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MathxMatrix on Instagram: "At its heart, a Taylor Series is a way to express a complicated function as an infinite sum of simpler polynomial terms. Near the point a , the Taylor Series gives a very accurate estimate of the function. The more terms you add, the better the approximation becomes. This series hugs the sine curve tightly near x = 0 , and it’s whispering the shape of sine just around the origin."
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AI • Machine Learning • Tech on Instagram: "You can think of a Taylor series as a very simple neural network that builds a function by adding together basic building blocks of the input. First, the input is expanded into features like the raw value, its squared version, its cubed version, and so on. Each of these features captures increasingly complex patterns in the data. A traditional Taylor series assigns fixed weights to these features, but a neural network can learn those weights from data
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mathswithmuza on Instagram: "A Taylor series is a way to approximate a function by expressing it as an infinite sum of polynomial terms based on the function’s derivatives at a single point. Starting from that point, usually called the center, the first term is the function’s value there, the next term involves its first derivative, and so on, with higher derivatives capturing more detail about the function’s behavior. This method allows complex functions, like exponentials, trigonometric functi
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