# custom_vjp and nondiff_argnums update guide¶

mattjj@ Oct 14 2020

This doc assumes familiarity with jax.custom_vjp, as described in the Custom derivative rules for JAX-transformable Python functions notebook.

## What to update¶

After JAX PR #4008, the arguments passed into a custom_vjp function’s nondiff_argnums can’t be Tracers (or containers of Tracers), which basically means to allow for arbitrarily-transformable code nondiff_argnums shouldn’t be used for array-valued arguments. Instead, nondiff_argnums should be used only for non-array values, like Python callables or shape tuples or strings.

Wherever we used to use nondiff_argnums for array values, we should just pass those as regular arguments. In the bwd rule, we need to produce values for them, but we can just produce None values to indicate there’s no corresponding gradient value.

For example, here’s the old way to write clip_gradient, which won’t work when hi and/or lo are Tracers from some JAX transformation.

from functools import partial
import jax

@partial(jax.custom_vjp, nondiff_argnums=(0, 1))
return x  # identity function

return x, None  # no residual values to save

return (jnp.clip(g, lo, hi),)



Here’s the new, awesome way, which supports arbitrary transformations:

import jax

@jax.custom_vjp  # no nondiff_argnums!
return x  # identity function

return x, (lo, hi)  # save lo and hi values as residuals

lo, hi = res
return (None, None, jnp.clip(g, lo, hi))  # return None for lo and hi



If you use the old way instead of the new way, you’ll get a loud error in any case where something might go wrong (namely when there’s a Tracer passed into a nondiff_argnums argument).

Here’s a case where we actually need nondiff_argnums with custom_vjp:

from functools import partial
import jax

@partial(jax.custom_vjp, nondiff_argnums=(0,))
def skip_app(f, x):
return f(x)

def skip_app_fwd(f, x):
return skip_app(f, x), None

def skip_app_bwd(f, _, g):
return (g,)

skip_app.defvjp(skip_app_fwd, skip_app_bwd)


## Explanation¶

Passing Tracers into nondiff_argnums arguments was always buggy. While there were some cases that worked correctly, others would lead to complex and confusing error messages.

The essence of the bug was that nondiff_argnums was implemented in a way that acted very much like lexical closure. But lexical closure over Tracers wasn’t at the time intended to work with custom_jvp/custom_vjp. Implementing nondiff_argnums that way was a mistake!

PR #4008 fixes all lexical closure issues with custom_jvp and custom_vjp. Woohoo! That is, now custom_jvp and custom_vjp functions and rules can close over Tracers to our hearts’ content. For all non-autodiff transformations, things will Just Work. For autodiff transformations, we’ll get a clear error message about why we can’t differentiate with respect to values over which a custom_jvp or custom_vjp closes:

Detected differentiation of a custom_jvp function with respect to a closed-over value. That isn’t supported because the custom JVP rule only specifies how to differentiate the custom_jvp function with respect to explicit input parameters.

Try passing the closed-over value into the custom_jvp function as an argument, and adapting the custom_jvp rule.

In tightening up and robustifying custom_jvp and custom_vjp in this way, we found that allowing custom_vjp to accept Tracers in its nondiff_argnums would take a significant amount of bookkeeping: we’d need to rewrite the user’s fwd function to return the values as residuals, and rewrite the user’s bwd function to accept them as normal residuals (rather than accepting them as special leading arguments, as happens with nondiff_argnums). This seems maybe manageable, until you think through how we have to handle arbitrary pytrees! Moreover, that complexity isn’t necessary: if user code treats array-like non-differentiable arguments just like regular arguments and residuals, everything already works. (Before #4039 JAX might’ve complained about involving integer-valued inputs and outputs in autodiff, but after #4039 those will just work!)

Unlike custom_vjp, it was easy to make custom_jvp work with nondiff_argnums arguments that were Tracers. So these updates only need to happen with custom_vjp.