Is there a way to only compute gradients of single member of the pytree?

[alonfnt]

Hi, maybe this is a very basic question, but I have a pytree where I'd like to calculate the gradient with respect to only some members and not the entire pytree

A minimal silly example:

import jax
from collections import namedtuple

PyTree = namedtuple('PyTree', ['a', 'b', 'c'])
x = PyTree(a=jax.numpy.arange(5.0), b=jax.numpy.ones(4), c=10.0)

f = lambda x: jax.numpy.sum(x.a * x.c)
g = jax.grad(f)

# This will yield the gradients of all 'a', 'b' and 'c'
grads = g(x)

# Returns a PyTree with gradients, but I only care about grads.a and would like to not compute the rest (grad.b and grad.c)
print(grads)
# PyTree(a=Array([10., 10., 10., 10., 10.], dtype=float32), b=Array([0., 0., 0., 0.], dtype=float32), c=Array(10., dtype=float32, weak_type=True))

Is there a trivial way to specify the element of the pytree for which to compute the gradients, similar to using the argnums keyword when having multiple inputs?

I understand that some wrapper where x.a is the first input and x is the second would work, but would that be efficient? And if, instead, I need the grad for more members, do I need to split them all separately as inputs?

[jakevdp]

No, there's no syntax to compute gradients with respect to a single element in a pytree, though it's been discussed (see #3875, #10614 and related discussions).

The easiest way to proceed is typically to take the gradient with respect to the whole pytree, then access the particular element you're interested and continue your computation. If this is wrapped in jit, the compiler will automatically elide any unnecessary computations. You can confirm this by using Ahead of time compilation to print the compiled HLO.

For example:

@jax.jit
def func(x):
  return g(x).a

print(func.lower(x).compile().as_text())

HloModule jit_func, entry_computation_layout={(f32[])->f32[5]{0}}, allow_spmd_sharding_propagation_to_output={true}

ENTRY %main.3 (Arg_0.1: f32[]) -> f32[5] {
  %Arg_0.1 = f32[] parameter(0), sharding={replicated}
  ROOT %broadcast.2 = f32[5]{0} broadcast(f32[] %Arg_0.1), dimensions={}, metadata={op_name="jit(func)/jit(main)/mul" source_file="<ipython-input-9-1e1fa7917511>" source_line=7}
}

When compared to the version that manually extracts the desired gradient, you'll see that the compiled HLO is essentially equivalent, because the compiler recognizes the unused parts of the computation and removes them from the compiled computation graph:

def f_wrapper(a, c):
  return jax.numpy.sum(a * c)

g_wrapper = jax.grad(f_wrapper, argnums=0)

@jax.jit
def func2(x):
  return g_wrapper(x.a, x.c)

print(func2.lower(x).compile().as_text())

HloModule jit_func2, entry_computation_layout={(f32[])->f32[5]{0}}, allow_spmd_sharding_propagation_to_output={true}

ENTRY %main.3 (Arg_0.1: f32[]) -> f32[5] {
  %Arg_0.1 = f32[] parameter(0), sharding={replicated}
  ROOT %broadcast.2 = f32[5]{0} broadcast(f32[] %Arg_0.1), dimensions={}, metadata={op_name="jit(func2)/jit(main)/mul" source_file="<ipython-input-10-ae40072ebf3a>" source_line=2}
}

[alonfnt]

I see. It relies on g(x) being jitable though, which is a bit annoying sometimes -- but understandable.
Thanks for the answer :)

[jakevdp]

If you can't use jit, then it's typically not too hard to write a wrapper function to pass the values individually.

But I agree it would be better to have a more granular way to specify autodiff arguments – I think we've gotten stuck on figuring out a natural API for this case; see the discussions in the issues I linked to.