**Mixture of Softmaxes** performs $K$ different softmaxes and mixes them. The motivation is that the traditional [softmax](https://paperswithcode.com/method/softmax) suffers from a softmax bottleneck, i.e. the expressiveness of the conditional probability we can model is constrained by the combination of a dot product and the softmax. By using a mixture of softmaxes, we can model the conditional probability more expressively.

Pixel-BERT is a pre-trained model trained to align image pixels with text. The end-to-end framework includes a CNN-based visual encoder and cross-modal transformers for visual and language embedding learning.
This model has three parts: one fully convolutional neural network that takes pixels of an image as input, one word-level token embedding based on BERT, and a multimodal transformer for jointly learning visual and language embedding.

For language, it uses other pretraining works to use Masked Language Modeling (MLM) to predict masked tokens with surrounding text and images. For vision, it uses the random pixel sampling mechanism that makes up for the challenge of predicting pixel-level features. This mechanism is also suitable for solving overfitting issues and improving the robustness of visual features. 

It applies Image-Text Matching (ITM) to classify whether an image and a sentence pair match for vision and language interaction. 

Image captioning is required to understand language and visual semantics for cross-modality tasks like VQA. Region-based visual features extracted from object detection models like Faster RCNN are used for better performance in the newer version of the model.

Pixel-BERT

Pixel-BERT: Aligning Image Pixels with Text by Deep Multi-Modal Transformers

Mixture of Softmaxes

Breaking the Softmax Bottleneck: A High-Rank RNN Language Model

**NICE**, or **Non-Linear Independent Components Estimation** is a framework for modeling complex high-dimensional densities. It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables.  The transformation is parameterised so that computing the determinant of the Jacobian and inverse Jacobian is trivial, yet it maintains the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood. The transformation used in NICE is the [affine coupling](https://paperswithcode.com/method/affine-coupling) layer without the scale term, known as additive coupling layer:

$$ y\_{I\_{2}} = x\_{I\_{2}} + m\left(x\_{I\_{1}}\right) $$

$$ x\_{I\_{2}} = y\_{I\_{2}} + m\left(y\_{I\_{1}}\right) $$

Source	Breaking the Softmax Bottleneck: A High-Rank RNN Language Model
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com