In image retrieval, standard evaluation metrics rely on score ranking, e.g.

As shown in Figure 1.a of the main paper, and discussed in Section 3.1 ("Comparison to SmoothAP"), 's score because the correct ordering is not reached (the negative instance This is illustrated on the toy dataset in Figure 1. We remind the reader of the definition of the decomposability gap given in Eq. (6) of the main paper. Proof of Eq. (8): Upper bound on the DG We choose a setting for the proof of the upper bound similar to the one used for training, i.e. all the batch have the same size, and the Eq. B.1 Metrics We detail here the performance metrics that we use to evaluate our models. The Recall@K metrics is often used in the literature.

In image retrieval, standard evaluation metrics rely on score ranking, e.g.

In image retrieval, standard evaluation metrics rely on score ranking, e.g. average precision (AP). In this paper, we introduce a method for robust and decomposable average precision (ROADMAP) addressing two major challenges for end-to-end training of deep neural networks with AP: non-differentiability and non-decomposability. Firstly, we propose a new differentiable approximation of the rank function, which provides an upper bound of the AP loss and ensures robust training. Secondly, we design a simple yet effective loss function to reduce the decomposability gap between the AP in the whole training set and its averaged batch approximation, for which we provide theoretical guarantees. Extensive experiments conducted on three image retrieval datasets show that ROADMAP outperforms several recent AP approximation methods and highlight the importance of our two contributions. Finally, using ROADMAP for training deep models yields very good performances, outperforming state-of-the-art results on the three datasets.