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Diffusion Models are Minimax Optimal Distribution Estimators
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited.
Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning
While variance reduction methods have shown great success in solving large scale optimization problems, many of them suffer from accumulated errors and, therefore, should periodically require the full gradient computation.
Excess Risk of Two-Layer ReLU Neural Networks in Teacher-Student Settings and its Superiority to Kernel Methods
While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established.
On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student Setting
Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically.
Benefit of deep learning with non-convex noisy gradient descent: Provable excess risk bound and superiority to kernel methods
Establishing a theoretical analysis that explains why deep learning can outperform shallow learning such as kernel methods is one of the biggest issues in the deep learning literature.
