The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
We report a systematic failure mode in predictive representation learning. Across 2695 neural network configurations trained to predict linear-Gaussian dynamics, the optimal encoder tracks the environment rather than the system it is meant to model. The mean causal fidelity -- the fraction of encoder sensitivity allocated to system degrees of freedom -- is 0.49, and only 2.5% of configurations exceed 0.70. The failure intensifies with dimension: at N=100, the optimal encoder becomes causally blind (fidelity ~10^{-8}) while achieving 92% lower prediction error than the causal representation. We prove this is not an optimization artifact but a structural property of the predictive objective...
| Authors | Kejun Liu |
|---|---|
| Primary category | cs.LG |
| Published | 6 May 2026 |
| Last updated at source | 6 May 2026 |
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