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Understanding Basic Recurrent Neural Networks (RNNs)
A Recurrent Neural Network (RNN) is a neural network designed to handle sequential data. Unlike traditional neural networks, RNNs maintain a “memory” of previous inputs, which makes them suitable for tasks like time-series analysis, language modeling, and more.
This article explains the basics of RNNs, provides the mathematical intuition behind them, and demonstrates a sample calculation using toy data.
Structure of a Basic RNN
- Input Layer: Accepts the sequential data (e.g., words in a sentence).
- Hidden Layer: Processes the input while maintaining a hidden state that evolves over time.
- Output Layer: Produces predictions based on the hidden state and current input.
Mathematical Intuition
1. Forward Propagation in RNN
At each time step t, the RNN processes an input xt and updates its hidden state ht as follows:
2. Loss Calculation
For classification tasks, the loss is typically calculated using Cross-Entropy Loss:
3. Backpropagation Through Time (BPTT)
RNNs use Backpropagation Through Time (BPTT) to compute gradients and update weights. This involves unrolling the network across all time steps and applying the chain rule to propagate errors backward through time.
Gradient updates:
Let’s go through the complete calculations for a Basic Recurrent Neural Network (RNN) with a simple example. We will cover each step in detail, including forward propagation, loss calculation, and backward propagation.
Problem Setup:
We want to predict the next number in a sequence. Let’s consider a toy example:
Step 1: Forward Propagation
