# A Decidability-Based Loss Function

arXiv: https://arxiv.org/abs/2109.05524 · HTML: https://mlsanity.com/paper/2109.05524/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 12 Sep 2021.

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

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [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)
- [CNN Features off-the-shelf: an Astounding Baseline for Recognition](https://mlsanity.com/paper/1403.6382/) (2014)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [L2-constrained Softmax Loss for Discriminative Face Verification](https://mlsanity.com/paper/1703.09507/) (2017)
- [Ranked List Loss for Deep Metric Learning](https://mlsanity.com/paper/1903.03238/) (2019)
- [Triplet-Center Loss for Multi-View 3D Object Retrieval](https://mlsanity.com/paper/1803.06189/) (2018)
- [Learning Deep Embeddings with Histogram Loss](https://mlsanity.com/paper/1611.00822/) (2016)
- [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)
- [Embedding Deep Metric for Person Re-identication A Study Against Large Variations](https://mlsanity.com/paper/1611.00137/) (2016)
- [Deep Metric Learning by Online Soft Mining and Class-Aware Attention](https://mlsanity.com/paper/1811.01459/) (2018)

## Built on by (most cited first, 1 of 1)

- [PD-Loss: Proxy-Decidability for Efficient Metric Learning](https://mlsanity.com/paper/2508.17082/) (2025)

## Abstract (arXiv)

Nowadays, deep learning is the standard approach for a wide range of problems, including biometrics, such as face recognition and speech recognition, etc. Biometric problems often use deep learning models to extract features from images, also known as embeddings. Moreover, the loss function used during training strongly influences the quality of the generated embeddings. In this work, a loss function based on the decidability index is proposed to improve the quality of embeddings for the verification routine. Our proposal, the D-loss, avoids some Triplet-based loss disadvantages such as the use of hard samples and tricky parameter tuning, which can lead to slow convergence. The proposed approach is compared against the Softmax (cross-entropy), Triplets Soft-Hard, and the Multi Similarity losses in four different benchmarks: MNIST, Fashion-MNIST, CIFAR10 and CASIA-IrisV4. The achieved results show the efficacy of the proposal when compared to other popular metrics in the literature. The D-loss computation, besides being simple, non-parametric and easy to implement, favors both the inter-class and intra-class scenarios.