The sounds of code

TENSORE (ML) Let  �  be a  field  such as the  real numbers   � . A tensor  �  is an  � 0 × � 1 × ⋯ � �  array over  � : � ∈ � � 0 × � 1 × … × � � . Here,  �  and  � 1 , � 2 , … , � �  are positive integers, and  �  is the number of dimensions. One basic approach (not the only way) to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2D function  � ( � , � )  with resolution  � × �  may be embedded in a mode-2 tensor as � ( � , � ) ↦ � ∈ � � × � . A color image with 3 channels for RGB might be embedded in a mode-3 tensor with three elements in an additional dimension: � � � � ( � , � ) ↦ � ∈ � � × � × 3 . In natural language processing, a word might be expressed as a vector  �  via the  Word2vec  algorithm. Thus  �  becomes a mode-1 tensor � ↦ � ∈ � � . The embedd...