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.


  • Tight integration with NumPy – Use numpy.ndarray in Theano-compiled functions.
  • Transparent use of a GPU – Perform data-intensive calculations up to 140x faster than with CPU.(float32 only)
  • Effcient symbolic differentiation – Theano does your derivatives for function with one or many inputs.
  • Speed and stability optimizations – Get the right answer for log(1+x) even when x is really tiny.
  • Dynamic C code generation – Evaluate expressions faster.
  • Extensive unit-testing and self-verification – Detect and diagnose many types of errors.


Theano is a library that handles multidimensional arrays, like Numpy. Used with other libs, it is well suited to data exploration and intended for research. Many academic researchers in the field of deep learning rely on Theano which is written in Python.

Theano’s user base enjoys an extensive volume of tutorials and documentation on how to do just about anything that is currently being done in artificial neural network research.


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.


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