Edgeworth Expansion for Semi-hard Triplet Loss
This provides theoretical insight for researchers and practitioners using triplet loss in metric learning, though it is incremental as it refines existing asymptotic analysis.
The paper tackles the problem of understanding the behavior of semi-hard triplet loss in embedding learning by developing a higher-order asymptotic analysis using Edgeworth expansion. The result provides explicit expansions that quantify the impact of the margin parameter and data skewness, offering guidance for parameter selection to ensure training stability.
We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are separated by a specified margin. By refining the classical central limit theorem, our approach quantifies the impact of the margin parameter and the skewness of the underlying data distribution on the loss behavior. In particular, we derive explicit Edgeworth expansions that reveal first-order corrections in terms of the third cumulant, thereby characterizing non-Gaussian effects present in the distribution of distance differences between anchor-positive and anchor-negative pairs. Our findings provide detailed insight into the sensitivity of the semi-hard triplet loss to its parameters and offer guidance for choosing the margin to ensure training stability.