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Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement (2401.10310v1)

Published 18 Jan 2024 in cs.LG, cs.AI, and cs.CC

Abstract: 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.

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Citations (4)
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Summary

  • The paper introduces a novel mathematical framework analyzing deep learning trustworthiness in addressing inverse problems under strict societal constraints.
  • It contrasts the limitations of Turing models with the promising modular enhancements in BSS models for achieving algorithmic transparency.
  • The findings suggest actionable adjustments in optimization and computation to align deep learning technologies with evolving judicial and societal standards.

Introduction

The field of machine learning has been fundamentally transformed by the emergence of deep learning, leveraging neural networks' capacity for tackling complex and varied tasks. Nonetheless, the advent of powerful models imposes substantial challenges in ensuring their trustworthiness. Trustworthiness embraces facets such as robustness, transparency, fairness, and safety, which are of paramount importance, especially when models assert profound societal impact. Regulatory frameworks like the European AI Act underscore these aspects, fueling debate on how these principles can be amalgamated within the mathematical prowess of deep learning systems, specifically in the context of ensuring algorithmic transparency.

Societal and Judicial Requirements for Trustworthiness

Responsiveness to societal and judicial mandates requires an alignment of AI systems with standards of transparency, accountability, and clarity in algorithmic decision-making. This necessity has sparked significant interest in exploring the potential for transparent implementation of algorithms, especially in settings where deep learning is employed to resolve inverse problems.

Algorithmic Solvability and Trustworthiness

The paper pivots on one crucial inquiry: Can deep learning be inherently trustworthy in algorithmic computation, particularly when addressing inverse problems? The research explores mathematical frameworks suitable for digital and analog computing paradigms, specifically Turing and Blum-Shub-Smale (BSS) machines. Findings indicate that while the Turing model exhibits inherent limitations in assuring algorithmic trustworthiness, the BSS model shows promise under certain conditions, particularly when additional modules or approximations are integrated.

Implications and Applications

In the field of inverse problems - fundamental in areas like imaging sciences - the disparity between Turing and BSS models’ proficiencies is stark. While modifications to optimization objectives can bridge the trustworthiness gap in BSS models, the Turing models grapple with intrinsic constraints that hinder the transparency of deep learning applications. These findings not only reflect the current capabilities and limitations of computing systems but also signify the directions for future adjustments in algorithms and computing technology that could ensure deep learning’s alignment with societal expectations for transparent and trustworthy AI.

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