Abstract: Causal representation learning aims to extract high-level latent causal factors from low-level sensory data. Many existing methods often identify these latent factors by assuming they are statistically independent. However, correlations and causal connections between factors are prevalent across applications. In this talk, we explore how geometric signatures of latent causal factors can facilitate causal representation learning with interventional data, without any assumptions about their distributions or dependency structure. The key observation is that the absence of causal connections between latent causal factors often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). Leveraging this fact, we can identify latent causal factors up to permutation and scaling with data from perfect do interventions. Moreover, we can achieve block affine identification with data from imperfect interventions. These results highlight the unique power of geometric signatures in causal representation learning.