Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizers

A new survey paper titled "Navigating LLM Valley" examines the evolving landscape of optimization algorithms for training large language models (LLMs). While AdamW remains the dominant optimizer, the study highlights a shift towards more computationally and memory-efficient alternatives necessary for extreme-scale training. The authors review recent advancements across various components of the optimization stack, including adaptive moment estimation, decoupled weight decay, and curvature approximation. The literature is categorized into classical first-order optimizers, adaptive methods, memory-efficient variants, second-order techniques, sign-based updates, and emerging matrix-based optimizers like Muon. Furthermore, the paper addresses critical benchmarking methodologies, emphasizing hyperparameter fairness, wall-clock efficiency, and token efficiency. It argues that optimizer research is transitioning from isolated speedup claims to rigorous, scale-aware comparisons that jointly evaluate convergence, stability, memory overhead, and implementation complexity. This comprehensive analysis provides a systems-and-optimization lens for understanding the next phase of LLM development, focusing on holistic performance metrics rather than single-algorithm improvements.