[CVPR 2025] SITH: Cracking the CLIP Code via Weight-Space Singular Vector Decomposition

TL;DR

SITH (Semantic Inspection of Transformer Heads) is a revolutionary data-free and training-free framework for interpreting CLIP. Instead of looking at image activations, it looks directly at the model weights. By decomposing attention matrices using SVD and a new algorithm called COMP, SITH identifies specific "concept vectors" inside attention heads. This allows for surgical model edits—like removing bias or NSFW content—simply by zeroing out specific singular values.

Impact: This work shifts mechanistic interpretability from a dataset-heavy task to a pure linear algebra problem, proving that CLIP’s weights are a direct map of human concepts.

The Motivation: Interpretation Without Bias

Most interpretability tools (like Sparse Autoencoders) are dataset-dependent. If your probe dataset is biased, your interpretation is biased. Furthermore, identifying that a "head" likes "colors" is too coarse. We need to know which specific feature inside that head represents "Fire-Engine Red" vs "Navy Blue."

SITH solves this by bypassing data entirely, looking at the Weight Space.

Methodology: The Core Mechanics

1. Weight Matrix Factorization

SITH focuses on the Value-Output (VO) matrix ($W_{VO}$) of each attention head. In the Transformer "circuit" view, the VO matrix determines what information is written into the residual stream.

SITH applies Singular Value Decomposition (SVD): $W_{VO}=U\Sigma V^T$

• Left Singular Vectors ($u_i$): What the head "reads" from the input.
• Right Singular Vectors ($v_i$): What the head "writes" to the output.
• Singular Values (${\sigma }_i$): The technical "strength" or importance of that feature.

2. COMP: Making Math Human-Readable

To turn abstract vectors into words, the authors developed COMP (Coherent Orthogonal Matching Pursuit). Standard matching pursuit just looks for the best mathematical fit. COMP adds a coherence term to ensure the words chosen make sense together (e.g., "sea," "ocean," and "beach" instead of "sea," "toaster," and "politics").

Figure 1: The SITH pipeline—from VO weight matrices to coherent concept clusters via SVD and COMP.

Interpretable Model Editing: Performance Results

Because SITH maps specific weights to specific concepts, we can "edit" the model without retraining.

Anti-Bias and Safety

• Spurious Correlations: On the "Waterbirds" dataset (birds on wrong backgrounds), SITH identifies "background" vectors. Setting ${\sigma }_i=0$ for those vectors improved accuracy significantly, outperforming head-level ablation methods like TextSpan.
• NSFW Filters: SITH identifies "unsafe" vectors. By suppressing them, the model becomes safer in retrieval tasks without losing general performance.

Fine-Tuning Insights

SITH reveals that when we fine-tune CLIP, we aren't learning new concepts. Instead, we are simply re-weighting the existing semantic basis. The "subspace shift" is subtle but task-aligned.

Figure 2: Substituting original singular vectors with SITH-reconstructed versions shows minimal loss in zero-shot accuracy, proving the fidelity of the decomposition.

Visual Evidence: Grounding Weights

Does a weight vector actually "see" what we think it does? The authors retrieved images from CC12M that most resembled specific singular vectors. The results are startling: a vector identified as "Two Children" consistently retrieves images of pairs of kids.

Figure 3: Top-3 images matched to singular vectors—confirming that the weight-based interpretations align with visual reality.

Deep Insight & Conclusion

The SITH framework is a masterclass in mechanistic interpretability. It proves that the "vision-language" alignment in models like CLIP is so robust that it is reflected directly in the geometry of its weights.

Takeaway: We no longer need massive datasets to understand or fix VLMs. By applying spectral analysis to model weights, we can achieve surgical, data-free interventions that make AI safer, more robust, and more transparent. The future of AI safety and adaptation may not lie in more data, but in better linear algebra.