Mathematician Explains How Geometry and Symmetry Can Unveil AI's Black Box

Henry Kvinge, a mathematician at Pacific Northwest National Laboratory (PNNL), is at the forefront of exploring the symbiotic relationship between mathematics and artificial intelligence (AI). His work highlights the critical role of mathematics in understanding, developing, and enhancing AI systems. This exploration is part of a larger initiative by PNNL, which is investing in the Mathematics for Artificial Reasoning in Science (MARS) program, aimed at uncovering the capabilities and limitations of AI. Math to Understand AI One of Kvinge's primary focuses is using mathematics to demystify the inner workings of AI models, particularly neural networks, which are often referred to as "black boxes." These models can make decisions based on complex inputs and outputs, and Kvinge argues that mathematical tools like curvature, shape, and symmetry can help researchers analyze and optimize these decision-making processes. By dissecting these models, mathematicians can identify underlying flaws and ensure that AI systems operate based on sound reasoning rather than faulty logic. This scrutiny is crucial for building trust in AI, especially in contexts where reliability is paramount. Math to Inspire AI Development Mathematics also plays a significant role in the design and improvement of AI systems. Kvinge explains that mathematical principles can guide the development of AI models, making them more efficient and effective. For example, the concept of a "loss landscape" in AI training involves visualizing models as topographical maps where shallow, broad valleys represent robust solutions. Mathematical techniques such as symmetry and curvature can help devise training algorithms that guide models toward these optimal solutions. This approach can significantly reduce training time and lower computational costs, making AI more accessible and practical for a wide range of applications. AI for Mathematics Conversely, AI is increasingly being seen as a powerful tool for advancing mathematical research. Kvinge and his team recently demonstrated that an AI algorithm could provide valuable insights into solving a difficult problem in algebraic combinatorics. By cracking open the black box and studying the algorithm's reasoning, they could understand how it arrived at its conclusions. This level of transparency and insight is still relatively rare in AI research due to the complexity and opaque nature of deep learning systems. Despite this, Kvinge believes that such successes will gradually win over the skepticism of traditional mathematicians and encourage more collaboration between the two fields. Challenges in Collaboration Collaboration between mathematicians and data engineers is essential for advancing AI. While mathematicians traditionally prefer working from first principles, they need to be open to applying their knowledge to problems derived from real-world systems. Engineers, on the other hand, can benefit from the abstract frameworks provided by mathematics, which help in making informed design decisions while the actual learning is left to algorithms. Kvinge emphasizes the importance of having humans in the loop to detect spurious correlations that AI models might exploit, ensuring that the models' outputs are reliable and meaningful. For instance, a model might perform well on a test set simply because it has learned the nuances of the test data rather than the underlying principles it is supposed to capture. PNNL's Investments and Future Directions Kvinge's work is part of PNNL's 4-year MARS investment, which has already yielded promising results. Building on this success, PNNL is now directing resources toward a new initiative called "Generative AI: Foundations for the Future." This project aims to leverage mathematicians' expertise in topology, algebra, and geometry to address fundamental data science challenges. Kvinge encourages the mathematics community to engage with the MARS project by exploring and contributing to the curated set of machine learning (ML) benchmarks in algebraic combinatorics, which are publicly available on GitHub. Industry Insights and Company Profile Industry insiders recognize the transformative potential of integrating mathematics and AI. They highlight that while AI has shown remarkable capabilities in various domains, its black-box nature often hinders wider adoption. Kvinge's research at PNNL is seen as a significant step towards making AI more transparent and trustworthy, bridging the gap between theoretical rigor and practical application. PNNL, a leading research institution, is well-positioned to continue pushing the boundaries of AI through interdisciplinary collaboration, ensuring that the technology serves scientific and societal needs effectively.