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.

How Many Bits Can an Adapter Write? Measuring the Capacity and Memorization of Parameter-Efficient Fine-Tuning

A LoRA adapter is a few megabytes that almost everyone treats as a skill rather than a record of the data behind it. We put that assumption on a scale. Extending compression-based memorization analysis to the frozen-base setting, we measure directly, in bits, how much a low-rank adapter writes into a model it never changes. The answer is both smaller than full fine-tuning and less lawful than parameter counting would predict. Adapters store a couple of bits per trainable parameter, well short of a full model's budget, but that figure turns less on how many parameters an adapter carries than on where they sit. Move the same parameter budget from attention into the MLP and it holds nearly twice as much; strip the frozen base of its structure and the capacity all but disappears. Applied to realistic fine-tunes of Qwen2.5, the same instrument shows privacy leakage rising with the bits an adapter writes rather than the parameters it nominally has, and it draws a clean line between supervised and reinforcement learning: the secrets that supervised fine-tuning copies down verbatim, an adapter trained on verifiable rewards never records. Measuring what fine-tuning writes, rather than attacking it after the fact, turns a piece of folklore into a quantity one can design against.