Introduction

These gradient APIs all answer the question "how do I compute derivatives," but they do it with different styles and levels of explicitness. The shortest way to think about them is this: tf.GradientTape is the modern, explicit TensorFlow approach, while implicit_gradients, gradients_function, and implicit_value_and_gradients came from older eager-style helper APIs that wrapped common gradient patterns.

tf.GradientTape: The Explicit Modern Tool

tf.GradientTape records operations and then lets you ask for gradients with respect to the variables or tensors you choose.

1import tensorflow as tf
2
3x = tf.Variable(3.0)
4
5with tf.GradientTape() as tape:
6    y = x * x + 2 * x
7
8grad = tape.gradient(y, x)
9print(grad.numpy())

This is explicit in two ways:

• you can see exactly what computation is being differentiated
• you choose exactly which sources to differentiate with respect to

That flexibility is why GradientTape became the standard API in TensorFlow 2.

gradients_function: Gradients With Respect to Explicit Arguments

The older gradients_function helper conceptually turns a Python function into another function that returns gradients with respect to the original function's explicit inputs.

Think of it as:

• you pass arguments in directly
• the gradient helper differentiates with respect to those arguments

That style is useful when the parameters you care about are regular function arguments rather than variables discovered automatically from a model or module.

In modern TensorFlow, you can express the same idea with GradientTape by watching the tensors explicitly and returning the gradient from a wrapper function.

implicit_gradients: Gradients With Respect to Captured Variables

implicit_gradients followed a different philosophy. Instead of telling TensorFlow "differentiate with respect to these explicit arguments," you wrote a function that closed over trainable variables, and the helper collected gradients with respect to those variables implicitly.

Conceptually, that means:

• your loss function reads model variables
• the helper finds those variables
• gradients are returned for the variables without listing them manually

That was convenient for eager training loops, but it was also less transparent. With GradientTape, you now usually write the variable list explicitly, which makes training code easier to inspect and debug.

implicit_value_and_gradients: Value Plus Implicit Gradients

implicit_value_and_gradients is similar to implicit_gradients, but it also returns the function value itself along with the gradients. That is useful when an optimizer step needs both:

• the scalar loss value
• the gradients of that loss

You can reproduce the same pattern directly with GradientTape.

1import tensorflow as tf
2
3w = tf.Variable(2.0)
4
5def loss_fn():
6    return (w - 5.0) ** 2
7
8with tf.GradientTape() as tape:
9    loss_value = loss_fn()
10
11grad = tape.gradient(loss_value, [w])
12print(loss_value.numpy(), grad[0].numpy())

This is the modern equivalent of "compute value and gradients in one go."

Why GradientTape Replaced the Older Style

The older helper functions were compact, but they hid too much:

• which variables were involved
• which tensors were being watched
• how nested or higher-order gradients were handled

GradientTape makes the differentiation boundary visible in ordinary TensorFlow code. That is a better fit for custom training loops, debugging, and mixed eager-graph workflows.

Which API Style to Prefer

For current TensorFlow code, prefer tf.GradientTape. It is the clearest and most future-proof mental model.

Use the older helper names mainly when:

• reading legacy eager-mode examples
• maintaining older TensorFlow code
• translating older tutorials into TensorFlow 2 style

The real conceptual distinction to remember is explicit versus implicit differentiation targets.

Common Pitfalls

The biggest pitfall is assuming all of these functions are different mathematical operations. They are mostly different interfaces around the same idea of automatic differentiation.

Another common mistake is confusing explicit arguments with implicitly captured variables. If you do not know which objects are being differentiated, training code becomes difficult to reason about.

Developers also trip over old documentation and examples that use helper APIs from earlier TensorFlow eager workflows. In modern TensorFlow, GradientTape is usually the right translation target.

Summary

• 'tf.GradientTape is the modern explicit API for automatic differentiation in TensorFlow.'
• 'gradients_function conceptually differentiates with respect to explicit function arguments.'
• 'implicit_gradients differentiates with respect to variables captured by the function.'
• 'implicit_value_and_gradients returns both the function value and its implicit gradients.'
• For new TensorFlow code, GradientTape is usually the clearest and safest choice.