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Mathematical Science and AI Lab
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A lab that spans physics, life science, and information science to explore the structures and laws of mathematics.
AboutAbout the lab
Exploring the mathematical structures and laws behind complexity.
Mathematical Science and AI Lab spans physics, life science, and information science to study the mathematical structures and universal laws behind complex systems.
Using mathematical concepts that do not depend on a particular model, such as "symmetry" and "topology," the lab aims to capture the essence shared by a wide range of seemingly different phenomena.
The lab pursues research in two directions: analyzing how AI works from the viewpoint of physics, and using AI to draw new scientific insights from experimental data.
Key terms
- Diffusion model
- One of the AI mechanisms widely used for image generation.
- Path integral
- Feynman's method in quantum mechanics for calculating a particle's behavior from all the paths it could take.
- Self-similarity
- The property that similar structures appear even when something is enlarged or reduced.
- Topology
- A field of mathematics that studies the properties preserved when a shape is continuously deformed.
- Robust perfect adaptation
- The property that the output returns to its original value even when the input stimulus changes.
NewsLab news
Paper on higher-form symmetries and dissipative photons published in Journal of High Energy Physics
Paper on generalized symmetries and self-similar inverse cascades published in Physical Review Letters
Paper on perfect adaptation in biochemical networks published in IEEE Control Systems
ResearchResearch themes
Mathematical Science and AI Lab spans physics, life science, and information science to explore the mathematical structures and universal laws behind complex systems. Its research includes analyzing AI from the viewpoint of physics, the control mechanisms of biological systems, and generalized symmetries and quantum phases.
*Illustrative imageUnderstanding diffusion models through path integrals
In research presented at ICML 2024, the lab proposed a new way to describe diffusion models using Feynman's path integral from quantum mechanics. This framework allows a deeper understanding of how diffusion models behave.
*Illustrative imageDiscovering self-similarity from data
Based on experimental data, the lab developed a method that uses neural networks to discover self-similarity in physical systems. Previously, a model had to be assumed in advance. This paper was selected as an Editors' Suggestion in Physical Review E.
*Illustrative imageDescribing quantum systems with neural networks
The lab proposed a mapping that writes a wide class of quantum mechanical systems in the form of a neural network. Particle trajectories in the Feynman path integral are approximated by a neural network.
*Illustrative imagePerfect adaptation in biochemical networks
The lab characterized "robust perfect adaptation," in which the output returns to its original value even when the input stimulus changes, in terms of the topology of general chemical reaction networks. It also shows how to construct the controllers that realize each case.
MembersFaculty
The members of Mathematical Science and AI Lab consist of faculty and doctoral and undergraduate students.
- Associate ProfessorYuji Hirono
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Mathematics (cryptography) on a blackboard” David Malone / CC BY 4.0 (cropped)
- Understanding diffusion models through path integrals: “Diffusion with ink” Zvonimir Lončarić / CC BY-SA 4.0 (cropped)
- Discovering self-similarity from data: “Cauliflower Fractal AVM” AVM / CC BY-SA 3.0 (cropped)
- Describing quantum systems with neural networks: “Artificial Neural Network with Chip” mikemacmarketing / original posted on flickr Liam Huang / clipped and posted on flickr / CC BY 2.0 (cropped)
- Perfect adaptation in biochemical networks: “Chemotaxis in bacterial populations” LivneNir / CC BY-SA 4.0 (cropped)
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