Challenge: Recent advances in memory-efficient zeroth-order methods have limited their widespread adoption due to performance drops and a high risk of divergence.
Approach: They propose a memory-efficient zeroth-order framework to improve performance and convergence of the MeZO methods by using only forward passes.
Outcome: The proposed framework improves performance and convergence of the proposed methods on Roberta-Large and Llama-2-7B models.

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MUZO: Leveraging Multiple Queries and Momentum for Zeroth-Order Fine-Tuning of Large Language Models (2025.emnlp-main)

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Challenge: Existing methods for fine-tuning large language models incur memory overhead due to the need for activation storage for back-propagation (BP).
Approach: They propose a method that estimates gradients through finite differences without activation storage for back-propagation.
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RoZO: Geometry-Aware Zeroth-Order Fine-Tuning on Low-Rank Adapters for Black-Box Large Language Models (2026.eacl-long)

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Challenge: Large language models (LLMs) have demonstrated exceptional performance across a wide range of tasks, yet fine-tuning them efficiently under black-box or memory-constrained settings remains challenging.
Approach: They propose a Riemannian zeroth-order optimization framework that constrains updates to the tangent space of the LoRA manifold.
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Global Adaptive Momentum Meets Local Personalized Perturbation: Efficient Federated LLM Fine-Tuning with Zeroth-Order Gradients (2026.acl-long)

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Challenge: federated fine-tuning of large language models provides privacy-preserving approach to deploying pervasive generative AI services.
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Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling (2026.findings-acl)

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Challenge: Existing methods for fine-tuning Large Language Models are slow and lack of performance.
Approach: They propose a Zeroth-Order optimization framework that uses forward passes to fine-tune Large Language Models.
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Hi-ZFO: Hierarchical Zeroth- and First-Order LLM Fine-Tuning via Importance-Guided Tensor Selection (2026.findings-acl)

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Challenge: generative tasks require a high degree of exploratory capacity, but zeroth-order methods suffer from slow convergence . generative task-specific methods tend to converge toward local minima, causing noise and inefficient estimation .
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HELENE: Hessian Layer-wise Clipping and Gradient Annealing for Accelerating Fine-tuning LLM with Zeroth-order Optimization (2025.emnlp-main)

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Challenge: Large language models (LLMs) face memory challenges due to the high cost of backpropagation.
Approach: They propose a zeroth-order (ZO) optimization that matches memory usage to inference . they propose scalable and memory-efficient zeroth order (ZE) optimizer that integrates annealed A-GNB gradients with diagonal Hessian estimation and layer-wise clipping as a second-order pre-conditioner.
Outcome: The proposed algorithm outperforms state-of-the-art methods with an average speedup of 20 over MeZO on RoBERTa-large and OPT-1.3B.
QuZO: Quantized Zeroth-Order Fine-Tuning for Large Language Models (2025.emnlp-main)

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Challenge: Large Language Models (LLMs) are quantized to lower precision to reduce memory cost and latency in inference.
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MobiZO: Enabling Efficient LLM Fine-Tuning at the Edge via Inference Engines (2025.emnlp-main)

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Challenge: Large Language Models (LLMs) are currently pre-trained and fine-tuned on large cloud servers . fine-timing on resource-constrained edge devices presents significant memory and computational demands .
Approach: They propose a resource-efficient fine-tuning framework for LLMs specifically designed for edge devices.
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LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models (2023.emnlp-main)

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Challenge: Large language models (LLMs) have shown unprecedented performance across various tasks.
Approach: They propose an easy-to-use framework that integrates adapters into LLMs . they evaluate adapters on 14 datasets from two different reasoning tasks .
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LoRETTA: Low-Rank Economic Tensor-Train Adaptation for Ultra-Low-Parameter Fine-Tuning of Large Language Models (2024.naacl-long)

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Challenge: Existing methods for parameter-efficient fine-tuning are limited by the growing number of trainable parameters with the rapid deployment of Large Language Models (LLMs).
Approach: They propose a parameter-efficient framework that reduces trainable parameters through tensor-train decomposition.
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