# Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations

arXiv: https://arxiv.org/abs/2406.15812 · HTML: https://mlsanity.com/paper/2406.15812/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 62 references that are in the map.
- First posted on arXiv 22 Jun 2024.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (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)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change](https://mlsanity.com/paper/1605.09096/) (2016)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Linearly Mapping from Image to Text Space](https://mlsanity.com/paper/2209.15162/) (2022)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [Reliability of CKA as a Similarity Measure in Deep Learning](https://mlsanity.com/paper/2210.16156/) (2022)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [Text-To-Concept (and Back) via Cross-Model Alignment](https://mlsanity.com/paper/2305.06386/) (2023)
- [Latent Space Translation via Semantic Alignment](https://mlsanity.com/paper/2311.00664/) (2023)
- [ASIF: Coupled Data Turns Unimodal Models to Multimodal Without Training](https://mlsanity.com/paper/2210.01738/) (2022)
- [N24News: A New Dataset for Multimodal News Classification](https://mlsanity.com/paper/2108.13327/) (2021)
- [Bridging Information-Theoretic and Geometric Compression in Language Models](https://mlsanity.com/paper/2310.13620/) (2023)

## Built on by (most cited first, 4 of 4)

- [Universally Converging Representations of Matter Across Scientific Foundation Models](https://mlsanity.com/paper/2512.03750/) (2025)
- [Large Vision-Language Models Get Lost in Attention](https://mlsanity.com/paper/2605.05668/) (2026)
- [Unsupervised detection of semantic correlations in big data](https://mlsanity.com/paper/2411.02126/) (2024)
- [Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension](https://mlsanity.com/paper/2510.01105/) (2025)

## Abstract (arXiv)

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear nature, which makes them challenging to detect using standard methods. This paper exploits the entanglement between intrinsic dimensionality and correlation to propose a metric that quantifies the (potentially nonlinear) correlation between high-dimensional manifolds. We first validate our method on synthetic data in controlled environments, showcasing its advantages and drawbacks compared to existing techniques. Subsequently, we extend our analysis to large-scale applications in neural network representations. Specifically, we focus on latent representations of multimodal data, uncovering clear correlations between paired visual and textual embeddings, whereas existing methods struggle significantly in detecting similarity. Our results indicate the presence of highly nonlinear correlation patterns between latent manifolds.