FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data

2026-08-11

AI Summary

This work addresses the challenge of accurately estimating the intrinsic dimensions of shared and private information in multimodal data, a task inadequately handled by existing methods that are often static or only implicitly model shared structures. To overcome this limitation, we propose FiGuRO, a fidelity-guided rank optimization framework that dynamically estimates the intrinsic dimensions of both unimodal and multimodal representations. FiGuRO adaptively adjusts low-rank projection dimensions under constraints of model capacity and hyperparameters, enabling the disentanglement of shared and private components to emerge naturally from the optimization process—without requiring complex auxiliary losses. The framework also supports efficient post-hoc disentanglement of pre-trained unimodal models. Experiments on both synthetic and real-world datasets demonstrate that FiGuRO consistently outperforms current approaches, robustly capturing multiscale intrinsic dimensions and subspace proportions while effectively separating shared and private information.

Abstract

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.

Problem

• Intrinsic Dimension
• Multi-Modal Data
• Disentangled Representations
• Dimension Estimation
• Shared and Private Information

Innovation

• Intrinsic Dimension Estimation
• Multi-Modal Representation Learning
• Disentangled Representation
• Low-Rank Projection
• Fidelity-Guided Optimization