关于tf.contrib.eager.custom_gradient中tape及dy含义的技术咨询

Hey there! Let's unpack your questions about custom gradients in TensorFlow Eager Execution—they’re super powerful but definitely take a minute to wrap your head around.

1. What’s the role of dy in the gradient function? #

Let’s start with the basics of automatic differentiation and the chain rule. When you define a custom gradient, dy represents the upstream gradient—this is the gradient of your final loss (or whatever value you’re optimizing) with respect to the output of your logexp function.

Think of it like this: your logexp function is just one step in a larger computation graph. Suppose you have something like:

x = tf.constant(2.0)
output = logexp(x)
loss = tf.square(output)

When you compute gradients of loss with respect to x, TensorFlow first calculates d(loss)/d(output) (which is 2*output in this case)—that’s exactly what dy is. Then, to get d(loss)/d(x), you use the chain rule: multiply dy by d(output)/d(x) (the local gradient of your function’s output with respect to its input).

In your example:

• The forward pass returns tf.log(1 + e) where e = tf.exp(x)
• The local gradient d(output)/d(x) is e/(1+e) (since derivative of log(1+e^x) is e^x/(1+e^x))
• Notice that 1 - 1/(1+e) simplifies to e/(1+e)—so your grad function is just applying the chain rule by multiplying dy (upstream gradient) with this local gradient.

If you were calling logexp directly (no extra loss computation), dy would be 1.0 (since the gradient of the output with respect to itself is 1), and you’d get the standard derivative of log(1+e^x) as your result.

2. How does the Gradient Tape work with custom_gradient? #

In Eager Execution, tf.GradientTape works by recording all differentiable operations you perform while the tape is active. Normally, when you compute gradients, it retraces these operations in reverse order to calculate derivatives using built-in rules for each TensorFlow op (like tf.exp, tf.log).

The @tfe.custom_gradient decorator changes this behavior:

• During the forward pass, the tape doesn’t record the individual operations inside your logexp function (like tf.exp or tf.log). Instead, it registers your function as a single "custom node" in the tape’s record.
• When you call tape.gradient() to compute backwards passes, instead of traversing the internal ops of logexp, the tape directly invokes the grad function you defined. It passes dy (the upstream gradient we talked about) to this function, and uses the returned value as the gradient of the input x.

Looking at the underlying implementation, here’s roughly what happens:

• The decorator wraps your function to create a special TensorFlow op that has your custom gradient logic attached.
• When the tape encounters this op during forward pass, it stores a reference to your grad function alongside the op’s inputs and outputs.
• During backpropagation, the tape retrieves this grad function, feeds it the upstream gradient dy, and uses the result to continue the reverse chain of gradient calculations.

This is why custom gradients are useful: they let you override the default gradient computation (maybe for numerical stability, like in your logexp example—computing 1 - 1/(1+e) is more stable than e/(1+e) when x is very large!) without changing the forward pass logic.

内容的提问来源于stack exchange，提问作者lifang