page_title: Tensor sketch
section_title: Compact multilinear pooling
hierarchical_section_title: Tensor sketch / Applications / Compact multilinear pooling
caption_attribution_description: English: A diagram of how Compact Multilinear Pooling is used to combine features in a neural network.
context_page_description: In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms.
context_section_description: Bilinear pooling is the technique of taking two input vectors,  from different sources, and using the tensor product  as the input layer to a neural network.
  In the authors considered using tensor sketch to reduce the number of variables needed.
  In 2017 another paper takes the FFT of the input features, before they are combined using the element-wise product.
  This again corresponds to the original tensor sketch.
caption: Tensor sketches can be used to decrease the number of variables needed when implementing Bilinear Pooling in a neural network.
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