Knockoffs are a popular statistical tool for conditional variable selection in high dimension.

Since itsintroduction inparametric design, knockofftechniques haveevolvedto handle arbitrary data distributions using deep learning-based generative models.

In artificial intelligence research, comprehending the internal representations of a large language model is still a fundamental challenge [Olah et al., 2020]. Neural network activations can now be broken down into interpretable features using sparse autoencoders (SAEs) [Cunningham et al., 2023, Templeton et al., 2024]. SAEs seek to deconstruct polysemantic neurons into monosemantic features that correlate to concepts that are comprehensible to humans by learning overcomplete sparse representations of model activations. Finding SAE features and confirming their legitimacy are not the same thing, though. The methods used in most interpretability research today are correlation with downstream tasks, automated explanation scoring, or manual inspection. These methods are unable to differentiate between real computational patterns and spurious correlations that result from the multiple testing problem, and they lack formal statistical guarantees. Random chance alone will yield a large number of apparent correlations with any target variable when thousands of candidate features are examined.

Causal discovery uncovers complex relationships between variables, enhancing predictions, decision-making, and insights into real-world systems, especially in nonlinear multivariate time series. However, most existing methods primarily focus on pairwise cause-effect relationships, overlooking interactions among groups of variables, i.e., subsystems and their collective causal influence. In this study, we introduce gCDMI, a novel multi-group causal discovery method that leverages group-level interventions on trained deep neural networks and employs model invariance testing to infer causal relationships. Our approach involves three key steps. First, we use deep learning to jointly model the structural relationships among groups of all time series. Second, we apply group-wise interventions to the trained model. Finally, we conduct model invariance testing to determine the presence of causal links among variable groups. We evaluate our method on simulated datasets, demonstrating its superior performance in identifying group-level causal relationships compared to existing methods. Additionally, we validate our approach on real-world datasets, including brain networks and climate ecosystems. Our results highlight that applying group-level interventions to deep learning models, combined with invariance testing, can effectively reveal complex causal structures, offering valuable insights for domains such as neuroscience and climate science.