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Tensor (machine learning)
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<p>In <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a>, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a <a href="/facts/Array_(data_type)/gHJJ3XPw">multidimensional array</a> (<i>M</i>-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a <a href="/facts/Tensor/pNjFo5tV">tensor</a> is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an <i>M</i>-way array ("data tensor"), may be analyzed either by <a href="/facts/Neural_network_(machine_learning)/6V1jMlkx">artificial neural networks</a> or <a href="/facts/Tensor_decomposition/5YNsQwfT">tensor methods</a>. </p><p><a href="/facts/Tensor_decomposition/5YNsQwfT">Tensor decomposition</a> factorizes data tensors into smaller tensors. Operations on data tensors can be expressed in terms of <a href="/facts/Matrix_multiplication/lYDB6Ro2">matrix multiplication</a> and the <a href="/facts/Kronecker_product/gABGx6I6">Kronecker product</a>. The computation of gradients, a crucial aspect of <a href="/facts/Backpropagation/lCsIdKHc">backpropagation</a>, can be performed using <a href="/facts/Library_(computing)/xRzL3P7q">software libraries</a> such as <a href="/facts/PyTorch/4Gv1t13B">PyTorch</a> and <a href="/facts/TensorFlow/kDwfBeNd">TensorFlow</a>. </p><p>Computations are often performed on <a href="/facts/Graphics_processing_unit/PTK1RQVp">graphics processing units</a> (GPUs) using <a href="/facts/CUDA/fvPpolot">CUDA</a>, and on dedicated hardware such as <a href="/facts/Google/GT9Sugza">Google</a>'s <a href="/facts/Tensor_Processing_Unit/aVlg0LFF">Tensor Processing Unit</a> or <a href="/facts/Nvidia/8QfCgqbu">Nvidia</a>'s <a href="/facts/Volta_(microarchitecture)/bxD4hpFL">Tensor core</a>. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. </p>