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About this paper
Gabriele D'Acunto, Paolo Di Lorenzo, Sergio Barbarossa
The paper develops a causal abstraction network in which agents with local, subjective causal models connect different-resolution representations through causally meaningful mappings and reconcile observational, interventional, or counterfactual distributions. In a synthetic Gaussian-mixture test, genuine linear causal abstraction reached MPW² below 10^-4, while a non-causal coarsening stayed above 10^-1. This result is dataset-specific, conditional on structural priors and converged trials.
Key insights
- Global causal coherence is encoded by the null space of the connection Laplacian: for a consistent connected network, its kernel identifies assignments that agree across all agents and abstraction paths.
- Repeated diffusion of local probability distributions can produce Gaussian mixtures, and under suitable connectivity and self-contribution conditions converges to a global section with shared latent covariance structure.
- Mixture-calsep separates probabilistic alignment from structural abstraction, allowing models with different mixture components and resolutions to be compared even when component correspondences are initially unknown.
Summary by alphaXiv.
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