Tensor

As explained in Deep Learning with Python, Third Edition

A tensor with three axes, used here for an image or feature-map representation with height, width, and depth.

A tensor is a structured array of values. In image processing, a rank-3 tensor has height, width, and depth (channels), organizing spatial data and learned features. section 8.1.1

From image to feature map

An RGB image can have shape (height, width, 3), because its depth contains red, green, and blue channels. A convolution can transform an MNIST input of shape (28, 28, 1) into (26, 26, 64): the first two axes remain spatial, while 64 output channels represent learned filters. Each channel forms a response map showing where its pattern appears. section 8.1.1

Figure 8.3 The concept of a response map: a 2D map of the presence of a pattern at different locations in an input

Use the response-map figure to visualize a depth channel as a two-dimensional map of a pattern’s presence across image locations. section 8.1.1

How Deep Learning with Python, Third Edition covers it

How deep it goes

Defines rank-3 dimensions and channels, then demonstrates convolutional transformation without detailing tensor operations beyond feature extraction.

Examples

Uses RGB images, black-and-white MNIST inputs, and a (28, 28, 1) to (26, 26, 64) transformation.

What you can do after

Evaluate/understand how spatial axes and channels encode images and learned visual patterns.

How it connects

Connects tensors to convolution, feature maps, channels, filters, and response maps.

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Related concepts

• rank-4 tensorproduces · A rank-4 tensor is a tensor with four axes, formed by stacking rank-3 tensors along an additional axis.
• arraykind of · An array is an indexed, ordered collection of elements arranged in one or more dimensions, with elements accessed by position.
• PyTorchused by · PyTorch is an open-source machine-learning framework for Python that provides tensor computation, automatic differentiation, and tools for building and training neural networks.
• vectorizationused by · Vectorization is the representation of data or computations as vectors or arrays so they can be processed numerically or collectively.
• scalarincludes · A scalar is a single, indivisible value rather than a collection or multidimensional structure; in mathematics, it is a quantity with magnitude and no direction.

This explainer was generated by Manning's knowledge graph from the text of Deep Learning with Python, Third Edition. The section links point to the parts of the book it draws on.