Vanilla recurrent neural networks (RNNs) form the basis of more sophisticated models, such as LSTMs and GRUs. There are lots of great articles, books, and videos that describe the functionality, mathematics, and behavior of RNNs so, don't worry, this isn't yet another rehash. (See below for a list of resources.) My goal is to present an explanation that avoids the neural network metaphor, stripping it down to its essence—a series of vector transformations that result in embeddings for variable-length input vectors.

My learning style involves pounding away at something until I'm able to re-create it myself from fundamental components. This helps me to understand exactly **what** a model is doing and **why** it is doing it. You can ignore this article if you're familiar with standard neural network layers and are comfortable with RNN explanations that use them as building blocks. Since I'm still learning the details of neural networks, I wanted to (1) peer through those layers to the matrices and vectors beneath and (2) investigate the details of the training process. My starting point was Karpathy's RNN code snippet associated with The Unreasonable Effectiveness of Recurrent Neural Networks and then I absorbed details from Chapter 12 from Jeremy Howard's / Sylvain Gugger's book Deep Learning for Coders with fastai and PyTorch and Chapter 12 from Andrew Trask's Grokking Deep Learning.