Recurrent Neural Networks (RNN)

RNN - Vanilla Code

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Original:

• https://gist.github.com/karpathy/d4dee566867f8291f086

Modified

import numpy as np
 
data = open('input.txt', 'r').read()
chars = list(set(data))
data_size, vocab_size = len(data), len(chars)
print('data has %d characters, %d unique.' % (data_size, vocab_size))
char_to_ix = {ch: i for i, ch in enumerate(chars)}
ix_to_char = {i: ch for i, ch in enumerate(chars)}
 
# hyperparameters
hidden_size = 100  # size of hidden layer of neurons
seq_length = 25  # number of steps to unroll the RNN for
learning_rate = 1e-1
 
# model parameters
Wxh = np.random.randn(hidden_size, vocab_size) * 0.01  # input to hidden
Whh = np.random.randn(hidden_size, hidden_size) * 0.01  # hidden to hidden
Why = np.random.randn(vocab_size, hidden_size) * 0.01  # hidden to output
bh = np.zeros((hidden_size, 1))  # hidden bias
by = np.zeros((vocab_size, 1))  # output bias
 
def lossFun(inputs, targets, hprev):
    """
    inputs,targets are both list of integers.
    hprev is Hx1 array of initial hidden state
    returns the loss, gradients on model parameters, and last hidden state
    """
    xs, hs, ys, ps = {}, {}, {}, {}
    hs[-1] = np.copy(hprev)
    loss = 0
 
    # forward pass
    for t in range(len(inputs)):
        xs[t] = np.zeros((vocab_size, 1))  # encode in 1-of-k representation
        xs[t][inputs[t]] = 1
        hs[t] = np.tanh(np.dot(Wxh, xs[t]) + np.dot(Whh, hs[t - 1]) + bh)  # hidden state
        ys[t] = np.dot(Why, hs[t]) + by  # unnormalized log probabilities for next chars
        ps[t] = np.exp(ys[t]) / np.sum(np.exp(ys[t]))  # probabilities for next chars
        loss += -np.log(ps[t][targets[t], 0])  # softmax (cross-entropy loss)
 
    # backward pass: compute gradients going backwards
    dWxh, dWhh, dWhy = np.zeros_like(Wxh), np.zeros_like(Whh), np.zeros_like(Why)
    dbh, dby = np.zeros_like(bh), np.zeros_like(by)
    dh_next = np.zeros_like(hs[0])
    for t in reversed(range(len(inputs))):
        dy = np.copy(ps[t])
        dy[targets[t]] -= 1  # backprop into y. see http://cs231n.github.io/neural-networks-case-study/#grad if confused here
 
        dWhy += np.dot(dy, hs[t].T)
        dby += dy
 
        dh = np.dot(Why.T, dy) + dh_next  # backprop into h
 
        dhraw = (1 - hs[t] * hs[t]) * dh  # backprop through tanh non-linearity
        dWxh += np.dot(dhraw, xs[t].T)
        dWhh += np.dot(dhraw, hs[t - 1].T)
        dbh += dhraw
 
        dh_next = np.dot(Whh.T, dhraw)
 
    for dparam in [dWxh, dWhh, dWhy, dbh, dby]:
        np.clip(dparam, -5, 5, out=dparam)  # clip to mitigate exploding gradients
 
    return loss, dWxh, dWhh, dWhy, dbh, dby, hs[len(inputs) - 1]
 
def sample(h, seed_ix, n):
    """
    sample a sequence of integers from the model
    h is memory state, seed_ix is seed letter for first time step
    """
    x = np.zeros((vocab_size, 1))
    x[seed_ix] = 1
    ixes = []
    for t in range(n):
        h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h) + bh)
        y = np.dot(Why, h) + by
        p = np.exp(y) / np.sum(np.exp(y))
        ix = np.random.choice(range(vocab_size), p=p.ravel())
        x = np.zeros((vocab_size, 1))
        x[ix] = 1
        ixes.append(ix)
    return ixes
 
n, p = 0, 0
hprev = np.zeros((hidden_size, 1))
 
# memory variables for Adagrad
mWxh, mWhh, mWhy = np.zeros_like(Wxh), np.zeros_like(Whh), np.zeros_like(Why)
mbh, mby = np.zeros_like(bh), np.zeros_like(by)
 
smooth_loss = -np.log(1.0 / vocab_size) * seq_length  # loss at iteration 0
 
while True:
    # prepare inputs (we're sweeping from left to right in steps seq_length long)
    if p + seq_length + 1 >= len(data) or n == 0:
        hprev = np.zeros((hidden_size, 1))  # reset RNN memory
        p = 0  # go from start of data
    inputs = [char_to_ix[ch] for ch in data[p:p + seq_length]]
    targets = [char_to_ix[ch] for ch in data[p + 1:p + seq_length + 1]]
 
    # forward seq_length characters through the net and fetch gradient
    loss, dWxh, dWhh, dWhy, dbh, dby, hprev = lossFun(inputs, targets, hprev)
    smooth_loss = smooth_loss * 0.999 + loss * 0.001
 
    # perform parameter update with Adagrad
    for param, dparam, mem in zip([Wxh, Whh, Why, bh, by],
                                  [dWxh, dWhh, dWhy, dbh, dby],
                                  [mWxh, mWhh, mWhy, mbh, mby]):
        mem += dparam * dparam
        param += -learning_rate * dparam / np.sqrt(mem + 1e-8)  # adagrad update
 
    if n % 100 == 0:
        # print current loss function
        print('iter %d, loss: %f' % (n, smooth_loss))
 
        # sample from the model now and then
        sample_ix = sample(hprev, inputs[0], 200)
        txt = ''.join(ix_to_char[ix] for ix in sample_ix)
        print('----\n %s \n----' % txt)
 
    p += seq_length  # move data pointer
    n += 1  # iteration counter

RNN - Types

• Hopfield Networks - Associative Memory Models - Ising–Lenz–Little Models - Nakano-Amari-Hopfield Networks

• Gated Recurrent Neural Networks (Gated RNN)

Resources

• Attention and Augmented Recurrent Neural Networks
• Andrej Karpathy - The Unreasonable Effectiveness of Recurrent Neural Networks
• https://explained.ai/rnn/index.html