# Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal Output Distributions

arXiv: https://arxiv.org/abs/2312.11735 · HTML: https://mlsanity.com/paper/2312.11735/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [Deep Directional Statistics: Pose Estimation with Uncertainty Quantification](https://mlsanity.com/paper/1805.03430/) (2018)
- [Confident Multiple Choice Learning](https://mlsanity.com/paper/1706.03475/) (2017)
- [DiverseNet: When One Right Answer is not Enough](https://mlsanity.com/paper/2008.10634/) (2020)
- [Diverse Multimedia Layout Generation with Multi Choice Learning](https://mlsanity.com/paper/2301.06629/) (2023)

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

- [MID-L: Matrix-Interpolated Dropout Layer with Layer-wise Neuron Selection](https://mlsanity.com/paper/2505.11416/) (2025)

## Abstract (arXiv)

In many real-world applications, from robotics to pedestrian trajectory prediction, there is a need to predict multiple real-valued outputs to represent several potential scenarios. Current deep learning techniques to address multiple-output problems are based on two main methodologies: (1) mixture density networks, which suffer from poor stability at high dimensions, or (2) multiple choice learning (MCL), an approach that uses M single-output functions, each only producing a point estimate hypothesis. This paper presents a Mixture of Multiple-Output functions (MoM) approach using a novel variant of dropout, Multiple Hypothesis Dropout. Unlike traditional MCL-based approaches, each multiple-output function not only estimates the mean but also the variance for its hypothesis. This is achieved through a novel stochastic winner-take-all loss which allows each multiple-output function to estimate variance through the spread of its subnetwork predictions. Experiments on supervised learning problems illustrate that our approach outperforms existing solutions for reconstructing multimodal output distributions. Additional studies on unsupervised learning problems show that estimating the parameters of latent posterior distributions within a discrete autoencoder significantly improves codebook efficiency, sample quality, precision and recall.