mlsanityData to 14 Oct 2026

Cardinality-Aware Set Prediction and Top-k Classification

arXiv 2407.07140 ↗First posted 9 Jul 2024cs.LG stat.MLcited by 23

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Abstract (arXiv)

We present a detailed study of cardinality-aware top-k classification, a novel approach that aims to learn an accurate top-k set predictor while maintaining a low cardinality. We introduce a new target loss function tailored to this setting that accounts for both the classification error and the cardinality of the set predicted. To optimize this loss function, we propose two families of surrogate losses: cost-sensitive comp-sum losses and cost-sensitive constrained losses. Minimizing these loss functions leads to new cardinality-aware algorithms that we describe in detail in the case of both top-k and threshold-based classifiers. We establish H-consistency bounds for our cardinality-aware surrogate loss functions, thereby providing a strong theoretical foundation for our algorithms. We report the results of extensive experiments on CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets demonstrating the effectiveness and benefits of our cardinality-aware algorithms.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 23 of its 61 references that are in the map. First posted on arXiv 9 Jul 2024.

Builds on

23 of 61 references.

References · 23

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2018Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labelscited by 997
  4. 2017Robust Loss Functions under Label Noise for Deep Neural Networkscited by 443
  5. 2023Cross-Entropy Loss Functions: Theoretical Analysis and Applicationscited by 210
  6. 2021Calibration and Consistency of Adversarial Surrogate Lossescited by 47
  7. 2018Smooth Loss Functions for Deep Top-k Classificationcited by 46
  8. 2015Loss Functions for Top-k Error: Analysis and Insightscited by 38
  9. 2023Principled Approaches for Learning to Defer with Multiple Expertscited by 38
  10. 2023Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithmscited by 36
  11. 2019On the Consistency of Top-k Surrogate Lossescited by 35
  12. 2023Learning to Reject with a Fixed Predictor: Application to Decontextualizationcited by 32
11 more
  1. 2023Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstentioncited by 32
  2. 2018Stochastic Negative Mining for Learning with Large Output Spacescited by 29
  3. 2023Revisiting Discriminative vs. Generative Classifiers: Theory and Implicationscited by 29
  4. 2024Regression with Multi-Expert Deferralcited by 29
  5. 2015Top-k Multiclass SVMcited by 28
  6. 2023Ranking with Abstentioncited by 27
  7. 2021A Finer Calibration Analysis for Adversarial Robustnesscited by 26
  8. 2024A Universal Growth Rate for Learning with Smooth Surrogate Lossescited by 24
  9. 2024H-Consistency Guarantees for Regressioncited by 21
  10. 2016Analysis and Optimization of Loss Functions for Multiclass, Top-k, and Multilabel Classificationcited by 20
  11. 2022Consistent Polyhedral Surrogates for Top-k Classification and Variantscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 11; 2026: 7.

23 papers.

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  1. 2024Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defercited by 26
  2. 2024Multi-Label Learning with Stronger Consistency Guaranteescited by 22
  3. 2024Enhanced H-Consistency Boundscited by 18
  4. 2024A Two-Stage Learning-to-Defer Approach for Multi-Task Learningcited by 17
  5. 2025Adversarial Robustness in Two-Stage Learning-to-Defer: Algorithms and Guaranteescited by 16
  6. 2025Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defercited by 16
  7. 2024Optimal Query Allocation in Extractive QA with LLMs: A Learning-to-Defer Framework with Theoretical Guaranteescited by 15
  8. 2025Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Datacited by 15
  9. 2025LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selectioncited by 13
  10. 2025Budgeted Multiple-Expert Deferralcited by 13
  11. 2025Improved Balanced Classification with Theoretically Grounded Loss Functionscited by 9
  12. 2025Why Ask One When You Can Ask k? Learning-to-Defer to the Top-k Expertscited by 7
11 more
  1. 2025Conformal Information Pursuit for Interactively Guiding Large Language Modelscited by 7
  2. 2025Beyond Tsybakov: Model Margin Noise and H-Consistency Boundscited by 7
  3. 2025Principled Algorithms for Optimizing Generalized Metrics in Binary Classificationcited by 6
  4. 2026Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Modelscited by 6
  5. 2025Adversarial Robustness in One-Stage Learning-to-Defercited by 5
  6. 2026A Theoretical Framework for Modular Learning of Robust Generative Modelscited by 4
  7. 2026SoftMoE: Soft Differentiable Routing for Mixture-of-Experts in LLMscited by 4
  8. 2026Optimized Deferral for Imbalanced Settingscited by 2
  9. 2026Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Predictioncited by 2
  10. 2026Online Learning-to-Defer with Varying Expertscited by 1
  11. 2026Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learningcited by 0