Why use 'torch.nn.Bilinear' in 'self.channelMixMLPs01' ?

[linhaojia13]

What's the purpose of using 'torch.nn.Bilinear'?
The formulation of a bilinear transformation is y= x_1^T A x_2 + b, and the formulation of a linear transformation is y=xA^T+b .
It seems that a bilinear layer just apply a slighter sophisticated linear transformation than the linear layer?

[LifeBeyondExpectations]

We empirically found that nn.Bilinear(...) results in a good performance.
I remember that the performance gap is quite big.
(ToDo) I will report the ablation study soon. ⚡

Nonetheless, in my personal opinion, this function can be seen as the 'simplest' version of a conditional MLP.

ECCV22-PointMixer/sem_seg/model/network/pointmixer.py

Lines 29 to 38 in bf1c3fb

	class BilinearFeedForward(nn.Module):
	def __init__(self, in_planes1, in_planes2, out_planes):
	super().__init__()
	self.bilinear = nn.Bilinear(in_planes1, in_planes2, out_planes)
	def forward(self, x):
	x = x.contiguous()
	x = self.bilinear(x, x)
	return x

As you can see the code above, the bilinear function takes the same input x (line 37).
Accordingly, we can say that

y = Bilinear(x, x) 
  = (xT W) x
  = W' x 
  = Linear(x | W')

where W' is conditioned to the input x.

In short, I think that not that much 'purpose' exists in this function.
However, nn.Bilinear(...) can be viewed as another type of MLP, as its name implies.

I hope you are satisfied with my understanding.

[linhaojia13]

Thank you for your detailed explanation. I think it is reasonable that regarding the bilinear layer as a simplest implementation of conditional MLP.
I'm looking forward to seeing the results of ablation study. Thank you!