Artificial intelligence is, at its core, applied mathematics. These math applications stands at the intersection of pure math and computer science, diving into the theoretical foundations of modern AI 📐. Explore complex research on gradient descent optimization, high-dimensional linear algebra, probabilistic reasoning, and the calculus of neural networks. From understanding the topology of deep learning models to the statistical theories explaining how massive language models generalize data, discover the mathematical proofs and equations that make artificial intelligence possible.
Sticky Brownian Motion — The Complete Trivariate Distribution, Finally Written Down Correctly | AI Trend Blend AITrendBlend Mathematics Machine Learning About Probability Theory · Journal of Mathematical Analysis and Applications 560 (2026) · Universidade Nova de Lisboa & Université de Lorraine · 12 min read A Particle That Gets Stuck — The Complete Mathematical Story […]
When Heat Refuses to Misbehave — Taming Ill-Posed Problems in Semi-Infinite Cylinders | AI Trend Blend AITrendBlend Mathematics Machine Learning About Applied Mathematics · Journal of Mathematical Analysis and Applications 561 (2026) · Universidade de Vigo & Universitat Politècnica de Catalunya · 12 min read When Heat Refuses to Misbehave — Taming Ill-Posed Problems in
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When the Only Symmetry Is a Flip of Sign — Isometries of James-Schreier and Lorentz Spaces | AI Trend Blend AITrendBlend Mathematics Machine Learning About Pure Mathematics · Journal of Mathematical Analysis and Applications 560 (2026) · Universidade de São Paulo & Universidade Estadual Paulista · 13 min read When the Only Symmetry Is a
Pinning Down the Zeros — New Uniform Asymptotic Expansions for Generalised Trigonometric Integrals | AI Trend Blend AITrendBlend Mathematics Machine Learning About Applied Mathematics · Journal of Mathematical Analysis and Applications 560 (2026) · San Diego State University · 13 min read Pinning Down the Zeros — How a Single Elegant Chain of Analysis Finally
When Matrices Draw Ellipses — The Hidden Geometry of Higher Rank Numerical Ranges | AI Trend Blend AITrendBlend Mathematics Machine Learning About Pure Mathematics · Journal of Mathematical Analysis and Applications 560 (2026) · University of Coimbra, University of Aveiro & University of Trás-os-Montes e Alto Douro, Portugal · 13 min read When Matrices Draw
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From Sparse to Dense Functional Data in High Dimensions: Phase Transitions Revisited | AI Trend Blend AITrendBlend Machine Learning Math About Functional Data Analysis · Journal of Machine Learning Research 26 (2025) 1–40 · 18 min read When Does Sampling Density Actually Matter? Phase Transitions in High-Dimensional Functional Data, Revisited A team from Renmin University
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Why Hard Training Examples Hurt Neural Networks — And How DPLS Fixes It | AI Trend Blend AITrendBlend Machine Learning Adversarial AI About Adversarial Robustness · Journal of Machine Learning Research 26 (2025) 1–48 · 16 min read Why Hard Training Examples Are Secretly Sabotaging Your Neural Network’s Robustness A team from Seoul National University
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Teaching Machines That the World Keeps Changing: Supervised Learning with Evolving Tasks and Performance Guarantees | AI Trend Blend AITrendBlend Machine Learning Math About Continual Learning · Journal of Machine Learning Research 26 (2025) 1–59 · BCAM · University of the Basque Country · 22 min read Teaching Machines That the World Keeps Changing: One
An Axiomatic Definition of Hierarchical Clustering: Why Hartigan Was Right All Along | AI Trend Blend AITrendBlend Machine Learning Math Computer Vision About Statistical Learning Theory · Journal of Machine Learning Research 26 (2025) 1–26 · 18 min read Three Rules That Define What a Cluster Actually Is: The Axiomatic Case for Hartigan’s Cluster Tree
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Bayes Meets Bernstein: Why Meta-Learning Finally Gets Fast — A PAC-Bayes Breakthrough | AI Trend Blend AITrendBlend Machine Learning Math About Machine Learning Theory · Journal of Machine Learning Research 26 (2025) · University of Tokyo, ESSEC Business School & CNRS / Sorbonne Université · 16 min read Why Meta-Learning Suddenly Gets Smarter the More
Bayes Meets Bernstein: Why Meta-Learning Finally Gets Fast — A PAC-Bayes Breakthrough Read More »