A Chosen Future Can Still Be Rewritten: Causal Writability in Video Models
Xingyun Wang, Haomin Zheng, Man Yuan, Leqian Yang, Ziming Liu
cs.LG, cs.CV
2026-09-15
After red-slow/blue-fast training, a 4-D edit from boundary state restores unused physical motion, until a sharp depth boundary where the same write stops working.
When a video model rolls out physically wrong motion, the pixels cannot tell you whether it never learned the right dynamics, or learned them and then ignored them. This paper isolates the second case.
Training videos pair red masses with slow oscillation and blue masses with fast oscillation. At test time a red mass arrives with fast motion already visible in the observed frames. The model often follows color and generates a slow future. A compact activation edit, predicted from simple physical variables, still restores the fast motion. The authors call this causal writability: whether an internal write can change motion in the fully decoded video.
The main testbed is Spring. A 488M latent flow-matching Transformer with 30 bidirectional DiT blocks sits on a frozen Wan2.1 VAE. Videos run at 20 fps: 65 observed frames, then 64 generated frames. Training support is only red-slow (ω U[2.2, 3.0] rad/s) and blue-fast (ω U[5.2, 6.4] rad/s). Long exposes all 65 observed frames. Short replaces the first 57 with a fixed background, leaving 8 motion frames.
Aligned and conflict rollouts share trajectory, boundary position and velocity, and generation seed; only color changes. Aligned follows observed motion. Conflict follows the color shortcut. Adding the aligned-minus-conflict activation difference on observed-frame tokens redirects the decoded future.
PCA on those differences shows that four coordinates keep nearly the full effect. Those coordinates trace smooth loops against boundary phase, so a first-harmonic controller can map target direction plus boundary phase onto the four coordinates, then reconstruct the write through a frozen PCA basis. No matched aligned activation is needed at test time.
A 31-site scan measures writability. At fixed strength a sharp depth boundary appears: the same edit changes the video before the boundary and does not after it. Closure marks commitment for that write. The motion signal remains detectable. A stronger downstream attention write can restore physical motion, and too much gain overshoots.
| Method | Metric | Result |
| Full activation difference | Held-out samples in target band | 92.4% |
| Top-4 PCA projection | Same | 87.8% |
| Boundary-phase controller | Same | 85.9% |
| Transfer across 3 training seeds | Decoded recovery R | 0.94–0.99 |
| Short training 5K→100K | Physics-follow | 0.52→0.60 |
| Remaining shortcut errors | Mean writable sites | 10.88→9.55 |
| Later-corrected errors | Extra writable sites at 5K | +3.79 |
| Wan 1.3B Neutral-first vs Direct | Conflict physics-follow | 80.5% vs 9.4% |
| Single-head V gain λ=8 | 48 strict failures | 56.3% physics-follow |
Independently trained Short models differ by about 22 percentage points in natural physics-follow rate, yet corrective edits transfer across all six directed run pairs with held-out decoded recovery R = 0.94–0.99. The models appear to share a physical solution and differ in how downstream computation uses it.
Component restoration pins the write to self-attention. Restoring the conflict post-attention future-frame state kills frequency recovery; restoring the following MLP output does not. Restoring Q barely matters. Restoring observed-frame K and V together removes recovery in all six groups. After closure the alternative-motion signal is still measurable. In one run, amplifying a single observed-frame V head at λ=8 lifts physics-follow to 56.3% on 48 held-out strict failures; at λ=16 every output stays valid but most leave the training-supported frequency bands.
The same pattern appears in a pretrained 1.3B Wan video DiT. Learning motion first on gray videos, then introducing the red-slow/blue-fast bias, yields 80.5% conflict physics-follow at 10K steps, against 9.4% for direct biased adaptation. Closure also moves later, from blocks 12–13 to 14–15. Pendulum repeats the oscillator result. Free Fall, with a donor-free [1, gtarget] controller, reaches median held-out recovery Rg = 0.967, but loses near-full direct writability after block 1.
For video generators and world models, a physically wrong rollout does not prove the right dynamics are missing. They may be present and unused. Training order is a real lever: motion-first pre-adaptation jumps conflict physics-follow from about one in ten to about eight in ten.
Early writability also splits errors that training will later fix from errors that persist, 3.79 sites on average, before the generated videos diverge. If that signal survives on more natural data, it is an earlier diagnostic than waiting for final sample quality.
This is a mechanism study, not a drop-in repair tool. Edits need paired activations or a fitted controller, and the quantitative claims sit on controlled mechanics videos.
The authors are explicit. Exact counterfactual matching and pixel-level scoring need synthetic dynamics. Learned edits follow the coupled appearance-dynamics modes in training. Closure is specific to observed-frame writes, tested sites, and checkpoints. Independent runs place the observed-to-future attention write on different K/V heads.
The open question is the one practitioners care about: do naturally occurring shortcuts in broadly pretrained world models have the same point of no return? The paper does not test that. Free Fall already closes after block 1, so how early commitment arrives depends on the dynamics. Springs are not a universal schedule.