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Last active February 7, 2023 23:56
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Minimal character-level language model with a Vanilla Recurrent Neural Network, in Python/numpy
Minimal character-level Vanilla RNN model. Written by Andrej Karpathy (@karpathy)
BSD License
import numpy as np
# data I/O
data = open('input.txt', 'r').read() # should be simple plain text file
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 xrange(len(inputs)):
xs[t] = np.zeros((vocab_size,1)) # encode in 1-of-k representation
xs[t][inputs[t]] = 1
hs[t] = np.tanh(, xs[t]) +, hs[t-1]) + bh) # hidden state
ys[t] =, 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)
dhnext = np.zeros_like(hs[0])
for t in reversed(xrange(len(inputs))):
dy = np.copy(ps[t])
dy[targets[t]] -= 1 # backprop into y. see if confused here
dWhy +=, hs[t].T)
dby += dy
dh =, dy) + dhnext # backprop into h
dhraw = (1 - hs[t] * hs[t]) * dh # backprop through tanh nonlinearity
dbh += dhraw
dWxh +=, xs[t].T)
dWhh +=, hs[t-1].T)
dhnext =, 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 xrange(n):
h = np.tanh(, x) +, h) + bh)
y =, 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
return ixes
n, p = 0, 0
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) # memory variables for Adagrad
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]]
# sample from the model now and then
if n % 100 == 0:
sample_ix = sample(hprev, inputs[0], 200)
txt = ''.join(ix_to_char[ix] for ix in sample_ix)
print '----\n %s \n----' % (txt, )
# 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
if n % 100 == 0: print 'iter %d, loss: %f' % (n, smooth_loss) # print progress
# 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
p += seq_length # move data pointer
n += 1 # iteration counter
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j8ahmed commented Oct 17, 2020

Wonderful code,but there are somecodes confused me.

# 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# 梯度的累加
        param += -learning_rate * dparam / np.sqrt(mem + 1e-8) # adagrad update

Wxh,..mby were defined as global variables,while param,dparam,mem are just local variables.How could Adagrad update change the value of global variables?I tried to test my thought by code like below.

import numpy as np
Wxh, Whh, Why, bh, by=1,2,3,4,5
dWxh, dWhh, dWhy, dbh, dby=1,2,3,4,5
mWxh, mWhh, mWhy, mbh, mby=1,2,3,4,5
while True:
    for param, dparam, mem in zip([Wxh, Whh, Why, bh, by], 
                                  [dWxh, dWhh, dWhy, dbh, dby], 
                                [mWxh, mWhh, mWhy, mbh, mby]):
        mem += dparam * dparam# 梯度的累加
        param += dparam / np.sqrt(mem + 1e-8) 
    print(Wxh)#Output never change!

It's might be a very simple problem.Just puzzled me!Someone helps?Thanks a lot.

Not sure if anyone ever addressed this further down the thread but I found an answer on stack overflow that addresses modifying mutable global variables like Wxh and the like within a local scope.

'param' is referencing all the weight arrays rather than copying their values in their original locations. It is not copying them into a new storage location. So when adding to all the values in 'param' with adagrad we are actually modifying the global values of Wxh, etc... not the values in param. I think?

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@MistryWoman We are trying to push our weights closer to zero, so that gradient doesn't vanish. For large weights , gradients become very small while using tanh. Please take a look at

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@karpathy Thank you for posting this. I had a small doubt in line 58. Why do we perform Whh.T in,dhraw)? Since Whh has (hidden_size,hidden_size) as shape, we can directly multiply it with dhraw. Or am I missing something here?

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Traceback (most recent call last):
File "", line 100, in
loss, dWxh, dWhh, dWhy, dbh, dby, hprev = lossFun(inputs, targets, hprev)
File "", line 43, in lossFun
loss += -np.log(ps[t][targets[t],0]) # softmax (cross-entropy loss)
IndexError: list index out of range

Why am I getting this error?

I was getting the same error but it seems like the reason is that your input file is too small. Try writing more stuff in your input.txt

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I made a two layer recurrent neural network based off of this and I am not sure why it does not work. So, if anyone could check out and make a PR if you find a problem?

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Hi, can anyone explain the line where we pass in the gradient through the softmax function " dy [targets[t]] -=1 ". Why are we doing this operation ??

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To anyone finding the code hard to understand, I provide detailed explanations here: Hope it helps

Good explanation for second part of lossFunction.

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pjoer commented Jan 31, 2023

Could someone explain how to use this? I can't generate text. It is running though.

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@pjoer, do you have an input.txt file (really any text file) in the same directory of this file which you should be running like python

It seems the above was written with python2 in mind, but I just updated a few lines and got it working on Python 3.9.6:

Good luck!

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