LLMs and string theory suggest that language and reality both emerge from projections across hidden dimensions.

Different branches of math might use different words for things — like “group” instead of “vector space” — but when you swap ... How do you go from strings of symbols and their statistics to this kind ...

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Royalty-free licenses let you pay once to use copyrighted images and video clips in personal and commercial projects on an ongoing basis without requiring additional payments each time you use that ...

DeepSeek and OpenAI’s o1 models performed the best across the various benchmarks, but all models still struggle in a range of ...

In the default model, the graph representing each individual enhancer can be arbitrarily complicated. To show how the ABC Score formula can arise from the default model, we need to impose the further ...

Under the conditions of the Hamiltonian principle, information is exchanged between two masses during an interaction by ...

The American Plains bison (Bison bison) is an iconic symbol of the American West ... logistic equation: The mathematical expression for a particular sigmoid growth curve in which the percentage ...

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They both return the optimal polynomial value found by the SB algorithm, along with its associated input vector. The optimization domain ... to define polynomials in a more natural way from ...

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