# Trustworthiness Preservation by Copies of Machine Learning Systems

arXiv: https://arxiv.org/abs/2506.05203 · HTML: https://mlsanity.com/paper/2506.05203/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 7 of 7)

- [A Lambda-Calculus Foundation for Universal Probabilistic Programming](https://mlsanity.com/paper/1512.08990/) (2015)
- [Twenty-Four Years of Empirical Research on Trust in AI: A Bibliometric Review of Trends, Overlooked Issues, and Future Directions](https://mlsanity.com/paper/2309.09828/) (2023)
- [A Probabilistic Dependent Type System based on Non-Deterministic Beta Reduction](https://mlsanity.com/paper/1602.06420/) (2016)
- [Checking Trustworthiness of Probabilistic Computations in a Typed Natural Deduction System](https://mlsanity.com/paper/2206.12934/) (2022)
- [Evaluating AI fairness in credit scoring with the BRIO tool](https://mlsanity.com/paper/2406.03292/) (2024)
- [A Type Theory for Probabilistic and Bayesian Reasoning](https://mlsanity.com/paper/1511.09230/) (2015)
- [Universal Semantics for the Stochastic Lambda-Calculus](https://mlsanity.com/paper/2011.13171/) (2020)

## Built on by (most cited first, 1 of 1)

- [Counting Worlds Branching Time Semantics for post-hoc Bias Mitigation in generative AI](https://mlsanity.com/paper/2604.19431/) (2026)

## Abstract (arXiv)

A common practice of ML systems development concerns the training of the same model under different data sets, and the use of the same (training and test) sets for different learning models. The first case is a desirable practice for identifying high quality and unbiased training conditions. The latter case coincides with the search for optimal models under a common dataset for training. These differently obtained systems have been considered akin to copies. In the quest for responsible AI, a legitimate but hardly investigated question is how to verify that trustworthiness is preserved by copies. In this paper we introduce a calculus to model and verify probabilistic complex queries over data and define four distinct notions: Justifiably, Equally, Weakly and Almost Trustworthy which can be checked analysing the (partial) behaviour of the copy with respect to its original. We provide a study of the relations between these notions of trustworthiness, and how they compose with each other and under logical operations. The aim is to offer a computational tool to check the trustworthiness of possibly complex systems copied from an original whose behavour is known.