Research map / Probabilistic and scientific modeling / Variational and generative sampling
From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows
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Proposes attributing predictions along least-action (Wasserstein-2 geodesic) generative transport paths from a reference distribution to data, using Rectified Flow/Reflow, with Aumann-Shapley line-integral credit allocation proven unique under fixed-path axioms.
Problem
Feature attributions depend on the counterfactual path from a reference state to the input (baseline, interpolation, generative trajectory), and the choice of path is often hand-designed or set by the model's own sensitivity geometry.
Approach
Separate attribution into fixed-path credit allocation (Aumann-Shapley line integral, shown unique under axioms) and path selection, where the path is a characteristic curve of a kinetic-action-minimizing generative flow from a reference distribution to the data distribution, approximated by Rectified Flow and Reflow.
Key results
- On CIFAR-10 Transport Flow reduces FCE to 0.005 versus about 1e4 for Integrated Gradients and 3.1e3 for DDIM, with best blur-deletion among path methods (1.311).
- Reflow (2-RF) lowers discrete kinetic action from 3179.2 to 3006.9 and raises SSIM of attribution maps from 0.716 to 0.911 relative to 1-RF.
- On CelebA-HQ DDIM has slightly better deletion scores (0.175 zero, 0.897 blur) while Transport Flow has FCE 1.780 versus 2.8e5 for DDIM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Reflow (2-RF) versus one-step Rectified Flow (1-RF) (ablation) | Rectified Flow path · seeds, path geometry | discrete kinetic action: 3179.2 to 3006.9 (lower) | Helped |
| Reflow versus one-step Rectified Flow (ablation) | Rectified Flow path · seeds, path geometry | attribution stability (SSIM, rank correlation, pixel variance): SSIM 0.716 to 0.911; rank corr 0.662 to 0.882; pixel var 0.0032 to 0.0010 | Helped |
| Increase integration steps K from 10 to 200 (ablation) | Aumann-Shapley discrete estimator · CUB-200 completeness | relative efficiency error: 19.30% to 1.34% | Helped |
| Rectified Flow/Reflow transport path instead of straight-line IG path | Integrated Gradients path · CIFAR-10 | FCE: ~1e4 to 0.005 | Helped |
| Transport path instead of DDIM generative path | DDIM path · CIFAR-10 | deletion blur: 1.360 to 1.311 | Helped |
| Transport path instead of DDIM generative path | DDIM path · CIFAR-10 | deletion zero: 0.444 to 0.456 | Hurt |
| Transport path instead of DDIM generative path | DDIM path · CelebA-HQ | FCE: 2.8e5 to 1.78 | Helped |
| Transport path instead of DDIM generative path | DDIM path · CelebA-HQ | deletion blur and EAS: deletion blur 0.897 to 0.926; EAS 0.147 to 0.091 | Hurt |
| Transport path instead of straight-line IG path | Integrated Gradients path · CIFAR-10 and CelebA-HQ | SATV and deletion: SATV 0.643 to 0.062 (CIFAR-10); deletion zero 0.670 to 0.456 (CIFAR-10) | Mixed |
| Transport path instead of straight-line IG path | Integrated Gradients path · CelebA-HQ | EAS: 0.060 (IG) to 0.091 (Transport Flow) | Mixed |
Surprising findings
- On CelebA-HQ, Transport Flow's FCE (1.78) is far larger than its CIFAR-10 value, and EAS is lower than DDIM and SmoothGrad-level baselines in some settings, so the method is not uniformly superior.
- Deletion faithfulness is not uniformly best; DDIM has better zero-deletion on CIFAR-10 and CelebA-HQ.
Limitations
- Paper explicitly does not claim data-manifold membership or universal superiority across metrics.
- Ideal optimal-transport geodesic is only approximated by Rectified Flow/Reflow; stability bound depends on uniform vector-field error assumptions that are not verified in high dimension.
- Completeness residual reported as nonzero (5.34% at K=50), and the backward-forward endpoint may not return to the input.
Experimental setup
Datasets: CIFAR-10 CelebA-HQ CUB-200
Benchmarks: CIFAR-10 CelebA-HQ CUB-200
Metrics: deletion zero deletion blur FCE SATV EAS GPS completeness residual SSIM rank correlation pixel variance
Baselines: SmoothGrad Guided Backpropagation GradientSHAP Integrated Gradients DDIM generative paths KernelSHAP-style baselines
Builds on: Integrated Gradients Rectified Flow Reflow Benamou-Brenier formulation Shapley value
Closest papers by meaning
- On the Relation between Rectified Flows and Optimal Transport (NeurIPS 2025 · similarity 0.88)
- Beckmann Transport Models: From Autonomous Flows to One-Step Maps (NeurIPS 2026 · similarity 0.87)
- Dynamic Conditional Optimal Transport through Simulation-Free Flows (NeurIPS 2024 · similarity 0.86)
- Metric Flow Matching for Smooth Interpolations on the Data Manifold (NeurIPS 2024 · similarity 0.86)
- One-Shot Generative Flows: Existence and Obstructions (NeurIPS 2026 · similarity 0.85)
- Path Choice Matters for Clear Attributions in Path Methods (ICLR 2024 · similarity 0.85)
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