The field of deep learning is moving towards a deeper understanding of optimization and generalization. Recent research has focused on developing new optimization algorithms and analyzing the properties of existing ones. A key direction is the development of more efficient and robust optimization methods, such as those that can handle non-convex landscapes and saddle points. Another important area is the study of generalization, including the role of regularization, normalization, and other techniques in improving the performance of deep neural networks. Noteworthy papers in this area include 'Gradient Descent as Loss Landscape Navigation: a Normative Framework for Deriving Learning Rules', which proposes a theoretical framework for understanding learning rules, and 'The Hidden Power of Normalization: Exponential Capacity Control in Deep Neural Networks', which provides a theoretical explanation for the success of normalization methods. Additionally, 'A Saddle Point Remedy: Power of Variable Elimination in Non-convex Optimization' provides a rigorous geometric explanation for the effectiveness of variable elimination algorithms.
Optimization and Generalization in Deep Learning
Sources
Gradient Descent as Loss Landscape Navigation: a Normative Framework for Deriving Learning Rules
Exploring Landscapes for Better Minima along Valleys
Learning an Efficient Optimizer via Hybrid-Policy Sub-Trajectory Balance
The Hidden Power of Normalization: Exponential Capacity Control in Deep Neural Networks
Regularization Implies balancedness in the deep linear network
A Saddle Point Remedy: Power of Variable Elimination in Non-convex Optimization
Estimation of Toeplitz Covariance Matrices using Overparameterized Gradient Descent
The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold
Bulk-boundary decomposition of neural networks
Matrix Sensing with Kernel Optimal Loss: Robustness and Optimization Landscape
Neural network initialization with nonlinear characteristics and information on spectral bias
Adam Reduces a Unique Form of Sharpness: Theoretical Insights Near the Minimizer Manifold
Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models
Relative entropy estimate and geometric ergodicity for implicit Langevin Monte Carlo
Mean square error analysis of stochastic gradient and variance-reduced sampling algorithms