# Mask2Cause: Temporal Causal Discovery Beyond Causality in Mean

arXiv: https://arxiv.org/abs/2605.07280 · HTML: https://mlsanity.com/paper/2605.07280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 17 of 17)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [CausalFormer: An Interpretable Transformer for Temporal Causal Discovery](https://mlsanity.com/paper/2406.16708/) (2024)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [Kolmogorov-Arnold Networks for Time Series Granger Causality Inference](https://mlsanity.com/paper/2501.08958/) (2025)
- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems](https://mlsanity.com/paper/2511.03168/) (2025)

## Abstract (arXiv)

One approach to discovering causal relationships in multivariate time series is to ask whether a variable's history improves prediction of another variable. When this improvement is measured solely by reductions in optimal squared error, the criterion misses relationships that affect the target's conditional variance without changing its conditional mean. We propose Mask2Cause, an end-to-end Transformer framework for causal discovery through conditional mean and variance prediction. Each variable's history is embedded as a separate token, and a single learnable adjacency matrix, shared across layers and attention heads, controls information exchange between tokens. Gaussian negative log-likelihood and a sparsity penalty on this matrix jointly train the forecasting model and graph. Our population analysis connects the optimal log-loss reduction to causally conditioned directed information, providing an information-theoretic motivation for the training objective. We introduce Mixed Physics, a benchmark with separately controlled mean and variance dependencies, to evaluate recovery of mean-only and variance-only edges. In its pure-variance setting, Mask2Cause achieves 1.000 off-diagonal AUROC, compared with 0.521 for a corresponding squared-error model. Experiments on linear, chaotic, biological, and real-data-derived benchmarks demonstrate competitive graph recovery, while the inferred graphs support downstream tasks such as causal pruning for efficient forecasting and root-cause localization.