On instabilities and trust in deep learning

Artificial Intelligence (AI) has become an integral part of daily life, influencing everything from search engines and voice assistants to medical diagnostics and self-driving cars. Recent advancements in large language models (LLMs) have brought AI closer to mimicking human-like text generation, raising discussions about AI’s potential to pass the Turing Test. Despite these successes, AI systems remain fragile, prone to hallucinations and adversarial examples, which expose the vulnerabilities in their decision-making processes. This thesis explores foundational issues in AI, particularly LLMs and neural networks, through the lens of computability theory and stability analysis. Chapter 1 provides relevant background material, outlining the motivation, objectives, and contributions of the research. The chapter introduces the key concepts of randomness, stability, and uncertainty in AI and highlights the importance of understanding these aspects to improve the reliability and robustness of AI systems. Chapter 2 investigates the phenomenon of hallucinations in LLMs and addresses the question of whether randomness in LLMs can solve non-computable problems. By drawing on established work on random Turing Machines, this chapter explores the implications of randomness on LLMs, particularly in the context of multivalued problems. In Chapter 3, the focus shifts to adversarial examples in neural networks, which occur when small perturbations in input data cause significant output changes. While traditional efforts have aimed to mitigate this by reducing the Lipschitz constant, classification tasks’ inherent discontinuity challenges these approaches. This chapter introduces a novel stability measure for classification tasks and presents two approximation theorems that link stability to neural networks’ ability to approximate discontinuous functions. Chapter 4 examines the feasibility of learning uncertainty estimates for models, focusing on the potential to develop methods that help neural networks gauge their own confidence. The chapter introduces ‘shadow properties’, a type of vulnerability that exists in models due to the geometry of the parameter space, and demonstrates how these properties impact a model’s ability to estimate certainty. Analytical and numerical results are provided to highlight the relationship between model parameters and shadow properties. This thesis provides a theoretical framework for understanding the limitations of AI, focusing on random algorithms, stability in neural networks, and the learnability of uncertainty estimates.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Liu, Zhen Ning David

Advisor dc:contributor.advisor

• Hansen, Anders C

• Mathematics
• Deep learning

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/3b34498c-d6c9-47b5-910c-201388aeebff/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.116302

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/380837