When Generative Models Act as Simulators

1 INTRODUCTION

• Generative models can supply plausible details beyond explicit specification, but lack a built-in way to set their environment state.Combining learned detail with interpretable control could support forecasting, planning, and persistent virtual environments.Source: §1 · pp. 1–2
• Editability asks whether setting a model's latent state makes its next prediction follow from a target simulator state.This is about accessible simulator-like functionality, not whether the model internally represents or advances state as a conventional simulator does.Source: §1 · p. 2
• The study holds architecture, training, and evaluation fixed while varying environments to isolate how rules or observations affect editability.The environments are Othello, with a discrete board determined by moves and rules, and Rayworld, with continuous disc positions viewed through partial 1D observations.Source: §1 · p. 2
• Representation steering decodes simulator state with probes and moves latent states along probe directions, whereas inverse mapping maps simulator state directly to a latent state.The inverse map overwrites one layer, leaving the model's remaining layers to carry that write through to its output.Source: §1 · p. 2
• Every model decodes its state well, yet Othello editability falls smoothly as rules are simplified, while Rayworld inverse mapping sets continuous positions despite failed probe steering.The inverse map can succeed even when it predicts the model's latent state poorly.Source: §1 · p. 2
• The evaluation framework tests edits against known simulator outcomes across diverse environments.The contributions also include evidence that simplifying rules can reduce editability and a demonstration that inverse maps can drive a model from simulator states.Source: §1 · p. 2

2 BACKGROUND AND RELATED WORK

• World-model studies distinguish whether models represent and use state in prediction from whether that state can be set.Prior work also tests whether identical states yield identical futures and different states yield different futures.Source: §2 · p. 2
• Controllable generation uses conditioning interfaces, latent-feature manipulation, or generative priors for explicit simulators, while this work tests edits in observation-trained models.Prior video-generator work reports accurate physical predictions within training distributions but poor extrapolation (Kang et al., 2025), while What-If World tests prompted physical changes.Source: §2 · p. 3
• Othello studies decode boards and steer predictions, but accurate board decoding can coexist with ineffective edits in late layers and shallow models (Hazineh et al., 2023).Other work finds probe-guided edits across rule variants when models train on paired variants, unlike this paper's separate model per variant (Chawla et al., 2026).Source: §2 · p. 3
• Probe interventions are evaluated in diverse settings, but this paper compares edited outputs with the corresponding directly edited simulator outputs.Its metrics capture both the targeted change and prediction quality, including whether properties outside the target are preserved.Source: §2 · p. 3
• Unlike StyleRig's editing losses or counterfactual-trained rollout edits, this inverse map uses state alone and ordinary state–activation pairs.It tests whether the intended output is produced when probe-derived editors cannot.Source: §2 · p. 3
• Causal abstraction aligns model interventions with a higher-level causal model, whereas this paper uses the simulator it aims to drive as its high-level model.The editors use paired latent and simulator states, without counterfactuals or optimization for intervention success.Source: §2 · p. 3

3 EXPERIMENTAL SETUP

• Across both environments, the simulator renders state into observations, the model encodes them into residual-stream latents, and the decoder predicts the next observation for comparison after an edit.The target is a simulator state edited from the original; its one-step-forward rendering provides the reference for the model’s edited prediction.Source: §3 · p. 3, Figure 2 · p. 4

3.1 OTHELLO

• Othello edits flip one token after a real 20-move opening, while variants alter placement rules, flipping, or both.Adjacent-flip retains flipping but averages 0.27 flipped tokens per move versus 2.2 in standard Othello; standard-noflip fills the same checkerboard in different orders.Source: §3.1 · p. 4

3.2 RAYWORLD

• Rayworld renders two constant-velocity discs through rays; edits teleport one disc while preserving velocities, and variants change visibility or observation detail.The appearance target groups positions that yield the same observation; blink hides discs for 1–12 frames, while the N-ray family uses 5, 8, 16, or 128 rays.Source: §3.2 · pp. 4–6

3.3 MODEL, TRAINING, AND PROBES

• All variants use the same eight-block, width-512 transformer, trained for 780,000 steps; linear and one-hidden-layer MLP probes decode simulator states from latent representations.Models have about 25M parameters and train on 18M sequences; probes use about 1.2M state–activation pairs, or 200,000 sequences for appearance targets.Source: §3.3 · p. 6

3.4 EDITORS

• Pseudoinverse injection and gradient steering edit latents through state-decoding probes, whereas the inverse map predicts a latent state directly from the target simulator state.The inverse map is an MLP trained on ordinary state–activation pairs; it is compared with overwriting the latent using the mean of the ten nearest training states.Source: §3.4 · p. 6

3.5 METRICS

• Probe Skill measures decoding against a trivial predictor, while Edit Index scores movement toward the edited target and Edit Fidelity measures whole-output accuracy.Edit Index ranges from −1 for matching the unedited observation to +1 for matching the edited one; settings are selected by highest Edit Index among those with nonnegative Edit Fidelity, with a fallback to highest fidelity.Source: §3.5 · p. 7

4 RESULTS

• Across two additional seeds per variant, trained-probe Probe Skill varies by at most 0.004 and successful editors’ Edit Index by less than 0.04.Every model predicts its environment well before probing or editing.Source: §4 · p. 7
• The state is decodable in every variant: MLP Probe Skill is at least 0.88, with the linear probe close behind.The inverse-map columns report R2 for predicting latent state from simulator state.Source: §4 · p. 7, Table 1 · p. 8
• In Rayworld, probe-derived editors fail on every continuous-position variant, while inverse mapping lands everywhere, including three further variants.At α = 1, the linear probe reads the edited state exactly even though the predicted frame does not move.Source: §4 · p. 7
• Every editor edits standard Othello, but rule changes break this; on adjacent-flip, inverse mapping lands while probe-derived editors reach at most +0.35 at low fidelity.Table 2 reports editability across variants and editors.Source: §4 · p. 7, Table 2 · p. 8
• At 5 rays, coarsened Rayworld targets raise the probe-derived editors’ scores to +0.51 and +0.60, though coarseness and target size remain confounded.At 8 rays, appearance bins improve most among the tested binning choices.Source: §4 · p. 8

5 DISCUSSION

• Othello editability declines as rules simplify: adjacency removes probe-steerable representations, yet inverse mapping edits the board.The inverse map also sets unreachable boards nearly as well as reachable ones; this generalization appears to degrade when token flipping is removed.Source: §5 · pp. 8–9
• Figure 5 shows qualitative edited predictions across Rayworld and Othello variants, with cyan and magenta marking changed discs or cells.The caption points to Table 2 for quantitative results.Source: Figure 5 · p. 9
• In Rayworld, probes cannot steer continuous positions, but discretized targets allow steering; inverse mapping sets continuous positions and partially succeeds when rigid-pair spacing is broken.Steering works best when the target state mirrors the observation space, unlike Othello’s board-like bottleneck.Source: §5 · p. 9
• In Rayworld, inverse mapping lands across residual points despite explaining only 0.32 to 0.58 of latent variance, and edited predictions appear smoother than the model’s own.The authors suggest the map produces a simplified latent that omits variance with little bearing on prediction.Source: §5 · p. 9

6 CONCLUSION

• In Othello, access to the model’s state narrows gradually as the game is simplified.In Rayworld, probe-derived editors cannot steer continuous state, but an inverse map sets the model from it despite predicting latent state poorly.Source: §6 · p. 9
• The paper evaluates editability at a single step, while a simulator must also carry state forward under consistent rules.Rewriting history lets an edit persist through a rollout.Source: §6 · p. 9
• The authors identify continuously driving a model from a simulator, or switching simulators over time, as next steps.Source: §6 · p. 9

8 REPRODUCIBILITY STATEMENT

• Code is released for every environment, model, probe, editor, and metric.Source: §8 · p. 10
• Trained weights, including seed replicates, and evaluation and edit datasets for every variant are available.Source: §8 · p. 10
• Training corpora are not hosted, but scripts regenerate them from recorded seeds.Source: §8 · p. 10

• Appendix sections cover predictive loss, metric variance and confidence intervals, and reachable versus unreachable Othello target states.Source: A APPENDIX · p. 14
• Rayworld supplements include matching GPT-style prediction, additional variants, residual-point trends, and comparisons of appearance bins and nearest-neighbor replacement.Source: A APPENDIX · p. 14
• Further sections address persistent transformer edits with history rewriting, selection by edit fidelity, implementation, and qualitative editability visualizations.Source: A APPENDIX · p. 14

• Editability is evaluated for one step only, leaving rollout metrics as a natural next step.The paper demonstrates history rewriting as one route for making an edit persist through a rollout.Source: §A.1 · p. 14
• Because every tested model is one transformer at one depth, some findings may reflect that architecture or depth rather than the environments.Recurrent and diffusion models may behave differently.Source: §A.1 · p. 14
• The environments differ in difficulty in ways the study cannot fully control, so difficulty unrelated to state representation may affect editability.Source: §A.1 · p. 14

• The Bayes floor is exact for Othello, while the Rayworld floor is approximated by averaging over sampled starting states consistent with observed frames.The Rayworld floor rises as rays coarsen and leave more of the state undetermined.Source: §A.2 · p. 14
• On 5-ray Rayworld, rollouts can keep a disc on the wrong ray for several steps.Source: §A.2 · p. 14
• In Othello, boards shaded by the model’s predicted distribution are nearly indistinguishable from boards shaded by the true legal moves.Source: §A.2 · p. 14
• Every model closes at least 99% of the gap from the trivial predictor to its Bayes floor.Table 3 compares held-out predictive loss with both references; Figures 6 and 7 show sampled predictive-accuracy demonstrations in Rayworld and Othello.Source: §A.2 · p. 14, Table 3 · p. 15, Figure 6 · p. 15

• The seed spread is small compared to the differences between variants.The comparison uses three seeds per variant at 512,000 steps.Source: §A.3 · p. 17
• No Probe Skill varies by more than 0.004, and the Edit Index of every successful editor varies by at most 0.034.Source: §A.3 · p. 17
• Three daggered cells mainly vary because each seed selects a different setting, while IM on adjacent-noflip remains unstable even with its setting fixed.For PI on the two adjacency variants, fixing the main run’s setting yields Edit Index variation of 0.05 to 0.07; IM on adjacent-noflip varies by 0.32 and one seed selects for highest fidelity after no setting passes the cutoff.Source: §A.3 · p. 17
• IM’s Edit Fidelity on adjacent-flip ranges from 0.40 to 0.59 despite a consistent Edit Index of 0.62 ± 0.03.The passage attributes this variation to neither selection nor different write points.Source: §A.3 · p. 17
• Edit Fidelity can differ by up to 0.26 when the selected setting shifts between checkpoints; PI on standard Othello has means of 0.48 against 0.70.Source: §A.3 · p. 17
• Refitting linear probes moves Probe Skill by at most 0.0007 and PI’s Edit Index by at most 0.016 on the tested settings.The MLP probes implementing GS were not refit.Source: §A.3 · p. 17

A.4 COMPARING REACHABLE VS UNREACHABLE TARGET STATES IN OTHELLO

• For single flips, standard Othello editors handle reachable and unreachable targets about equally well, while IM does better on reachable adjacent-flip boards.Neither no-flip variant has a reachable single-flip board, so its failures are all on unreachable targets.Source: §A.4 · p. 17, Table 5 · p. 18
• On reachable adjacent-noflip two-token edits, IM reaches +0.88 Edit Index and 0.78 Edit Fidelity, while PI and GS fail.On unreachable pairs, IM moves changed cells toward the target (+0.65) but degrades the rest of the prediction (Edit Fidelity 0.08); no editor lands on standard-noflip pairs.Source: Table 6 · p. 18, §A.4 · p. 18

A.5 MATCHING GPT-STYLE PREDICTION IN RAYWORLD

• The 8-ray token model matches the frame model’s decodability and prediction, and changing the interface leaves editability patterns intact: probes fail on continuous positions while IM lands.Categorical targets improve probe-derived editors; exact-frame scoring gives lower scores when a prediction is one ray off.Source: §A.5 · pp. 18–19, Table 8 · p. 19

A.6 ADDITIONAL RAYWORLD VARIANTS

• On smooth and obs5 Rayworld, better-readable continuous positions still do not make PI or GS steer successfully, while IM lands; on pair, IM reaches +0.41 Edit Index and 0.30 Edit Fidelity.For pair, the corresponding standard-Rayworld results are +0.59 and 0.66; the pair edit bench teleports one disc and breaks the rigid-pair invariant.Source: Table 9 · p. 20, §A.6 · p. 20

A.7 INVERSE MAPPING TRENDS ACROSS RESIDUAL POINTS

• At Othello residual points, IM lands only at points 4 and 5, whereas in Rayworld it edits at every point and reaches +0.59 Edit Index with 0.66 Edit Fidelity at point 6.Othello’s inverse-map fit rises from R2 0.39 at the embedding to 0.83 at point 5, then dips to 0.73 at point 7; Rayworld’s R2 falls to about 0.3 from point 1 onward.Source: §A.7 · pp. 20–21, Table 10 · p. 21, Figure 8 · p. 21

A.8 APPEARANCE BINS AGAINST EVENLY SPACED BINS

• On the 8-ray model, appearance bins raise GS to +0.59 Edit Index and 0.56 Edit Fidelity, versus +0.35 to +0.39 for uniform grids; snapping regression back to bin centers returns it to −0.05 and 0.07.The passage reports that the appearance bins match the observation space and that grid probes decode worse than the continuous position target despite editing better.Source: Table 11 · p. 22, §A.8 · p. 22

A.9 COMPARING INVERSE MAPPING TO NEAREST NEIGHBOR REPLACEMENT

• The inverse map beats nearest-neighbor replacement on latent-state prediction in every variant, edits better on every Rayworld variant, and is the only one that edits Othello successfully.The control writes the mean latent state of the ten nearest training examples, so the inverse map’s advantage is not just recall of nearby examples.Source: §A.9 · p. 22, Table 12 · p. 23

A.10 PERSISTENT TRANSFORMER EDITS WITH HISTORY REWRITING

• History rewriting holds a Rayworld edit through rollout, while a single inverse-map write largely reverts after one step; the method rewrites earlier frames so history agrees with the edit.It relies on reversible Rayworld dynamics, and rewritten frames drift from true renders, risking compounded errors over longer horizons.Source: §A.10 · p. 23, Figure 9 · p. 24

A.11 SELECTING FOR EDIT FIDELITY INSTEAD OF EDIT INDEX

• When settings are chosen for highest Edit Fidelity rather than the main rule’s no-harm Edit Index criterion, the main text’s qualitative conclusions remain unchanged.PI and GS mostly take smaller steps, while IM’s Edit Index changes by at most 0.10.Source: §A.11 · p. 24, Table 13 · p. 25

A.12 IMPLEMENTATION DETAILS

• Implementation uses disjoint sequence splits for fitting and held-out evaluation, and fit-to-held-out skill gaps stay within 0.003 for linear probes and 0.005 for MLP probes.The inverse map’s two R2 values agree to three decimals.Source: §A.12 · pp. 25–26