A Question about the Calculation of cauchy_cross_entroy Loss

[MaxChanger]

Hello, I recently looked at the DCH method in the DeepHash library, but I encountered some incomprehension, as shown in the following figure

The parameter v and label_v in function cauchy_cross_entroy is always None, so in function cauchy_cross_entroy, the part in the red box is always executed. So u and v are the same.

At the same time, I'm also looking at HashNet's pytorch code implementation. And It also requires two sets to calculate the loss, but outputs1 and outputs2 in the figure below take two batches from the entire data, which are different.

So now I'm wondering why you set U and V to the same directly.
In the paper, h_i and h_j are also used to represent two sets, which are not the same.

I hope I can get your answer. Thank you.

[bl0]

Hi, I think that calculating the loss within the batch and cross two batches are both ok.
But obviously within the batch is more convenient.

[MaxChanger]

I found this problem when I tried to modify the DCH based on the HashNet code, because I was more familiar with pytorch. I modified the loss function of HashNet according to the DCH paper and tensorflow code, but if I used the image data from two batches to calculate loss, the result would be nan. But if the settings in the picture above come from the same batch, I can get a map on coco that is similar to the one in the paper, 0.73.

[MaxChanger]

I can't understand why it's set to come from the same batch.
I think if u and v come from the same batch, the values of h_i and h_j should be equal, h_i = h_j.
And if it's true, then dist(h_i,h_j) = dist(h_i,h_i) , what's the mean about dist(h_i,h_i)
I don't know if I understand it correctly.

[bl0]

Hi, a batch also contains some samples. So i and j can be any number in [0, batch_size) and we can calculate the cross entropy loss for all pair (i, j) within the batch.

[bl0]

PYI: In our implementation, ip_1 and label_ip both have shape [bs, bs] where bs is the batch size.

[MaxChanger]

Hi, I think the u in the code is batch_size×hash_bits, for example 128×48, represent the batch has 128 images and the length of hash code is 48, the label_u is batch_size×label_bits, the label_bits depend on the train.txt/database.txt. Hence, as you said, ip_1 and label_ip both have shape [batch_size, batch_size].

But I understand that h_i or h_j is a row of u matrices, and if ip_1= tf.matmul(u, tf.transpose(v) represent matrix u is multiplied by v's transposition. if u and v are the same, It is equivalent to ip_1 = tf.matmul(u, tf.transpose(u), the value of ip_1[i][j] represents the dot product of u[h_i] row and u^T[h_j] column, but is the value of ip[i][i] meaningful?

[bl0]

Why ip[i][i] is not meaningful? They come from different i and j.

[MaxChanger]

ip[i][j] is meaningful, they come from different i and j, but ip[i][i] is dist(h_i, h_i) not dist(h_i, h_j), it represents a hash code of an image dot product by itself

[bl0]

Ok, I understand your question now.
Yes, ip[i, i] may not be meaningful. But the loss for pair (i, i) will be zero and don't affect the training. So we need not worry that.

[MaxChanger]

Thank you for your answer. Through the discussion with you, I am more convinced that my understanding is correct or not.
But I still need to find why I set two different batch in my code as input led to the loss is nan, but the same batch can work perfectly.
If I have some progress, I will show in this issue again. Thanks

[bl0]

Ok. Welcome to discuss with me.