The recent developments in the field of deep learning and neural network optimization have shown a significant shift towards more stable and scalable algorithms. Researchers are increasingly focusing on understanding and improving the generalization capabilities of models, particularly through the lens of optimization techniques like Sharpness-Aware Minimization (SAM) and its variants. The field is witnessing a trend towards more theoretical grounding of optimization methods, with efforts to mathematically characterize the behavior of these methods, especially in the context of large-scale models and datasets. Additionally, there is a growing interest in developing convex optimization algorithms that can scale to high-dimensional data, as evidenced by the introduction of CRONOS and CRONOS-AM. These algorithms not only promise better performance but also provide theoretical guarantees of convergence. Furthermore, the design of neural operators is being informed by rigorous mathematical analysis, aiming to enhance stability, convergence, and computational efficiency. The integration of these theoretical insights with practical design strategies is paving the way for next-generation neural operators with improved performance and reliability. Notably, the work on $\mu$P$^2$ and ADOPT stands out for their contributions to the stability and convergence of neural networks, offering new parameterizations and adaptive gradient methods that address long-standing issues in optimization. These advancements collectively suggest a maturing of the field, where theoretical rigor and practical scalability are increasingly being prioritized.
Theoretical Rigor and Scalability in Neural Network Optimization
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$\boldsymbol{\mu}\mathbf{P^2}$: Effective Sharpness Aware Minimization Requires Layerwise Perturbation Scaling
Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond
CRONOS: Enhancing Deep Learning with Scalable GPU Accelerated Convex Neural Networks
Guiding Neural Collapse: Optimising Towards the Nearest Simplex Equiangular Tight Frame
1st-Order Magic: Analysis of Sharpness-Aware Minimization
Rethinking Weight Decay for Robust Fine-Tuning of Foundation Models
How Analysis Can Teach Us the Optimal Way to Design Neural Operators
Local Loss Optimization in the Infinite Width: Stable Parameterization of Predictive Coding Networks and Target Propagation
Cost-Gain Analysis of Sequence Selection for Nonlinearity Mitigation
Theoretical characterisation of the Gauss-Newton conditioning in Neural Networks
A Convex Relaxation Approach to Generalization Analysis for Parallel Positively Homogeneous Networks
ADOPT: Modified Adam Can Converge with Any $\beta_2$ with the Optimal Rate
PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic Devices
Deriving Analytical Solutions Using Symbolic Matrix Structural Analysis: Part 1 -- Continuous Beams