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convolutions


Meanings
  • noun

    The mathematical operation of multiplying a function or signal with a kernel and sliding the kernel over the function or signal, producing a new function or signal.

    - "In image processing, convolutions are used to extract features from an image by applying filters."
    - "Convolutions are a fundamental operation in deep learning neural networks for feature extraction."

Variants
List of all variants of convolutions that leads to same result
convolution , convolutions
Etymology
origin and the way in which meanings have changed throughout history.

The term 'convolution' comes from the Latin word 'convolutus,' meaning 'twisted together.' In mathematics, it refers to the twisting or rolling of one function or signal over another.


Trivia
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  1. Convolutions were first introduced in mathematics by the French mathematician Augustin-Louis Cauchy in 1823.

  2. Convolutional neural networks were invented by Yann LeCun in 1989 and have since become a fundamental tool in deep learning and artificial intelligence.

  3. Convolutions are used in various applications such as speech recognition, object detection, and facial recognition.


Related Concepts
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  1. Filters: Convolutions are often implemented using filters, which are mathematical functions used to modify or extract specific features from signals.

  2. Deep Learning: Convolutional neural networks (CNNs) are a type of deep learning neural network that use convolutions as a primary mechanism for feature extraction.


Culture
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Convolutions have been extensively used in various fields such as mathematics, physics, engineering, image processing, and deep learning neural networks. They are an essential tool for feature extraction and pattern recognition.

How to Memorize "convolutions"

  1. visualize

    - Imagine a function or signal as a 2D image, and the kernel as a small filter that slides over the image. The output at each position is the sum of the products of the corresponding elements in the image and the filter.
    - Visualize the mathematical operation of multiplying the kernel with the image, and then sliding the kernel over the image to produce the output.

  2. associate

    - Associate the term 'convolution' with the idea of extracting features from signals or images by sliding a filter over them.
    - Think of convolutions as a way of 'looking' at a signal or image from different perspectives by applying different filters.

  3. mnemonics

    - Use the mnemonic 'Cats Nibble Fish' to remember the order of operations in a convolution: C for Convolve, N for Negate, I for Input, B for Buffer, F for Filter, and S for Sum.


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