Although it would be hard for me to precisely review the accuracy of these new statements about batchnorm, what I can say here is that this additional information is not necessarily needed in the context of describing the behavior of this operation during model inference.

For instance, the paragraph starts with "Batch normalization modifies the mean and variance...". This isn't true for the inference pass. The mean and variance values are simply given as inputs to the inference pass of batchnorm. They were previously computed during the training pass, but WebNN only concerns itself with inference operation and not training, therefore the behavior of how these values came to be maybe irrelevant. The only reason it is even mentioned in the original text that means and variance values are previously computed is only to draw a distinction with the other similar operation instanceNormalization where both value vectors are computed on the fly and only within a single batch during the inference pass.

My recommendation is to keep the original text as-is.

axis is an unsigned long type. I believe that's what we agreed on, which is consistent with other operations with the same param. Why do we change it here to long?

Also, please keep the existing description of the axis param. The new description doesn't read well to me. For instance, the index is to the "feature count" dimension of the input shape, and not the "feature" dimension. Nor was it collapsed for the calculation of the means and variance values. Those wordings just seem wrong.

The additional text added here (about the gamma and beta param) aren't necessary and could well be confusing to readers since neither is a parameter of the batchnorm API.

According to the batchnorm calculations, the epsilon value is added to the square of the corresponding variance value of the mini-batch being inspected. I think this is an extra information that may not be needed in the description of epsilon because the spec already provides a reference to the full paper (that includes all the calculations relevant to batchnorm). However, the additional wording being introduced here, in my opinion, may cause more confusion as it sounds like each of the precomputed variance value is adjusted by the epsilon amount, which will be incorrect from the mathematical aspect of the behavior. My recommendation is to keep the existing wording.

This is redundant to what already stated above this section.

If we feel compelled to add this note, there may be a better way to express it. The current wording doesn't read well because it doesn't explain what "fuse" in this context means, and what is "it" that the statement refers to. For example, a more complete wording may be "At the graph execution time, the implementation may choose to combine the execution of the standard batch normalization operation with the optional activation function provided by options.activation to improve the overall execution performance of the combined operation." etc.

I agree, but I think the use of "fuse" should be handled in a separate issue/PR, consistently over the whole spec.