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

• URL: http://arxiv.org/abs/2606.01520v1
• Date: Mon, 01 Jun 2026 00:50:59 GMT
• Title: TERRA: Task-Embedded Reasoning and Representation Architecture for Cross-Domain Applications
• Abstract summary: A single action-conditioned latent predictive architecture can be trained on the structured state of a driving scene, a robot workspace, or a financial order book.<n>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.<n>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
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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