Coordinated Disentanglement with Iterative Mode Discovery Under Hidden Correlations

Supervised disentangled representation learning (DRL) typically assumes independence between attributes. However, real-world data often contain hidden correlations, where specific attribute values exhibit multi-modal distributions (modes) that are themselves correlated with other attributes. The authors investigate how to achieve robust disentanglement in these scenarios without losing critical mode information, while avoiding the catastrophic error amplification that occurs when disentanglement and mode discovery modules are trained naively.

The authors propose Coordinated Disentanglement with Iterative mode Discovery (CoDID). The framework consists of three main components:

1. Disentanglement Module: Learns representations while enforcing conditional independence based on cluster labels, using a dynamic architecture that adapts to an evolving number of modes.
2. Mode Discovery Module: Uses a Dirichlet Process Gaussian Mixture Model (DPGMM) to perform non-parametric clustering, allowing the model to infer the number of modes end-to-end without pre-specification.
3. Meta-Coordination Mechanism: A novel meta-optimization layer that assigns weights to marginal representations during conditional mutual information (CMI) minimization. This mechanism identifies and corrects within-cluster correlations, preventing the model from collapsing mode information and guiding cluster splits to refine the discovery process.

CoDID addresses the cycle of error amplification where inaccurate clustering leads to poor disentanglement, which in turn degrades future clustering. By using meta-learned weights, the model effectively differentiates correlated modes within clusters. Empirical evaluations across seven diverse datasets show that CoDID outperforms state-of-the-art baselines, achieving an average improvement of 7.8% in accuracy and 7.9% in macro F1 score, particularly under correlation shift and out-of-distribution tasks.