Fine-tuning vision language models (VLMs) has achieved remarkable performance across various downstream tasks; yet, it requires access to model gradients through backpropagation (BP), making them unsuitable for memory-constrained, inference-only edge devices. To address this limitation, previous work has explored various BP-free fine-tuning methods. However, these approaches often rely on high-variance evolutionary strategies (ES) or zeroth-order (ZO) optimization, and often fail to achieve satisfactory performance. In this paper, we propose a hybrid Sharpness-aware Zeroth-order optimization (SharpZO) approach, specifically designed to enhance the performance of ZO VLM fine-tuning via a sharpness-aware warm-up training. SharpZO features a two-stage optimization process: a sharpness-aware ES stage that globally explores and smooths the loss landscape to construct a strong initialization, followed by a fine-grained local search via sparse ZO optimization. The entire optimization relies solely on forward passes. Detailed theoretical analysis and extensive experiments on CLIP models demonstrate that SharpZO significantly improves accuracy and convergence speed, achieving up to 7% average gain over state-of-the-art forward-only methods.

More detailed comparisons with DFO and ZOO methods will be added in the revision. It is indeed valuable to enrich our related work on DFO. We will compare our method with existing DFO solvers, e.g., A preliminary comparison with COBYLA was illustrated in AE. Many benchmark black-box attack methods were built on ZO optimization, e.g., ZO-SignSGD Thus, we focus on the application in adversarial learning. It is shown from Eq. (19) that " should be added at the end of Y es, the stepsize interval should be reversed.

Large language models have demonstrated exceptional capabilities across diverse tasks, but their fine-tuning demands significant memory, posing challenges for resource-constrained environments. Zeroth-order (ZO) optimization provides a memory-efficient alternative by eliminating the need for backpropagation. However, ZO optimization suffers from high gradient variance, and prior research has largely focused on single-task learning, leaving its application to multi-task learning unexplored. Multi-task learning is crucial for leveraging shared knowledge across tasks to improve generalization, yet it introduces unique challenges under ZO settings, such as amplified gradient variance and collinearity. In this paper, we present MaZO, the first framework specifically designed for multi-task LLM fine-tuning under ZO optimization. MaZO tackles these challenges at the parameter level through two key innovations: a weight importance metric to identify critical parameters and a multi-task weight update mask to selectively update these parameters, reducing the dimensionality of the parameter space and mitigating task conflicts. Experiments demonstrate that MaZO achieves state-of-the-art performance, surpassing even multi-task learning methods designed for first-order optimization.

Large language models (LLMs) excel across various tasks, but standard first-order (FO) fine-tuning demands considerable memory, significantly limiting real-world deployment. Recently, zeroth-order (ZO) optimization stood out as a promising memory-efficient training paradigm, avoiding backward passes and relying solely on forward passes for gradient estimation, making it attractive for resource-constrained scenarios. However, ZO method lags far behind FO method in both convergence speed and accuracy. To bridge the gap, we introduce a novel layer-wise divergence analysis that uncovers the distinct update pattern of FO and ZO optimization. Aiming to resemble the learning capacity of FO method from the findings, we propose \textbf{Di}vergence-driven \textbf{Z}eroth-\textbf{O}rder (\textbf{DiZO}) optimization. DiZO conducts divergence-driven layer adaptation by incorporating projections to ZO updates, generating diverse-magnitude updates precisely scaled to layer-wise individual optimization needs. Our results demonstrate that DiZO significantly reduces the needed iterations for convergence without sacrificing throughput, cutting training GPU hours by up to 48\% on various datasets. Moreover, DiZO consistently outperforms the representative ZO baselines in fine-tuning RoBERTa-large, OPT-series, and Llama-series on downstream tasks and, in some cases, even surpasses memory-intensive FO fine-tuning.

Recently, zeroth-order (ZO) optimization plays an essential role in scenarios where gradient information is inaccessible or unaffordable, such as black-box systems and resource-constrained environments. While existing adaptive methods such as ZO-AdaMM have shown promise, they are fundamentally limited by their underutilization of moment information during optimization, usually resulting in underperforming convergence. To overcome these limitations, this paper introduces Refined Adaptive Zeroth-Order Optimization (R-AdaZO). Specifically, we first show the untapped variance reduction effect of first moment estimate on ZO gradient estimation, which improves the accuracy and stability of ZO updates. We then refine the second moment estimate based on these variance-reduced gradient estimates to better capture the geometry of the optimization landscape, enabling a more effective scaling of ZO updates. We present rigorous theoretical analysis to show (I) the first analysis to the variance reduction of first moment estimate in ZO optimization, (II) the improved second moment estimates with a more accurate approximation of its variance-free ideal, (III) the first variance-aware convergence framework for adaptive ZO methods, which may be of independent interest, and (IV) the faster convergence of R-AdaZO than existing baselines like ZO-AdaMM. Our extensive experiments, including synthetic problems, black-box adversarial attack, and memory-efficient fine-tuning of large language models (LLMs), further verify the superior convergence of R-AdaZO, indicating that R-AdaZO offers an improved solution for real-world ZO optimization challenges.

Backpropagation provides a generalized configuration for overcoming catastrophic forgetting. Like, SGD and Adam are commonly used for weight updates in continual learning and continual pre-training. In practice, permission to access gradient information is not always granted (the gradient ban), such as black-box APIs, hardware limitations, and non-differentiable systems. To bridge this gap, we introduce the first benchmark ZeroFlow to evaluate gradient-free optimization algorithms for overcoming forgetting. This benchmark examines a suite of forward pass methods across multiple methods, forgetting scenarios, and datasets. We find that forward passes alone are enough to overcome forgetting. Our findings reveal new optimization principles that highlight the potential of forward-pass in mitigating forgetting, managing task conflicts, and reducing memory demands, alongside novel enhancements that further mitigate forgetting with just one forward pass. This work provides essential insights and tools for advancing forward pass methods to overcome forgetting.

In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard. Yet, as LLMs grow {in size}, the substantial memory overhead from back-propagation (BP) for FO gradient computation presents a significant challenge. Addressing this issue is crucial, especially for applications like on-device training where memory efficiency is paramount. This paper proposes a shift towards BP-free, zeroth-order (ZO) optimization as a solution for reducing memory costs during LLM fine-tuning, building on the initial concept introduced by MeZO. Unlike traditional ZO-SGD methods, our work expands the exploration to a wider array of ZO optimization techniques, through a comprehensive, first-of-its-kind benchmarking study across five LLM families (Roberta, OPT, LLaMA, Vicuna, Mistral), three task complexities, and five fine-tuning schemes. Our study unveils previously overlooked optimization principles, highlighting the importance of task alignment, the role of the forward gradient method, and the balance between algorithm complexity and fine-tuning performance. We further introduce novel enhancements to ZO optimization, including block-wise descent, hybrid training, and gradient sparsity. Our study offers a promising direction for achieving further memory-efficient LLM fine-tuning. Codes to reproduce all our experiments are at https://github.com/ZO-Bench/ZO-LLM .

Zeroth-order (ZO) optimization has become a popular technique for solving machine learning (ML) problems when first-order (FO) information is difficult or impossible to obtain. However, the scalability of ZO optimization remains an open problem: Its use has primarily been limited to relatively small-scale ML problems, such as sample-wise adversarial attack generation. To our best knowledge, no prior work has demonstrated the effectiveness of ZO optimization in training deep neural networks (DNNs) without a significant decrease in performance. To overcome this roadblock, we develop DeepZero, a principled ZO deep learning (DL) framework that can scale ZO optimization to DNN training from scratch through three primary innovations. First, we demonstrate the advantages of coordinatewise gradient estimation (CGE) over randomized vector-wise gradient estimation in training accuracy and computational efficiency. Second, we propose a sparsityinduced ZO training protocol that extends the model pruning methodology using only finite differences to explore and exploit the sparse DL prior in CGE. Third, we develop the methods of feature reuse and forward parallelization to advance the practical implementations of ZO training. Our extensive experiments show that DeepZero achieves state-of-the-art (SOTA) accuracy on ResNet-20 trained on CIFAR-10, approaching FO training performance for the first time. Furthermore, we show the practical utility of DeepZero in applications of certified adversarial defense and DL-based partial differential equation error correction, achieving 10-20% improvement over SOTA. We believe our results will inspire future research on scalable ZO optimization and contribute to advancing DL with black box. Codes are available at https://github.com/OPTML-Group/DeepZero.

Backward propagation (BP) is widely used to compute the gradients in neural network training. However, it is hard to implement BP on edge devices due to the lack of hardware and software resources to support automatic differentiation. This has tremendously increased the design complexity and time-to-market of on-device training accelerators. This paper presents a completely BP-free framework that only requires forward propagation to train realistic neural networks. Our technical contributions are three-fold. Firstly, we present a tensor-compressed variance reduction approach to greatly improve the scalability of zeroth-order (ZO) optimization, making it feasible to handle a network size that is beyond the capability of previous ZO approaches. Secondly, we present a hybrid gradient evaluation approach to improve the efficiency of ZO training. Finally, we extend our BP-free training framework to physics-informed neural networks (PINNs) by proposing a sparse-grid approach to estimate the derivatives in the loss function without using BP. Our BP-free training only loses little accuracy on the MNIST dataset compared with standard first-order training. We also demonstrate successful results in training a PINN for solving a 20-dim Hamiltonian-Jacobi-Bellman PDE. This memory-efficient and BP-free approach may serve as a foundation for the near-future on-device training on many resource-constraint platforms (e.g., FPGA, ASIC, micro-controllers, and photonic chips).