jax.checkpoint

jax.checkpoint(fun, concrete=False, prevent_cse=True, policy=None)

Make fun recompute internal linearization points when differentiated.

The jax.checkpoint() decorator, aliased to jax.remat, provides a way to trade off computation time and memory cost in the context of automatic differentiation, especially with reverse-mode autodiff like jax.grad() and jax.vjp() but also with jax.linearize().

When differentiating a function in reverse-mode, by default all the linearization points (e.g. inputs to elementwise nonlinear primitive operations) are stored when evaluating the forward pass so that they can be reused on the backward pass. This evaluation strategy can lead to a high memory cost, or even to poor performance on hardware accelerators where memory access is much more expensive than FLOPs.

An alternative evaluation strategy is for some of the linearization points to be recomputed (i.e. rematerialized) rather than stored. This approach can reduce memory usage at the cost of increased computation.

This function decorator produces a new version of fun which follows the rematerialization strategy rather than the default store-everything strategy. That is, it returns a new version of fun which, when differentiated, doesn’t store any of its intermediate linearization points. Instead, these linearization points are recomputed from the function’s saved inputs.

See the examples below.

Parameters

• fun (Callable) – Function for which the autodiff evaluation strategy is to be changed from the default of storing all intermediate linearization points to recomputing them. Its arguments and return value should be arrays, scalars, or (nested) standard Python containers (tuple/list/dict) thereof.

• concrete (bool) – Optional, boolean indicating whether fun may involve value-dependent Python control flow (default False). Support for such control flow is optional, and disabled by default, because in some edge-case compositions with jax.jit() it can lead to some extra computation.

• prevent_cse (bool) – Optional, boolean indicating whether to prevent common subexpression elimination (CSE) optimizations in the HLO generated from differentiation. This CSE prevention has costs because it can foil other optimizations, and because it can incur high overheads on some backends, especially GPU. The default is True because otherwise, under a jit or pmap, CSE can defeat the purpose of this decorator. But in some settings, like when used inside a scan, this CSE prevention mechanism is unnecessary, in which case prevent_cse can be set to False.

• policy (Optional[Callable[…, bool]]) – This is an experimental feature and the API is likely to change. Optional callable, one of the attributes of jax.checkpoint_policies, which takes as input a type-level specification of a first-order primitive application and returns a boolean indicating whether the corresponding output value(s) can be saved as a residual (or, if not, instead must be recomputed in the (co)tangent computation).

Return type

Callable

Returns

A function (callable) with the same input/output behavior as fun but which, when differentiated using e.g. jax.grad(), jax.vjp(), or jax.linearize(), recomputes rather than stores intermediate linearization points, thus potentially saving memory at the cost of extra computation.

Here is a simple example:

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

>>> @jax.checkpoint
... def g(x):
...   y = jnp.sin(x)
...   z = jnp.sin(y)
...   return z
...
>>> jax.value_and_grad(g)(2.0)
(DeviceArray(0.78907233, dtype=float32, weak_type=True), DeviceArray(-0.2556391, dtype=float32, weak_type=True))

Here, the same value is produced whether or not the jax.checkpoint() decorator is present. When the decorator is not present, the values jnp.cos(2.0) and jnp.cos(jnp.sin(2.0)) are computed on the forward pass and are stored for use in the backward pass, because they are needed on the backward pass and depend only on the primal inputs. When using jax.checkpoint(), the forward pass will compute only the primal outputs and only the primal inputs (2.0) will be stored for the backward pass. At that time, the value jnp.sin(2.0) is recomputed, along with the values jnp.cos(2.0) and jnp.cos(jnp.sin(2.0)).

While jax.checkpoint controls what values are stored from the forward-pass to be used on the backward pass, the total amount of memory required to evaluate a function or its VJP depends on many additional internal details of that function. Those details include which numerical primitives are used, how they’re composed, where jit and control flow primitives like scan are used, and other factors.

The jax.checkpoint() decorator can be applied recursively to express sophisticated autodiff rematerialization strategies. For example:

>>> def recursive_checkpoint(funs):
...   if len(funs) == 1:
...     return funs[0]
...   elif len(funs) == 2:
...     f1, f2 = funs
...     return lambda x: f1(f2(x))
...   else:
...     f1 = recursive_checkpoint(funs[:len(funs)//2])
...     f2 = recursive_checkpoint(funs[len(funs)//2:])
...     return lambda x: f1(jax.checkpoint(f2)(x))
...