# Variance & Greediness: A comparative study of metric-learning losses

arXiv: https://arxiv.org/abs/2601.21450 · HTML: https://mlsanity.com/paper/2601.21450/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [Feature Learning based Deep Supervised Hashing with Pairwise Labels](https://mlsanity.com/paper/1511.03855/) (2015)
- [Deep Triplet Neural Networks with Cluster-CCA for Audio-Visual Cross-modal Retrieval](https://mlsanity.com/paper/1908.03737/) (2019)
- [Fisher Discriminant Triplet and Contrastive Losses for Training Siamese Networks](https://mlsanity.com/paper/2004.04674/) (2020)
- [Complete Cross-triplet Loss in Label Space for Audio-visual Cross-modal Retrieval](https://mlsanity.com/paper/2211.03434/) (2022)
- [Center Contrastive Loss for Metric Learning](https://mlsanity.com/paper/2308.00458/) (2023)
- [Two-Stage Triplet Loss Training with Curriculum Augmentation for Audio-Visual Retrieval](https://mlsanity.com/paper/2310.13451/) (2023)
- [Anchor-aware Deep Metric Learning for Audio-visual Retrieval](https://mlsanity.com/paper/2404.13789/) (2024)
- [Metric Learning with Progressive Self-Distillation for Audio-Visual Embedding Learning](https://mlsanity.com/paper/2501.09608/) (2025)
- [Learning Audio-Visual Embeddings with Inferred Latent Interaction Graphs](https://mlsanity.com/paper/2601.11995/) (2026)

## Abstract (arXiv)

Metric learning is central to retrieval, yet its effects on embedding geometry and optimization dynamics are not well understood. We introduce a diagnostic framework, VARIANCE (intra-/inter-class variance) and GREEDINESS (active ratio and gradient norms), to compare seven representative losses, i.e., Contrastive, Triplet, N-pair, InfoNCE, ArcFace, SCL, and CCL, across five image-retrieval datasets. Our analysis reveals that Triplet and SCL preserve higher within-class variance and clearer inter-class margins, leading to stronger top-1 retrieval in fine-grained settings. In contrast, Contrastive and InfoNCE compact embeddings are achieved quickly through many small updates, accelerating convergence but potentially oversimplifying class structures. N-pair achieves a large mean separation but with uneven spacing. These insights reveal a form of efficiency-granularity trade-off and provide practical guidance: prefer Triplet/SCL when diversity preservation and hard-sample discrimination are critical, and Contrastive/InfoNCE when faster embedding compaction is desired.