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FaCT: Faithful Concept Traces for Explaining Neural Network Decisions
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Proposes FaCT, a B-cos network with bias-free sparse autoencoder bottlenecks that yields shared, faithful concept decompositions (logit = sum of concept contributions, concept activation = sum of pixel attributions), and a DINOv2-based C²-score for concept consistency.
Problem
Post-hoc concept explanations are often unfaithful to the model and rely on restrictive assumptions (class-specificity, small spatial extent, predefined concept sets), and existing consistency metrics depend on human part annotations.
Approach
Insert bias-free TopK sparse autoencoders into B-cos networks at intermediate layers so concepts are part of the forward pass; the dynamic-linear structure of B-cos then gives exact concept-to-logit contributions and exact pixel-level attributions per concept. Also a class-agnostic consistency metric (C²-score) using DINOv2 features with LoftUp upsampling and random-attribution baseline.
Key results
- C2-score for DenseNet-121 Block 3/4 rises from 0.11 to 0.39 with under 3% ImageNet accuracy drop relative to B-cos.
- Concept consistency across concepts improves from 0.09 (B-cos channels) to 0.37 (FaCT) in C2-score.
- User study with 38 participants rated FaCT concepts as significantly more interpretable than B-cos channels, with input attributions raising early-layer scores by about 0.5/5 on average.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace B-cos channels with FaCT concepts | DenseNet-121 Block 3/4 · ImageNet | C²-score: 0.11→0.39 | Helped |
| replace B-cos channels with FaCT concepts | ImageNet models · ImageNet | C²-score: 0.09→0.37 | Helped |
| use FaCT's sparse concept representation instead of the original B-cos model | ImageNet models · ImageNet | accuracy: < 3% | Hurt |
| add faithful input attributions to FaCT concept visualizations | FaCT concepts · ImageNet, user study | interpretability score: about 0.5/5 average increase | Helped |
| add faithful input attributions to early-layer FaCT concept visualizations | FaCT early-layer concepts · ImageNet, user study | interpretability score: +3.0/5; +2.5/5 | Helped |
| rank concepts using C²-score | DenseNet-121 late-layer concepts · ImageNet, user study | Spearman correlation with user ratings: 33/38; 20/38 | Helped |
Surprising findings
- Random baseline C2-score per-class (0.40) is far higher than the shared-set random baseline (0.0005), showing that per-class evaluation inflates consistency.
- A small set of concepts causes sharp accuracy drops when deleted at Block 2/4, and these concepts always contribute to every decision.
Limitations
- Concept-to-logit faithfulness depends on the B-cos architecture; standard models are not directly supported.
- Accuracy drops slightly (under 3%) relative to original B-cos models.
- C2-score depends on foundation model features (DINOv2) and upsampler (LoftUp) with centering needed for baseline similarity.
Experimental setup
Datasets: ImageNet PartImageNet
Benchmarks: ImageNet PartImageNet
Metrics: top-1 accuracy C2-score logit deletion drop overall accuracy drop under concept deletion spatial extent (80% attribution pixels) user interpretability score (5-point)
Baselines: B-cos channels CRAFT CRP Saliency Sobol indices PartImageNet annotations
Builds on: B-cos networks TopK sparse autoencoder CRAFT DINOv2 CLIP-Dissect
Closest papers by meaning
- Visual Concept Connectome (VCC): Open World Concept Discovery and their Interlayer Connections in Deep Models (CVPR 2024 · similarity 0.88)
- Understanding Inter-Concept Relationships in Concept-Based Models (ICML 2024 · similarity 0.87)
- Show and Tell: Visually Explainable Deep Neural Nets via Spatially-Aware Concept Bottleneck Models (CVPR 2025 · similarity 0.87)
- Keep the Faith: Faithful Explanations in Convolutional Neural Networks for Case-Based Reasoning (AAAI 2024 · similarity 0.86)
- FastCAV: Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks (ICML 2025 · similarity 0.86)
- FACE: Faithful Automatic Concept Extraction (NeurIPS 2025 · similarity 0.86)
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