# Loss Functions for Top-k Error: Analysis and Insights

arXiv: https://arxiv.org/abs/1512.00486 · HTML: https://mlsanity.com/paper/1512.00486/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2015.

## Built on by (most cited first, 30 of 38)

- [Set-valued classification -- overview via a unified framework](https://mlsanity.com/paper/2102.12318/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Fast, Differentiable and Sparse Top-k: a Convex Analysis Perspective](https://mlsanity.com/paper/2302.01425/) (2023)
- [A Universal Growth Rate for Learning with Smooth Surrogate Losses](https://mlsanity.com/paper/2405.05968/) (2024)
- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
- [sigmoidF1: A Smooth F1 Score Surrogate Loss for Multilabel Classification](https://mlsanity.com/paper/2108.10566/) (2021)
- [Cardinality-Aware Set Prediction and Top-k Classification](https://mlsanity.com/paper/2407.07140/) (2024)
- [Differentiable Top-k Classification Learning](https://mlsanity.com/paper/2206.07290/) (2022)
- [Surrogate Regret Bounds for Polyhedral Losses](https://mlsanity.com/paper/2110.14031/) (2021)
- [An Embedding Framework for the Design and Analysis of Consistent Polyhedral Surrogates](https://mlsanity.com/paper/2206.14707/) (2022)
- [LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selection](https://mlsanity.com/paper/2503.06242/) (2025)
- [Label Distributionally Robust Losses for Multi-class Classification: Consistency, Robustness and Adaptivity](https://mlsanity.com/paper/2112.14869/) (2021)
- [Stochastic smoothing of the top-K calibrated hinge loss for deep imbalanced classification](https://mlsanity.com/paper/2202.02193/) (2022)
- [List Sample Compression and Uniform Convergence](https://mlsanity.com/paper/2403.10889/) (2024)
- [Optimizing Partial Area Under the Top-k Curve: Theory and Practice](https://mlsanity.com/paper/2209.01398/) (2022)
- [Consistent Polyhedral Surrogates for Top-k Classification and Variants](https://mlsanity.com/paper/2207.08873/) (2022)
- [Dual-Encoders for Extreme Multi-Label Classification](https://mlsanity.com/paper/2310.10636/) (2023)
- [Why Ask One When You Can Ask k? Learning-to-Defer to the Top-k Experts](https://mlsanity.com/paper/2504.12988/) (2025)
- [Don't Ignore the Tail: Decoupling top-K Probabilities for Efficient Language Model Distillation](https://mlsanity.com/paper/2602.20816/) (2026)
- [Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics](https://mlsanity.com/paper/2408.16862/) (2024)
- [FEDS -- Filtered Edit Distance Surrogate](https://mlsanity.com/paper/2103.04635/) (2021)
- [Top-k Classification and Cardinality-Aware Prediction](https://mlsanity.com/paper/2403.19625/) (2024)
- [An Optimal Sauer Lemma Over k-ary Alphabets](https://mlsanity.com/paper/2604.12952/) (2026)
- [SoftMoE: Soft Differentiable Routing for Mixture-of-Experts in LLMs](https://mlsanity.com/paper/2606.17952/) (2026)
- [Tensor Normalization and Full Distribution Training](https://mlsanity.com/paper/2109.02345/) (2021)
- [A Stochastic Bundle Method for Interpolating Networks](https://mlsanity.com/paper/2201.12678/) (2022)
- [Set-valued prediction in hierarchical classification with constrained representation complexity](https://mlsanity.com/paper/2203.06676/) (2022)
- [Smooth and Stepwise Self-Distillation for Object Detection](https://mlsanity.com/paper/2303.05015/) (2023)
- [Classification Under Ambiguity: When Is Average-K Better Than Top-K?](https://mlsanity.com/paper/2112.08851/) (2021)
- [Identify ambiguous tasks combining crowdsourced labels by weighting Areas Under the Margin](https://mlsanity.com/paper/2209.15380/) (2022)

## Abstract (arXiv)

In order to push the performance on realistic computer vision tasks, the number of classes in modern benchmark datasets has significantly increased in recent years. This increase in the number of classes comes along with increased ambiguity between the class labels, raising the question if top-1 error is the right performance measure. In this paper, we provide an extensive comparison and evaluation of established multiclass methods comparing their top-k performance both from a practical as well as from a theoretical perspective. Moreover, we introduce novel top-k loss functions as modifications of the softmax and the multiclass SVM losses and provide efficient optimization schemes for them. In the experiments, we compare on various datasets all of the proposed and established methods for top-k error optimization. An interesting insight of this paper is that the softmax loss yields competitive top-k performance for all k simultaneously. For a specific top-k error, our new top-k losses lead typically to further improvements while being faster to train than the softmax.