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On the Joint Interaction of Models, Data, and Features
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Introduces an interaction tensor linking models, data, and PCA-based features to empirically study feature learning, then proposes a combinatorial dominant/rare feature framework that derives closed-form accuracy and agreement and explains GDE without calibration assumptions.
Problem
Theoretical understanding of what features deep networks learn and how different random-seed models learn different features is underdeveloped; existing feature models (multi-view) conflict with observations, and the Generalization Disagreement Equality (GDE) has previously required a calibration as
Approach
Define features as PCA projections of last-layer activations, cluster them across models into an interaction tensor, observe a long-tailed feature distribution and that low-confidence data has more features, then model features as dominant vs rare with sampling-without-replacement learning and derive closed-form accuracy and agreement that yield GDE without calibration.
Key results
- Feature frequency in CIFAR-10 is long-tailed, and low-confidence data contain more low-frequency features (O.1, O.2).
- Merging CIFAR-10 classes into 2, 3, 5 superclasses keeps the accuracy-agreement difference near 0.04-0.05, while re-partitioning data by blue intensity yields differences from 0.05 to 0.10 across groups.
- The closed-form framework with dominant/rare features reproduces GDE approximately when rare-feature parameters are coupled to dominant ones (alpha = 0.2).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Merge CIFAR-10 classes into superclasses | ResNet18 ensemble · CIFAR-10 merged classes | accuracy-agreement difference: 0.05, 0.04, 0.04, 0.05 | No clear effect |
| Re-partition CIFAR-10 by blue-intensity quantiles | ResNet18 ensemble · CIFAR-10 blue-intensity groups | accuracy-agreement difference: 0.08, 0.07, 0.10, 0.05, 0.05 | Mixed |
| Use the interaction tensor to compare feature frequency across training | ResNet18 models on CIFAR-10 · CIFAR-10 training set | tail-feature frequency | Hurt |
| Have fewer features present in a data point | ResNet18 ensemble · CIFAR-10 test set | ensemble confidence | Helped |
| Have more low-frequency features present in a data point | ResNet18 ensemble · CIFAR-10 test set | ensemble confidence | Hurt |
| Increase a feature's frequency in the dataset | ResNet18 models · CIFAR-10 test set | number of models learning the feature | Helped |
| Increase the number of features shared between models | ResNet18 model pairs · CIFAR-10 test set | shared error | Helped |
| Vary dominant-data proportion or model capacity (ablation) | Combinatorial feature-learning framework · Numerical simulation | accuracy-agreement tracking | No clear effect |
| Vary rare-feature count or rare features per data point independently (ablation) | Combinatorial feature-learning framework · Numerical simulation | accuracy-agreement tracking | Hurt |
| Couple rare and dominant feature/data parameters proportionally (ablation) | Combinatorial feature-learning framework · Numerical simulation | accuracy-agreement tracking | Helped |
Surprising findings
- Low-confidence data tend to contain more features, contradicting the multi-view model in which multi-view data are classified correctly by all models.
- Breaking GDE is possible with natural i.i.d. data partitions, without adversarial construction, implying the ensemble is not calibrated on those partitions.
Limitations
- The framework does not describe how features are learned mechanistically via optimization.
- Features are assumed to be a simplified binary dominant/rare dichotomy and a single feature suffices for classification.
- The framework is derived for binary classification; the multi-class extension is not analytically resolved.
Experimental setup
Datasets: CIFAR-10 SVHN
Benchmarks: CIFAR-10 SVHN
Metrics: accuracy agreement accuracy-agreement difference (GDE gap)
Baselines: multi-view model neural tangent kernel
Builds on: multi-view data model (Allen-Zhu & Li) generalization disagreement equality (Jiang et al.) neural tangent kernel
Closest papers by meaning
- Exploring the cloud of feature interaction scores in a Rashomon set (ICLR 2024 · similarity 0.86)
- Factor Augmented Tensor-on-Tensor Neural Networks (AAAI 2025 · similarity 0.84)
- Explaining Generalization Power of a DNN Using Interactive Concepts (AAAI 2024 · similarity 0.84)
- Feature Contamination: Neural Networks Learn Uncorrelated Features and Fail to Generalize (ICML 2024 · similarity 0.84)
- Interaction Asymmetry: A General Principle for Learning Composable Abstractions (ICLR 2025 · similarity 0.84)
- Monitoring Primitive Interactions During the Training of DNNs (AAAI 2025 · similarity 0.83)
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