Latent-Space Denoising for Temporal Causal Representation Learning with Mechanism Sparsity

Observation noise poses a major challenge to causal representation learning. In temporal data, noise affects latent representations at successive time steps, making temporal dependencies harder to estimate and causal structures harder to recover. To address this challenge, we integrate our latent-space denoising module with an existing mechanism-sparsity method to form a joint learning framework, Latent Denoising with Mechanism Sparsity (LDMS). The framework uses free-energy-guided particle dynamics to refine the latent distribution and combines denoising regularization with variational reconstruction and sparse transition estimation to improve the representations used for temporal mechanism learning. Our theoretical analysis considers the effects of both latent states and auxiliary variables at the preceding time step on the current latent state. We establish stability bounds for mechanism strengths after denoising, sufficient conditions for preserving sparse dependencies, and consistency conditions for joint denoising and mechanism estimation. These results quantify how denoising error affects mechanism estimation and graph recovery, providing a theoretical basis for the joint framework. Experimental results show that LDMS improves latent factor alignment and graph recovery, demonstrating the benefits of latent-space denoising for existing temporal causal representation learning methods and its potential as a plug-and-play module.