# Quantifying Structure in CLIP Embeddings: A Statistical Framework for Concept Interpretation

arXiv: https://arxiv.org/abs/2506.13831 · HTML: https://mlsanity.com/paper/2506.13831/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [The iWildCam 2020 Competition Dataset](https://mlsanity.com/paper/2004.10340/) (2020)
- [SPINE: SParse Interpretable Neural Embeddings](https://mlsanity.com/paper/1711.08792/) (2017)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Sparse Overcomplete Word Vector Representations](https://mlsanity.com/paper/1506.02004/) (2015)
- [Interpreting the Second-Order Effects of Neurons in CLIP](https://mlsanity.com/paper/2406.04341/) (2024)
- [Concentration and regularization of random graphs](https://mlsanity.com/paper/1506.00669/) (2015)
- [Decomposing and Interpreting Image Representations via Text in ViTs Beyond CLIP](https://mlsanity.com/paper/2406.01583/) (2024)
- [Vintage Factor Analysis with Varimax Performs Statistical Inference](https://mlsanity.com/paper/2004.05387/) (2020)
- [Understanding Regularized Spectral Clustering via Graph Conductance](https://mlsanity.com/paper/1806.01468/) (2018)
- [Spectral Neural Networks: Approximation Theory and Optimization Landscape](https://mlsanity.com/paper/2310.00729/) (2023)

## Built on by (most cited first, 6 of 6)

- [SpaceVLM: Sub-Space Modeling of Negation in Vision-Language Models](https://mlsanity.com/paper/2511.12331/) (2025)
- [SCoCCA: Multi-modal Sparse Concept Decomposition via Canonical Correlation Analysis](https://mlsanity.com/paper/2603.13884/) (2026)
- [Interpreting ResNet-based CLIP via Neuron-Attention Decomposition](https://mlsanity.com/paper/2509.19943/) (2025)
- [Explaining, Verifying, and Aligning Semantic Hierarchies in Vision-Language Model Embeddings](https://mlsanity.com/paper/2603.26798/) (2026)
- [Adaptive Subspace Projection for Generative Personalization](https://mlsanity.com/paper/2605.07257/) (2026)
- [COMET: Concept Space Dissection of the Modality Gap in Audio-Text Multimodal Contrastive Embeddings](https://mlsanity.com/paper/2605.29628/) (2026)

## Abstract (arXiv)

Concept-based approaches, which aim to identify human-understandable concepts within a model's internal representations, are a promising method for interpreting embeddings from deep neural network models, such as CLIP. While these approaches help explain model behavior, current methods lack statistical rigor, making it challenging to validate identified concepts and compare different techniques. To address this challenge, we introduce a hypothesis testing framework that quantifies rotation-sensitive structures within the CLIP embedding space. Once such structures are identified, we propose a post-hoc concept decomposition method. Unlike existing approaches, it offers theoretical guarantees that discovered concepts represent robust, reproducible patterns (rather than method-specific artifacts) and outperforms other techniques in terms of reconstruction error. Empirically, we demonstrate that our concept-based decomposition algorithm effectively balances reconstruction accuracy with concept interpretability and helps mitigate spurious cues in data. Applied to a popular spurious correlation dataset, our method yields a 22.6% increase in worst-group accuracy after removing spurious background concepts.