Using semi-hard negative miner with NT-Xent loss

[lemuelatQSA]

I was analyzing what happens when we use BatchEasyHardMiner(neg_strategy=BatchEasyHardMiner.SEMIHARD) along with the NTXentLoss, and I realized that it basically computes

$$ \mathcal{L_{NT}} = - \log \frac {\exp( sim(x_a, x_p) / \tau )} {\exp( sim(x_a, x_p) / \tau ) + \exp( sim(x_a, x_n) / \tau )} $$

Where $sim(\cdot)$ represents the cosine similarity, and $x_a,x_p,x_n$ are the anchor, positive and negative respectively. Is there anyone who can confirm that? Can we still call this "NT-Xent loss"? I believe so, since it looks like a simplified version of it. Indeed, not involving other negatives from other classes will slower the convergence since we're optimizing the distance only w.r.t. $x_n$ class.

Any comment/opinion is appreciated! :)

[KevinMusgrave]

That looks correct to me. The easy/hard mining paper has a relevant section:

I think it's fine to call it "NT-Xent" or "InfoNCE" because that's what you would call it if you did no mining and the batch naturally had only 1 negative.

[lemuelatQSA]

I agree. Thank you!