Institute for Pure & Applied Mathematics (IPAM) Courses

Multiresolution Tensor Learning for Efficient and Interpretable Spatial Analysis

Explore efficient and interpretable spatial analysis using multiresolution tensor learning, with applications in geology, sports, and climate science. Discover improved methods for handling complex spatial data.

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

The Effectiveness of Nonconvex Tensor Completion - Fast Convergence and Uncertainty Quantification

Explores nonconvex optimization for tensor completion, proposing a two-stage algorithm with guaranteed success, linear convergence, and statistical accuracy. Discusses distribution characterization and confidence interval construction.

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

Implicit and Explicit Regularization in Deep Neural Networks

Explores implicit and explicit regularization in deep neural networks, connecting learning algorithms to H-infinity control and explaining convergence behavior in over-parametrized models, offering insights into generalization abilities.

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

Understanding, Interpreting and Designing Neural Network Models Through Tensor Representations

Explore tensor representations for neural networks, enhancing interpretability, expressive power, generalization, and robustness in deep learning models through spectral methods and innovative architecture design.

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

Principal Components along Quiver Representations

Explore principal components in quiver representations, a generalization of multi-indexed data tensors, and their applications in optimization and data analysis.

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

Beyond Lazy Training for Over-parameterized Tensor Decomposition

Explore tensor decomposition in over-parameterized settings, analyzing gradient descent variants and their performance beyond lazy training regimes for improved optimization in neural networks.

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

The Kikuchi Hierarchy and Tensor PCA

Explores advanced algorithms for tensor PCA, introducing a new hierarchy inspired by Kikuchi free energy to improve belief propagation performance and match sum-of-squares methods.

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

Strictly-Correlated Electron Functional and Multimarginal Optimal Transport

Explore convex optimization methods for multi-marginal transport problems in density functional theory, including relaxation techniques and rounding schemes for energy bounds.

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

News on Tensor Network Simulations for Quantum Matter and Beyond

Explore recent developments in tensor network simulations for quantum systems and their applications beyond physics, including portfolio optimization in finance.

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

Emergent Gapless Quantum Spin Liquid from Deconfined Quantum Critical Point

Explores emergent gapless quantum spin liquid near deconfined quantum critical point using tensor network state methods, providing evidence for its existence in antiferromagnetic Heisenberg models.

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

Hyper-Optimized Tensor Network Contraction - Simplifications, Applications and Approximations

Explore tensor network contraction optimization through hyper-graph partitioning, simplifications, and approximations, with applications in quantum circuit simulation and beyond.

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

Phase Transitions in the Complexity of Simulating Random Shallow Quantum Circuits

Explores phase transitions in simulating random shallow quantum circuits, discussing computational complexity, tensor network contraction, and mapping 2D circuits to 1D processes with implications for quantum computing.

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

Tensor Networks for Machine Learning and Applications

Explore tensor networks in machine learning, their benefits, and applications. Learn about model functions, optimization algorithms, and potential insights for matching architectures to data types.

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

Tropical Tensor Networks

Unified tensor network approach for spin glasses using tropical algebra, enabling ground state energy computation, optimal configuration identification, and solution counting. Combines graphical models and quantum circuit simulation.

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

Low Rank Tensor Completion

Explore low-rank tensor completion methods for recovering tensors from partial observations, including matrix composition, multilinear ranks, and approaches for initialization and recovery.

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