Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order

Fine-tuning Large Language Models (LLMs) is essential for adapting pre-trained models to downstream tasks. Yet traditional first-order optimizers such as Stochastic Gradient Descent (SGD) and Adam incur prohibitive memory and computational costs that scale poorly with model size. In this paper, we investigate zero-order (ZO) optimization methods as a memory- and compute-efficient alternative, particularly in the context of parameter-efficient fine-tuning techniques like LoRA. We propose $\texttt{JAGUAR SignSGD}$, a ZO momentum-based algorithm that extends ZO SignSGD, requiring the same number of parameters as the standard ZO SGD and only $\mathcal{O}(1)$ function evaluations per iteration. To the best of our knowledge, this is the first study to establish rigorous convergence guarantees for SignSGD in the stochastic ZO case. We further propose $\texttt{JAGUAR Muon}$, a novel ZO extension of the Muon optimizer that leverages the matrix structure of model parameters, and we provide its convergence rate under arbitrary stochastic noise. Through extensive experiments on challenging LLM fine-tuning benchmarks, we demonstrate that the proposed algorithms meet or exceed the convergence quality of standard first-order methods, achieving significant memory reduction. Our theoretical and empirical results establish new ZO optimization methods as a practical and theoretically grounded approach for resource-constrained LLM adaptation. Our code is available at https://github.com/brain-mmo-lab/ZO_LLM

Quality and Cost Trade-offs in Passage Re-ranking Task

Deep learning models named transformers achieved state-of-the-art results in a vast majority of NLP tasks at the cost of increased computational complexity and high memory consumption. Using the transformer model in real-time inference becomes a major challenge when implemented in production, because it requires expensive computational resources. The more executions of a transformer are needed the lower the overall throughput is, and switching to the smaller encoders leads to the decrease of accuracy. Our paper is devoted to the problem of how to choose the right architecture for the ranking step of the information retrieval pipeline, so that the number of required calls of transformer encoder is minimal with the maximum achievable quality of ranking. We investigated several late-interaction models such as Colbert and Poly-encoder architectures along with their modifications. Also, we took care of the memory footprint of the search index and tried to apply the learning-to-hash method to binarize the output vectors from the transformer encoders. The results of the evaluation are provided using TREC 2019-2021 and MS Marco dev datasets.