[Paper Review] Rethinking Feature Discrimination and Polymerization for Large-scale Recognition

Yü Liu, Hongyang Li+1 more|arXiv (Cornell University)|Oct 2, 2017

Face and Expression Recognition38 references112 citations

TL;DR

The paper introduces the congenerous cosine (COCO) loss, which jointly optimizes intra-class polymerization and inter-class discrimination by leveraging class centroids and cosine similarity, enabling stable end-to-end training for large-scale recognition.

ABSTRACT

Feature matters. How to train a deep network to acquire discriminative features across categories and polymerized features within classes has always been at the core of many computer vision tasks, specially for large-scale recognition systems where test identities are unseen during training and the number of classes could be at million scale. In this paper, we address this problem based on the simple intuition that the cosine distance of features in high-dimensional space should be close enough within one class and far away across categories. To this end, we proposed the congenerous cosine (COCO) algorithm to simultaneously optimize the cosine similarity among data. It inherits the softmax property to make inter-class features discriminative as well as shares the idea of class centroid in metric learning. Unlike previous work where the center is a temporal, statistical variable within one mini-batch during training, the formulated centroid is responsible for clustering inner-class features to enforce them polymerized around the network truncus. COCO is bundled with discriminative training and learned end-to-end with stable convergence. Experiments on five benchmarks have been extensively conducted to verify the effectiveness of our approach on both small-scale classification task and large-scale human recognition problem.

Motivation & Objective

• Motivate the need for features that are both discriminative across categories and polymerized within a class in ultra-large scale recognition.
• Propose a new loss (COCO) that optimizes cosine similarity with class centroids to achieve both goals.
• Ensure end-to-end trainability with stable convergence across small- and large-scale benchmarks.

Proposed method

• Define cosine similarity between features and class centroids.
• Formulate the COCO loss as a cross-entropy over normalized, scaled features and centroids.
• Update class centroids jointly with network parameters during training (no separate center loss term).
• Provide gradients for features and centroids to enable backpropagation within standard CNN pipelines.
• Theoretically relate the scale factor alpha to network and class count, and derive an optimal lower bound.
• Demonstrate stability and convergence advantages over triplet and center losses.

Experimental results

Research questions

• RQ1 Can a cosine-based, centroid-guided objective produce both tight intra-class clustering and large inter-class margins at ultra-large class counts?
• RQ2 Does COCO enable stable end-to-end training and better scalability than existing metric-learning losses (e.g., triplet, center loss) for large-scale recognition tasks?

Key findings

• COCO achieves competitive or superior accuracy on MNIST and CIFAR-10 without data augmentation, outperforming several baselines.
• On large-scale face recognition benchmarks, COCO yields state-of-the-art or competitive results in verification and identification tasks (e.g., LFW and MegaFace).
• COCO produces clearer intra-class polymerization and larger inter-class separation in cosine-distance visualizations compared to softmax and triplet losses.
• An optimal scale factor alpha can be determined, with a derived lower bound guiding practical settings (alpha ≈ 0.5 log(K-1) + 3).
• The method maintains stable convergence and avoids the training instability sometimes observed with triplet loss on large class counts.