JAXbind: Bind any function to JAX

JAXbind API documentation: nifty-ppl.github.io/JAXbind/ | Found a bug? github.com/NIFTy-PPL/JAXbind/issues | Need help? github.com/NIFTy-PPL/JAXbind/discussions

Summary

The existing interface in JAX for connecting fully differentiable custom code requires deep knowledge of JAX and its C++ backend. The aim of JAXbind is to drastically lower the burden of connecting custom functions implemented in other programming languages to JAX. Specifically, JAXbind provides an easy-to-use Python interface for defining custom, so-called JAX primitives. Via JAXbind, any function callable from Python can be exposed as a JAX primitive. JAXbind allows to interface the JAX function transformation engine with custom derivatives and batching rules, enabling all JAX transformations for the custom primitive. In contrast, the JAX built-in external callback interface also has a Python endpoint but the external callbacks cannot be fully integrated into the JAX transformation engine, as only the Jacobian-vector product or the vector-Jacobian product can be added but not both.

Automatic Differentiation and Code Example

Automatic differentiation is a core feature of JAX and often one of the main reasons for using it. Thus, it is essential that custom functions registered with JAX support automatic differentiation. In the following, we will outline which functions our package respectively JAX requires to enable automatic differentiation. For simplicity, we assume that we want to connect the nonlinear function $f(x_1,x_2) = x_1x_2^2$ to JAX. The JAXbind package expects the Python function for $f$ to take three positional arguments. The first argument, out, is a tuple into which the function results are written. The second argument is also a tuple containing the input to the function, in our case, $x_1$ and $x_2$. Via kwargs_dump, potential keyword arguments given to the later registered Jax primitive can be forwarded to f in serialized form.

import jaxbind

def f(out, args, kwargs_dump):
    kwargs = jaxbind.load_kwargs(kwargs_dump)
    x1, x2 = args
    out[0][()] = x1 * x2**2

JAX's automatic differentiation engine can compute the Jacobian-vector product jvp and vector-Jacobian product vjp of JAX primitives. The Jacobian-vector product in JAX is a function applying the Jacobian of $f$ at a position $x$ to a tangent vector. In mathematical nomenclature this operation is called the pushforward of $f$ and can be denoted as $\partial f(x): T_x X \mapsto T_{f(x)} Y$, with $T_x X$ and $T_{f(x)} Y$ being the tangent spaces of $X$ and $Y$ at the positions $x$ and $f(x)$. As the implementation of $f$ is not JAX native, JAX cannot automatically compute the jvp. Instead, an implementation of the pushforward has to be provided, which JAXbind will register as the jvp of the JAX primitive of $f$. For our example, this Jacobian-vector-product function is given by $\partial f(x_1,x_2)(dx_1,dx_2) = x_2^2dx_1 + 2x_1x_2dx_2$.

def f_jvp(out, args, kwargs_dump):
    kwargs = jaxbind.load_kwargs(kwargs_dump)
    x1, x2, dx1, dx2 = args
    out[0][()] = x2**2 * dx1 + 2 * x1 * x2 * dx2

The vector-Jacobian product vjp in JAX is the linear transpose of the Jacobian-vector product. In mathematical nomenclature this is the pullback $(\partial f(x))^{T}: T_{f(x)}Y \mapsto T_x X$ of $f$. Analogously to the jvp, the user has to implement this function as JAX cannot automatically construct it. For our example function, the vector-Jacobian product is $(\partial f(x_1,x_2))^{T}(dy) = (x_2^2dy, 2x_1x_2dy)$.

def f_vjp(out, args, kwargs_dump):
    kwargs = jaxbind.load_kwargs(kwargs_dump)
    x1, x2, dy = args
    out[0][()] = x2**2 * dy
    out[1][()] = 2 * x1 * x2 * dy

To just-in-time compile the function, JAX needs to abstractly evaluate the code, i.e. it needs to be able to know the shape and dtype of the output of the custom function given only the shape and dtype of the input. We have to provide these abstract evaluation functions returning the output shape and dtype given an input shape and dtype for f as well as for the vjp application. The output shape of the jvp is identical to the output shape of f itself and does not need to be specified again. Due to the internals of JAX the abstract evaluation functions take normal keyword arguments and not serialized keyword arguments.

def f_abstract(*args, **kwargs):
    assert args[0].shape == args[1].shape
    return ((args[0].shape, args[0].dtype),)

def f_abstract_T(*args, **kwargs):
    return (
        (args[0].shape, args[0].dtype),
        (args[0].shape, args[0].dtype),
    )

We have now defined all ingredients necessary to register a JAX primitive for our function $f$ using the JAXbind package.

f_jax = jaxbind.get_nonlinear_call(
    f, (f_jvp, f_vjp), f_abstract, f_abstract_T
)

f_jax is a JAX primitive registered via the JAXbind package supporting all JAX transformations. We can now compute the jvp and vjp of the new JAX primitive and even jit-compile and batch it.

import jax
import jax.numpy as jnp

inp = (jnp.full((4,3), 4.), jnp.full((4,3), 2.))
tan = (jnp.full((4,3), 1.), jnp.full((4,3), 1.))
res, res_tan = jax.jvp(f_jax, inp, tan)

cotan = [jnp.full((4,3), 6.)]
res, f_vjp = jax.vjp(f_jax, *inp)
res_cotan = f_vjp(cotan)

f_jax_jit = jax.jit(f_jax)
res = f_jax_jit(*inp)

Higher Order Derivatives and Linear Functions

JAX supports higher order derivatives and can differentiate a jvp or vjp with respect to the position at which the Jacobian was taken. Similar to first derivatives, JAX can not automatically compute higher derivatives of a general function $f$ that is not natively implemented in JAX. Higher order derivatives would again need to be provided by the user. For many algorithms, first derivatives are sufficient, and higher order derivatives are often not implemented by the high-performance codes. Therefore, the current interface of JAXbind is, for simplicity, restricted to first derivatives. In the future, the interface could be easily expanded if specific use cases require higher order derivatives.

In scientific computing, linear functions such as, e.g., spherical harmonic transforms are widespread. If the function $f$ is linear, differentiation becomes trivial. Specifically for a linear function $f$, the pushforward respectively the jvp of $f$ is identical to $f$ itself and independent of the position at which it is computed. Expressed in formulas, $\partial f(x)(dx) = f(dx)$ if $f$ is linear in $x$. Analogously, the pullback respectively the vjp becomes independent of the initial position and is given by the linear transpose of $f$, thus $(\partial f(x))^{T}(dy) = f^T(dy)$. Also, all higher order derivatives can be expressed in terms of $f$ and its transpose. To make use of these simplifications, JAXbind provides a special interface for linear functions, supporting higher order derivatives, only requiring an implementation of the function and its transpose.

Demos and Documentation

Additional demos can be found in the demos folder. Specifically, there is a basic demo 01_linear_function.py showcasing the interface for linear functions and custom batching rules. 02_multilinear_function.py binds a multi-linear function as a JAX primitive. Finally, 03_nonlinear_function.py demonstrates the interface for non-linear functions and shows how to deal with fixed arguments, which cannot be differentiated. The documentation of the JAXbind API is available here.

Platforms

Currently, JAXbind only has CPU but no GPU support. With some expertise on Python bindings for GPU kernels adding GPU support should be fairly simple. The Interfacing with the JAX automatic differentiation engine is identical for CPU and GPU. Contributions are welcome!

Installation

Binary wheels for JAXbind can be obtained and installed from PyPI via:

pip install jaxbind

To install JAXbind from source, clone the repository and install the package via pip.

git clone https://github.com/NIFTy-PPL/jaxbind.git
cd jaxbind
pip install .

Contributing

Contributions are highly appreciated! Please open an issue first if you think your PR changes current code substanitally. Please format your code using black. PRs affecting the public API, including adding new features, should update the public documentation. If possible, add appropriate tests to your PR. Feel free to open a PR early on in the development process, we are happy to help in the development process and provide feedback along the way.

Licensing terms

All source code in this package is released under the 2-clause BSD license. All of JAXbind is distributed without any warranty.