Before Diffusion Models: The Mathematical Genius Behind the Invention of Measure Theory.
The Life & Work of Henri Lebesgue.
Dear Network,
The Quantum Formalism (QF) team has recently released an eBook on LinkedIn exploring the profound indirect contributions of the legendary French mathematician Henri Lebesgue to the development of the mathematical framework underlying quantum mechanics. While Lebesgue is most famous for his pioneering work in Measure Theory, his influence extends far beyond pure mathematics, touching on key areas such as probability theory and quantum information sciences. Indeed, Lebesgue’s ideas laid the foundation for Andrey Kolmogorov’s rigorous mathematical framework of probability, which in turn has impacted a wide range of applied disciplines, including modern artificial intelligence (AI).
For those interested in AI, Diffusion Models offer a good example of how Lebesgue’s foundational work continues to shape cutting-edge technologies. These models, also known as diffusion probabilistic models or score-based generative models, leverage Measure Theory to simulate the diffusion process. In simple terms, a diffusion model learns how data evolves through random processes, allowing it to generate new, high-quality data points similar to the original dataset.
Since the model operates in high-dimensional data spaces (e.g., image pixel values), measure theory is required as the foundational mathematical framework for defining probabilities in these spaces. In particular, a probability measure is needed to assign probabilities to events (sets of possible outcomes), which allows the model to handle continuous probability distributions effectively.
If you’re passionate about the intersection of AI and advanced branches of mathematics, or if you want to better understand the mathematical principles driving today’s AI breakthroughs, this 10 page eBook is for you.
Download your copy below and learn about Henri Lebesgue’s life and pioneering work in France during the vibrant period of 'La Belle Époque'.
Measure Theory Crash Course
I am currently delivering the QF’s 'Abstract Mathematics 101 Bootcamp', which began in May and runs until December. We are currently in Module I, having just started the Topology section. Following this, Module II, covering Measure Theory, will begin around the second week of November. If you’re interested in joining for Module II, you can sign up using this form: https://forms.gle/tqTPQ4rdZzXsKYAK8.
Below, you'll find the resources for Module I, in case you'd like to review Topology before starting Module II.
Thank you for reading my newsletter. I wish you a fantastic rest of the weekend!
Best wishes,
Bambordé