On Performance and Trustworthiness of AI: from inverse problems to Artificial General Intelligence
Artificial Intelligence (AI) has emerged as a powerful problem-solving tool, both in the mathematical field of inverse problems and, more recently, in broader applications with the advent of modern chatbots. However, AI systems have repeatedly been shown to be prone to producing hallucinations, plausible yet false solutions that could be mistaken for correct answers. This vulnerability undermines trust in AI systems, and thus an examination of the trustworthiness of AI is urgently needed. This thesis investigates the concept of trust in AI, examining its performance, stability, verifiability, and explainability. Starting with an in-depth assessment of the best performance achievable by an AI for inverse problems, the analysis of trustworthy AI culminates in the Consistent Reasoning Paradox. This paradox shows the intricacy involved in creating an artificial general intelligence capable of human-like behaviour - the goal modern chatbots aim to achieve. The resolution to the paradox lies in providing AI with the ability to confess `I don't know' when relevant, and thus the concept of an `I don't know' function is introduced as a necessary tool to develop reliable and trustworthy AI systems.
Consistent Reasoning Paradox, Kernel size, Trustworthy AI, Artificial General Intelligence (AGI), AI Trust, AI Hallucinations, Inverse Problems, AI Performance Bounds
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