Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality. Our code is available at https://github.com/lingbai-kong/CausalFormer.

This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks. Our study primarily focuses on a proof-of-concept investigation based on simulated neural dynamics, for which the ground-truth causality is known through the underlying connectivity matrix. For transformer models trained to forecast neuronal population dynamics, we show that the cross attention module effectively captures the causal relationship among neurons, with an accuracy equal or superior to that for the most popular Granger causality analysis method. While we acknowledge that real-world neurobiology data will bring further challenges, including dynamic connectivity and unobserved variability, this research offers an encouraging preliminary glimpse into the utility of the transformer model for causal representation learning in neuroscience.