RNNs may compute strongly nonlinear functions over many timesteps, leading to derivatives with either very small (vanishing) or very large (exploding) magnitudes. One example of this is the objective function, whose "landscape" creates "cliffs" in the function space. This makes finding an acceptable step size (learning rate) for gradient descent very difficult.

Reason for Gradient Clipping



One solution to gradient problems is called "clipping the gradient". There are different ways to accomplish this; element-wise clipping is one option, norm-clipping is another. Although these methods produce slightly different mathematical results, there is experimental evidence that both work similarly in practice. 

University of Massachusetts at Amherst

- Identity RNN with ReLU activation (solving vanishing gradient problem only)
- Gradient clipping
- Skip connections
- LSTM
- GRU

Solutions for vanishing/exploding gradient

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

Gated Recurrent Units (GRUs) resolve the vanishing gradients problem in simple RNNs and also ease the burden of introducing a considerable number of additional parameters in the LSTMs, by dispensing with the use of a separate context vector, and by reducing the number of gates to 2 — a reset/relevance gate and an update gate.
The purpose of the reset gate is to decide which aspects of the previous hidden state are relevant to the current context and what can be ignored. It computes an intermediate representation for the new hidden state at the current time.
The purpose of the update gate is to determine which aspects of this new state will be used directly in the new hidden state and which aspects of the previous state need to be preserved for future use.

Gated recurrent unit (GRU)

Clipping Gradients

The long short-term memory (LSTM) network is an extension to RNNs, in addressing problems such as the vanishing gradient problem and the inability of RNNs to carry forward critical information.

LSTMs divide the context management problem into two sub-problems: 
- Removing information no longer needed from the context
- Adding information likely to be needed for later decision making

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