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Interpreting CLIP with Hierarchical Sparse Autoencoders
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Introduces Matryoshka SAE (MSAE), which applies TopK at multiple nested k values during training, and applies it to CLIP to get a better sparsity-reconstruction Pareto frontier and extract concepts for similarity search and CelebA bias analysis.
Problem
Sparse autoencoders for CLIP embeddings face a trade-off between reconstruction quality and sparsity: L1 causes activation shrinkage while TopK imposes rigid sparsity, making CLIP representations hard to interpret and control.
Approach
Train one SAE with multiple TopK granularities (k_i = 2^i, nested) and sum the reconstruction losses across granularities with weights, then use the full ReLU latent at inference, giving hierarchical features without a single rigid k.
Key results
- MSAE reaches about 0.99 cosine similarity and FVU below 0.1 at roughly 80% sparsity on CLIP, establishing a better sparsity-fidelity Pareto frontier than ReLU and TopK SAEs.
- Matryoshka (UW) at expansion 8 on ViT-L/14 reports FVU 0.002 and CS 0.999 with 0 dead neurons, versus TopK k=256 with FVU 0.011 and 296 dead neurons.
- Over 120 validated concept neurons are extracted, with TopK k=32 yielding more valid concepts (216) than MSAE RW (140) under the strictest validation filter.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use hierarchical Matryoshka training instead of TopK SAE | CLIP ViT-L/14 SAE · ImageNet-1k training | FVU: .011_{±.003} -> .007_{±.003} | Helped |
| Use hierarchical Matryoshka training instead of BatchTopK SAE | CLIP ViT-L/14 SAE · ImageNet-1k training | FVU: .010_{±.005} -> .007_{±.003} | Helped |
| Use reverse weighting rather than uniform weighting (ablation) | Matryoshka SAE · ImageNet-1k training | L0: .748_{±.006} -> .829_{±.008} | Helped |
| Use reverse weighting rather than uniform weighting (ablation) | Matryoshka SAE · ImageNet-1k training | FVU: .002_{±.001} -> .007_{±.003} | Hurt |
| Train MSAE on text rather than image data (ablation) | Matryoshka SAE · ImageNet-1k | CKNNA: .809_{±.002} -> .782_{±.008} | Helped |
| Train MSAE on text rather than image data (ablation) | Matryoshka SAE · CC3M validation text | FVU: .060_{±.052} -> .008_{±.003} | Helped |
| Add activation soft-capping (ablation) | Matryoshka RW, size 12288 · ImageNet-1k validation | L0: 0.884_{±.006} -> 0.889_{±.005} | Helped |
| Add activation soft-capping (ablation) | Matryoshka RW, size 12288 · ImageNet-1k validation | FVU: 0.005_{±.003} -> 0.007_{±.003} | Hurt |
| Add activation soft-capping (ablation) | Matryoshka RW, size 12288 · ImageNet-1k validation | dead neurons: 32(124) -> 11(66) | Helped |
| Add activation soft-capping (ablation) | Matryoshka UW, size 12288 · ImageNet-1k validation | FVU: 0.000_{±.000} -> 0.001_{±.001} | Hurt |
| Train with Matryoshka granularities [128,256] rather than a single TopK threshold (ablation) | SAE · ImageNet-1k | EVR | Helped |
| Use multiple reconstruction granularities rather than a single TopK threshold | SAE progressive recovery · ImageNet-1k | CKNNA | Helped |
Surprising findings
- Under the strictest concept validation, TopK with k=32 yields more valid concept neurons than MSAE, contrary to the paper's framing of MSAE as more interpretable.
- Training SAEs on the text modality gave better cross-modal generalization and higher sparsity with no dead neurons than training on images.
Limitations
- Training requires multiple decoder passes with different TopK activations, adding computational overhead.
- Concept mapping relies on a unigram vocabulary and a similarity threshold, and many neurons do not map to clear concepts.
- Only 1-3% of MSAE neurons pass the concept validation at expansion rate 8, so concept learning evidence is limited.
Experimental setup
Datasets: CC3M ImageNet-1k CelebA LAION-400m vocabulary
Benchmarks: ImageNet-1k CC3M CelebA
Metrics: L0 FVU explained variance ratio cosine similarity CKNNA linear probe KL linear probe accuracy decoder orthogonality dead neuron count
Baselines: ReLU SAE TopK SAE BatchTopK SAE
Builds on: Matryoshka representation learning TopK SAE ReLU SAE BatchTopK Sparse autoencoders for CLIP (Rao et al.)
Closest papers by meaning
- Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models (NeurIPS 2025 · similarity 0.91)
- From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit (NeurIPS 2025 · similarity 0.90)
- Learning Multi-Level Features with Matryoshka Sparse Autoencoders (ICML 2025 · similarity 0.90)
- Sparse Autoencoders, Again? (ICML 2025 · similarity 0.89)
- SASA: Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretability (NeurIPS 2026 · similarity 0.89)
- Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE) (NeurIPS 2024 · similarity 0.89)
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