∇²f(x) ≻ 0 𝔼[X²] − 𝔼[X]² ≥ 0 Tr(AB) ≤ ‖A‖·‖B‖ ∂L/∂θ ← θ − η∇L H(p,q) = −Σ p log q Rₙ(𝒻) ≤ 2𝔊ₙ(ℱ) + ε Attention(Q,K,V) = softmax(QKᵀ/√d)V

Workshop · Peking University

Mathematical Foundations
of Modern Machine Learning

Dates 3–5 July, 2026

Venue Peking University, Beijing

Format Invited Talks & Discussion

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About the Workshop

Mathematical insight
meets modern ML practice

Modern machine learning has developed rapidly in both methodology and scale, while its mathematical foundations remain incomplete. Understanding the structural principles governing expressivity, representation, generalization, optimization, and scaling in large learning systems has become a central problem at the interface of applied mathematics and ML theory.

This workshop aims to advance the mathematical foundations of modern machine learning, with particular emphasis on connecting rigorous analysis to phenomena observed in large-scale practice. We bring together researchers working on approximation theory, high-dimensional generalization, optimization dynamics, statistical physics perspectives, and the theory of large language models.

Planned Session Topics

01 Approximation, generalization, and optimization in deep learning

02 Statistical physics perspectives on learning and training dynamics

03 Theoretical foundations of large language models

Invited Speakers