AI summaryⓘ
The authors propose a theoretical framework to understand when a learning model trained in one structured environment, like driving scenes, can be transferred to a similar but different domain, such as financial order books. They break down each domain into parts that are specific to it and parts that are shared, and use mathematical tools to measure how closely these parts align across domains. Their work establishes precise conditions and limits for effective transfer of learned representations, predicts how errors might accumulate over time, and suggests experiments to test their ideas. Importantly, this is a proposal with no experimental results yet, focusing on turning common assumptions about transfer learning into a testable theory.
structured-state domainlatent predictive modelMarkov decision processbisimulationGromov-Wasserstein distanceaction-conditioned transitiondomain adaptationtransfer learningLipschitz continuityvalue regret
Abstract
A single action-conditioned latent predictive architecture can in principle be trained on the structured state of a driving scene, a robot workspace, or a financial order book. The ingredients for doing so within any one domain already exist and are individually validated: masked-latent prediction, action-conditioned latent world models, discrete action tokenization, and joint-embedding prediction on voxelized state. What is not established, and what TERRA addresses, is the transfer question: when does a representation or predictor learned in one structured-state domain carry over to a structurally analogous but otherwise unrelated domain, and by how much. We give this question a formal treatment. We model each domain as a controlled Markov process on a graded latent grid, factor any instantiation into thin domain adapters and a shared domain-invariant core, and identify a cross-domain correspondence with an approximate Markov decision process homomorphism whose quality is measured by a lax bisimulation discrepancy and, for domains lacking a shared coordinate system, by a Gromov-Wasserstein distance between their action-conditioned transition operators. Under a Lipschitz predictor we derive a transfer bound that separates source-model error from structural mismatch, grows geometrically in the prediction horizon, and is certified from below by the Gromov-Wasserstein distance; we then connect latent error to decision regret through the Lipschitz value property of bisimulation metrics. The resulting Structured-State Transfer Hypothesis is stated as a falsifiable claim with a preregistered experimental program, centered on a transfer test from driving scenes to order books, including conditions under which it is refuted. We present no empirical results: this is a research proposal that converts a widely repeated intuition into testable theory.