Title: TERRA: Task-Embedded Reasoning and Representation Architecture for Cross-Domain Applications

Abstract:

It is theoretically feasible to train a single action-conditioned latent predictive model on the structured states of diverse environments, ranging from financial order books and robot workspaces to driving scenes. The foundational components required for such training within any specific domain are already established and individually validated. These include masked-latent prediction, discrete action tokenization, joint-embedding prediction on voxelized states, and action-conditioned latent world models. However, a critical gap remains: the transferability question. Specifically, it is unclear under what conditions a representation or predictor acquired in one structured-state domain can be applied to a structurally similar but otherwise unrelated domain, and to what extent.

TERRA addresses this gap by providing a formal treatment of cross-domain transfer. In this framework, each domain is modeled as a controlled Markov process situated on a graded latent grid. We decompose any specific instantiation into a shared, domain-invariant core and thin domain-specific adapters. We define cross-domain correspondence through an approximate Markov decision process homomorphism. The fidelity of this correspondence is quantified using a lax bisimulation discrepancy; for domains that do not share a common coordinate system, we employ the Gromov-Wasserstein distance between their action-conditioned transition operators.

Assuming a Lipschitz predictor, we derive a transfer bound that distinguishes between source-model error and structural mismatch. This bound expands geometrically with the prediction horizon and is lower-bounded by the Gromov-Wasserstein distance. Furthermore, we link latent error to decision regret by leveraging the Lipschitz value property of bisimulation metrics. Based on these findings, we propose the Structured-State Transfer Hypothesis—a falsifiable claim supported by a preregistered experimental program. This program focuses on a transfer test from driving scenes to order books, explicitly outlining the conditions under which the hypothesis would be refuted. Please note that this document serves as a research proposal rather than a report of empirical results; its purpose is to transform a commonly held intuition into a testable theoretical framework.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC