# Scaffolding Sets

arXiv: https://arxiv.org/abs/2111.03135 · HTML: https://mlsanity.com/paper/2111.03135/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 64 references that are in the map.
- First posted on arXiv 4 Nov 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Understanding self-supervised Learning Dynamics without Contrastive Pairs](https://mlsanity.com/paper/2102.06810/) (2021)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Learning One-hidden-layer Neural Networks with Landscape Design](https://mlsanity.com/paper/1711.00501/) (2017)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [The Power of Contrast for Feature Learning: A Theoretical Analysis](https://mlsanity.com/paper/2110.02473/) (2021)
- [Metric Learning for Individual Fairness](https://mlsanity.com/paper/1906.00250/) (2019)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [Top-label calibration and multiclass-to-binary reductions](https://mlsanity.com/paper/2107.08353/) (2021)
- [Distribution-free calibration guarantees for histogram binning without sample splitting](https://mlsanity.com/paper/2105.04656/) (2021)
- [Adversarial Training Helps Transfer Learning via Better Representations](https://mlsanity.com/paper/2106.10189/) (2021)
- [Learning Two-layer Neural Networks with Symmetric Inputs](https://mlsanity.com/paper/1810.06793/) (2018)

## Built on by (most cited first, 8 of 8)

- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data](https://mlsanity.com/paper/2302.06232/) (2023)
- [Multicalibration as Boosting for Regression](https://mlsanity.com/paper/2301.13767/) (2023)
- [Freeze then Train: Towards Provable Representation Learning under Spurious Correlations and Feature Noise](https://mlsanity.com/paper/2210.11075/) (2022)
- [HappyMap: A Generalized Multi-calibration Method](https://mlsanity.com/paper/2303.04379/) (2023)
- [Last-Layer Fairness Fine-tuning is Simple and Effective for Neural Networks](https://mlsanity.com/paper/2304.03935/) (2023)
- [FIFA: Making Fairness More Generalizable in Classifiers Trained on Imbalanced Data](https://mlsanity.com/paper/2206.02792/) (2022)
- [On the Richness of Calibration](https://mlsanity.com/paper/2302.04118/) (2023)

## Abstract (arXiv)

Predictors map individual instances in a population to the interval [0,1]. For a collection mathcal C of subsets of a population, a predictor is multi-calibrated with respect to mathcal C if it is simultaneously calibrated on each set in mathcal C. We initiate the study of the construction of scaffolding sets, a small collection mathcal S of sets with the property that multi-calibration with respect to mathcal S ensures correctness, and not just calibration, of the predictor. Our approach is inspired by the folk wisdom that the intermediate layers of a neural net learn a highly structured and useful data representation.