In what manner does the lambda layer in TensorFlow Keras propagate gradients?

The lambda layer in TensorFlow Keras is a custom layer that allows you to define a simple Python function that will be applied to the input data during the forward pass. During the backward pass, the gradient of the loss with respect to the output of the lambda layer is computed and propagated to the input of the lambda layer.

More specifically, when you define a lambda layer in TensorFlow Keras, you can provide a function that maps the input tensor to the output tensor. This function can be any valid Python function that operates on tensors and returns a tensor. During the forward pass, the lambda layer simply applies this function to the input tensor and returns the output tensor.

During the backward pass, TensorFlow Keras computes the gradient of the loss with respect to the output tensor of the lambda layer. This gradient is then propagated back to the input tensor of the lambda layer using the chain rule of calculus. The exact details of how the gradient is computed depending on the specific function that you provide to the lambda layer.

Note that in some cases, the gradient of the lambda layer may not be well-defined or may be computationally difficult to compute. In these cases, you may need to use a different type of layer or define a custom layer with a more explicit gradient computation.