In the realm of deep learning and PyTorch, understanding when and why to use `torch.sum()` before calling the `.backward()` function is crucial for efficient backpropagation and gradient computation. This article dives deep into the technical reasons, examples, and implications of this approach.

Understanding Backward Propagation

In neural networks, backpropagation is the primary mechanism for training models, allowing the gradients of loss with respect to each model parameter to be computed. The compute graph, built during the forward pass, is traversed in reverse to determine these gradients when `.backward()` is called.

The Role of Scalar `Loss` Functions

By design, the `.backward()` function computes the gradients of a scalar value. This scalar value typically represents the loss, indicating how far off the current predictions of your neural network are from the actual outputs. The gradients can then be used to adjust weights and biases within the model to minimize this loss.

Why Use `torch.sum()`?

Essentially, `torch.sum()` is employed to ensure that the output provided to `.backward()` is a scalar. However, the reasons are both practical and mathematical, as detailed below:

1. Ensuring Scalar Outputs:
   • In many cases, the direct output of the model after the forward pass isn't a scalar but a tensor. The `torch.sum()` function aggregates a tensor into a single scalar value, making it suitable for `.backward()`.
2. Handling Batched Inputs:
   • Deep learning models often deal with batches of data. After computing the batch-wise loss (e.g., per sample), `torch.sum()` aggregates these losses into a single value. This is important for models that compute per-sample loss to ensure a unified gradient computation.
3. Facilitating Gradient Flow:
   • Using `torch.sum()` harmonizes the gradient computation, as it aggregates errors from all outputs in the network, simplifying how the error signals are propagated backwards.
4. Variance Adjustments:
   • Aggregating the losses over a batch can also stabilize variance issues that might occur from noisy samples within batches, promoting smoother convergence during training.

Example Usage

Here's a practical example demonstrating the use of `torch.sum()` alongside `.backward()`:

• Summing across all dimensions (`torch.sum(tensor)`) results in a scalar.
• Summing across specific dimensions can preserve certain dimensional features, which might be advantageous based on the model objective.