# Ahead-of-time lowering and compilation#

JAX offers several transformations, such as jax.jit and jax.pmap, returning a function that is compiled and runs on accelerators or the CPU. As the JIT acronym indicates, all compilation happens just-in-time for execution.

Some situations call for ahead-of-time (AOT) compilation instead. When you want to fully compile prior to execution time, or you want control over when different parts of the compilation process take place, JAX has some options for you.

First, let’s review the stages of compilation. Suppose that f is a function/callable output by jax.jit(), say f = jax.jit(F) for some input callable F. When it is invoked with arguments, say f(x, y) where x and y are arrays, JAX does the following in order:

1. Stage out a specialized version of the original Python callable F to an internal representation. The specialization reflects a restriction of F to input types inferred from properties of the arguments x and y (usually their shape and element type).

2. Lower this specialized, staged-out computation to the XLA compiler’s input language, StableHLO.

3. Compile the lowered HLO program to produce an optimized executable for the target device (CPU, GPU, or TPU).

4. Execute the compiled executable with the arrays x and y as arguments.

JAX’s AOT API gives you direct control over steps #2, #3, and #4 (but not #1), plus some other features along the way. An example:

>>> import jax
>>> import jax.numpy as jnp
>>> import numpy as np

>>> def f(x, y): return 2 * x + y
>>> x, y = 3, 4

>>> lowered = jax.jit(f).lower(x, y)

>>> # Print lowered HLO
>>> print(lowered.as_text())
module @jit_f.0 {
func.func public @main(%arg0: tensor<i32>, %arg1: tensor<i32>) -> tensor<i32> {
%0 = stablehlo.constant dense<2> : tensor<i32>
%1 = stablehlo.multiply %0, %arg0 : tensor<i32>
%2 = stablehlo.add %1, %arg1 : tensor<i32>
return %2 : tensor<i32>
}
}

>>> compiled = lowered.compile()

>>> # Query for cost analysis, print FLOP estimate
>>> compiled.cost_analysis()[0]['flops']
2.0

>>> # Execute the compiled function!
>>> compiled(x, y)
DeviceArray(10, dtype=int32)


See the jax.stages documentation for more details on what functionality the lowering and compiled functions provide.

In place of jax.jit above, you can also lower(...) the result of jax.pmap(), as well as pjit and xmap (from jax.experimental.pjit and jax.experimental.maps respectively). In each case, you can compile() the result similarly.

All optional arguments to jit—such as static_argnums—are respected in the corresponding lowering, compilation, and execution. Again the same goes for pmap, pjit, and xmap.

In the example above, we can replace the arguments to lower with any objects that have shape and dtype attributes:

>>> i32_scalar = jax.ShapeDtypeStruct((), jnp.dtype('int32'))
>>> jax.jit(f).lower(i32_scalar, i32_scalar).compile()(x, y)
DeviceArray(10, dtype=int32)


More generally, lower only needs its arguments to structurally supply what JAX must know for specialization and lowering. For typical array arguments like the ones above, this means shape and dtype fields. For static arguments, by contrast, JAX needs actual array values (more on this below).

Invoking an AOT-compiled function with arguments that are incompatible with its lowering raises an error:

>>> x_1d = y_1d = jnp.arange(3)
>>> jax.jit(f)(i32_scalar, i32_scalar).compile(x_1d, y_1d)
...
TypeError: Computation compiled for input types:
ShapedArray(int32[]), ShapedArray(int32[])
called with:
ShapedArray(int32[3]), ShapedArray(int32[3])

>>> x_f = y_f = 72.0
>>> jax.jit(f)(i32_scalar, i32_scalar).compile(x_f, y_f)
...
TypeError: Computation compiled for input types:
ShapedArray(int32[]), ShapedArray(int32[])
called with:
ShapedArray(float32[]), ShapedArray(float32[])


Relatedly, AOT-compiled functions cannot be transformed by JAX’s just-in-time transformations such as jax.jit, jax.grad(), and jax.vmap().

## Lowering with static arguments#

Lowering with static arguments underscores the interaction between options passed to jax.jit, the arguments passed to lower, and the arguments needed to invoke the resulting compiled function. Continuing with our example above:

>>> lowered_with_x = jax.jit(f, static_argnums=0).lower(7, 8)

>>> # Lowered HLO, specialized to the *value* of the first argument (7)
>>> print(lowered_with_x.as_text())
module @jit_f.1 {
func.func public @main(%arg0: tensor<i32>) -> tensor<i32> {
%0 = stablehlo.constant dense<14> : tensor<i32>
%1 = stablehlo.add %0, %arg0 : tensor<i32>
return %1 : tensor<i32>
}
}
>>> lowered_with_x.compile()(5)
DeviceArray(19, dtype=int32)


Note that lower here takes two arguments as usual, but the subsequent compiled function accepts only the remaining non-static second argument. The static first argument (value 7) is taken as a constant at lowering time and built into the lowered computation, where it is possibly folded in with other constants. In this case, its multiplication by 2 is simplified, resulting in the constant 14.

Although the second argument to lower above can be replaced by a hollow shape/dtype structure, it is necessary that the static first argument be a concrete value. Otherwise, lowering would err:

>>> jax.jit(f, static_argnums=0).lower(i32_scalar, i32_scalar)
TypeError: unsupported operand type(s) for *: 'int' and 'ShapeDtypeStruct'

>>> jax.jit(f, static_argnums=0).lower(10, i32_scalar).compile()(5)
DeviceArray(25, dtype=int32)


## AOT-compiled functions cannot be transformed#

Compiled functions are specialized to a particular set of argument “types,” such as arrays with a specific shape and element type in our running example. From JAX’s internal point of view, transformations such as jax.vmap() alter the type signature of functions in a way that invalidates the compiled-for type signature. As a policy, JAX simply disallows compiled functions to be involved in transformations. Example:

>>> def g(x):
...   assert x.shape == (3, 2)
...   return x @ jnp.ones(2)

>>> def make_z(*shape):
...   return jnp.arange(np.prod(shape)).reshape(shape)

>>> z, zs = make_z(3, 2), make_z(4, 3, 2)

>>> g_jit = jax.jit(g)
>>> g_aot = jax.jit(g).lower(z).compile()

>>> jax.vmap(g_jit)(zs)
DeviceArray([[ 1.,  5.,  9.],
[13., 17., 21.],
[25., 29., 33.],
[37., 41., 45.]], dtype=float32)

>>> jax.vmap(g_aot)(zs)
TypeError: Cannot apply JAX transformations to a function lowered and compiled for a particular signature. Detected argument of Tracer type <class 'jax.interpreters.batching.BatchTracer'>.


A similar error is raised when g_aot is involved in autodiff (e.g. jax.grad()). For consistency, transformation by jax.jit is disallowed as well, even though jit does not meaningfully modify its argument’s type signature.

## Debug information and analyses, when available#

In addition to the primary AOT functionality (separate and explicit lowering, compilation, and execution), JAX’s various AOT stages also offer some additional features to help with debugging and gathering compiler feedback.

For instance, as the initial example above shows, lowered functions often offer a text representation. Compiled functions do the same, and also offer cost and memory analyses from the compiler. All of these are provided via methods on the jax.stages.Lowered and jax.stages.Compiled objects (e.g., lowered.as_text() and compiled.cost_analysis() above).

These methods are meant as an aid for manual inspection and debugging, not as a reliably programmable API. Their availability and output vary by compiler, platform, and runtime. This makes for two important caveats:

1. If some functionality is unavailable on JAX’s current backend, then the method for it returns something trivial (and False-like). For example, if the compiler underlying JAX does not provide a cost analysis, then compiled.cost_analysis() will be None.

2. If some functionality is available, there are still very limited guarantees on what the corresponding method provides. The return value is not required to be consistent—in type, structure, or value—across JAX configurations, backends/platforms, versions, or even invocations of the method. JAX cannot guarantee that the output of compiled.cost_analysis() on one day will remain the same on the following day.

When in doubt, see the package API documentation for jax.stages.

## Inspecting staged-out computations#

Stage #1 in the list at the top of this note mentions specialization and staging, prior to lowering. JAX’s internal notion of a function specialized to the types of its arguments is not always a reified data structure in memory. To explicitly construct a view of JAX’s specialization of a function in the internal Jaxpr intermediate language, see jax.make_jaxpr().