Deep learning still has drawbacks in terms of trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated to trustworthiness have been proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a central question is to what extent trustworthy deep learning can be realized. Establishing the described properties constituting trustworthiness requires that the factors influencing an algorithmic computation can be retraced, i.e., the algorithmic implementation is transparent. Motivated by the observation that the current evolution of deep learning models necessitates a change in computing technology, we derive a mathematical framework which enables us to analyze whether a transparent implementation in a computing model is feasible. We exemplarily apply our trustworthiness framework to analyze deep learning approaches for inverse problems in digital and analog computing models represented by Turing and Blum-Shub-Smale Machines, respectively. Based on previous results, we find that Blum-Shub-Smale Machines have the potential to establish trustworthy solvers for inverse problems under fairly general conditions, whereas Turing machines cannot guarantee trustworthiness to the same degree.

翻译：深度学习在可信性方面仍存在不足，可信性描述了一种可理解、公平、安全且可靠的方法。为降低人工智能的潜在风险，相关监管指南（如《欧洲人工智能法案》）已提出与可信性相关的明确义务。因此，核心问题在于可信深度学习能在多大程度上得以实现。要建立构成可信性的上述属性，需要能够追溯影响算法计算的因素，即算法实现需具备透明性。基于当前深度学习模型的演进必然要求计算技术变革这一观察，我们推导出一个数学框架，用于分析在计算模型中实现透明算法的可行性。我们以数字与模拟计算模型（分别由图灵机和Blum-Shub-Smale机器表征）中的逆问题深度学习方法为例，应用该可信性框架进行分析。基于已有结果发现，Blum-Shub-Smale机器在相当普遍的条件下具有建立可信逆问题求解器的潜力，而图灵机则无法保证同等程度的可信性。