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Monitoring Primitive Interactions During the Training of DNNs
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Redefines AND-OR interactions on top principal intermediate-layer feature components to summarize DNN learning dynamics into a few interaction primitives, and categorizes them into five learning-efficiency groups.
Problem
Explaining the highly complex learning dynamics of DNNs by summarizing them into a few simple, faithful interaction-based primitives, which is hard because parameter-level changes are high-dimensional and chaotic.
Approach
Define AND-OR interactions over principal feature components (PCA of intermediate-layer features across training checkpoints) rather than raw input variables, yielding much sparser interactions among fewer than 10 variables, and use their trajectories to classify learning behavior into reliable, withdrawn, forgotten, betraying, and fluctuating groups.
Key results
- Using top-10 principal feature components keeps classification accuracy nearly unchanged (e.g., CIFAR-10 ResNet 0.89 raw vs 0.89 with P10).
- Using fewer than 10% of salient interactions matches network outputs well; the minimum needed is on average 3.0% to 30.9% of 2^(r+1) interactions depending on the model.
- Interactions split into five groups (reliable, withdrawn, forgotten, betraying, fluctuating); e.g., RN-20 on MNIST has 49.6 reliable interactions on average versus 44.2 for VGG-11 on MNIST among the top 100.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | MLP-5 · income | classification accuracy: 0.92 -> 0.94 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | MLP-5 · TV news | classification accuracy: 0.86 -> 0.85 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | MLP-8 · income | classification accuracy: 0.95 -> 0.90 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | ResNet · MNIST | classification accuracy: 1.00 -> 1.00 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | ResNet · CIFAR-10 | classification accuracy: 0.89 -> 0.89 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | VGG · MNIST | classification accuracy: 1.00 -> 1.00 | No clear effect |
| Use the top 10 feature components plus the average feature instead of the raw feature (ablation) | VGG · CIFAR-10 | classification accuracy: 0.98 -> 0.97 | No clear effect |
| Define interactions on principal feature components rather than raw input variables | Interaction-based explanation · income, TV news, bike, SST-2, MNIST, CIFAR-10, ShapeNet | interaction sparsity | Helped |
Surprising findings
- High-order interactions are usually fluctuating or withdrawn, representing complex and unstable features.
- DNNs tend to use high-order interactions to classify abnormal samples (e.g., noisy labels) more than normal samples.
Limitations
- Interactions encode mixed semantics and are not equivalent to semantically meaningful concepts.
- Sparsity proof relies on three assumed conditions that are hard to verify in real DNNs.
- Analysis restricted to features from roughly the mid-depth layer of each network.
Experimental setup
Datasets: census income TV news bike sharing SST-2 MNIST CIFAR-10 Tiny ImageNet ShapeNet
Benchmarks: census income TV news bike sharing SST-2 MNIST CIFAR-10 Tiny ImageNet ShapeNet
Metrics: matching error of interaction-based approximation classification accuracy with top-10 components eigenvalue significance relative interaction strength interaction group counts
Baselines: raw input-variable interactions
Builds on: AND-OR interactions Shapley value interaction Defining and quantifying the emergence of sparse concepts in DNNs Does a neural network really encode symbolic concept? Information bottleneck learning dynamics (Shwartz-Ziv and Tishby 2017)
Closest papers by meaning
- Towards the Dynamics of a DNN Learning Symbolic Interactions (NeurIPS 2024 · similarity 0.91)
- Layerwise Change of Knowledge in Neural Networks (ICML 2024 · similarity 0.90)
- Defining and extracting generalizable interaction primitives from DNNs (ICLR 2024 · similarity 0.90)
- Three Mechanisms of Feature Learning in a Linear Network (ICLR 2025 · similarity 0.86)
- Explaining Generalization Power of a DNN Using Interactive Concepts (AAAI 2024 · similarity 0.86)
- Learning dynamics in linear recurrent neural networks (ICML 2025 · similarity 0.86)
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