N-model ModelStock merging

Hey,

Thanks for your great implementation, very useful for the community. I have a question about the ModelStock N-model merging. I see a comment in the implementation here:

mergekit/mergekit/merge_methods/model_stock.py

Lines 72 to 76 in 57e7d14

    
           # now there is a question of how to come up with a value for theta. 
        
           # in the two-vector case, we can get an exact angle between the two vectors 
        
           # but the paper doesn't explicitly say what to do in the multi-vector case - 
        
           # they keep using a singular theta value and don't elaborate on how to 
        
           # calculate it. i'm going to assume an average of pairwise angles for now? i guess?

.

I see that you've taken a pairwise angles average for the implementation:

mergekit/mergekit/merge_methods/model_stock.py

Lines 78 to 91 in 57e7d14

    
           cos_thetas = [] 
        
           for i, w_0_offset in enumerate(offsets): 
        
               for j in range(i + 1, len(offsets)): 
        
                   w_1_offset = offsets[j] 
        
                   norm_product = torch.norm(w_0_offset, dim=-1) * torch.norm( 
        
                       w_1_offset, dim=-1 
        
                   ) 
        
                   cos_theta = ( 
        
                       (w_0_offset * w_1_offset).sum(dim=-1) / norm_product.clamp(min=1e-6) 
        
                   ).clamp(-1, 1) 
        
                   cos_thetas.append(cos_theta) 
        
           cos_theta = torch.stack(cos_thetas).mean(dim=0).unsqueeze(-1)

However, from the ModelStock paper fig Da in page 24, it seems like the theta is taken as the max of any two pairwise angles? I am wondering if you ran any N-model merging experiments, and saw any strange results or if they roughly followed that of the paper? I'd be curious to see if the mean or the max is the right aggregation method here.

Thanks and looking forward to your response.

EDIT: the authors of the ModelStock confirmed that it is indeed the average of all pairwise angles that is used for computing the theta fo N-model merging, see this linked issue: naver-ai/model-stock#2

	# now there is a question of how to come up with a value for theta.
	# in the two-vector case, we can get an exact angle between the two vectors
	# but the paper doesn't explicitly say what to do in the multi-vector case -
	# they keep using a singular theta value and don't elaborate on how to
	# calculate it. i'm going to assume an average of pairwise angles for now? i guess?

	cos_thetas = []
	for i, w_0_offset in enumerate(offsets):
	for j in range(i + 1, len(offsets)):
	w_1_offset = offsets[j]

	norm_product = torch.norm(w_0_offset, dim=-1) * torch.norm(
	w_1_offset, dim=-1
	)
	cos_theta = (
	(w_0_offset * w_1_offset).sum(dim=-1) / norm_product.clamp(min=1e-6)
	).clamp(-1, 1)
	cos_thetas.append(cos_theta)

	cos_theta = torch.stack(cos_thetas).mean(dim=0).unsqueeze(-1)