# Theano at a Glance¶

Theano is a Python library that lets you 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:

- use of GPU for computations
- constant folding
- merging of similar subgraphs, to avoid redundant calculation
- arithmetic simplification (e.g.
`x*y/x -> y`

,`--x -> x`

) - inserting efficient BLAS operations (e.g.
`GEMM`

) in a variety of contexts - using memory aliasing to avoid calculation
- using inplace operations wherever it does not interfere with aliasing
- loop fusion for elementwise sub-expressions
- improvements to numerical stability (e.g. and )
- for a complete list, see Optimizations

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).

## Sneak peek¶

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 as tt
# declare two symbolic floating-point scalars
a = tt.dscalar()
b = tt.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

- declare variables (
`a,b`

) and give their types - build expressions for how to put those variables together
- compile expression graphs to functions in order to use them for computation.

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.

## What does it do that they don’t?¶

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?

*execution speed optimizations*: Theano can use g++ or nvcc to compile parts your expression graph into CPU or GPU instructions, which run much faster than pure Python.*symbolic differentiation*: Theano can automatically build symbolic graphs for computing gradients.*stability optimizations*: Theano can recognize [some] numerically unstable expressions and compute them with more stable algorithms.

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).

If numpy is to be compared to MATLAB and sympy to Mathematica, Theano is a sort of hybrid of the two which tries to combine the best of both worlds.

## Getting started¶

- Installing Theano
- Instructions to download and install Theano on your system.
- Tutorial
- Getting started with Theano’s basic features. Go here if you are new!
- API Documentation
- Details of what Theano provides. It is recommended to go through the Tutorial first though.

A PDF version of the online documentation may be found here.

## Theano Vision¶

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
- Graph Transformations
- Differentiation/higher order differentiation
- ‘R’ and ‘L’ differential operators
- Speed/memory optimizations
- Numerical stability optimizations

- Can use many compiled languages, instructions sets: C/C++, CUDA, OpenCL, PTX, CAL, AVX, …
- Lazy evaluation
- Loop
- 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.

## Theano Vision State¶

Here is the state of that vision as of November 15th, 2017 (after Theano 1.0.0):

- MILA will stop developing Theano..
We will provide support for one year, starting from
`1.0`

release (November 15th, 2017 to November 15th, 2018). - We support tensors using the numpy.ndarray object and we support many operations on them.
- We support sparse types by using the scipy.{csc,csr,bsr}_matrix object and support some operations on them.
- We have implementing/wrapping more advanced linear algebra operations. Still more possible.
- We have basic support for the creation of new operations from graphs at runtime. It supports well gradient overload for every input and inlining at the start of compilation. We don’t cover well the case when it is not inlined.
- We have many graph transformations that cover the 4 categories listed above.
- We can improve the graph transformation with better storage optimization
and instruction selection.
- Similar to auto-tuning during the optimization phase, but this doesn’t apply to only 1 op.
- Example of use: Determine if we should move computation to the GPU or not depending on the input size.

- We support Python 2 and Python 3.
- We have a new CUDA backend for tensors with many dtype support.
- Loops work, but not all related optimizations are currently done.
- The cvm linker allows lazy evaluation. It is the current default linker.
- How to have DebugMode check it? Right now, DebugMode checks the computation non-lazily.

- SIMD parallelism on the CPU comes from the compiler.
- Multi-core parallelism support limited. If the external BLAS implementation supports it, many dot are parallelized via gemm, gemv and ger. Also, element-wise operation are supported. See Multi cores support in Theano.
- No multi-node support.
- Most, but not all NumPy functions/aliases are implemented.
- Wrapping an existing Python function in easy and documented.
- We know how to separate the shared variable memory storage location from its object type (tensor, sparse, dtype, broadcast flags), but we need to do it.

## Contact us¶

Questions and bug reports should be submitted in the form of an issue at pymc-theano-dev

We welcome all kinds of contributions. If you have any questions regarding how to extend Theano, please feel free to ask.