Incorrect Jacobian of `jax.scipy.special.logsumexp` when `b` contains a `0`

[Adrien-Kahn]

Description

The gradient of jax.scipy.special.logsumexp along b is wrong when b contains a 0. In the following example, the gradient of $f(x_1, x_2) = \log(x_1 + x_2)$ should be:

\nabla_x f(x) = \left( \frac{1}{x_1 + x_2}, \frac{1}{x_1 + x_2} \right)

but JAX outputs that the gradient at (1,0) is (1,0) when it should be (1,1):

import jax
import jax.numpy as jnp

fun = lambda x: jax.scipy.special.logsumexp(jnp.zeros(2), axis=0, b=x)
a = jnp.array([1, 0], dtype=float)

jax.jacfwd(fun)(a)

output:

Array([1., 0.], dtype=float32)

There is only a problem for an exact 0: the gradient taken at (1,1e-30) outputs the correct value of (1,1):

a = jnp.array([1, 1e-30], dtype=float)
jax.jacfwd(fun)(a)

output:

Array([1., 1.], dtype=float32)

Furthermore, if the logsumexp is implemented manually, the gradient at (1, 0) is also correct:

fun_2 = lambda x: jnp.log(jnp.sum(x * jnp.exp(jnp.zeros(2))))
a = jnp.array([1, 0], dtype=float)
jax.jacfwd(fun_2)(a)

output:

Array([1., 1.], dtype=float32)

cc @PhilipVinc

System info (python version, jaxlib version, accelerator, etc.)

jax:    0.4.30
jaxlib: 0.4.30
numpy:  1.24.4
python: 3.11.6 | packaged by conda-forge | (main, Oct  3 2023, 10:37:07) [Clang 15.0.7 ]
jax.devices (1 total, 1 local): [CpuDevice(id=0)]
process_count: 1
platform: uname_result(system='Darwin', node='mba-10836208', release='23.4.0', version='Darwin Kernel Version 23.4.0: Fri Mar 15 00:19:22 PDT 2024; root:xnu-10063.101.17~1/RELEASE_ARM64_T8112', machine='arm64')

[jakevdp]

Hi - thanks for the clear report! Indeed this looks like a bug in the logsumexp implementation; I think the root cause is this line: https://github.com/google/jax/blob/46103f6ff3f4cbac2881fece37d145bba7d3e60d/jax/_src/ops/special.py#L74

It removes the dependence of the output on b for b = 0. I suspect the best way of fixing this will be to add a custom JVP rule.

[NDOWAH]

Hello @superbobry, though a beginner, i would like to give this a look to make my first contribution. Any documentation or idea to get me started would be appreciated. I have a clear understanding of how Jacobian is being computed.