Stochasticity and Uncertainty › Summary
Michael BrenndoerferJune 23, 20262 min read
World Models HandbookAll chapters Part 4 of 12Space, Physics, and Causality
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- World-model transitions are generally conditional distributions; deterministic functions are degenerate cases. Expected squared-error minimization targets the conditional mean, which can fall in a low-density gap for separated multimodal futures.
- Aleatoric uncertainty is conditional spread relative to a specified information set. Epistemic uncertainty reflects limited knowledge and can shrink when informative data and suitable structure identify the model. The boundary depends on representation and assumptions.
- Mixture heads, discrete latents, autoregressive models, and diffusion or flow models offer different ways to preserve multimodal structure. Without semantic supervision or identifiability constraints, these architectures do not guarantee that learned components match physical branches.
- Distributional heads model within-model spread. Ensembles provide empirical between-member disagreement, while Bayesian approximations target parameter or function uncertainty. Their interpretations and calibration require validation.
- Calibration connects claimed probabilities to observed frequencies. For feedback deployment, evaluate on representative closed-loop data or use appropriate sequential methods rather than assuming one-step IID calibration transfers.
- Recursive uncertainty can grow in locally expanding dynamics and can shrink or remain bounded in contractive systems. Moment methods, particles, and member propagation make different approximation and cost tradeoffs.
- Whether apparent noise is hidden structure involves observability, system identification, and sometimes causal assumptions. That question leads naturally to the next chapter's treatment of compositional structure and generalization.