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Kasai Lab
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The lab studies modern machine learning as an object of mathematical study.
AboutAbout the lab
Reading the inside of models through mathematics.
Kasai Lab studies the models of modern machine learning as objects of mathematical study.
Beyond statistical learning theory, the lab seeks to clarify the representations and states inside models, as well as the mechanisms by which they generate outputs.
The lab draws on a wide range of mathematical ideas, including geometry, probability theory, dynamical systems, and optimization.
Another goal is to clarify where the limits of what models can do lie.
Key terms
- Optimization
- A field of mathematics that uses mathematical formulas to find the best answer under given conditions
- Dynamical systems
- A field of mathematics that expresses the mechanisms of things that change over time in mathematical formulas and investigates them
- Geometry
- A field of mathematics that investigates the shapes and connectedness of figures and spaces
ResearchResearch themes
The lab studies the models of modern machine learning as objects of mathematical study. Using geometry, probability theory, and other tools, it seeks to clarify the representations and states inside models, the mechanisms by which they generate outputs, and the limits of what they can and cannot do.
*Illustrative imageGeometry and Optimal Transport
The lab studies how probability distributions change from one to another, using geometry, optimal transport, and gradient flows.
*Illustrative imageStochastic Processes and Dynamical Systems
The lab studies the mathematical properties of randomly changing phenomena and of systems that evolve over time.
*Illustrative imageOptimization and Variational Analysis
The lab studies the mathematical mechanisms of optimization and functional analysis that underlie machine learning algorithms.
*Illustrative imageInternal Representations of AI Models
The lab studies what information is represented, stored, and interpretable inside AI models.
MembersFaculty
The members of Kasai Lab consist of faculty, secretaries, and doctoral, master's, and undergraduate students.As of 2026
- ProfessorHiroyuki Kasai
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: “Koch V3 85 Grad K HQ OpenCL” PantheraLeo1359531 / CC BY 4.0 (cropped)
- Geometry and Optimal Transport: “Modelle von Flächen zweiter Ordnung nach A. Brill -Schilling, Cartonmodelle- (3)” Ramona Trusheim / CC BY-SA 3.0 (cropped)
- Stochastic Processes and Dynamical Systems: “Asset-Prices-Simulated-using-the-Brownian-Motion-Stochastic-Process-Many” NivedRajeev / CC BY-SA 4.0 (cropped)
- Optimization and Variational Analysis: “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped)
- Internal Representations of AI Models: “Museo de Informática Histórica (MIH) – UNIZAR – Magnetic-core memory 8k x 12 bit H-212 – close up” José Luis Briz Velasco / CC BY-SA 4.0 (cropped)
- Related lab (前原研究室): “Advanced Technology Demonstrator radar antenna array 01” NOAA / Public domain (cropped)
- Related lab (小川研究室): “Spectrogram - It Rains a Lot in Portland” Aaron Parecki / CC BY 2.0 (cropped)
- Related lab (甲藤研究室): “Studio A broadcast area ( )” Atomic Taco from Seattle, WA, USA / CC BY-SA 2.0 (cropped)
- Related lab (河原研究室): “Kanji (Unsplash)” Niketh Vellanki / CC0 (cropped)
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