# Learning with Batch-wise Optimal Transport Loss for 3D Shape Recognition

## TL;DR

This paper introduces a batch-wise optimal transport loss for deep metric learning, which automatically emphasizes hard samples, accelerates convergence, and improves 3D shape recognition performance.

## Contribution

It proposes a novel batch-wise optimal transport loss that enhances deep metric learning by focusing on hard examples and improving convergence speed.

## Key findings

- Accelerates convergence significantly.
- Achieves state-of-the-art recognition performance.
- Outperforms existing methods in 3D shape recognition after fewer epochs.

## Abstract

Deep metric learning is essential for visual recognition. The widely used pair-wise (or triplet) based loss objectives cannot make full use of semantical information in training samples or give enough attention to those hard samples during optimization. Thus, they often suffer from a slow convergence rate and inferior performance. In this paper, we show how to learn an importance-driven distance metric via optimal transport programming from batches of samples. It can automatically emphasize hard examples and lead to significant improvements in convergence. We propose a new batch-wise optimal transport loss and combine it in an end-to-end deep metric learning manner. We use it to learn the distance metric and deep feature representation jointly for recognition. Empirical results on visual retrieval and classification tasks with six benchmark datasets, i.e., MNIST, CIFAR10, SHREC13, SHREC14, ModelNet10, and ModelNet40, demonstrate the superiority of the proposed method. It can accelerate the convergence rate significantly while achieving a state-of-the-art recognition performance. For example, in 3D shape recognition experiments, we show that our method can achieve better recognition performance within only 5 epochs than what can be obtained by mainstream 3D shape recognition approaches after 200 epochs.