The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
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| Format: | Preprint |
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2026
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| _version_ | 1866917464545165312 |
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| author | Liu, Kejun |
| author_facet | Liu, Kejun |
| contents | 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: when environment modes are slower or less noisy than system modes, every minimizer of the population risk encodes the former. The set of dynamics exhibiting this predictive-causal gap is open and of positive measure in parameter space. In a nonlinear Duffing-GRU sweep, unconstrained predictors learn environment-dominant representations in 55% of tasks (95% CI 41--68%) versus 24% under operational grounding (p=2.3e-3); the median out-of-distribution MSE inflation under environment shift is 1.82x versus 1.00x. Operational grounding -- restricting the loss to system observables -- partially suppresses the gap, but causal fidelity is never recovered without an explicit system-environment boundary. The results identify the predictive-causal gap as a structural limit of learning, with implications for self-supervised representation learning, world models, and the scaling paradigm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence Liu, Kejun Machine Learning 68T07, 62M45, 37M10, 81S2268T07, 62M45, 37M10, 81S22 68T07, 62M45, 37M10, 81S22 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: when environment modes are slower or less noisy than system modes, every minimizer of the population risk encodes the former. The set of dynamics exhibiting this predictive-causal gap is open and of positive measure in parameter space. In a nonlinear Duffing-GRU sweep, unconstrained predictors learn environment-dominant representations in 55% of tasks (95% CI 41--68%) versus 24% under operational grounding (p=2.3e-3); the median out-of-distribution MSE inflation under environment shift is 1.82x versus 1.00x. Operational grounding -- restricting the loss to system observables -- partially suppresses the gap, but causal fidelity is never recovered without an explicit system-environment boundary. The results identify the predictive-causal gap as a structural limit of learning, with implications for self-supervised representation learning, world models, and the scaling paradigm. |
| title | The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence |
| topic | Machine Learning 68T07, 62M45, 37M10, 81S2268T07, 62M45, 37M10, 81S22 68T07, 62M45, 37M10, 81S22 |
| url | https://arxiv.org/abs/2605.05029 |