Triplet Loss

The goal of Triplet loss, in the context of Siamese Networks, is to maximize the joint probability among all score-pairs i.e. the product of all probabilities. By using its negative logarithm, we can get the loss formulation as follows:

$$L\_{t}\left(\mathcal{V}\_{p}, \mathcal{V}\_{n}\right)=-\frac{1}{M N} \sum\_{i}^{M} \sum\_{j}^{N} \log \operatorname{prob}\left(v p\_{i}, v n\_{j}\right)$$

where the balance weight $1/MN$ is used to keep the loss with the same scale for different number of instance sets.