Operational certificates for world models
Certifying Physical Language through Response Substitution
and Ordered Execution
1New York University · 2Carnegie Mellon University · 3Columbia University
The capability ladder
Each rung changes exactly one element of physical-language use while the response vocabulary stays fixed. A certificate that returns a single verdict cannot tell them apart.
Can one observation recover a physical variable?
prior workDo two sensors denote the same response function?
certified · 4.5× · 19/19Does the joint predictive law actually improve?
beats both; diagonal tiesDoes the phrase preserve the intervention law?
certified at 25× budgetDemonstration I · Cluster Haptic
A robot scans 118 surfaces. Audio and acceleration are compiled by separate models on disjoint query panels — no matching loss, no entity identifier — then decoded by one frozen chart. Pick a held-out surface: the two sensors land on the same response. Pick a wrong surface for either one and they part.
Demonstration II · live simulation in your browser
A unit mass on a spring, a dashpot and a plastic slider. The slider remembers: once a pulse yields it, the rest position moves. So A then B does not settle where B then A does. Run them and watch. This is the exact system, integrated live at Δt = 0.005.
The certificate
The gate has a prerequisite: before any learned inference is scored, the exact chart coordinate must execute a held-out program better than the population response. At the pre-registered budget it does not — so the gate refuses, correctly. Train the executor to convergence and the same chart clears it. Swap the executor's factorization and the gate stops it again.
Oracle NMSE against executor updates. The registered 1.2k budget misses; the crossing sits between 6k and 12k.
Absolute NMSE vs. an entity-blind predictor, log scale. The program-level executor is better on words it was fitted on, and collapses on an unseen adjacency.
Held-out joint energy score. Fusion improves on both modalities; its diagonal restriction does slightly better, the sole remaining gate failure.
The paper
Certifying Physical Language through Response Substitution and Ordered Execution.
@article{tan2027certifying,
title = {Beyond Multimodal Alignment:
Certifying Physical Language through Response Substitution and Ordered Execution},
author = {Tan, Kaizhen and Xu, Xin and Tao, Siru and Li, Yixiao
and Hong, Hanzhe and Feng, Yang and Du, Heqing},
year = {2027}
}