Using cubic splines to improve factorization machine accuracy with numerical features

The **Truncation Trick** is a latent sampling procedure for generative adversarial networks, where we sample $z$ from a truncated normal (where values which fall outside a range are resampled to fall inside that range). 
The original implementation was in [Megapixel Size Image Creation with GAN](https://paperswithcode.com/paper/megapixel-size-image-creation-using).
In [BigGAN](http://paperswithcode.com/method/biggan), the authors find this provides a boost to the Inception Score and FID.

Truncation Trick

Megapixel Size Image Creation using Generative Adversarial Networks

FM with splines

Basis Function Encoding of Numerical Features in Factorization Machines for Improved Accuracy

**TSRUc**, or **Transformation-based Spatial Recurrent Unit c**, is a modification of a [ConvGRU](https://paperswithcode.com/method/cgru) used in the [TriVD-GAN](https://paperswithcode.com/method/trivd-gan) architecture for video generation.

Instead of computing the reset gate $r$ and resetting $h\_{t−1}$, the TSRUc computes the parameters of a transformation $\theta$, which we use to warp $h\_{t−1}$. The rest of our model is unchanged (with $\hat{h}\_{t-1}$ playing the role of $h'\_{t}$ in $c$’s update equation from ConvGRU. The TSRUc module is described by the following equations:

$$ \theta\_{h,x} = f\left(h\_{t−1}, x\_{t}\right) $$

$$ \hat{h}\_{t-1} = w\left(h\_{t-1}; \theta\_{h, x}\right) $$

$$ c = \rho\left(W\_{c} \star\_{n}\left[\hat{h}\_{t-1};x\_{t}\right] + b\_{c} \right) $$

$$ u = \sigma\left(W\_{u} \star\_{n}\left[h\_{t-1};x\_{t}\right] + b\_{u} \right) $$

$$ h\_{t} = u \odot h\_{t-1} + \left(1-u\right) \odot c $$

In these equations $\sigma$ and $\rho$ are the elementwise sigmoid and [ReLU](https://paperswithcode.com/method/relu) functions respectively and the $\star\_{n}$ represents a [convolution](https://paperswithcode.com/method/convolution) with a kernel of size $n \times n$. Brackets are used to represent a feature concatenation.

Source	Basis Function Encoding of Numerical Features in Factorization Machines for Improved Accuracy
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com

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What is: Factorization machines with cubic splines for numerical features?

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