# On the Joint Interaction of Models, Data, and Features

arXiv: https://arxiv.org/abs/2306.04793 · HTML: https://mlsanity.com/paper/2306.04793/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 65 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [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)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)

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

- [InternalInspector I2: Robust Confidence Estimation in LLMs through Internal States](https://mlsanity.com/paper/2406.12053/) (2024)
- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- [DASH: Warm-Starting Neural Network Training in Stationary Settings without Loss of Plasticity](https://mlsanity.com/paper/2410.23495/) (2024)
- [OOD-Chameleon: Is Algorithm Selection for OOD Generalization Learnable?](https://mlsanity.com/paper/2410.02735/) (2024)
- [What Do Students Learn? A Feature-Level Analysis of Dark Knowledge](https://mlsanity.com/paper/2606.03052/) (2026)

## Abstract (arXiv)

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. With the interaction tensor, we make several key observations about how features are distributed in data and how models with different random seeds learn different features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form. We demonstrate that the proposed framework can explain empirically observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only unlabeled data. Further, our theory also provides explicit construction of natural data distributions that break the GDE. Thus, we believe this work provides valuable new insight into our understanding of feature learning.