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我试图区分一个函数，该函数在给定偏移平均值的情况下近似包含在 2 个限制（截断的高斯）内的高斯分数。 jnp.grad不允许我区分添加布尔过滤器（注释行），所以我不得不即兴使用 sigmoid。

但是，现在当截断边界很高时梯度总是 nan 我不明白为什么。

在下面的示例中，我正在计算具有 0 均值和 std=1 的高斯梯度，然后我用x.

如果我减小边界，则函数的行为符合预期。但这不是解决方案。当边界很高时，始终belows 变为 1。但如果是这种情况并且x对下面没有影响，那么它对梯度的贡献应该是0而不是nan。但如果我返回belows[0][0]而不是返回jnp.mean(filt, axis=0)，我仍然得到nan。

有任何想法吗？提前致谢（github上也有一个问题）

import os

from tqdm import tqdm

os.environ["XLA_FLAGS"] = '--xla_force_host_platform_device_count=4' # Use 8 CPU devices
import numpy as np
from jax.config import config
config.update("jax_enable_x64", True)
import jax
import jax.numpy as jnp
from jax import vmap

from functools import reduce

def sigmoid(x, scale=100):
    return 1 / (1 + jnp.exp(-x*scale))

def above_lower(x, l, scale=100):
    return sigmoid(x - l, scale)

def below_upper(x, u, scale=100):
    return 1 - sigmoid(x - u, scale)

def combine_soft_filters(a):
    return jnp.prod(jnp.stack(a), axis=0)


def fraction_not_truncated(mu, v, limits, stdnorm_samples):
    L = jnp.linalg.cholesky(v)
    y = vmap(lambda x: jnp.dot(L, x))(stdnorm_samples) + mu
    # filt = reduce(jnp.logical_and, [(y[..., i] > l) & (y[..., i] < u) for i, (l, u) in enumerate(limits)])
    aboves = [above_lower(y[..., i], l) for i, (l, u) in enumerate(limits)]
    belows = [below_upper(y[..., i], u) for i, (l, u) in enumerate(limits)]
    filt = combine_soft_filters(aboves+belows)
    return jnp.mean(filt, axis=0)

limits = np.array([
        [0.,1000],
])

stdnorm_samples = np.random.multivariate_normal([0], np.eye(1), size=1000)

def func(x):
    return fraction_not_truncated(jnp.zeros(1)+x, jnp.eye(1), limits, stdnorm_samples)

_x = np.linspace(-2, 2, 500)
gradfunc = jax.grad(func)
vals = [func(x) for x in tqdm(_x)]
grads = [gradfunc(x) for x in tqdm(_x)]
print(vals)
print(grads)
import matplotlib.pyplot as plt
plt.plot(_x, np.asarray(vals))
plt.ylabel('f(x)')
plt.twinx()
plt.plot(_x, np.asarray(grads), c='r')
plt.ylabel("f(x)'")
plt.title('Fraction not truncated')
plt.axhline(0, color='k', alpha=0.2)
plt.xlabel('shift')
plt.tight_layout()
plt.show()

在此处输入图像描述

[DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64), DeviceArray(1., dtype=float64)]
[DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64), DeviceArray(nan, dtype=float64)]
4

1 回答 1

2

问题是您的sigmoid函数的实现方式使得自动确定的梯度对于较大的负值不稳定x：

import jax.numpy as jnp
import jax

def sigmoid(x, scale=100):
    return 1 / (1 + jnp.exp(-x*scale))

print(jax.grad(sigmoid)(-1000.0))
# nan

jax.make_jaxpr您可以使用该函数内省自动确定的渐变产生的操作来了解为什么会发生这种情况（评论是我的注释）：

>>> jax.make_jaxpr(jax.grad(sigmoid))(-1000.0)
{ lambda  ; a.                    # a = -1000
  let b = neg a                   # b = 1000
      c = mul b 100.0             # c = 100,000
      d = exp c                   # d = inf
      e = add d 1.0
      _ = div 1.0 e
      f = integer_pow[ y=-2 ] e   # f = 0
      g = mul 1.0 f               # g = 0
      h = mul g 1.0               # h = 0
      i = neg h                   # i = 0
      j = mul i d                 # j = 0 * inf = NaN
      k = mul j 100.0             # k = NaN
      l = neg k                   # l = NaN
  in (l,) }                       # return NaN

这是 64 位浮点运算失败的情况之一：它没有处理exp(100000).

所以，你可以做什么？一个重量级的选择是使用自定义衍生规则来告诉 autodiff 如何以sigmoid更稳定的方式处理函数。sigmoid但是，在这种情况下，一个更简单的选择是根据在 autodiff 转换下表现更好的东西来重新表达函数。一种选择是：

def sigmoid(x, scale=100):
    return 0.5 * (jnp.tanh(x * scale / 2) + 1)

在您的脚本中使用此版本可解决此问题。

于 2021-07-07T23:21:04.817 回答