How does PyTorch handle broadcasting errors

1. Singleton Dimensions: If one tensor has a singleton dimension (size 1), it can be broadcasted to match the size of the corresponding dimension in the other tensor.
2. Matching Dimensions: Dimensions that are not singleton must match exactly.

If these conditions are not met, PyTorch will raise an error. For example, if you try to add two tensors where one has a shape that cannot be broadcasted to match the other, you will encounter a `RuntimeError` indicating that the sizes do not match at a non-singleton dimension.

Here's an example from the search results:

python
X = torch.tensor([[1,5,2,7],[8,2,5,3]])  # Shape: (2, 4)
Y = torch.tensor([[2,9],[11,4],[9,2],[22,7]])  # Shape: (4, 2)

# Attempting to add X and Y will raise an error because their shapes are not compatible for broadcasting.
print(X + Y)

This will result in a `RuntimeError` because the shapes `(2, 4)` and `(4, 2)` cannot be broadcasted for addition.

To resolve such errors, you need to ensure that the tensors are reshaped or broadcasted appropriately before performing operations. You can use methods like `unsqueeze` or `repeat` to add dimensions or repeat values to make tensors compatible for broadcasting.

For instance, if you want to perform an operation where the mean and variance need to be applied across different dimensions, you might need to reshape or unsqueeze these tensors to match the input shape:

python
input = torch.randint(1, 5, size=(2, 2, 3, 3)).float()
my_mean = torch.tensor([1.0, 2.0, 3.0])  # Assuming mean for each channel
my_var = torch.tensor([4.0, 5.0, 6.0])  # Assuming variance for each channel

# Reshape mean and variance to match input dimensions
my_mean = my_mean.unsqueeze(0).unsqueeze(1).unsqueeze(2).repeat(2, 2, 3, 1)
my_var = my_var.unsqueeze(0).unsqueeze(1).unsqueeze(2).repeat(2, 2, 3, 1)

# Now you can perform operations like normalization
normalized_input = (input - my_mean) / my_var