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Binomial filter

As explained in Inside Deep Learning: Math, Algorithms, Models

A smoothing kernel whose weights follow binomial coefficients, emphasizing the center more than the edges.

A binomial filter is a blurring convolution kernel whose weights follow binomial coefficients. It emphasizes the center and gradually reduces the contribution of farther pixels, producing a weighted average that helps suppress aliasing. section 14.1.2

For a kernel of width k, compute one-dimensional weights from the binomial distribution, normalize them to sum to 1, and expand them across one, two, or three dimensions. A BlurLayer exposes kernel_size, stride, and input dimensionality D. section 14.1.2

Anti-aliased max pooling

Apply max pooling with stride 1, then pass the result through BlurLayer with a larger stride. The blur shrinks the representation while retaining distinctions that naive strided max pooling can lose. section 14.1.2

How Inside Deep Learning: Math, Algorithms, Models covers it

How deep it goes
Defines the weighting pattern and demonstrates multidimensional kernel construction, but omits a full derivation.
Examples
Uses multidimensional BlurLayer code and a max-pooling pipeline applied to an image.
What it assumes
Assumes convolution and max-pooling familiarity while specifying the layer’s dimensionality, kernel size, and stride.
What you can do after
Builds a configurable blur layer with SciPy and PyTorch, then inserts it into an anti-aliased pooling pipeline.
How it connects
Connects convolution, blurring, max pooling, anti-aliasing, and the binomial distribution.
Cover of Inside Deep Learning: Math, Algorithms, Models
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This explainer was generated by Manning's knowledge graph from the text of Inside Deep Learning: Math, Algorithms, Models. The section links point to the parts of the book it draws on.