import theano import theano.tensor as T import numpy as np x_t = T.matrix('input') h_prev = T.matrix('hidden_prev') W_xh = theano.shared(np.random.randn(input_dim, hidden_dim)) W_hh = theano.shared(np.random.randn(hidden_dim, hidden_dim)) b_h = theano.shared(np.zeros(hidden_dim))
They can remember information for hundreds of steps, making them ideal for text generation, speech recognition, and complex time series. GRU (Gated Recurrent Unit) GRUs are a simpler, faster alternative to LSTMs. They merge the forget and input gates into a single "update gate" and combine the cell state with the hidden state. GRUs perform similarly to LSTMs on many tasks but with fewer parameters. import theano import theano
Vanilla RNNs suffer from the vanishing/exploding gradient problem — they can't learn long-range dependencies (e.g., information from 50 steps ago). This is where LSTM and GRU come in. LSTM (Long Short-Term Memory) LSTMs introduce a cell state (a conveyor belt of information) and three gates: forget, input, and output. These gates learn what to remember, what to write, and what to output. GRUs perform similarly to LSTMs on many tasks
Let’s dive in. A standard dense layer assumes no temporal order. It doesn't know that the word following "I ate" is likely food-related, or that yesterday's stock price influences today's. RNNs solve this with a hidden state — a vector that gets passed from one time step to the next. The Simple RNN (Vanilla RNN) The simplest form has a loop. At each time step t , it takes the current input x_t and the previous hidden state h_t-1 , and produces a new hidden state h_t . LSTM (Long Short-Term Memory) LSTMs introduce a cell
In Python (with Theano-style tensors), a naive implementation looks like: