# Disentangling Model Multiplicity in Deep Learning

arXiv: https://arxiv.org/abs/2206.08890 · HTML: https://mlsanity.com/paper/2206.08890/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [PAC-Bayesian Theory Meets Bayesian Inference](https://mlsanity.com/paper/1605.08636/) (2016)
- [Analyzing the Role of Model Uncertainty for Electronic Health Records](https://mlsanity.com/paper/1906.03842/) (2019)
- [Model Selection Techniques -- An Overview](https://mlsanity.com/paper/1810.09583/) (2018)
- [Smooth activations and reproducibility in deep networks](https://mlsanity.com/paper/2010.09931/) (2020)
- [Beyond Point Estimate: Inferring Ensemble Prediction Variation from Neuron Activation Strength in Recommender Systems](https://mlsanity.com/paper/2008.07032/) (2020)

## Built on by (most cited first, 5 of 5)

- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [Algorithmic Arbitrariness in Content Moderation](https://mlsanity.com/paper/2402.16979/) (2024)
- [The Costs of Pretending That There Are Data-Generating Probability Distributions in the Social World](https://mlsanity.com/paper/2407.17395/) (2024)
- [On Hardware-efficient Inference in Probabilistic Circuits](https://mlsanity.com/paper/2405.13639/) (2024)
- [Revisiting the Relation Between Robustness and Universality](https://mlsanity.com/paper/2510.19427/) (2025)

## Abstract (arXiv)

Model multiplicity is a well-known but poorly understood phenomenon that undermines the generalisation guarantees of machine learning models. It appears when two models with similar training-time performance differ in their predictions and real-world performance characteristics. This observed 'predictive' multiplicity (PM) also implies elusive differences in the internals of the models, their 'representational' multiplicity (RM). We introduce a conceptual and experimental setup for analysing RM by measuring activation similarity via singular vector canonical correlation analysis (SVCCA). We show that certain differences in training methods systematically result in larger RM than others and evaluate RM and PM over a finite sample as predictors for generalizability. We further correlate RM with PM measured by the variance in i.i.d. and out-of-distribution test predictions in four standard image data sets. Finally, instead of attempting to eliminate RM, we call for its systematic measurement and maximal exposure.