Consider the scalar-valued sum function $$y = \sum x_i$$, which computes the sum of the elements of a vector $$\mathbf{x}$$. The gradient of this function with respect to $$\mathbf{x}$$ is a vector of ones. When calculating this gradient in deep learning frameworks, it is often necessary to first reset or clear the gradient buffer to prevent the new gradient from accumulating with any previously stored gradients.

Example: Gradient of the Sum Function $$y = \sum x_i$$

In deep learning frameworks, the behavior of the gradient buffer after a backward pass varies. PyTorch accumulates newly calculated gradients by adding them to the existing values stored in the buffer. This accumulation is advantageous when optimizing the sum of multiple objective functions, but it requires the programmer to explicitly reset the gradients to zero before computing gradients for a new iteration. In contrast, frameworks like MXNet and TensorFlow automatically reset the gradient buffer whenever a new gradient is recorded, overwriting the previously stored values.

Claude

Before computing the gradient of a function with respect to its parameters, memory must be allocated to store the resulting gradient vector. In deep learning frameworks, this is done to avoid allocating new memory for every derivative calculation, as gradients are computed successively with respect to the same parameters numerous times, which could exhaust available memory.

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