# Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles

arXiv: https://arxiv.org/abs/1606.07839 · HTML: https://mlsanity.com/paper/1606.07839/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2016.

## Built on by (most cited first, 30 of 77)

- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [MoViNets: Mobile Video Networks for Efficient Video Recognition](https://mlsanity.com/paper/2103.11511/) (2021)
- [DICE: Diversity in Deep Ensembles via Conditional Redundancy Adversarial Estimation](https://mlsanity.com/paper/2101.05544/) (2021)
- [Residual Mixture of Experts](https://mlsanity.com/paper/2204.09636/) (2022)
- [HPNet: Dynamic Trajectory Forecasting with Historical Prediction Attention](https://mlsanity.com/paper/2404.06351/) (2024)
- [Divide-and-Conquer for Lane-Aware Diverse Trajectory Prediction](https://mlsanity.com/paper/2104.08277/) (2021)
- [Probabilistic Modeling of Semantic Ambiguity for Scene Graph Generation](https://mlsanity.com/paper/2103.05271/) (2021)
- [Diversity and Generalization in Neural Network Ensembles](https://mlsanity.com/paper/2110.13786/) (2021)
- [Embracing Uncertainty: Decoupling and De-bias for Robust Temporal Grounding](https://mlsanity.com/paper/2103.16848/) (2021)
- [Uncertainty Estimation via Response Scaling for Pseudo-mask Noise Mitigation in Weakly-supervised Semantic Segmentation](https://mlsanity.com/paper/2112.07431/) (2021)
- [Bootstrap Motion Forecasting With Self-Consistent Constraints](https://mlsanity.com/paper/2204.05859/) (2022)
- [Using Soft Labels to Model Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/2109.12622/) (2021)
- [DP-SSL: Towards Robust Semi-supervised Learning with A Few Labeled Samples](https://mlsanity.com/paper/2110.13740/) (2021)
- [Verification-Aided Deep Ensemble Selection](https://mlsanity.com/paper/2202.03898/) (2022)
- [Trajectory Mamba: Efficient Attention-Mamba Forecasting Model Based on Selective SSM](https://mlsanity.com/paper/2503.10898/) (2025)
- [Class-Incremental Experience Replay for Continual Learning under Concept Drift](https://mlsanity.com/paper/2104.11861/) (2021)
- [TENET: Transformer Encoding Network for Effective Temporal Flow on Motion Prediction](https://mlsanity.com/paper/2207.00170/) (2022)
- [That Label's Got Style: Handling Label Style Bias for Uncertain Image Segmentation](https://mlsanity.com/paper/2303.15850/) (2023)
- [Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysis](https://mlsanity.com/paper/2311.01052/) (2023)
- [Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealing](https://mlsanity.com/paper/2407.15580/) (2024)
- [MCL-GAN: Generative Adversarial Networks with Multiple Specialized Discriminators](https://mlsanity.com/paper/2107.07260/) (2021)
- [R-U-SURE? Uncertainty-Aware Code Suggestions By Maximizing Utility Across Random User Intents](https://mlsanity.com/paper/2303.00732/) (2023)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2303.13123/) (2023)
- [A Holistic Assessment of the Reliability of Machine Learning Systems](https://mlsanity.com/paper/2307.10586/) (2023)
- [Simple or Complex? Complexity-Controllable Question Generation with Soft Templates and Deep Mixture of Experts Model](https://mlsanity.com/paper/2110.06560/) (2021)
- [Diverse Multimedia Layout Generation with Multi Choice Learning](https://mlsanity.com/paper/2301.06629/) (2023)
- [MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views](https://mlsanity.com/paper/2207.09086/) (2022)
- [Self-Activating Neural Ensembles for Continual Reinforcement Learning](https://mlsanity.com/paper/2301.00141/) (2022)
- [Understanding and Improving Model Averaging in Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2305.07845/) (2023)

## Abstract (arXiv)

Many practical perception systems exist within larger processes that include interactions with users or additional components capable of evaluating the quality of predicted solutions. In these contexts, it is beneficial to provide these oracle mechanisms with multiple highly likely hypotheses rather than a single prediction. In this work, we pose the task of producing multiple outputs as a learning problem over an ensemble of deep networks -- introducing a novel stochastic gradient descent based approach to minimize the loss with respect to an oracle. Our method is simple to implement, agnostic to both architecture and loss function, and parameter-free. Our approach achieves lower oracle error compared to existing methods on a wide range of tasks and deep architectures. We also show qualitatively that the diverse solutions produced often provide interpretable representations of task ambiguity.