Learning Causal Graphs at Scale: A Foundation Model Approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918067949273088 |
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| author | Yin, Naiyu Gao, Tian Yu, Yue |
| author_facet | Yin, Naiyu Gao, Tian Yu, Yue |
| contents | Due to its human-interpretability and invariance properties, Directed Acyclic Graph (DAG) has been a foundational tool across various areas of AI research, leading to significant advancements. However, DAG learning remains highly challenging, due to its super-exponential growth in computational cost and identifiability issues, particularly in small-sample regimes. To address these two challenges, in this work we leverage the recent success of linear transformers and develop a foundation model approach for discovering multiple order-consistent DAGs across tasks. In particular, we propose Attention-DAG (ADAG), a novel attention-mechanism-based architecture for learning multiple linear Structural Equation Models (SEMs). ADAG learns the mapping from observed data to both graph structure and parameters via a nonlinear attention-based kernel, enabling efficient multi-task estimation of the underlying linear SEMs. By formulating the learning process across multiple tasks as a continuous optimization problem, the pre-trained ADAG model captures the common structural properties as a shared low-dimensional prior, thereby reducing the ill-posedness of downstream DAG learning tasks in small-sample regimes. We evaluate our proposed approach on benchmark synthetic datasets and find that ADAG achieves substantial improvements in both DAG learning accuracy and zero-shot inference efficiency. To the best of our knowledge, this is the first practical approach for pre-training a foundation model specifically designed for DAG learning, representing a step toward more efficient and generalizable down-stream applications in causal discovery. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Causal Graphs at Scale: A Foundation Model Approach Yin, Naiyu Gao, Tian Yu, Yue Machine Learning Artificial Intelligence Due to its human-interpretability and invariance properties, Directed Acyclic Graph (DAG) has been a foundational tool across various areas of AI research, leading to significant advancements. However, DAG learning remains highly challenging, due to its super-exponential growth in computational cost and identifiability issues, particularly in small-sample regimes. To address these two challenges, in this work we leverage the recent success of linear transformers and develop a foundation model approach for discovering multiple order-consistent DAGs across tasks. In particular, we propose Attention-DAG (ADAG), a novel attention-mechanism-based architecture for learning multiple linear Structural Equation Models (SEMs). ADAG learns the mapping from observed data to both graph structure and parameters via a nonlinear attention-based kernel, enabling efficient multi-task estimation of the underlying linear SEMs. By formulating the learning process across multiple tasks as a continuous optimization problem, the pre-trained ADAG model captures the common structural properties as a shared low-dimensional prior, thereby reducing the ill-posedness of downstream DAG learning tasks in small-sample regimes. We evaluate our proposed approach on benchmark synthetic datasets and find that ADAG achieves substantial improvements in both DAG learning accuracy and zero-shot inference efficiency. To the best of our knowledge, this is the first practical approach for pre-training a foundation model specifically designed for DAG learning, representing a step toward more efficient and generalizable down-stream applications in causal discovery. |
| title | Learning Causal Graphs at Scale: A Foundation Model Approach |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2506.18285 |