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

TERRA introduces a theoretical framework for transferring machine learning representations across structurally similar but unrelated domains—from driving scenes to robot workspaces to financial markets. The research formalizes when and how well a model trained in one domain generalizes to another through mathematical constructs like Markov decision process homomorphisms and Gromov-Wasserstein distances, presenting a preregistered experimental program without empirical validation.

This arXiv paper addresses a fundamental challenge in artificial intelligence: understanding cross-domain transfer learning through rigorous mathematical theory rather than empirical intuition. The authors propose TERRA, which models different structured-state environments as controlled Markov processes and factorizes them into shared, domain-invariant cores with thin domain-specific adapters. This architecture theoretically enables representations learned from driving scenes—a well-studied domain—to transfer to financial order books, a significantly different application area.

The research builds on established techniques including masked-latent prediction and action-conditioned world models, but innovates by formalizing the transfer question through bisimulation metrics and Gromov-Wasserstein distances. The framework derives transfer bounds that quantify how source-model error compounds across prediction horizons, providing certified lower bounds on structural mismatch quality. This mathematical rigor transforms an industry intuition—that similar structures should transfer—into falsifiable claims.

For AI practitioners and financial technologists, this work carries substantial implications. If validated empirically, cross-domain transfer could dramatically reduce training costs for specialized models in finance, robotics, and autonomous systems by leveraging representations from data-rich domains. The preregistered experimental program, intentionally designed to include conditions for refutation, raises the research standard for transfer learning claims. However, without empirical results, the framework remains theoretical; its practical utility depends on successful validation against the financial order book test case.

The significance extends beyond academia. Financial institutions exploring AI-driven trading systems face expensive data collection and model validation. A validated transfer mechanism from driving scenes—where massive labeled datasets exist—could accelerate deployment timelines. The honest framing acknowledging the absence of results positions this as foundational work rather than breakthrough, setting expectations appropriately for the research community.

• →TERRA provides mathematical framework for transferring representations across structurally similar domains using Markov homomorphisms and Gromov-Wasserstein distances
• →Transfer bounds separate source-model error from structural mismatch, growing geometrically with prediction horizon and certified by formal distance metrics
• →Preregistered experimental program explicitly includes conditions for refutation, establishing higher validation standards for cross-domain transfer claims
• →Framework enables potential transfer from data-rich domains like autonomous driving to data-scarce domains like financial market analysis if empirically validated
• →Research is theoretical proposal without empirical results, requiring future validation against driving-to-order-book test case to prove practical utility