Introduction to Theano¶
Credits: Forked from summerschool2015 by mila-udem
Slides¶
Refer to the associated Introduction to Theano slides and use this notebook for hands-on practice of the concepts.
Basic usage¶
Defining an expression¶
In [1]:
import theano
from theano import tensor as T
x = T.vector('x')
W = T.matrix('W')
b = T.vector('b')
In [2]:
dot = T.dot(x, W)
out = T.nnet.sigmoid(dot + b)
Graph visualization¶
In [3]:
from theano.printing import debugprint
debugprint(dot)
dot [@A] '' |x [@B] |W [@C]
In [4]:
debugprint(out)
sigmoid [@A] ''
|Elemwise{add,no_inplace} [@B] ''
|dot [@C] ''
| |x [@D]
| |W [@E]
|b [@F]
Compiling a Theano function¶
In [5]:
f = theano.function(inputs=[x, W], outputs=dot)
g = theano.function([x, W, b], out)
h = theano.function([x, W, b], [dot, out])
i = theano.function([x, W, b], [dot + b, out])
Graph visualization¶
In [6]:
debugprint(f)
CGemv{inplace} [@A] '' 3
|AllocEmpty{dtype='float64'} [@B] '' 2
| |Shape_i{1} [@C] '' 1
| |W [@D]
|TensorConstant{1.0} [@E]
|InplaceDimShuffle{1,0} [@F] 'W.T' 0
| |W [@D]
|x [@G]
|TensorConstant{0.0} [@H]
In [7]:
debugprint(g)
Elemwise{ScalarSigmoid}[(0, 0)] [@A] '' 2
|CGemv{no_inplace} [@B] '' 1
|b [@C]
|TensorConstant{1.0} [@D]
|InplaceDimShuffle{1,0} [@E] 'W.T' 0
| |W [@F]
|x [@G]
|TensorConstant{1.0} [@D]
In [8]:
from theano.printing import pydotprint
pydotprint(f, outfile='pydotprint_f.png')
The output file is available at pydotprint_f.png
In [9]:
from IPython.display import Image
Image('pydotprint_f.png', width=1000)
Out[9]:
In [10]:
pydotprint(g, outfile='pydotprint_g.png')
Image('pydotprint_g.png', width=1000)
The output file is available at pydotprint_g.png
Out[10]:
In [11]:
pydotprint(h, outfile='pydotprint_h.png')
Image('pydotprint_h.png', width=1000)
The output file is available at pydotprint_h.png
Out[11]:
Executing a Theano function¶
In [12]:
import numpy as np
np.random.seed(42)
W_val = np.random.randn(4, 3)
x_val = np.random.rand(4)
b_val = np.ones(3)
f(x_val, W_val)
Out[12]:
array([ 1.79048354, 0.03158954, -0.26423186])
In [13]:
g(x_val, W_val, b_val)
Out[13]:
array([ 0.9421594 , 0.73722395, 0.67606977])
In [14]:
h(x_val, W_val, b_val)
Out[14]:
[array([ 1.79048354, 0.03158954, -0.26423186]), array([ 0.9421594 , 0.73722395, 0.67606977])]
In [15]:
i(x_val, W_val, b_val)
Out[15]:
[array([ 2.79048354, 1.03158954, 0.73576814]), array([ 0.9421594 , 0.73722395, 0.67606977])]
In [16]:
pydotprint(f, compact=False, outfile='pydotprint_f_notcompact.png')
Image('pydotprint_f_notcompact.png', width=1000)
The output file is available at pydotprint_f_notcompact.png
Out[16]:
In [17]:
r = T.row('r')
print(r.broadcastable)
(True, False)
In [18]:
c = T.col('c')
print(c.broadcastable)
(False, True)
In [19]:
f = theano.function([r, c], r + c)
print(f([[1, 2, 3]], [[.1], [.2]]))
[[ 1.1 2.1 3.1] [ 1.2 2.2 3.2]]
In [20]:
x_ = T.vector('x_')
x_n = (x_ - x_.mean()) / x_.std()
f_n = theano.function([x_, W], dot, givens={x: x_n})
f_n(x_val, W_val)
Out[20]:
array([ 1.90651511, 0.60431744, -0.64253361])
Cloning with replacement¶
In [21]:
dot_n, out_n = theano.clone([dot, out], replace={x: (x - x.mean()) / x.std()})
f_n = theano.function([x, W], dot_n)
f_n(x_val, W_val)
Out[21]:
array([ 1.90651511, 0.60431744, -0.64253361])
In [22]:
y = T.vector('y')
C = ((out - y) ** 2).sum()
dC_dW = theano.grad(C, W)
dC_db = theano.grad(C, b)
# dC_dW, dC_db = theano.grad(C, [W, b])
Using the gradients¶
In [23]:
cost_and_grads = theano.function([x, W, b, y], [C, dC_dW, dC_db])
y_val = np.random.uniform(size=3)
print(cost_and_grads(x_val, W_val, b_val, y_val))
[array(0.6137821438190066), array([[ 0.01095277, 0.07045955, 0.051161 ],
[ 0.01889131, 0.12152849, 0.0882424 ],
[ 0.01555008, 0.10003427, 0.07263534],
[ 0.01048429, 0.06744584, 0.04897273]]), array([ 0.03600015, 0.23159028, 0.16815877])]
In [24]:
upd_W = W - 0.1 * dC_dW
upd_b = b - 0.1 * dC_db
cost_and_upd = theano.function([x, W, b, y], [C, upd_W, upd_b])
print(cost_and_upd(x_val, W_val, b_val, y_val))
[array(0.6137821438190066), array([[ 0.49561888, -0.14531026, 0.64257244],
[ 1.52114073, -0.24630622, -0.2429612 ],
[ 1.57765781, 0.7574313 , -0.47673792],
[ 0.54151161, -0.47016228, -0.47062703]]), array([ 0.99639999, 0.97684097, 0.98318412])]
In [25]:
pydotprint(cost_and_upd, outfile='pydotprint_cost_and_upd.png')
Image('pydotprint_cost_and_upd.png', width=1000)
The output file is available at pydotprint_cost_and_upd.png
Out[25]: