Institute for Pure & Applied Mathematics (IPAM) Courses

Solving Overparametrized Systems of Nonlinear Equations

Explore overparametrized nonlinear equation systems, their solutions, and implications for neural network optimization landscapes with Stanford's Andrea Montanari at IPAM's EnCORE Workshop.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Sample Complexity of Estimation in Logistic Regression - Lecture

Explore sample complexity in logistic regression, examining parameter estimation across temperature regimes. Gain insights into non-asymptotic analysis and critical points in the complexity curve.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Provably Learning a Multi-Head Attention Layer

Explore algorithmic approaches and computational challenges in learning multi-head attention layers, with insights on provable algorithms and lower bounds for transformer model learnability.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Memory as a Lens to Understand Efficient Learning and Optimization

Exploring memory's role in optimization, discussing convergence rates of memory-limited algorithms vs. computationally expensive methods, and examining new problem structures to improve gradient descent variants.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Robust Learning of a Single Neuron - Bridging Computational Gaps Using Optimization

Explore robust learning of a single neuron with ReLU activation, focusing on optimization techniques to achieve near-optimal mean square loss in adversarial settings. Discover novel approaches for various activation functions.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Fast Multipole Attention: A Divide-and-Conquer Attention Mechanism for Long Sequences

Innovative divide-and-conquer strategy for efficient attention in long sequences, reducing complexity while maintaining global receptive field. Potential to enhance large language models with extended context processing.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Testing Dependency of Databases - Lecture

Explore statistical methods for detecting dependencies between random databases, including hypothesis testing and phase transitions in error probability based on database dimensions and distributions.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Complexity of Sparse Linear Regression

Explore new methods for solving sparse linear regression, overcoming limitations of traditional approaches and exploiting structural properties of covariance matrices in machine learning and statistics.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Beyond Worst-case Guarantees for Sequential Prediction - Robustness via Abstention

Explore sequential prediction with adversarial examples, introducing a model allowing learners to abstain from predictions. Discover algorithms handling stochastic and adversarial data while maintaining optimal regret scaling.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Algorithms Approaching the Threshold for Semirandom Planted Clique

Explore advanced algorithms for semirandom planted clique problems with Princeton researcher Pravesh Kothari, discussing computational and statistical challenges in learning and optimization.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Symmetric Functions: Foundations and Applications in Combinatorics - Part 1

Explore symmetric functions in algebraic combinatorics, representation theory, and statistical mechanics. Learn formulas, combinatorial models, and key properties with applications and open problems.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Dimer Models and Random Tilings - Part 1

Explore dimer models and random tilings with Cédric Boutillier. Learn about Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for studying perfect matchings on lattices.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Gaussian Free Field and Schramm-Loewner Evolution - Part 1

Explore the Gaussian free field and Schramm-Loewner Evolution, two key concepts in random geometry. Learn their applications in statistical physics and connections to critical phenomena.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Introduction to Cluster Algebras - Part 2

Explore the Laurent phenomenon in cluster algebras, focusing on octahedron recurrences. Gain insights into geometric and algebraic aspects of this advanced mathematical topic.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Gaussian Free Field and Schramm-Loewner Evolution - Part 2

Explore Gaussian free field and Schramm-Loewner Evolution in random geometry. Discover connections between these canonical objects and their applications in statistical physics and conformal field theory.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video