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Sum-of-Parts: Self-Attributing Neural Networks with End-to-End Learning of Feature Groups
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Proposes Sum-of-Parts (SOP), a model-agnostic framework that converts any differentiable pretrained model into a group-based self-attributing network with end-to-end learned feature groups, supported by theory showing per-feature SANNs have exponentially growing error on correlated features.
Problem
Self-attributing neural networks (SANNs) that decompose predictions into feature-subset contributions suffer large performance trade-offs, especially when features are highly correlated in high-dimensional vision and language data.
Approach
Learn feature groups end-to-end per input with a self-attention group generator (binary top-20% masks), run a frozen pretrained backbone on each masked group, and aggregate group logits with a sparsemax cross-attention group selector, so any differentiable model becomes a group-based SANN without group supervision.
Key results
- SOP achieves ImageNet-S error 0.267 vs. 0.306 for the best baseline (SHAP-F) and IOU 0.630 vs. 0.511 (FG-F).
- SOP achieves CosmoGrid MSE 0.025 vs. 0.028 for SHAP-F, and purity 0.647.
- Group probing on ImageNet-S yields random-level accuracy (0.10%) for SOP groups versus 13.40% for FG-F groups.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learned feature groups with SOP instead of the strongest listed SANN baseline | ImageNet-S with ViT · ImageNet-S | error rate: 0.306 ± 0.027 -> 0.267 ± 0.017 | Helped |
| Use learned feature groups with SOP instead of FG-F | ImageNet-S with ViT · ImageNet-S | IOU: 0.511 ± 0.018 -> 0.630 ± 0.006 | Helped |
| Use learned feature groups with SOP instead of SHAP-F | CosmoGrid with CNN · CosmoGrid | MSE: 0.028 ± 0.002 -> 0.025 ± 0.002 | Helped |
| Use learned feature groups with SOP instead of FG-F | CosmoGrid with CNN · CosmoGrid | purity: 0.529 ± 0.016 -> 0.647 ± 0.011 | Helped |
| Use learned feature groups with SOP instead of RISE-F | MultiRC with BERT · MultiRC | error rate: 0.366 ± 0.025 -> 0.366 ± 0.021 | No clear effect |
| Use learned feature groups with SOP instead of LIME-F | MultiRC with BERT · MultiRC | IOU: 0.177 ± 0.012 -> 0.176 ± 0.008 | Hurt |
| Use SOP instead of SHAP-F | ImageNet with ViT · ImageNet | insertion: 0.878 ± 0.007 -> 0.930 ± 0.003 | Helped |
| Use SOP instead of XDNN | ImageNet with ViT · ImageNet | deletion: 0.210 ± 0.003 -> 0.109 ± 0.000 | Helped |
| Increase SOP group count from 2 to 5 (ablation) | SOP on ImageNet-S · ImageNet-S | error rate: 6 percentage points | Helped |
| Increase SOP group count beyond 5, up to 20 (ablation) | SOP on ImageNet-S · ImageNet-S | performance | No clear effect |
| Train SOP at one group sparsity and evaluate at other inference-time sparsities (ablation) | SOP · ImageNet-S | error rate | Helped |
| Evaluate SOP at untrained sparsity levels on MultiRC (ablation) | SOP versus FRESH · MultiRC | performance | Hurt |
Surprising findings
- Group probing from SHAP-F-style post-hoc groups leaks label information (FG-F 13.40%), while SOP groups do not.
- For MultiRC, FRESH slightly outperforms SOP at untrained sparsity levels.
Limitations
- Per-feature SANN error bounds are proven only for specific binomial and monomial polynomials; the general exponential trend is a conjecture supported by fitted curves.
- Group probing and faithfulness results depend on chosen metrics; deletion metric biases toward few-feature models.
- Each group uses a fixed 20% feature budget and max 20 groups, and performance on MultiRC is not uniformly best.
Experimental setup
Datasets: ImageNet-S CosmoGrid MultiRC
Benchmarks: ImageNet-S CosmoGrid MultiRC
Metrics: error rate MSE IOU purity insertion deletion fidelity group probing accuracy
Baselines: LIME-F SHAP-F IG-F GC-F FG-F RISE-F Archipelago-F MFABA-F AGI-F AMPE-F BCos-F XDNN
Builds on: self-explaining neural networks BagNet Neural Additive Models FRESH sparsemax
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