Tuesday, September 9, 4 pm, East Hall 1324: Science 2.0 - Evolving the Scientific Method in the Age of AI
There will be a reception after the Tuesday Colloquium in the Math Upper Atrium.
Wednesday, September 10, 4 pm, East Hall 1360: Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning
Thursday, September 11, 4 pm, East Hall 4448: From Big Data to Right Data: Information-Theoretic Optimal Experimental Design
Tuesday, September 9, 4 pm, East Hall 1324: Science 2.0 - Evolving the Scientific Method in the Age of AI
This lecture addresses the historical trade-off between interpretable but expertise-dependent deductive models and scalable but non-interpretable data-driven approaches by introducing hybrid AI frameworks that transcend this divide. We present AI-Descartes (generator-verifier paradigm), AI-Hilbert (unified hypothesis generation and testing), and AI-Noether (algebraic-geometric theory revision via abductive reasoning) as transformative approaches to mathematical model discovery. These frameworks advocate for conceptual evolution of the scientific method toward deeper AI integration in pursuing both interpretable and universal models.
Wednesday, September 10, 4 pm, East Hall 1360: Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning
This lecture introduces a novel tensor-tensor algebra that preserves essential matrix-algebraic properties while overcoming limitations of conventional tensorial frameworks, culminating in an Eckart-Young-like theorem that resolves a decades-long open problem in tensor analysis. We demonstrate how this framework enables seamless retrofitting of existing computational workflows (Hamiltonian neural networks, tensor Graph Convolutional Networks) and extends to tensor group symmetry theory for equivariant learning applications. This work opens pathways to new tensorial algebras that can reveal deeper patterns in high-dimensional information previously inaccessible to traditional methods.
Thursday, September 11, 4 pm, East Hall 4448: From Big Data to Right Data: Information-Theoretic Optimal Experimental Design
This lecture addresses the modern paradox where unprecedented data accumulation capabilities make selective identification of informative samples more critical than ever for meaningful model development. We review theoretical foundations of experimental design within inverse problems frameworks, examining strategies for well-posed and ill-posed settings while establishing approaches for design preferences, budget allocation, and risk assessment. Through information-theoretic principles, we demonstrate how optimal experimental design creates a paradigm shift from data volume to information content, with transformative implications for resource-constrained scientific methodology.
Dr. Lior Horesh is a Principal Research Scientist, Master Inventor and a Senior Manager of the Mathematics & Theoretical Computer Science (formerly Mathematics of AI) department at IBM Research. His department’s mission is to approach some of the big challenges the field of AI is facing, from a principled mathematical angle. Additionally, Dr. Horesh holds an adjunct Associate Professor position at the Computer Science department of Columbia University where he teaches graduate level Advanced Machine Learning and Quantum Computing courses. Dr. Horesh Received his Ph.D. in 2006 from UCL and joined IBM in 2009.
The Ziwet Lectures were established in 1934 through a bequest from Professor Ziwet, Chair of the UM Department of Mathematics from 1888-1925. He stipulated that his estate “should be used for the promotion of scientific work.” The Ziwet lectures have been one of the most prestigious lecture series in the department.
There will be a reception after the Tuesday Colloquium in the Math Upper Atrium.
Wednesday, September 10, 4 pm, East Hall 1360: Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning
Thursday, September 11, 4 pm, East Hall 4448: From Big Data to Right Data: Information-Theoretic Optimal Experimental Design
Tuesday, September 9, 4 pm, East Hall 1324: Science 2.0 - Evolving the Scientific Method in the Age of AI
This lecture addresses the historical trade-off between interpretable but expertise-dependent deductive models and scalable but non-interpretable data-driven approaches by introducing hybrid AI frameworks that transcend this divide. We present AI-Descartes (generator-verifier paradigm), AI-Hilbert (unified hypothesis generation and testing), and AI-Noether (algebraic-geometric theory revision via abductive reasoning) as transformative approaches to mathematical model discovery. These frameworks advocate for conceptual evolution of the scientific method toward deeper AI integration in pursuing both interpretable and universal models.
Wednesday, September 10, 4 pm, East Hall 1360: Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning
This lecture introduces a novel tensor-tensor algebra that preserves essential matrix-algebraic properties while overcoming limitations of conventional tensorial frameworks, culminating in an Eckart-Young-like theorem that resolves a decades-long open problem in tensor analysis. We demonstrate how this framework enables seamless retrofitting of existing computational workflows (Hamiltonian neural networks, tensor Graph Convolutional Networks) and extends to tensor group symmetry theory for equivariant learning applications. This work opens pathways to new tensorial algebras that can reveal deeper patterns in high-dimensional information previously inaccessible to traditional methods.
Thursday, September 11, 4 pm, East Hall 4448: From Big Data to Right Data: Information-Theoretic Optimal Experimental Design
This lecture addresses the modern paradox where unprecedented data accumulation capabilities make selective identification of informative samples more critical than ever for meaningful model development. We review theoretical foundations of experimental design within inverse problems frameworks, examining strategies for well-posed and ill-posed settings while establishing approaches for design preferences, budget allocation, and risk assessment. Through information-theoretic principles, we demonstrate how optimal experimental design creates a paradigm shift from data volume to information content, with transformative implications for resource-constrained scientific methodology.
Dr. Lior Horesh is a Principal Research Scientist, Master Inventor and a Senior Manager of the Mathematics & Theoretical Computer Science (formerly Mathematics of AI) department at IBM Research. His department’s mission is to approach some of the big challenges the field of AI is facing, from a principled mathematical angle. Additionally, Dr. Horesh holds an adjunct Associate Professor position at the Computer Science department of Columbia University where he teaches graduate level Advanced Machine Learning and Quantum Computing courses. Dr. Horesh Received his Ph.D. in 2006 from UCL and joined IBM in 2009.
The Ziwet Lectures were established in 1934 through a bequest from Professor Ziwet, Chair of the UM Department of Mathematics from 1888-1925. He stipulated that his estate “should be used for the promotion of scientific work.” The Ziwet lectures have been one of the most prestigious lecture series in the department.
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