What does the bins parameter mean in NSF?

[Bill-Gots]

I checked the article Neural Spine Flows and searched for the keyword bins. Then I got it' s related to some transforms like rantional-quadratic transform. But that article seemed so hard for me that I still don't understand why bins are related to the shapes parameter in flows.MAF. Could someone tell me some information about that?

[francois-rozet]

Hello, the number of bins is the number of knots minus one. The space between two knots is a bin. A spline is a piecewise function, meaning that each bin defines a different function, with different parameters. In the case of the rational-quadratic spline, each bin has 3 parameters: a width, a height and a slope. Hence, for the entire spline the parameters are 3 vectors of size bins (minus one for the slope due to boundary conditions). In comparison, for an affine transformation, the parameters are 2 scalars (tensor of shape ()).

[Bill-Gots]

Thanks for reply! Just one more problem: how are the knots generated? Are they from neural networks whose input are randomly generated?

[francois-rozet]

The number of knots is chosen by the user. Their position is learned by the transformation during training. This is what the hyper network (hyper) returns.

[Bill-Gots]

Ok I got it. Thanks for your time!

[simonschnake]

The flows.MAF implementation creates a masked autoregressive flow (MAF). The architecture does not use a spline transform by default. There is an option to set univariate=MonotonicRQSTransform to use a Neural Spline architecture. As @francois-rozet explained, the number of bins is related to the number of knots in the spline transformation. Have a look at the graphic in the paper that should clarify the purpose of the knots.