# Shadow loss: Memory-linear deep metric learning for efficient training

arXiv: https://arxiv.org/abs/2311.14012 · HTML: https://mlsanity.com/paper/2311.14012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 15 of 15)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [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)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [Ranked List Loss for Deep Metric Learning](https://mlsanity.com/paper/1903.03238/) (2019)
- [A Benchmark for Studying Diabetic Retinopathy: Segmentation, Grading, and Transferability](https://mlsanity.com/paper/2008.09772/) (2020)
- [Learning Local Image Descriptors with Deep Siamese and Triplet Convolutional Networks by Minimising Global Loss Functions](https://mlsanity.com/paper/1512.09272/) (2015)
- [A Theoretically Sound Upper Bound on the Triplet Loss for Improving the Efficiency of Deep Distance Metric Learning](https://mlsanity.com/paper/1904.08720/) (2019)
- [The Group Loss for Deep Metric Learning](https://mlsanity.com/paper/1912.00385/) (2019)

## Abstract (arXiv)

Deep metric learning objectives (e.g., triplet loss) require storing and comparing high-dimensional embeddings, making the per-batch loss buffer scale as O(S· D), where S is the number of samples in a batch and D is the feature dimension, thus limiting training on memory-constrained hardware. We propose Shadow Loss, a proxy-free, parameter-free objective that measures similarity via scalar projections onto the anchor direction, reducing the loss-specific buffer from O(S· D) to O(S) while preserving the triplet structure. We analyze gradients, provide a Lipschitz continuity bound, and show that Shadow Loss penalizes trivial collapse for stable optimization. Across fine-grained retrieval (CUB-200, CARS196), large-scale product retrieval (Stanford Online Products, In-Shop Clothes), and standard/medical benchmarks (CIFAR-10/100, Tiny-ImageNet, HAM-10K, ODIR-5K), Shadow Loss consistently outperforms recent objectives (Triplet, Soft-Margin Triplet, Angular Triplet, SoftTriple, Multi-Similarity). It also converges in ≈ 1.5-2× fewer epochs under identical backbones and mining. Furthermore, it improves representation separability as measured by higher silhouette scores. The design is architecture-agnostic and vectorized for efficient implementation. By decoupling discriminative power from embedding dimensionality and reusing batch dot-products, Shadow Loss enables memory-linear training and faster convergence, making deep metric learning practical on both edge and large-scale systems.