia.org/wiki/Embedding
However, this does not apply to immersions; for instance, R P 2 {\displaystyle \mathbb {R} \mathrm {P} ^{2}} can be immersed in R 3 {\displaystyle \mathbb {R} ^{3}} as is explicitly shown by Boy's surface—which has self-intersections
https://en.wikipedia.org/wiki/Ideal_(ring_theory)
An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group
https://en.wikipedia.org/wiki/Noncommutative_ring
x n ⟩ / ( x i x j − q i j x j x i ) {\displaystyle \mathbb {C} \langle x_{1},\ldots ,x_{n}\rangle /(x_{i}x_{j}-q_{ij}x_{j}x_{i})} , called a quantum plane, where q i j ∈ C {\displaystyle q_{ij}\in \mathbb {C} }
Any Clifford algebra can be described explicitly using an algebra presentation: given an F {\
https://en.wikipedia.org/wiki/Semigroup
A semigroup without an identity element can be easily turned into a monoid by just adding an identity element
https://en.wikipedia.org/wiki/De_Havilland_Venom
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https://en.wikipedia.org/wiki/Inference_rule
Rules of inference include rules of implication, which operate only in one direction from premises to conclusions, and rules of replacement, which state that two expressions are equivalent and can be freely swapped
https://en.wikipedia.org/wiki/Group_(mathematics)
In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory
https://en.wikipedia.org/wiki/Continent
1 Early concepts of the Old World continents
5
https://en.wikipedia.org/wiki/Gnome
[19] appears to be a misattribution, for Paracelsus states: \"The mountain manikins [gnomes] are endowed with speech like the nymphs [undines, water], and the vulcans [salamanders, fire] speak nothing, yet they can speak but roughly and rarely\
https://en.wikipedia.org/wiki/Appeasement
1 Avoiding mistakes of First World War
2
https://en.wikipedia.org/wiki/De_Havilland_Mosquito
98 Mosquito was a British twin-engined, multi-role combat aircraft, introduced during the Second World War
https://en.wikipedia.org/wiki/Historicity_of_Jesus
[note 1] However, scholars distinguish between the 'Christ of faith' as presented in the New Testament and the subsequent Christian theology, and a minimal 'Jesus of history', about whom almost nothing can be known
https://en.wikipedia.org/wiki/Machine_learning
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