Theano is a Python library that lets you to define, optimize, and evaluate mathematical expressions, especially ones with multi-dimensional arrays (numpy.ndarray). Using Theano it is possible to attain speeds rivaling hand-crafted C implementations for problems involving large amounts of data. It can also surpass C on a CPU by many orders of magnitude by taking advantage of recent GPUs.
Theano combines aspects of a computer algebra system (CAS) with aspects of an optimizing compiler. It can also generate customized C code for many mathematical operations. This combination of CAS with optimizing compilation is particularly useful for tasks in which complicated mathematical expressions are evaluated repeatedly and evaluation speed is critical. For situations where many different expressions are each evaluated once Theano can minimize the amount of compilation/analysis overhead, but still provide symbolic features such as automatic differentiation.
Theano’s compiler applies many optimizations of varying complexity to these symbolic expressions. These optimizations include, but are not limited to:
Theano was written at the LISA lab to support rapid development of efficient machine learning algorithms. Theano is named after the Greek mathematician, who may have been Pythagoras’ wife. Theano is released under a BSD license (link).
Here is an example of how to use Theano. It doesn’t show off many of Theano’s features, but it illustrates concretely what Theano is.
import theano from theano import tensor # declare two symbolic floating-point scalars a = tensor.dscalar() b = tensor.dscalar() # create a simple expression c = a + b # convert the expression into a callable object that takes (a,b) # values as input and computes a value for c f = theano.function([a,b], c) # bind 1.5 to 'a', 2.5 to 'b', and evaluate 'c' assert 4.0 == f(1.5, 2.5)
Theano is not a programming language in the normal sense because you write a program in Python that builds expressions for Theano. Still it is like a programming language in the sense that you have to
It is good to think of theano.function as the interface to a compiler which builds a callable object from a purely symbolic graph. One of theano’s most important features is that theano.function can optimize a graph and even compile some or all of it into native machine instructions.
Theano is a Python library and optimizing compiler for manipulating and evaluating expressions, especially matrix-valued ones. Manipulation of matrices is typically done using the numpy package, so what does Theano do that Python and numpy do not?
The closest Python package to Theano is sympy. Theano focuses more on tensor expressions than Sympy, and has more machinery for compilation. Sympy has more sophisticated algebra rules and can handle a wider variety of mathematical operations (such as series, limits, and integrals).
A PDF version of the online documentation may be found here.
This is the vision we have for Theano. This is give people an idea of what to expect in the future of Theano, but we can’t promise to implement all of it. This should also help you to understand where Theano fits in relation to other computational tools.
Support tensor and sparse operations
Support linear algebra operations
Can use many compiled languages, instructions sets: C/C++, CUDA, OpenCL, PTX, CAL, AVX, ...
Parallel execution (SIMD, multi-core, multi-node on cluster, multi-node distributed)
Support all NumPy/basic SciPy functionality
Easy wrapping of library functions in Theano
Note: There is no short term plan to support multi-node computation.
Here is the state of that vision as of October 1st, 2012 (after Theano release 0.6rc1):
Discussion about Theano takes place in the theano-dev and theano-users mailing lists. People interested in development of Theano should check the former, while the latter is reserved for issues that concern the end users.
Questions, comments, praise, criticism as well as bug reports should be submitted to these mailing lists.
We welcome all kinds of contributions. If you have any questions regarding how to extend Theano, please feel free to ask on the theano-dev mailing list.