Question about Figure 5

[Jiahao Wang]

Hi, Peihao!

This is an amazing paper with fantastic visualization results.

I have 2 questions about Visualize the spectrum of attention maps (Figure 5), that is:

1. Is the model on which the plot in Figure 5 is based the pre-trained DeiT-S? I plotted some plots based on the visualization code you provided and the pre-trained weights open to DeiT, but they don't seem to match Figure 5.
2. Is the matrix on which Figure 5 is plotted an attention map after softmax? Or is it from another location?

Thanks for replying!

[Peter]

Dear Jiahao,

Thanks for your interest.

1. Yes, I guess you can get the similar visualization of the spectrum using pre-trained DeiT-S if it is computed correctly.
2. The Figure 5 plots the post-softmax attention matrix.

Best,
Peihao

[Jiahao Wang]

Hi, Peihao!

Thanks for the nice reply.

I have plot the post-softmax attention matrix using the open-source DeiT-S pretrained model and get the results. But I found that the results in layer 5 has been shown like this:

I also found that attention matrix after layer 2 shows a similar pattern, which are not similar with Figure.5.

Is it possible that I am wrong somewhere? Can you provide the full code for this part please? Thanks a lot.

[Jiahao Wang]

Besides, I plot the attention matrix through code as:

class Attention(nn.Module):
def init(self, dim, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0.):
super().init()
self.num_heads = num_heads
head_dim = dim // num_heads
# NOTE scale factor was wrong in my original version, can set manually to be compat with prev weights
self.scale = qk_scale or head_dim ** -0.5

    self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
    self.attn_drop = nn.Dropout(attn_drop)
    self.proj = nn.Linear(dim, dim)
    self.proj_drop = nn.Dropout(proj_drop)

def forward(self, x):
    B, N, C = x.shape
    qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
    q, k, v = qkv[0], qkv[1], qkv[2]   # make torchscript happy (cannot use tensor as tuple)

    attn = (q @ k.transpose(-2, -1)) * self.scale
    attn = attn.softmax(dim=-1)
    attn = self.attn_drop(attn)

    x = (attn @ v).transpose(1, 2).reshape(B, N, C)
    x = self.proj(x)
    x = self.proj_drop(x)
    return x, attn

Am I doing the same as you? Thanks for the reply~

[Peter]

Hi Jiahao,

Thanks for the follow-up. I guess we are using the same code for computing attention. I do think the figure you showed above has the right shape as we expect - a peak around the DC component and a long tail across the high-frequency bands. However, I'm not very convinced that the frequencies other than DC have zero responses. This is not possible, otherwise the attention map will turn out to be a (normalized) all-one matrix. I would suggest you first visualize the attention map directly, and try with different batches of images.

Best,
Peihao

[Jiahao Wang]

Hi Peihao,

Thanks for the quick and nice reply!
I saw the paper say that "Below we provide a complete spectral visualization of attention maps computed from a random sample in ImageNet validation set", which mean that Figure.5 was drawn from only 1 sample.

Do you mean that figure 5 is obtained from the data of a batch validation data? If so, how big is the data in this batch?

[Jiahao Wang]

Hi Peihao,

Yes, as you say, the attention matrix after layer 2 indeed turns out to be a (normalized) all-one matrix like:

tensor([[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051],
[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051],
[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051],
...,
[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051],
[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051],
[0.0051, 0.0051, 0.0051, ..., 0.0051, 0.0051, 0.0051]],
grad_fn=)

I wonder why it be like this? since I directly use the pretrained open-sourced DeiT-S checkpoint.

[Jiahao Wang]

Hi Peihao,

Thanks for the quick and nice reply!
I saw the paper say that "Below we provide a complete spectral visualization of attention maps computed from a random sample in ImageNet validation set", which mean that Figure.5 was drawn from only 1 sample.

Do you mean that figure 5 is obtained from the data of a batch validation data? If so, how big is the data in this batch?

[Peter]

Hi Jiahao,

Thanks for your continued interest and sorry for the late reply. Getting uniformly distributed attention maps does not make sense to me. Have you ever tested the test accuracy?

Fig. 5 is visualized for one sample (i.e., one image) not a batch. As far as I remember, this was not cherry picky. An arbitrary sample can produce the similar results.

Peihao

[gcxamy]

Hello, I really love your paper. Both the results and visualization are incredible. I am very curious about how you visualize Figure 5, could I have your code about it?

[Peter]

Hi, thanks for your interest. The code to visualize the spectrum of attention can be found here: #1 (comment). Hope you find this helpful!

[Peter]

Feel free to reopen this thread if any further issues.