Recurrent Neural Networks (RNNs): Sequence Modeling

Learning Objectives Define sequence data and explain why traditional neural networks are insufficient for processing it. Diagram the architecture of a simple RNN, including inputs, hidden states, and outputs across multiple timesteps. Trace the flow of information through an RNN by calculating the hidden state at each timestep for a given short sequence. Explain the concept of Backpropagation Through Time (BPTT) and its role in training RNNs. Identify and describe the vanishing and exploding gradient problems as they relate to RNNs. Map real-world problems like machine translation and sentiment analysis to appropriate RNN-based solutions. Ever wonder how your phone's keyboard predicts the next word you're about to type? 🔮 That's the magic of a neural network...

TermDefinitionExample Sequence DataData where the order of elements is crucial to its meaning. Each element depends on the ones that came before it.The sentence 'The dog chased the cat' has a different meaning from 'The cat chased the dog'. The sequence of words matters. Recurrent Neural Network (RNN)A type of neural network that contains a feedback loop, allowing it to maintain an internal state or 'memory' of past inputs.When processing the word 'is' in 'The sky is blue', the RNN's memory already contains information about the subject 'sky', helping it predict the color 'blue'. Hidden State (h_t)A vector that acts as the RNN's memory at a specific timestep (t). It's a compressed representation of all re...

Hidden State Update Rule h_t = tanh(W_hh * h_{t-1} + W_xh * x_t + b_h) This is the core formula of an RNN. At each timestep 't', the new hidden state (h_t) is calculated by combining the previous hidden state (h_{t-1}) and the current input (x_t) using weight matrices (W_hh, W_xh) and a bias (b_h), then passing the result through an activation function like tanh. Output Calculation Rule y_t = softmax(W_hy * h_t + b_y) This formula computes the final output (y_t) for the current timestep. It takes the current hidden state (h_t), applies a weight matrix (W_hy) and a bias (b_y), and often uses a softmax activation function to convert the result into a probability distribution over possible outputs (e.g., all words in a vocabulary). Shared Weights Principle The w...