# (Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models

arXiv: https://arxiv.org/abs/2409.02628 · HTML: https://mlsanity.com/paper/2409.02628/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 61 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [MaxViT: Multi-Axis Vision Transformer](https://mlsanity.com/paper/2204.01697/) (2022)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Supermasks in Superposition](https://mlsanity.com/paper/2006.14769/) (2020)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)

## Built on by (most cited first, 15 of 15)

- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [Agentic Uncertainty Quantification](https://mlsanity.com/paper/2601.15703/) (2026)
- [Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification](https://mlsanity.com/paper/2604.17112/) (2026)
- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [Position: agentic AI orchestration should be Bayes-consistent](https://mlsanity.com/paper/2605.00742/) (2026)
- [From predictions to confidence intervals: an empirical study of conformal prediction methods for in-context learning](https://mlsanity.com/paper/2504.15722/) (2025)
- [Uncertainty Estimation using Variance-Gated Distributions](https://mlsanity.com/paper/2509.08846/) (2025)
- [Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?](https://mlsanity.com/paper/2605.22593/) (2026)
- [Scaling Laws for Uncertainty in Deep Learning](https://mlsanity.com/paper/2506.09648/) (2025)
- [Rethinking Uncertainty Quantification and Entanglement in Image Segmentation](https://mlsanity.com/paper/2603.18792/) (2026)
- [Entropy-regularized Gradient Estimators for Approximate Bayesian Inference](https://mlsanity.com/paper/2503.11964/) (2025)
- [Covariance Last-Layer Ensembles: Function-Space Diversity for Efficient Uncertainty Quantification](https://mlsanity.com/paper/2607.23856/) (2026)
- [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://mlsanity.com/paper/2607.28248/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Structural Limits of the Information-Theoretic Uncertainty Decomposition](https://mlsanity.com/paper/2609.39591/) (2026)

## Abstract (arXiv)

Epistemic uncertainty is crucial for safety-critical applications and data acquisition tasks. Yet, we find an important phenomenon in deep learning models: an epistemic uncertainty collapse as model complexity increases, challenging the assumption that larger models invariably offer better uncertainty quantification. We introduce implicit ensembling as a possible explanation for this phenomenon. To investigate this hypothesis, we provide theoretical analysis and experiments that demonstrate uncertainty collapse in explicit ensembles of ensembles and show experimental evidence of similar collapse in wider models across various architectures, from simple MLPs to state-of-the-art vision models including ResNets and Vision Transformers. We further develop implicit ensemble extraction techniques to decompose larger models into diverse sub-models, showing we can thus recover epistemic uncertainty. We explore the implications of these findings for uncertainty estimation.