We are collecting here answers to frequently asked questions. Contributions welcome!
If you have a Python function that changes behavior after using :func:`jax.jit`, perhaps
your function uses global state, or has side-effects. In the following code, the
impure_func uses the global y and has a side-effect due to print:
y = 0
# @jit # Different behavior with jit
def impure_func(x):
print("Inside:", y)
return x + y
for y in range(3):
print("Result:", impure_func(y))
Without jit the output is:
Inside: 0 Result: 0 Inside: 1 Result: 2 Inside: 2 Result: 4
and with jit it is:
Inside: 0 Result: 0 Result: 1 Result: 2
For :func:`jax.jit`, the function is executed once using the Python interpreter, at which time the
Inside printing happens, and the first value of y is observed. Then, the function
is compiled and cached, and executed multiple times with different values of x, but
with the same first value of y.
Additional reading:
Let's first look at the principles of data and computation placement in JAX.
In JAX, the computation follows data placement. JAX arrays have two placement properties: 1) the device where the data resides; and 2) whether it is committed to the device or not (the data is sometimes referred to as being sticky to the device).
By default, JAX arrays are placed uncommitted on the default device
(jax.devices()[0]).
>>> from jax import numpy as jnp
>>> print(jnp.ones(3).device_buffer.device()) # doctest: +SKIP
gpu:0Computations involving uncommitted data are performed on the default device and the results are uncommitted on the default device.
Data can also be placed explicitly on a device using :func:`jax.device_put`
with a device parameter, in which case the data becomes committed to the device:
>>> import jax
>>> from jax import device_put
>>> print(device_put(1, jax.devices()[2]).device_buffer.device()) # doctest: +SKIP
gpu:2Computations involving some committed inputs will happen on the committed device and the result will be committed on the same device. Invoking an operation on arguments that are committed to more than one device will raise an error.
You can also use :func:`jax.device_put` without a device parameter. If the data
is already on a device (committed or not), it's left as-is. If the data isn't on any
device—that is, it's a regular Python or NumPy value—it's placed uncommitted on the default
device. You can also use :func:`jax.device_put` without a device parameter.
Jitted functions behave like any other primitive operations—they will follow the data and will show errors if invoked on data committed on more than one device.
(As of April 2020, :func:`jax.jit` has a device parameter that affects the device placement. That parameter is experimental, is likely to be removed or changed, and its use is not recommended.)
For a worked-out example, we recommend reading through
test_computation_follows_data in
multi_device_test.py.
If you are getting an error that a library function is called with "Abstract tracer value encountered where concrete value is expected", you may need to change how you invoke JAX transformations. Below is an example and a couple of possible solutions, followed by the details of what is actually happening, if you are curious or the simple solution does not work for you.
Some library functions take arguments that specify shapes or axes, such as the second and third arguments for :func:`jax.numpy.split`:
# def np.split(arr, num_sections: Union[int, Sequence[int]], axis: int): np.split(np.zeros(2), 2, 0) # works
If you try the following code:
jax.jit(np.split)(np.zeros(4), 2, 0)
you will get the following error:
ConcretizationTypeError: Abstract tracer value encountered where concrete value is expected (in jax.numpy.split argument 1). Use transformation parameters such as `static_argnums` for `jit` to avoid tracing input values. See `https://jax.readthedocs.io/en/latest/faq.html#abstract-tracer-value-where-concrete-value-is-expected-error`. Encountered value: Traced<ShapedArray(int32[], weak_type=True):JaxprTrace(level=-1/1)>
You must change the way you use :func:`jax.jit` to ensure that the num_sections
and axis arguments use their concrete values (2 and 0 respectively).
The best mechanism is to use special transformation parameters
to declare some arguments to be static, e.g., static_argnums for :func:`jax.jit`:
jax.jit(np.split, static_argnums=(1, 2))(np.zeros(4), 2, 0)
An alternative is to apply the transformation to a closure
that encapsulates the arguments to be protected, either manually as below
or by using functools.partial:
jax.jit(lambda arr: np.split(arr, 2, 0))(np.zeros(4))
Note a new closure is created at every invocation, which defeats the compilation caching mechanism, which is why static_argnums is preferred.
To understand more subtleties having to do with tracers vs. regular values, and concrete vs. abstract values, you may want to read Different kinds of JAX values.
In the process of transforming functions, JAX replaces some function arguments with special tracer values.
You could see this if you use a print statement:
def func(x): print(x) return np.cos(x) res = jax.jit(func)(0.)
The above code does return the correct value 1. but it also prints
Traced<ShapedArray(float32[])> for the value of x. Normally, JAX
handles these tracer values internally in a transparent way, e.g.,
in the numeric JAX primitives that are used to implement the
jax.numpy functions. This is why np.cos works in the example above.
More precisely, a tracer value is introduced for the argument of
a JAX-transformed function, except the arguments identified by special
parameters such as static_argnums for :func:`jax.jit` or
static_broadcasted_argnums for :func:`jax.pmap`. Typically, computations
that involve at least a tracer value will produce a tracer value. Besides tracer
values, there are regular Python values: values that are computed outside JAX
transformations, or arise from above-mentioned static arguments of certain JAX
transformations, or computed solely from other regular Python values.
These are the values that are used everywhere in absence of JAX transformations.
A tracer value carries an abstract value, e.g., ShapedArray with information
about the shape and dtype of an array. We will refer here to such tracers as
abstract tracers. Some tracers, e.g., those that are
introduced for arguments of autodiff transformations, carry ConcreteArray
abstract values that actually include the regular array data, and are used,
e.g., for resolving conditionals. We will refer here to such tracers
as concrete tracers. Tracer values computed from these concrete tracers,
perhaps in combination with regular values, result in concrete tracers.
A concrete value is either a regular value or a concrete tracer.
Most often values computed from tracer values are themselves tracer values.
There are very few exceptions, when a computation can be entirely done
using the abstract value carried by a tracer, in which case the result
can be a regular value. For example, getting the shape of a tracer
with ShapedArray abstract value. Another example, is when explicitly
casting a concrete tracer value to a regular type, e.g., int(x) or
x.astype(float).
Another such situation is for bool(x), which produces a Python bool when
concreteness makes it possible. That case is especially salient because
of how often it arises in control flow.
Here is how the transformations introduce abstract or concrete tracers:
- :func:`jax.jit`: introduces abstract tracers for all positional arguments except those denoted by
static_argnums, which remain regular values.- :func:`jax.pmap`: introduces abstract tracers for all positional arguments except those denoted by
static_broadcasted_argnums.- :func:`jax.vmap`, :func:`jax.make_jaxpr`, :func:`xla_computation`: introduce abstract tracers for all positional arguments.
- :func:`jax.jvp` and :func:`jax.grad` introduce concrete tracers for all positional arguments. An exception is when these transformations are within an outer transformation and the actual arguments are themselves abstract tracers; in that case, the tracers introduced by the autodiff transformations are also abstract tracers.
- All higher-order control-flow primitives (:func:`lax.cond`, :func:`lax.while_loop`, :func:`lax.fori_loop`, :func:`lax.scan`) when they process the functionals introduce abstract tracers, whether or not there is a JAX transformation in progress.
All of this is relevant when you have code that can operate only on regular Python values, such as code that has conditional control-flow based on data:
def divide(x, y): return x / y if y >= 1. else 0.
If we want to apply :func:`jax.jit`, we must ensure to specify static_argnums=1
to ensure y stays a regular value. This is due to the boolean expression
y >= 1., which requires concrete values (regular or tracers). The
same would happen if we write explicitly bool(y >= 1.), or int(y),
or float(y).
Interestingly, jax.grad(divide)(3., 2.), works because :func:`jax.grad`
uses concrete tracers, and resolves the conditional using the concrete
value of y.
If you define a function using where to avoid an undefined value, if you
are not careful you may obtain a NaN for reverse differentiation:
def my_log(x): return np.where(x > 0., np.log(x), 0.) my_log(0.) ==> 0. # Ok jax.grad(my_log)(0.) ==> NaN
A short explanation is that during grad computation the adjoint corresponding
to the undefined np.log(x) is a NaN and when it gets accumulated to the
adjoint of the np.where. The correct way to write such functions is to ensure
that there is a np.where inside the partially-defined function, to ensure
that the adjoint is always finite:
def safe_for_grad_log(x): return np.log(np.where(x > 0., x, 1.) safe_for_grad_log(0.) ==> 0. # Ok jax.grad(safe_for_grad_log)(0.) ==> 0. # Ok
The inner np.where may be needed in addition to the original one, e.g.:
def my_log_or_y(x, y): """Return log(x) if x > 0 or y""" return np.where(x > 0., np.log(np.where(x > 0., x, 1.), y)
Additional reading: