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Chapter 11
Using Theano, we can define many types of functions working on scalars, arrays,
and matrices, as well as other mathematical expressions. For instance, we can create
a function that computes the length of the hypotenuse of a right-angled triangle:
import theano
from theano import tensor as T
First, we define the two inputs, a and b. These are simple numerical values, so we
define them as scalars:
a = T.dscalar()
b = T.dscalar()
Then, we define the output, c. This is an expression based on the values of a and b:
c = T.sqrt(a ** 2 + b ** 2)
Note that c isn't a function or a value here—it is simply an expression, given a and b.
Note also that a and b don't have actual values—this is an algebraic expression, not
an absolute one. In order to compute on this, we define a function:
f = theano.function([a,b], c)
This basically tells Theano to create a function that takes values for a and b
as inputs, and returns c as an output, computed on the values given. For example,
f(3, 4) returns 5.
While this simple example may not seem much more powerful than what we
can already do with Python, we can now use our function or our mathematical
expression c in other parts of code and the remaining mappings. In addition, while
we defined c before the function was defined, no actual computation was done until
we called the function.
An introduction to Lasagne
Theano isn't a library to build neural networks. In a similar way, NumPy isn't a
library to perform machine learning; it just does the heavy lifting and is generally
used from another library. Lasagne is such a library, designed specifically around
building neural networks, using Theano to perform the computation.
Lasagne implements a number of modern types of neural network layers, and the
building blocks for building them.
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