# Cross-Modal Redundancy and the Geometry of Vision-Language Embeddings

arXiv: https://arxiv.org/abs/2602.06218 · HTML: https://mlsanity.com/paper/2602.06218/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in MLLM training and visual instruction tuning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 60 of its 78 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- Multimodal LLMs / vision-language models / [MLLM training and visual instruction tuning](https://mlsanity.com/mllm/mllm-training-and-visual-instruction-tuning/)

## Builds on (most cited first, 30 of 60)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Evaluating Explainable AI: Which Algorithmic Explanations Help Users Predict Model Behavior?](https://mlsanity.com/paper/2005.01831/) (2020)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)

## Built on by (most cited first, 10 of 10)

- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Out of Sight, Still in Mind: Token Compression for Omni-LLMs](https://mlsanity.com/paper/2607.21179/) (2026)
- [When Language Overwrites Vision: Over-Alignment and Geometric Debiasing in Vision-Language Models](https://mlsanity.com/paper/2605.08245/) (2026)
- [A Unifying Framework for Concept-Based Representational Similarity](https://mlsanity.com/paper/2606.09653/) (2026)
- [Same Concept, Different Directions: Cross-Modal Feature Heterogeneity in Sparse Autoencoders](https://mlsanity.com/paper/2606.29888/) (2026)
- [The Hyperspherical Geometry of CLIP Latent Space: A Semantic Mixture Model](https://mlsanity.com/paper/2607.13660/) (2026)
- [Decoder-Preserving Sparse Autoencoders: Which Readouts Survive Sparse Compression?](https://mlsanity.com/paper/2607.17425/) (2026)
- [Linguistic Context Recodes Visual Representations in Vision-Language Models](https://mlsanity.com/paper/2608.00035/) (2026)
- [From Interpretability Methods to Interpretable Models](https://mlsanity.com/paper/2609.05399/) (2026)
- [Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility](https://mlsanity.com/paper/2610.20139/) (2026)

## Abstract (arXiv)

Vision-language models (VLMs) align images and text with remarkable success, yet the geometry of their shared embedding space remains poorly understood. To probe this geometry, we begin from the Iso-Energy Assumption, which exploits cross-modal redundancy: a concept that is truly shared should exhibit the same average energy across modalities. We operationalize this assumption with an Aligned Sparse Autoencoder (SAE) that encourages energy consistency during training while preserving reconstruction. We find that this inductive bias changes the SAE solution without harming reconstruction, giving us a representation that serves as a tool for geometric analysis. Sanity checks on controlled data with known ground truth confirm that alignment improves when Iso-Energy holds and remains neutral when it does not. Applied to foundational VLMs, our framework reveals a clear structure with practical consequences: (i) sparse bimodal atoms carry the entire cross-modal alignment signal; (ii) unimodal atoms act as modality-specific biases and fully explain the modality gap; (iii) removing unimodal atoms collapses the gap without harming performance; (iv) restricting vector arithmetic to the bimodal subspace yields in-distribution edits and improved retrieval. These findings suggest that the right inductive bias can both preserve model fidelity and render the latent geometry interpretable and actionable.