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Word problem (mathematics) In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Word problem for groups. In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group is the algorithmic problem of deciding whether two words in the generators represent the same element. The word problem is a well-known example of an undecidable problem .
History Initial developments. Generative pretraining (GP) was a long-established concept in machine learning applications. It was originally used as a form of semi-supervised learning, as the model is trained first on an unlabelled dataset (pretraining step) by learning to generate datapoints in the dataset, and then it is trained to classify a labelled dataset.
Solutions of the Einstein field equations. Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact .
Solution of a travelling salesperson problem: the black line shows the shortest possible loop that connects every red dot. The travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns ...
OpenAI's GPT-4 model is released in March 2023 and is regarded as an impressive improvement over GPT-3.5, with the caveat that GPT-4 retains many of the same problems of the earlier iteration. Unlike previous iterations, GPT-4 is multimodal, allowing image input as well as text. GPT-4 is integrated into ChatGPT as a subscriber service.
In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and ...
The Scunthorpe problem is the unintentional blocking of online content by a spam filter or search engine because their text contains a string (or substring) of letters that appear to have an obscene or otherwise unacceptable meaning. Names, abbreviations, and technical terms are most often cited as being affected by the issue.
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