How to write in English (1)
… conveys that …
As sketched in Section 2, …
We hereby provide a quick sketch.
We demonstrate that …
Table 2 presents the split for four DML losses.
This link can be drawn from two different perspectives, …
This information theoretic argument reinforces our conclusion …
… highlight the fact that …
the preliminary experiments we provide in the supplementary material indicate that CE and SPCE exhibit similar behaviors at training time.
Throughout this paper, we revealed non-obvious relations between the cross-entropy loss, widely adopted in classification tasks, and pairwise losses commonly used in DML.
This connection becomes particularly apparent when writing mutual information in both its generative and discriminative views.
We concede that … (尽管不情愿但也得承认)
- Datasets are divided into train and evaluation
splits. - In-Shop is divided into a query and a gallery
set.
Recently, substantial research efforts … focused on …
Specifically, the current paradigm is to …
The recent success of deep neural networks at learning complex, nonlinear mappings of high-dimensional data aligns with the problem of learning a suitable embedding.
While such formulations seem intuitive, …
Admittedly, the objective of doing …
… most likely due to its apparent irrelevance for …
To the best of our knowledge, …
We show that four of the most prominent pairwise metric-learning losses…
… establish tight links between … and …
an upper bound on …
… represents a proxy for …
We consistently obtained state-of-the-art results, outperforming many recent and complex DML methods.
The tightness part encourages
samples from the same class to be close to each other and form tight clusters. As for the contrastive part, it forces samples from different classes to stand far apart from one another in the embedded feature space.
This bound is tight when …
A similar analysis can be carried out on other
Lemma 1
引理 1
sth. is exhaustively studied in …
We now completely change gear to focus on the widely used unary classification loss: cross-entropy.
On the surface, …
intractable
auxiliary function
proposition
观点，主张，命题
Proposition 1 casts a new light on the cross-entropy loss by …
i.e. = id est
In echo to Lemma 1, …
In order to remove the dependence upon λ …
Contrary to …
This fact alone is not enough to explain why the cross-entropy is able to consistently achieve better results than DML losses as shown in Section 5.
be substantially easier
it simplifies the implementation, thus increasing its potential applicability in real-world problems.
[1] Boudiaf, M., Rony, J., Ziko, I. M., Granger, E., Pedersoli, M., Piantanida, P., & Ayed, I. B. (2020, August). A unifying mutual information view of metric learning: cross-entropy vs. pairwise losses. In European conference on computer vision (pp. 548-564). Springer, Cham.