the loss function in paper

[wcyjerry]

Hi, I have read ur paper again today and read with codes, still got a question that why Lc works, our purpose seems to minimize the dissimilarity but the function have a '-' , I think with the '-' it just do the opposite work.

[ChongjianGE]

Hi @q671383789 ，
Thx for the question.
We truly want to minimize the dissimilarity of the two vectors ${f_1}, {f_2}$, i.e., maximizing the similarity of the two vectors.
The subtraction in $L_c$ loss term truly does the right job here.

Specifically, the <,> operation in $L_c$ could be considered as the dot product. Taking ${f_1}=(1,0)$ for example, where (1,0) is the vector, the $f_2$ should be close to (1,0) to maximize the similarity. Under this case, <$f_1$, $f_2$&gt; meets the maximum value when $f_2$ is close to (1,0). However, the training procedure strives for decreasing the loss term of $L_c$. That's why we use the subtraction in $L_c$ to meet the consistency.

[wcyjerry]

Hi @q671383789 ， Thx for the question. We truly want to minimize the dissimilarity of the two vectors ${f_1}, {f_2}$, i.e., maximizing the similarity of the two vectors. The subtraction in $L_c$ loss term truly does the right job here.

Specifically, the <,> operation in $L_c$ could be considered as the dot product. Taking ${f_1}=(1,0)$ for example, where (1,0) is the vector, the $f_2$ should be close to (1,0) to maximize the similarity. Under this case, <$f_1$, $f_2$&gt; meets the maximum value when $f_2$ is close to (1,0). However, the training procedure strives for decreasing the loss term of $L_c$. That's why we use the subtraction in $L_c$ to meet the consistency.

However, I don't see the L2_norm in the codes.

[ChongjianGE]

The L2 norm is implemented by the network module in fc layer

CARE/models/resnet_care.py

Line 347 in 3187afb

Normalize(),

[wcyjerry]

@ChongjianGE Thxs, But codes seem to be different with paper. it seems like that the both the numerator and denominator are L2_normed matrix not only the denominator term.

[ChongjianGE]

The implementation is mathematically equivalent to the loss term in the paper.

[wcyjerry]

ok, thx and forgive my poor math, I'll do more research. thx again.

…

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[ChongjianGE]

That's alright~
I will close this issue first. Please feel free to reopen it again if there are further questions.