Research map / Probabilistic and scientific modeling / Causal discovery
A Fixed-Point Approach for Causal Generative Modeling
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Reformulates SCMs as DAG-free fixed-point problems on topologically ordered variables, then combines a zero-shot topological-order predictor (trained by sequentially predicting leaves) with an attention-based fixed-point SCM learner for causal discovery and counterfactual generation.
Problem
Learning structural causal models from observational data is an NP-hard, ill-posed inverse problem because the mechanisms depend on an unknown DAG; existing amortized DAG inference does not guarantee acyclicity and scales quadratically.
Approach
Express SCMs as fixed-point equations on causally ordered variables (no DAG instantiation), prove weak identifiability given the topological order, amortize zero-shot topological-order inference by sequentially predicting graph leaves, and parameterize the fixed-point map with a causal-attention transformer whose attention rows can sum to less than one so it can represent DAGs.
Key results
- FiP achieves directed F1 of 0.76 on LIN OUT and 0.81 on RFF OUT, the best among compared methods (AVICI 0.73 and 0.74).
- FiP counterfactual re-scaled l2 error is 0.13 on both LIN OUT and RFF OUT, versus 0.39 for DECI and 0.20/0.16 for DoWhy-AVICI.
- With the true graph, the ANM model achieves counterfactual errors near 0.01-0.03 median, while using true TOs yields up to about 0.12 mean error.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FiP instead of AVICI for causal discovery | Causal discovery · LIN OUT | directed F1: 0.73 (0.16) -> 0.76 (0.20) | Helped |
| Use FiP instead of AVICI for causal discovery | Causal discovery · RFF OUT | directed F1: 0.74 (0.17) -> 0.81 (0.15) | Helped |
| Use FiP instead of DoWhy - AVICI | Counterfactual prediction · LIN OUT | re-scaled ℓ2 error: 0.20 (0.18) -> 0.13~(0.10) | Helped |
| Use FiP instead of DoWhy - AVICI | Counterfactual prediction · RFF OUT | re-scaled ℓ2 error: 0.16 (0.096) -> 0.13 (0.096) | Helped |
| Use the true graph instead of the true topological order | T_ANM · LIN IN | re-scaled ℓ2 error: 0.037 / 0.066 (0.057) -> 0.012 / 0.039 (0.060) | Helped |
| Use the true graph instead of the true topological order | T_ANM · LIN OUT | re-scaled ℓ2 error: 0.065 / 0.11 (0.084) -> 0.017 / 0.034 (0.048) | Helped |
| Use the true graph instead of the true topological order | T_ANM · RFF IN | re-scaled ℓ2 error: 0.065 / 0.10 (0.089) -> 0.033 / 0.059 (0.075) | Helped |
| Use the true graph instead of the true topological order | T_ANM · RFF OUT | re-scaled ℓ2 error: 0.11 / 0.12 (0.088) -> 0.033 / 0.042 (0.040) | Helped |
| Use the true graph instead of the true topological order | T_ANM · C-Suite | re-scaled ℓ2 error: 0.026 / 0.032 (0.030) -> 0.022 / 0.025 (0.022) | Helped |
| Compute d-TOE on a subsampled set of indices during training (ablation) | TO inference model M · Synthetic TO inference | topological ordering score | No clear effect |
Surprising findings
- Sub-sampling only 10% of the d-TOE loss terms during training yields performance similar to full training, with memory scaling linearly in d_max.
Experimental setup
Datasets: synthetic SCM datasets (P_IN training) C-Suite SynTReN protein measurements dataset
Benchmarks: LIN OUT RFF OUT C-Suite LIN IN RFF IN
Metrics: topological ordering score directed F1 re-scaled l2 counterfactual error
Baselines: PC GES GOLEM DAG-GNN GraN-DAG DP-DAG DECI AVICI DoWhy
Builds on: DECI AVICI autoregressive flows transformer attention
Closest papers by meaning
- Standardizing Structural Causal Models (ICLR 2025 · similarity 0.91)
- Learning Structural Causal Models from Ordering: Identifiable Flow Models (AAAI 2025 · similarity 0.90)
- Causal Abstraction Learning based on the Semantic Embedding Principle (ICML 2025 · similarity 0.88)
- Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inference (ICML 2024 · similarity 0.88)
- DCILP: A Distributed Approach for Large-Scale Causal Structure Learning (AAAI 2025 · similarity 0.88)
- Causal learning with the invariance principle (NeurIPS 2026 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.