**RMSProp** is an unpublished adaptive learning rate optimizer [proposed by Geoff Hinton](http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf). The motivation is that the magnitude of gradients can differ for different weights, and can change during learning, making it hard to choose a single global learning rate. RMSProp tackles this by keeping a moving average of the squared gradient and adjusting the weight updates by this magnitude. The gradient updates are performed as:

$$E\left[g^{2}\right]\_{t} = \gamma E\left[g^{2}\right]\_{t-1} + \left(1 - \gamma\right) g^{2}\_{t}$$

$$\theta\_{t+1} = \theta\_{t} - \frac{\eta}{\sqrt{E\left[g^{2}\right]\_{t} + \epsilon}}g\_{t}$$

Hinton suggests $\gamma=0.9$, with a good default for $\eta$ as $0.001$.

Image: [Alec Radford](https://twitter.com/alecrad)

**Residual Networks**, or **ResNets**, learn residual functions with reference to the layer inputs, instead of learning unreferenced functions. Instead of hoping each few stacked layers directly fit a desired underlying mapping, residual nets let these layers fit a residual mapping. They stack [residual blocks](https://paperswithcode.com/method/residual-block) ontop of each other to form network: e.g. a ResNet-50 has fifty layers using these blocks. 

Formally, denoting the desired underlying mapping as $\mathcal{H}(x)$, we let the stacked nonlinear layers fit another mapping of $\mathcal{F}(x):=\mathcal{H}(x)-x$. The original mapping is recast into $\mathcal{F}(x)+x$.

There is empirical evidence that these types of network are easier to optimize, and can gain accuracy from considerably increased depth.

ResNet

Deep Residual Learning for Image Recognition

RMSProp

**Stochastic Weight Averaging** is an optimization procedure that averages multiple points along the trajectory of [SGD](https://paperswithcode.com/method/sgd), with a cyclical or constant learning rate. On the one hand it averages weights, but it also has the property that, with a cyclical or constant learning rate, SGD proposals are approximately sampling from the loss surface of the network, leading to stochastic weights and helping to discover broader optima.

Year	2013
Data Source	CC BY-SA - https://paperswithcode.com