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Explaining Generalization Power of a DNN Using Interactive Concepts
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Explains DNN generalization via Harsanyi-interaction-based interactive concepts, showing high-order concepts are more inconsistent under noise and over-fitted DNNs encode stronger high-order concepts.
Problem
Explaining why a DNN generalizes, and why high-order (complex) interactive concepts generalize worse than low-order ones, without a universally accepted definition of DNN concepts.
Approach
Takes sparse Harsanyi interactions as interactive concepts and defines concept generalization as train/test distribution similarity; proves the variance of an interaction's effect under Gaussian input perturbation grows roughly exponentially with its order, explaining higher inconsistency and lower generalization of high-order concepts.
Key results
- Low-order concepts show higher train-test similarity than high-order concepts across MLP, AlexNet, VGG-11 and ResNet-20 settings.
- The ratio of inconsistent salient concepts under adversarial perturbation increases with concept order.
- Theory and experiments show the variance of interaction effects under Gaussian perturbation grows roughly exponentially with order.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use low-order rather than high-order interactive concepts | DNN concept distributions · Training vs. testing samples | concept-distribution similarity | Helped |
| increase the order of interactive concepts | DNN concepts under adversarial perturbations · Noisy samples | ratio of inconsistent concepts | Hurt |
| increase the order of interactive concepts | DNN concepts under Gaussian perturbations · Gaussian input perturbations | interaction-effect variance | Hurt |
| increase the ratio of incorrect training labels | AlexNet, ResNet-20, and VGG-11 · MNIST and CIFAR-10 | high-order interaction strength | Hurt |
| decrease the ratio of incorrect training labels | AlexNet, ResNet-20, and VGG-11 · MNIST and CIFAR-10 | early-epoch learning progress of low-order concepts | Helped |
| train the DNN to fit a high-order rather than low-order target concept | Five-layer MLP · Boolean-polynomial concept fitting, n=10 | directness of concept learning | Hurt |
Surprising findings
- Over-fitted DNNs (trained with more label noise) encode stronger high-order interactive concepts than normal DNNs.
- High-order concepts are learned via a detouring dynamic: the DNN first learns low-order mixtures before shifting to the target high-order concept.
Limitations
- Theory uses only Gaussian perturbations as noise and a simplified baseline/masking setting.
- Interactive concepts are a simplified definition not proven to match human cognition.
- Experiments are on small MLPs and CIFAR/MNIST-scale CNNs.
Experimental setup
Datasets: census dataset TV news dataset MNIST CIFAR-10
Benchmarks: census TV news MNIST CIFAR-10
Metrics: Jaccard similarity of concept distributions between train an ratio of inconsistent concepts under adversarial perturbatio interaction strength by order variance of interaction effect by order
Builds on: Harsanyi interaction interaction-based explanation of DNNs
Closest papers by meaning
- Defining and extracting generalizable interaction primitives from DNNs (ICLR 2024 · similarity 0.88)
- Towards the Dynamics of a DNN Learning Symbolic Interactions (NeurIPS 2024 · similarity 0.88)
- Layerwise Change of Knowledge in Neural Networks (ICML 2024 · similarity 0.87)
- Monitoring Primitive Interactions During the Training of DNNs (AAAI 2025 · similarity 0.86)
- What Variables Affect Out-of-Distribution Generalization in Pretrained Models? (NeurIPS 2024 · similarity 0.85)
- Data Distributional Properties As Inductive Bias for Systematic Generalization (CVPR 2025 · similarity 0.85)
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