Memory-Efficient LLM Training with Dynamic Sparsity: From Stability to Practical Scaling

Communication increasingly dominates the cost of Large Language Model (LLM) pre-training, especially under data-parallel and sharded training schemes, where gradient synchronization and parameter reconstruction overhead increase with model size and system scale. Existing communication-reduction methods either sparsify raw gradients, which can be unstable for modern Adam-style optimizers at high sparsity, or quantize communication, whose savings are fundamentally bounded by bit width and often incur additional runtime overhead. We present SCAPE, a communication-efficient distributed optimizer for LLM training that exploits the stability of AdamS's first-moment to enable aggressive sparsification without loss of LLM quality. Instead of constructing masks from raw gradients, SCAPE derives them from first-moment-based statistics, partitions mask generation across workers to align with optimizer sharding, and delays mask usage by one step so that mask synchronization can overlap with computation. SCAPE also reconstructs the quantities required for second-moment updates from a single synchronized sparse buffer, avoiding an additional collective. We implement SCAPE in Megatron-LM and evaluate its convergence by pre-training GPT-345M on OpenWebText and Llama-500M on SlimPajama-6B using 32 NVIDIA GH200 GPUs on TACC Vista. In both models, SCAPE preserves training stability, validation loss, and downstream task accuracy under 90% and 99% sparsity. For Llama-500M, SCAPE reduces end-to-end pre-training wall-clock time by up to 43.3% while maintaining model quality comparable to dense AdamW and AdamS. For Llama-1.8B, SCAPE achieves up to 3.26$\times$ speedup per step compared to dense AdamS.

Large language models (LLMs) achieve strong generation and reasoning performance, but the Transformer architecture incurs high inference cost. Existing acceleration methods often rely on task-specific fine-tuning or training from scratch, increasing adaptation cost and limiting cross-task usability. We present an Adaptive Depth Sparse Framework (AdaDSF) that converts off-the-shelf pre-trained LLMs into depth-sparse models without full retraining. Our key insight is that layers contribute unequally to representation transformation, characterized by the cosine similarity between layer input and output hidden states. Based on this, AdaDSF assigns layer-wise token retention ratios from similarity statistics, uses a lightweight router to select informative tokens at each layer, and introduces a feature-preserving alignment objective to match intermediate and final representations between sparse and dense models. On GPT-NeoX and Qwen2.5 over language modeling and commonsense reasoning, AdaDSF substantially reduces inference FLOPs while preserving performance close to dense counterparts. Under comparable sparsity, AdaDSF consistently yields smaller accuracy degradation than strong baselines including MoD, D-LLM, and DLO.

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale language-model pretraining and fine-tuning, recent work has revisited nearly every component of the optimization stack: adaptive moment estimation, decoupled weight decay, memory footprint, curvature approximation, sign-based updates, large-batch stability, low-rank gradient structure, and matrix-wise orthogonalized updates. This survey reviews optimizer design for large language models through a systems-and-optimization lens. We organize the literature into classical first-order optimizers, adaptive optimizers, memory-efficient variants, second-order and curvature-aware methods, sign-based and discovered optimizers, low-rank and projection-based methods, and matrix-based optimizers such as Muon. We also discuss benchmarking methodology, including hyperparameter fairness, scale dependence, wall-clock efficiency, token efficiency, memory overhead, and downstream evaluation. We argue that optimizer research for LLMs is entering a new phase: moving from single-algorithm speedup claims toward rigorous, scale-aware comparisons that jointly evaluate convergence, stability, memory, and implementation complexity.