Kaizhen Tan
Publications
What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representations
A central premise of latent world models is that predicting the future forces a representation to internalize the physics of its environment. Which physical quantities does a trained latent actually contain, and what decides this? We answer with controlled interventions in POKEWORLD, an interactive environment whose visually identical objects hide mass, drag, and contact stiffness. A certificate-gated protocol first certifies each parameter as recoverable from raw observations, then measures whether it enters the latent, so a null result can be attributed to the objective rather than to the environment. The resulting identifiability map has two organizing mechanisms and one frontier. Inputs limit what can be known, while prediction targets decide what is retained. Stiffness enters the latent only when touch is forecast ($R^2=0.50$, compared with $-0.02$ when the same signal is merely fused into the input), and under single-step prediction a vision-only latent discards even perfectly visible object state. Drag marks the frontier. It carries a recoverability certificate of 0.89 yet plateaus near 0.13 under every deterministic prediction objective we test, while a supervised head on the same trunk reaches 0.45. Parameters whose readout is slow and ratio-type under the sensed coordinates fall outside what these objectives acquire. On RH20T, an input-target factorial across scaling curves reproduces both mechanisms across two robots and 4,258 episodes. Every arm missing information or prediction pressure stays flat over a fivefold data range, and only the full multimodal objective forecasts force beyond a persistence baseline, with held-out gains that grow with scale. Objective structure determines which physical parameters a latent acquires, and additional data improves only the parameters it already acquires.
Collusion with Competitive Marginals: Price-Level Audits Are Blind by Construction
Empirical work on algorithmic collusion asks one question of the data: are prices supracompetitive? We show this can be answered "no" by a conspiracy that is nonetheless profitable. Consider bidding agents that couple only through the joint distribution of their unexplained bid components, leaving every agent's own bid law exactly at the competitive law. Any test whose input is a single agent's price or bid history then has power exactly equal to its false-positive rate, for every coupling strength up to comonotonicity. The published detection methodology is therefore blind to this conduct by construction rather than underpowered, and no sample size repairs it. Three empirical results follow. First, the mechanism appears in real language-model agents: twenty models from nineteen independent developers, three deployment prompts each, show residual correlation of $+0.053$ between two deployments of one model against $+0.0001$ across models, with a 95% interval clustered by developer of $[0.030, 0.078]$, under an auditor that sees every order feature and is fitted out of sample. Second, the coupling falls monotonically as sampling temperature rises ($p=0.002$), turning a deployment parameter into a candidate mitigation. Third, on 24 days of Ethereum block-building auction data covering 77,684 bids from 39 bidders, the honest population of bidder pairs is itself so dependent that a screen held at a 5% false-positive rate must sit above a floor of $+0.50$ to $+0.81$, which is 20 to 32 times the family-wise sampling threshold and does not fall as the audit window grows. Since lawful multi-identity operation and conspiracy are behaviourally indistinguishable here, the tractable regulatory target is not detection but counting: resolving 40 bidding identities into 23 operators raises the Herfindahl index by 247.5%, and adding behavioural clusters from public bid streams reaches 324.5%.
Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks
A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.