使用 vmap 时，Jax 不支持不可散列的静态参数

这与这个问题 https://stackoverflow.com/questions/65612989/jax-cannot-find-the-static-argnums。经过一些工作，我设法将其更改为最后一个错误。代码现在看起来像这样。

import jax.numpy as jnp
from jax import grad, jit, value_and_grad
from jax import vmap, pmap
from jax import random
import jax
from jax import lax
from jax import custom_jvp


def p_tau(z, tau, alpha=1.5):
    return jnp.clip((alpha - 1) * z - tau, 0) ** (1 / (alpha - 1))


def get_tau(tau, tau_max, tau_min, z_value):
    return lax.cond(z_value < 1,
                    lambda _: (tau, tau_min),
                    lambda _: (tau_max, tau),
                    operand=None
                    )


def body(kwargs, x):
    tau_min = kwargs['tau_min']
    tau_max = kwargs['tau_max']
    z = kwargs['z']
    alpha = kwargs['alpha']

    tau = (tau_min + tau_max) / 2
    z_value = p_tau(z, tau, alpha).sum()
    taus = get_tau(tau, tau_max, tau_min, z_value)
    tau_max, tau_min = taus[0], taus[1]
    return {'tau_min': tau_min, 'tau_max': tau_max, 'z': z, 'alpha': alpha}, None

@jax.partial(jax.jit, static_argnums=(2,))
def map_row(z_input, alpha, T):
    z = (alpha - 1) * z_input

    tau_min, tau_max = jnp.min(z) - 1, jnp.max(z) - z.shape[0] ** (1 - alpha)
    result, _ = lax.scan(body, {'tau_min': tau_min, 'tau_max': tau_max, 'z': z, 'alpha': alpha}, xs=None,
                         length=T)
    tau = (result['tau_max'] + result['tau_min']) / 2
    result = p_tau(z, tau, alpha)
    return result / result.sum()

@jax.partial(jax.jit, static_argnums=(1,3,))
def _entmax(input, axis=-1, alpha=1.5, T=20):
    result = vmap(jax.partial(map_row, alpha, T), axis)(input)
    return result

@jax.partial(custom_jvp, nondiff_argnums=(1, 2, 3,))
def entmax(input, axis=-1, alpha=1.5, T=10):
    return _entmax(input, axis, alpha, T)

@jax.partial(jax.jit, static_argnums=(0,2,))    
def _entmax_jvp_impl(axis, alpha, T, primals, tangents):
    input = primals[0]
    Y = entmax(input, axis, alpha, T)
    gppr = Y  ** (2 - alpha)
    grad_output = tangents[0]
    dX = grad_output * gppr
    q = dX.sum(axis=axis) / gppr.sum(axis=axis)
    q = jnp.expand_dims(q, axis=axis)
    dX -= q * gppr
    return Y, dX


@entmax.defjvp
def entmax_jvp(axis, alpha, T, primals, tangents):
    return _entmax_jvp_impl(axis, alpha, T, primals, tangents)

import numpy as np
input = jnp.array(np.random.randn(64, 10)).block_until_ready()
weight = jnp.array(np.random.randn(64, 10)).block_until_ready()

def toy(input, weight):
    return (weight*entmax(input, 0, 1.5, 20)).sum()

jax.jit(value_and_grad(toy))(input, weight)

这导致（我希望的）是最终的错误，即

Non-hashable static arguments are not supported, as this can lead to unexpected cache-misses. Static argument (index 2) of type <class 'jax.interpreters.batching.BatchTracer'> for function map_row is non-hashable.

这很奇怪，因为我想我已经标记了每个地方axis看起来是静态的，但它仍然告诉我它是被追踪的。

当你写一个partial带有位置参数的函数，这些参数首先被传递。所以这：

jax.partial(map_row, alpha, T)

本质上等价于：

lambda z_input: map_row(alpha, T, z_input)

注意参数的顺序不正确——这就是导致错误的原因：你正在传递z_input，一个不可散列的跟踪器，指向一个预计是静态的参数。

您可以通过替换来修复此问题partial上面的声明：

lambda z: map_row(z, alpha, T)

然后你的代码就会正确运行。