  We study causal representation learning, the task of recovering high-level
latent variables and their causal relationships in the form of a causal graph
from low-level observed data (such as text and images), assuming access to
observations generated from multiple environments. Prior results on the
identifiability of causal representations typically assume access to
single-node interventions which is rather unrealistic in practice, since the
latent variables are unknown in the first place. In this work, we provide the
first identifiability results based on data that stem from general
environments. We show that for linear causal models, while the causal graph can
be fully recovered, the latent variables are only identified up to the
surrounded-node ambiguity (SNA) \citep{varici2023score}. We provide a
counterpart of our guarantee, showing that SNA is basically unavoidable in our
setting. We also propose an algorithm, \texttt{LiNGCReL} which provably
recovers the ground-truth model up to SNA, and we demonstrate its effectiveness
via numerical experiments. Finally, we consider general non-parametric causal
models and show that the same identification barrier holds when assuming access
to groups of soft single-node interventions.
