“Theano: A Python framework for fast computation of mathematical expressions” was submitted to arXiv on May 9, 2016, credited to the Theano Development Team, a list of more than a hundred contributors that included Yoshua Bengio and Ian Goodfellow. The project was created and maintained at MILA (the Montreal Institute for Learning Algorithms) at the University of Montreal.
The paper describes Theano as a Python library that lets users define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. It compiled symbolic expressions down to fast CPU or GPU code and computed gradients automatically, which made it one of the most used mathematical compilers in the machine learning community. The paper benchmarks Theano against Torch7 and TensorFlow and surveys its features, limitations, and community.
Theano predates and influenced the frameworks that displaced it. Its symbolic-graph-plus-autodiff design shaped how later tools approached the problem, and higher-level libraries such as Keras originally ran on top of it. In September 2017 MILA announced it would cease major development after the 1.0 release, citing the rise of well-funded industrial frameworks; Theano 1.0 shipped in November 2017. By then the ideas it pioneered had been absorbed across the field.