Getting Started#

PyTensor is a Python library that allows one to define, optimize/rewrite, and evaluate mathematical expressions, especially ones involving multi-dimensional arrays (e.g. numpy.ndarrays). Using PyTensor, it is possible to attain speeds rivaling hand-crafted C implementations for problems involving large amounts of data.

PyTensor combines aspects of a computer algebra system (CAS) with aspects of an optimizing compiler. It can also generate customized code for multiple compiled languages and/or their Python-based interfaces, such as C, Numba, and JAX. This combination of CAS features with optimizing compilation and transpilation 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, PyTensor can minimize the amount of compilation and analysis overhead, but still provide symbolic features such as automatic differentiation.

PyTensor’s compiler applies many default optimizations of varying complexity. These optimizations include, but are not limited to:

  • constant folding

  • merging of similar sub-graphs, to avoid redundant calculations

  • arithmetic simplifications (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 unnecessary calculations

  • using in-place operations wherever it does not interfere with aliasing

  • loop fusion for element-wise sub-expressions

  • improvements to numerical stability (e.g. \(\log(1+\exp(x))\) and \(\log(\sum_i \exp(x[i]))\))

For more information see Optimizations.


The library that PyTensor is based on, Theano, was written at the LISA lab to support rapid development of efficient machine learning algorithms but while Theano was commonly referred to as a “deep learning” (DL) library, PyTensor is not a DL library.

Designations like “deep learning library” reflect the priorities/goals of a library; specifically, that the library serves the purposes of DL and its computational needs. PyTensor is not explicitly intended to serve the purpose of constructing and evaluating DL models, but that doesn’t mean it can’t serve that purpose well.

The designation “tensor library” is more apt, but, unlike most other tensor libraries (e.g. TensorFlow, PyTorch, etc.), PyTensor is more focused on what one might call the symbolic functionality.

Most tensor libraries perform similar operations to some extent, but many do not expose the underlying operations for use at any level other than internal library development. Furthermore, when they do, many libraries cross a large language barrier that unnecessarily hampers rapid development (e.g. moving from Python to C++ and back).

If you follow the history of this project, you can see that it grew out of work on PyMC, and PyMC is a library for domain-specific (i.e. probabilistic modeling) computations. Likewise, the other pymc-devs projects demonstrate the use of PyTensor graphs as an intermediate representation (IR) for a domain-specific language/interface (e.g. aeppl provides a graph representation for a PPL) and advanced automations based on IR (e.g. aemcmc as a means of constructing custom samplers from IR, aeppl as a means of automatically deriving log-probabilities for basic tensor operations represented in IR).

This topic is a little more advanced and doesn’t really have parallels in other tensor libraries, but it’s one of the things that PyTensor uniquely facilitates.

The PyMC/probabilistic programming connection is similar to the DL connection Theano had, but—unlike Theano—we don’t want PyTensor to be conflated with one of its domains of application—like probabilistic modeling. Those primary domains of application will always have some influence on the development of PyTensor, but that’s also why we need to avoid labels/designations like “deep learning library” and focus on the functionality, so that we don’t unnecessarily compromise PyTensor’s general applicability, relative simplicity, and/or prevent useful input/collaboration from other domains.

Sneak peek#

Here is an example of how to use PyTensor. It doesn’t show off many of its features, but it illustrates concretely what PyTensor is.

import pytensor
from pytensor import tensor as pt

# declare two symbolic floating-point scalars
a = pt.dscalar()
b = pt.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 = pytensor.function([a, b], c)

# bind 1.5 to 'a', 2.5 to 'b', and evaluate 'c'
assert 4.0 == f(1.5, 2.5)

PyTensor is not a programming language in the normal sense because you write a program in Python that builds expressions for PyTensor. Still it is like a programming language in the sense that you have to

  • declare variables a and b and give their types,

  • build expressions graphs using those variables,

  • compile the expression graphs into functions that can be used for computation.

It is good to think of pytensor.function() as the interface to a compiler which builds a callable object from a purely symbolic graph. One of PyTensor’s most important features is that pytensor.function() can optimize a graph and even compile some or all of it into native machine instructions.

What does it do that NumPy doesn’t#

PyTensor is a essentially an optimizing compiler for manipulating and evaluating expressions, especially tensor-valued ones. Manipulation of tensors is typically done using the NumPy package, so what does PyTensor do that Python and NumPy don’t do?

  • execution speed optimizations: PyTensor can use C, Numba, or JAX to compile parts your expression graph into CPU or GPU instructions, which run much faster than pure Python.

  • symbolic differentiation: PyTensor can automatically build symbolic graphs for computing gradients.

  • stability optimizations: PyTensor can recognize some numerically unstable expressions and compute them with more stable algorithms.

The closest Python package to PyTensor is sympy. PyTensor 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, PyTensor is a sort of hybrid of the two which tries to combine the best of both worlds.

Getting started#

Installing PyTensor

Instructions to download and install PyTensor on your system.


Getting started with PyTensor’s basic features. Go here if you are new!

API Documentation

Details of what PyTensor provides. It is recommended to go through the Tutorial first though.

Contact us#

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

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