Predictive Statistics Shape Emergent World Representations of Grid Walkers
Next-token predictors often appear to develop internal representations of the latent world and its rules. The probabilistic nature of these models suggests a deep connection between the structure of the world and the geometry of probability distributions. In order to understand this link more precisely, we use a minimal stochastic process as a controlled setting: constrained random walks on a two-dimensional lattice that must reach a fixed endpoint after a predetermined number of steps. Optimal prediction of this process solely depends on a sufficient vector determined by the walker's position relative to the target and the remaining time horizon; in other words, the probability distribut...
| Authors | Sasha Brenner, Thomas R. Knösche, Nico Scherf |
|---|---|
| Primary category | cs.LG |
| Published | 17 March 2026 |
| Last updated at source | 5 June 2026 |
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