*(Crossposted on the Google Open Source Blog)*

Tangent is a new, free, and open-source Python library for automatic differentiation. In contrast to existing machine learning libraries, Tangent is a source-to-source system, consuming a Python function f and emitting a new Python function that computes the gradient of f. This allows much better user visibility into gradient computations, as well as easy user-level editing and debugging of gradients. Tangent comes with many more features for debugging and designing machine learning models:

- Easily debug your backward pass
- Fast gradient surgery
- Forward mode automatic differentiation
- Efficient Hessian-vector products
- Code optimizations

Neural networks (NNs) have led to great advances in machine learning models for images, video, audio, and text. The fundamental abstraction that lets us train NNs to perform well at these tasks is a 30-year-old idea called reverse-mode automatic differentiation (also known as backpropagation), which comprises two passes through the NN. First, we run a “forward pass” to calculate the output value of each node. Then we run a “backward pass” to calculate a series of derivatives to determine how to update the weights to increase the model’s accuracy.

Training NNs, and doing research on novel architectures, requires us to compute these derivatives correctly, efficiently, and easily. We also need to be able to debug these derivatives when our model isn’t training well, or when we’re trying to build something new that we do not yet understand. Automatic differentiation, or just “autodiff,” is a technique to calculate the derivatives of computer programs that denote some mathematical function, and nearly every machine learning library implements it.

Existing libraries implement automatic differentiation by tracing a program’s execution (at runtime, like TF Eager, PyTorch and Autograd) or by building a dynamic data-flow graph and then differentiating the graph (ahead-of-time, like TensorFlow). In contrast, Tangent performs ahead-of-time autodiff on the Python source code itself, and produces Python source code as its output.

As a result, you can finally read your automatic derivative code just like the rest of your program. Tangent is useful to researchers and students who not only want to write their models in Python, but also read and debug automatically-generated derivative code without sacrificing speed and flexibility.

You can easily inspect and debug your models written in Tangent, without special tools or indirection. Tangent works on a large and growing subset of Python, provides extra autodiff features other Python ML libraries don’t have, is high-performance, and is compatible with TensorFlow and NumPy.

**Automatic differentiation of Python code**

How do we automatically generate derivatives of plain Python code? Math functions like tf.exp or tf.log have derivatives, which we can compose to build the backward pass. Similarly, pieces of syntax, such as subroutines, conditionals, and loops, also have backward-pass versions. Tangent contains recipes for generating derivative code for each piece of Python syntax, along with many NumPy and TensorFlow function calls.

Tangent has a one-function API:

Here’s an animated graphic of what happens when we call tangent.grad on a Python function:

If you want to print out your derivatives, you can run:

Under the hood, tangent.grad first grabs the source code of the Python function you pass it. Tangent has a large library of recipes for the derivatives of Python syntax, as well as TensorFlow Eager functions. The function tangent.grad then walks your code in reverse order, looks up the matching backward-pass recipe, and adds it to the end of the derivative function. This reverse-order processing gives the technique its name: reverse-mode automatic differentiation.

The function df above only works for scalar (non-array) inputs. Tangent also supports

- Using TensorFlow Eager functions, for processing arrays of numbers.
- Subroutines
- Control flow

**Next Steps**

Tangent is open source now at github.com/google/tangent. Go check it out for download and installation instructions. Tangent is still an experiment, so expect some bugs. If you report them to us on GitHub, we will do our best to fix them quickly.

We are working to add support in Tangent for more aspects of the Python language (e.g., closures, inline function definitions, classes, more NumPy and TensorFlow functions). We also hope to add more advanced automatic differentiation and compiler functionality in the future, such as automatic trade-off between memory and compute (Griewank and Walther 2000; Gruslys et al., 2016), more aggressive optimizations, and lambda lifting.

We intend to develop Tangent together as a community. We welcome pull requests with fixes and features. Happy differentiating!

**Acknowledgments**

Bart van MerriĆ«nboer contributed immensely to all aspects of Tangent during his internship, and Dan Moldovan led TF Eager integration, infrastructure and benchmarking. Also, thanks to the Google Brain team for their support of this post and special thanks to Sanders Kleinfeld, Matt Johnson and Aleks Haecky for their valuable contribution for the technical aspects of the post.