# Deep Metric Learning with Chance Constraints

arXiv: https://arxiv.org/abs/2209.09060 · HTML: https://mlsanity.com/paper/2209.09060/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 89 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 30 of 49)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [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)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [Cross-Batch Memory for Embedding Learning](https://mlsanity.com/paper/1912.06798/) (2019)
- [Deep Metric Learning with Hierarchical Triplet Loss](https://mlsanity.com/paper/1810.06951/) (2018)
- [ProxyNCA++: Revisiting and Revitalizing Proxy Neighborhood Component Analysis](https://mlsanity.com/paper/2004.01113/) (2020)
- [Revisiting Training Strategies and Generalization Performance in Deep Metric Learning](https://mlsanity.com/paper/2002.08473/) (2020)
- [Smart Mining for Deep Metric Learning](https://mlsanity.com/paper/1704.01285/) (2017)
- [Ranked List Loss for Deep Metric Learning](https://mlsanity.com/paper/1903.03238/) (2019)
- [Attention-based Ensemble for Deep Metric Learning](https://mlsanity.com/paper/1804.00382/) (2018)
- [Hardness-Aware Deep Metric Learning](https://mlsanity.com/paper/1903.05503/) (2019)
- [Recall@k Surrogate Loss with Large Batches and Similarity Mixup](https://mlsanity.com/paper/2108.11179/) (2021)
- [Hard-Aware Deeply Cascaded Embedding](https://mlsanity.com/paper/1611.05720/) (2016)
- [MIC: Mining Interclass Characteristics for Improved Metric Learning](https://mlsanity.com/paper/1909.11574/) (2019)
- [Metric Learning with Adaptive Density Discrimination](https://mlsanity.com/paper/1511.05939/) (2015)
- [DiVA: Diverse Visual Feature Aggregation for Deep Metric Learning](https://mlsanity.com/paper/2004.13458/) (2020)
- [Divide and Conquer the Embedding Space for Metric Learning](https://mlsanity.com/paper/1906.05990/) (2019)
- [Fewer is More: A Deep Graph Metric Learning Perspective Using Fewer Proxies](https://mlsanity.com/paper/2010.13636/) (2020)
- [Learning Intra-Batch Connections for Deep Metric Learning](https://mlsanity.com/paper/2102.07753/) (2021)
- [Non-isotropy Regularization for Proxy-based Deep Metric Learning](https://mlsanity.com/paper/2203.08547/) (2022)

## Built on by (most cited first, 3 of 3)

- [Generalizable Embeddings with Cross-batch Metric Learning](https://mlsanity.com/paper/2307.07620/) (2023)
- [Generalized Sum Pooling for Metric Learning](https://mlsanity.com/paper/2308.09228/) (2023)
- [ReliableNet: A Chance-Constrained Approach to Trustworthy Classification in Deep Learning](https://mlsanity.com/paper/2608.09768/) (2026)

## Abstract (arXiv)

Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer of proxy-based DML satisfies certain chance constraints, and that the worst case generalization performance of the proxy-based methods can be characterized by the radius of the smallest ball around a class proxy to cover the entire domain of the corresponding class samples, suggesting multiple proxies per class helps performance. To provide a scalable algorithm as well as exploiting more proxies, we consider the chance constraints implied by the minimizers of proxy-based DML instances and reformulate DML as finding a feasible point in intersection of such constraints, resulting in a problem to be approximately solved by iterative projections. Simply put, we repeatedly train a regularized proxy-based loss and re-initialize the proxies with the embeddings of the deliberately selected new samples. We applied our method with 4 well-accepted DML losses and show the effectiveness with extensive evaluations on 4 popular DML benchmarks. Code is available at: https://github.com/yetigurbuz/ccp-dml