# TopoAlign: Topology-Aware Visual Representation Alignment

arXiv: https://arxiv.org/abs/2605.25541 · HTML: https://mlsanity.com/paper/2605.25541/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 78 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 30 of 35)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Explainable Artificial Intelligence for Autonomous Driving: A Comprehensive Overview and Field Guide for Future Research Directions](https://mlsanity.com/paper/2112.11561/) (2021)
- [Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challenges](https://mlsanity.com/paper/2412.11427/) (2024)
- [Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiples](https://mlsanity.com/paper/1912.04853/) (2019)
- [Beyond Supervised vs. Unsupervised: Representative Benchmarking and Analysis of Image Representation Learning](https://mlsanity.com/paper/2206.08347/) (2022)
- [ReSi: A Comprehensive Benchmark for Representational Similarity Measures](https://mlsanity.com/paper/2408.00531/) (2024)
- [EmbeddingVis: A Visual Analytics Approach to Comparative Network Embedding Inspection](https://mlsanity.com/paper/1808.09074/) (2018)
- [Emblaze: Illuminating Machine Learning Representations through Interactive Comparison of Embedding Spaces](https://mlsanity.com/paper/2202.02641/) (2022)
- [embComp: Visual Interactive Comparison of Vector Embeddings](https://mlsanity.com/paper/1911.01542/) (2019)
- [The Effects of Randomness on the Stability of Node Embeddings](https://mlsanity.com/paper/2005.10039/) (2020)
- [Visual Comparison of Language Model Adaptation](https://mlsanity.com/paper/2208.08176/) (2022)
- [Universally Converging Representations of Matter Across Scientific Foundation Models](https://mlsanity.com/paper/2512.03750/) (2025)
- [VAC-CNN: A Visual Analytics System for Comparative Studies of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2110.13252/) (2021)
- [Measuring Representational Robustness of Neural Networks Through Shared Invariances](https://mlsanity.com/paper/2206.11939/) (2022)
- [Experimental Observations of the Topology of Convolutional Neural Network Activations](https://mlsanity.com/paper/2212.00222/) (2022)
- [Mapper Interactive: A Scalable, Extendable, and Interactive Toolbox for the Visual Exploration of High-Dimensional Data](https://mlsanity.com/paper/2011.03209/) (2020)
- [Inter-layer Information Similarity Assessment of Deep Neural Networks Via Topological Similarity and Persistence Analysis of Data Neighbour Dynamics](https://mlsanity.com/paper/2012.03793/) (2020)
- [Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution](https://mlsanity.com/paper/2303.03964/) (2023)
- [VISLIX: An XAI Framework for Validating Vision Models with Slice Discovery and Analysis](https://mlsanity.com/paper/2505.03132/) (2025)
- [MOUNTAINEER: Topology-Driven Visual Analytics for Comparing Local Explanations](https://mlsanity.com/paper/2406.15613/) (2024)
- [Explainable Mapper: Charting LLM Embedding Spaces Using Perturbation-Based Explanation and Verification Agents](https://mlsanity.com/paper/2507.18607/) (2025)

## Abstract (arXiv)

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different models, layers, or training conditions produce similar representations for the same inputs, with important implications for model interpretation, selection, and robustness analysis. Existing approaches to measure alignment primarily rely on geometric properties, such as neighborhood and cluster similarity, offering limited insight into the global organization of representations. In this work, we present TopoAlign, a topology-aware framework for visually comparing model representations from a structural perspective. Leveraging mapper graphs from topological data analysis, TopoAlign jointly analyzes graphs constructed from representations of shared inputs across different models or layers. The framework supports a top-down comparative workflow: it first performs global structure alignment via joint force-directed optimization to produce coordinated graph layouts; it then identifies local correspondences through automated detection of structurally matching regions, visualized with Bubble Sets; and finally it enables fine-grained pattern inspection through motif-based queries and membrane-inspired visualizations. We demonstrate TopoAlign through case studies on language and multimodal models, complemented by expert feedback. Our results show that TopoAlign provides meaningful insights into representation structure and alignment from a topological perspective.