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Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models
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Proposes Archetypal SAEs (A-SAE) and relaxed RA-SAE, which constrain SAE decoder atoms to the convex hull of K-Means-distilled activations to improve dictionary stability in vision models, along with new plausibility and soft identifiability benchmarks.
Problem
Sparse autoencoders trained on vision model activations are unstable: identical models trained on similar data or with different seeds yield very different concept dictionaries, undermining interpretability.
Approach
Parameterize the SAE decoder dictionary as row-stochastic convex combinations of K-Means centroids of the data (archetypal dictionary), so atoms lie in conv(data) and the codes reconstruct within cone(data); a relaxed variant adds a small norm-bounded offset to match TopK reconstruction.
Key results
- On DINOv2 with 2000 concepts, RA-SAE reaches R^2 89.34 (vs TopK 89.52) while raising stability from 0.542 (TopK) to 0.927.
- On the soft identifiability benchmark, A-SAE reaches 0.9482 on DINOv2 and 0.9631 on ResNet versus best non-archetypal baseline around 0.83.
- Plausibility scores for RA-SAE are substantially higher than TopK SAE baseline across ConvNeXt, ResNet and ViT at all dictionary sizes (e.g., ResNet 0.6213 vs 0.3125 at 32k).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Constrain dictionary atoms to the data convex hull | SAE on the Soft Identifiability benchmark · DINOv2 | soft identifiability accuracy: 0.8135 -> 0.9482 | Helped |
| Constrain dictionary atoms to the data convex hull | SAE on the Soft Identifiability benchmark · ResNet | soft identifiability accuracy: 0.8150 -> 0.9631 | Helped |
| Constrain dictionary atoms to the data convex hull | SAE on the Soft Identifiability benchmark · SigLIP | soft identifiability accuracy: 0.8289 -> 0.9602 | Helped |
| Constrain dictionary atoms to the data convex hull | SAE on the Soft Identifiability benchmark · ViT | soft identifiability accuracy: 0.8328 -> 0.9615 | Helped |
| Replace the free TopK dictionary with a relaxed archetypal dictionary | TopK SAE on DINOv2 · DINOv2 | stability: 0.542 -> 0.927 | Helped |
| Replace the free TopK dictionary with a relaxed archetypal dictionary | TopK SAE on DINOv2 · DINOv2 | OOD score: 0.551 -> 0.060 | Helped |
| Use a relaxed archetypal dictionary instead of TopK SAE | TopK SAE on DINOv2 · DINOv2 | R²: 89.52 -> 89.34 | Hurt |
| Relax the convex-hull constraint with δ=1.0 rather than δ=0 (ablation) | A-SAE on ConvNeXt · ConvNeXt, 32k dictionary | plausibility score: 0.3999 -> 0.5581 | Helped |
| Relax the convex-hull constraint with δ=1.0 rather than δ=0 (ablation) | A-SAE on ResNet · ResNet, 32k dictionary | plausibility score: 0.6133 -> 0.6213 | Helped |
| Relax the convex-hull constraint with δ=1.0 rather than δ=0 (ablation) | A-SAE on ViT · ViT, 32k dictionary | plausibility score: 0.3721 -> 0.5014 | Helped |
| Relax the convex-hull constraint with δ=1.0 rather than δ=0 (ablation) | A-SAE on DINOv2 · DINOv2 | soft identifiability accuracy: 0.9482 -> 0.9447 | Hurt |
Surprising findings
- Classical SAEs with dictionaries of up to 32k atoms still show limited alignment with true classification directions.
- Stability of TopK SAE on DINOv2 is around 0.5, meaning roughly half of concepts change across seeds.
Limitations
- Archetypal dictionary requires distilling data into centroids, with an approximation to the full convex hull.
- Evaluated only on vision models; extension to LLMs is proposed but not tested.
- Relaxation parameter delta trades off stability against reconstruction and plausibility; larger delta degrades stability toward baseline.
Experimental setup
Datasets: ImageNet Soft identifiability synthetic gem collages (12 datasets)
Benchmarks: Plausibility benchmark Soft Identifiability benchmark ImageNet reconstruction R^2
Metrics: R^2 dead codes stability max cosine OOD score stable rank effective rank coherence connectivity negative interference
Baselines: Vanilla SAE TopK SAE JumpReLU SAE Semi-NMF Convex-NMF KMeans ICA Sparse PCA SVD PCA ACE ICE
Builds on: Archetypal analysis TopK SAE JumpReLU SAE Convex-NMF Semi-NMF
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