避免在Python中使用softplus函数溢出 [英] Avoid overflow with softplus function in python

问题描述

我正在尝试实现以下softplus功能:

I am trying to implement the following softplus function:

log(1 + exp(x))

我已经尝试使用math/numpy和float64作为数据类型，但是只要x太大(例如x = 1000)，结果就是inf.

I've tried it with math/numpy and float64 as data type, but whenever x gets too large (e.g. x = 1000) the result is inf.

您能协助我成功地大量处理此功能吗?

Can you assist me on how to successfully handle this function with large numbers?

推荐答案

有一种关系可以使用:

log(1+exp(x)) = log(1+exp(x)) - log(exp(x)) + x = log(1+exp(-x)) + x

因此，从数学上讲，安全的实施方式应该是:

So a safe implementation, as well as mathematically sound, would be:

log(1+exp(-abs(x))) + max(x,0)

这既适用于数学函数又适用于numpy函数(例如:np.log，np.exp，np.abs，np.maximum).

This works both for math and numpy functions (use e.g.: np.log, np.exp, np.abs, np.maximum).

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