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Conclusion

We presented ACIA, a measure-theoretic framework for anti-causal representation learning. ACIA provides:

• a unified interventional kernel formulation that accommodates both perfect and imperfect interventions without requiring explicit causal structure knowledge;
• a novel causal dynamic that captures anti-causal structure from raw observations, together with a causal abstraction that distills environment-invariant relationships;
• a principled optimization framework based on a min–max objective with causal regularizers; and
• provable out-of-distribution generalization guarantees that bound the performance gap between training and unseen environments.

Overall, ACIA opens new directions for causal representation learning in settings where traditional assumptions—such as perfect interventions or known causal structures—do not hold.

Future Work

In future, we plan to generalize ACIA to handle more complex causal structures—such as confounded-descendant or mixed causal-anticausal scenarios.