The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence

TL;DR

This paper demonstrates a fundamental limitation in predictive neural models, showing they tend to encode environment rather than system dynamics, especially in high-dimensional, noisy, or slow environments, with implications for AI modeling.

Contribution

It proves a structural property of predictive objectives causing models to encode environment modes over system modes, supported by large-scale neural evidence and theoretical analysis.

Findings

Optimal encoders predominantly track environment rather than system.

The gap worsens with increasing environment dimension, becoming causally blind at high N.

Operational grounding reduces but does not eliminate the predictive-causal gap.

Abstract

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.