# FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data

arXiv: https://arxiv.org/abs/2608.10857 · HTML: https://mlsanity.com/paper/2608.10857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 70 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 30 of 38)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Domain Separation Networks](https://mlsanity.com/paper/1608.06019/) (2016)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Balanced Multimodal Learning via On-the-fly Gradient Modulation](https://mlsanity.com/paper/2203.15332/) (2022)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [Learning Factorized Multimodal Representations](https://mlsanity.com/paper/1806.06176/) (2018)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [What Makes Multi-modal Learning Better than Single (Provably)](https://mlsanity.com/paper/2106.04538/) (2021)
- [Multimodal Representation Learning by Alternating Unimodal Adaptation](https://mlsanity.com/paper/2311.10707/) (2023)
- [AudioMNIST: Exploring Explainable Artificial Intelligence for Audio Analysis on a Simple Benchmark](https://mlsanity.com/paper/1807.03418/) (2018)
- [Image-to-image translation for cross-domain disentanglement](https://mlsanity.com/paper/1805.09730/) (2018)
- [A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models](https://mlsanity.com/paper/2406.03537/) (2024)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Intrinsic Dimensionality Estimation within Tight Localities: A Theoretical and Experimental Analysis](https://mlsanity.com/paper/2209.14475/) (2022)
- [Structural Learning and Integrative Decomposition of Multi-View Data](https://mlsanity.com/paper/1707.06573/) (2017)
- [Learning Manifold Dimensions with Conditional Variational Autoencoders](https://mlsanity.com/paper/2302.11756/) (2023)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)
- [Estimating the effective dimension of large biological datasets using Fisher separability analysis](https://mlsanity.com/paper/1901.06328/) (2019)
- [Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis](https://mlsanity.com/paper/2006.00436/) (2020)
- [Improving Multimodal Accuracy Through Modality Pre-training and Attention](https://mlsanity.com/paper/2011.06102/) (2020)
- [Unity by Diversity: Improved Representation Learning in Multimodal VAEs](https://mlsanity.com/paper/2403.05300/) (2024)
- [An Information Criterion for Controlled Disentanglement of Multimodal Data](https://mlsanity.com/paper/2410.23996/) (2024)
- [A Survey of Dimension Estimation Methods](https://mlsanity.com/paper/2507.13887/) (2025)
- [Multi-View Independent Component Analysis with Shared and Individual Sources](https://mlsanity.com/paper/2210.02083/) (2022)

## Abstract (arXiv)

Determining the complexity, or Intrinsic Dimension (ID), of data is fundamental to efficient and interpretable representation learning. This is particularly challenging in multi-modal settings when trying to learn disentangled representations for shared and private information. Existing techniques leave a critical gap: they are often static, uni-modal, or in the case of contrastive methods, adapt only to the shared ID implicitly. We introduce Fidelity-Guided Rank Optimization (FiGuRO), a framework for approximating the ID of uni- and multi-modal data under constraints of model capacity and hyperparameters. FiGuRO learns the dimensions of low-rank projections using truncated singular value decomposition and an algorithm that determines when to reduce or increase dimension and in which latent space. Disentanglement of shared and private information arises as an emergent property of this optimization, eliminating the need for complex auxiliary loss functions. We demonstrate that FiGuRO outperforms existing ID estimation techniques and is more robust to hyperparameter changes. Across simulations and real-world data, FiGuRO captures distinct ID scales and varying subspace ratios, and decomposes shared and private information successfully. Furthermore, we show that FiGuRO can be applied to modern uni-modal pretrained models, enabling efficient, post-hoc disentanglement of multi-modal representations.