arXiv:2606.08113v1 Announce Type: new Abstract: A small Wasserstein distance does not certify that a transformation is admissible. In evidence-constrained, semantic, causal, physical, monotone, or risk-sensitive learning, one must ask not only how far two probability laws are, but whether mass has moved in a direction allowed by available information. We introduce conditional random ordered transport spaces (CROTS), a class of \(L^0\)-valued spaces of random probability measures equipped with a Wasserstein ambient metric, a closed stochastic order, hard and soft ordered transport discrepancies
The increasing complexity and safety demands of AI applications, especially in areas requiring explainability and ethical constraints, necessitate more robust mathematical frameworks for understanding probabilistic transformations.
This research introduces a novel mathematical framework for more nuanced and constrained probabilistic modeling, crucial for developing trustworthy and interpretable AI systems beyond simple similarity metrics.
The ability to assess how mass moves in 'allowed' directions, rather than just how 'far' it moves, provides a critical tool for building AI that adheres to evidence-based, semantic, causal, or risk-sensitive rules.
- · AI safety researchers
- · Developers of explainable AI (XAI)
- · Industries with high regulatory or ethical stakes (e.g., healthcare, finance)
- · Machine learning theoreticians
- · AI systems relying solely on traditional statistical similarity
- · Black-box AI development approaches
Improved theoretical foundations for AI systems requiring constrained and interpretable data transformations.
Development of new AI algorithms and evaluation metrics that incorporate these ordered transport concepts, leading to more reliable and auditable AI.
Increased adoption of 'safe by design' principles in AI, potentially accelerating regulatory clarity and public trust in advanced AI applications.
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Read at arXiv cs.LG