**DiCENet** is a convolutional neural network architecture that utilizes dimensional convolutions (and dimension-wise fusion). The dimension-wise convolutions apply light-weight convolutional filtering across each dimension of the input tensor while dimension-wise fusion efficiently combines these dimension-wise representations; allowing the [DiCE Unit](https://paperswithcode.com/method/dice-unit) in the network to efficiently encode spatial and channel-wise information contained in the input tensor.

A **QRNN**, or **Quasi-Recurrent Neural Network**, is a type of recurrent neural network that alternates convolutional layers, which apply in parallel across timesteps, and a minimalist recurrent pooling function that applies in parallel across channels. Due to their increased parallelism, they can be up to 16 times faster at train and test time than [LSTMs](https://paperswithcode.com/method/lstm).

Given an input sequence $\mathbf{X} \in \mathbb{R}^{T\times{n}}$ of $T$ n-dimensional vectors $\mathbf{x}\_{1}, \dots, \mathbf{x}\_{T}$, the convolutional subcomponent of a QRNN performs convolutions in the timestep dimension with a bank of $m$ filters, producing a sequence $\mathbf{Z} \in \mathbb{R}^{T\times{m}}$ of m-dimensional candidate vectors $\mathbf{z}\_{t}$. Masked convolutions are used so filters can not access information from future timesteps (implementing with left padding).

Additional convolutions are applied with separate filter banks to obtain sequences of vectors for the
elementwise gates that are needed for the pooling function. While the candidate vectors are passed
through a $\tanh$ nonlinearity, the gates use an elementwise sigmoid. If the pooling function requires a
forget gate $f\_{t}$ and an output gate $o\_{t}$ at each timestep, the full set of computations in the convolutional component is then:

$$ \mathbf{Z} = \tanh\left(\mathbf{W}\_{z} ∗ \mathbf{X}\right) $$
$$ \mathbf{F} = \sigma\left(\mathbf{W}\_{f} ∗ \mathbf{X}\right) $$
$$ \mathbf{O} = \sigma\left(\mathbf{W}\_{o} ∗ \mathbf{X}\right) $$

where $\mathbf{W}\_{z}$, $\mathbf{W}\_{f}$, and $\mathbf{W}\_{o}$, each in $\mathbb{R}^{k×n×m}$, are the convolutional filter banks and ∗ denotes a [masked convolution](https://paperswithcode.com/method/masked-convolution) along the timestep dimension.  Dynamic [average pooling](https://paperswithcode.com/method/average-pooling) by Balduzzi & Ghifary (2016) is used, which uses only a forget gate:

$$ \mathbf{h}\_{t} = \mathbf{f}\_{t} \odot{\mathbf{h}\_{t−1}} + \left(1 − \mathbf{f}\_{t}\right) \odot{\mathbf{z}\_{t}} $$ 

Which is denoted f-pooling. The function may also include an output gate:

$$ \mathbf{c}\_{t} = \mathbf{f}\_{t} \odot{\mathbf{c}\_{t−1}} + \left(1 − \mathbf{f}\_{t}\right) \odot{\mathbf{z}\_{t}} $$ 

$$ \mathbf{h}\_{t} = \mathbf{o}\_{t} \odot{\mathbf{c}\_{t}} $$

Which is denoted fo-pooling. Or the recurrence relation may include an independent input and forget gate:

$$ \mathbf{c}\_{t} = \mathbf{f}\_{t} \odot{\mathbf{c}\_{t−1}} + \mathbf{i}\_{t}\odot{\mathbf{z}\_{t}} $$ 

$$ \mathbf{h}\_{t} = \mathbf{o}\_{t} \odot{\mathbf{c}\_{t}} $$

Which is denoted ifo-pooling. In each case $h$ or $c$ is initialized to zero. The recurrent part sof these functions must be calculated for each timestep in the sequence, but parallelism along feature dimensions means evaluating them even over long sequences requires a negligible amount of computation time.

A single QRNN layer thus performs an input-dependent pooling, followed by a gated linear combination of convolutional features. As with convolutional neural networks, two or more QRNN layers should be stacked to create a model with the capacity to approximate more complex functions.

QRNN

Quasi-Recurrent Neural Networks

DiCENet

DiCENet: Dimension-wise Convolutions for Efficient Networks

**DeepSIM** is a generative model for conditional image manipulation based on a single image. The network learns to map between a primitive representation of the image to the image itself. At manipulation time, the generator allows for making complex image changes by modifying the primitive input representation and mapping it through the network. The choice of a primitive representations has an impact on the ease and expressiveness of the manipulations and can be automatic (e.g. edges), manual, or hybrid such as edges on top of segmentations.

Source	DiCENet: Dimension-wise Convolutions for Efficient Networks
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com