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While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO)…

Machine Learning · Computer Science 2026-02-17 Yong Liu , Zirui Zhu , Chaoyu Gong , Minhao Cheng , Cho-Jui Hsieh , Yang You

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient…

Machine Learning · Computer Science 2023-06-13 Louis Fournier , Stéphane Rivaud , Eugene Belilovsky , Michael Eickenberg , Edouard Oyallon

This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A…

Neural and Evolutionary Computing · Computer Science 2019-07-11 Yi-Fei PU , Jian Wang

We study the problem of training neural networks with quantized parameters. Learning low-precision quantized parameters by enabling computation of gradients via the Straight-Through Estimator (STE) can be challenging. While the STE enables…

Machine Learning · Computer Science 2025-10-29 Ningfeng Yang , Tor M. Aamodt

We propose a memory efficient method, named Stochastic Backpropagation (SBP), for training deep neural networks on videos. It is based on the finding that gradients from incomplete execution for backpropagation can still effectively train…

Computer Vision and Pattern Recognition · Computer Science 2022-04-01 Feng Cheng , Mingze Xu , Yuanjun Xiong , Hao Chen , Xinyu Li , Wei Li , Wei Xia

A major challenge of applying zeroth-order (ZO) methods is the high query complexity, especially when queries are costly. We propose a novel gradient estimation technique for ZO methods based on adaptive lazy queries that we term as LAZO.…

Machine Learning · Computer Science 2022-06-16 Quan Xiao , Qing Ling , Tianyi Chen

Fine-tuning is powerful for adapting large language models to downstream tasks, but it often results in huge memory usages. A promising approach to mitigate this is using Zeroth-Order (ZO) optimization, which estimates gradients to replace…

Machine Learning · Computer Science 2024-10-15 Fei Wang , Li Shen , Liang Ding , Chao Xue , Ye Liu , Changxing Ding

Fine-tuning large pretrained language models (LLMs) is a cornerstone of modern NLP, yet its growing memory demands (driven by backpropagation and large optimizer States) limit deployment in resource-constrained settings. Zero-order (ZO)…

Machine Learning · Computer Science 2026-02-17 Valery Parfenov , Grigoriy Evseev , Andrey Veprikov , Nikolay Bushkov , Stanislav Moiseev , Aleksandr Beznosikov

There is an increasing need for algorithms that can accurately detect changepoints in long time-series, or equivalent, data. Many common approaches to detecting changepoints, for example based on penalised likelihood or minimum description…

Methodology · Statistics 2014-09-08 Robert Maidstone , Toby Hocking , Guillem Rigaill , Paul Fearnhead

Gradient descent and backpropagation have enabled neural networks to achieve remarkable results in many real-world applications. Despite ongoing success, training a neural network with gradient descent can be a slow and strenuous affair. We…

Machine Learning · Computer Science 2020-11-19 Varun Ranganathan , Alex Lewandowski

Zeroth-Order Optimization (ZOO) provides powerful tools for optimizing functions where explicit gradients are unavailable or expensive to compute. However, the underlying mechanisms of popular ZOO methods, particularly those employing…

Machine Learning · Computer Science 2025-06-18 Junbin Qiu , Zhengpeng Xie , Xiangda Yan , Yongjie Yang , Yao Shu

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance reduced ZO proximal algorithms have been proposed to speed up ZO optimization for…

Optimization and Control · Mathematics 2024-10-04 Bin Gu , Xiyuan Wei , Hualin Zhang , Yi Chang , Heng Huang

Fine-tuning large language models (LLMs) using zeroth-order (ZO) optimization has emerged as a promising alternative to traditional gradient-based methods due to its reduced memory footprint requirement. However, existing ZO methods suffer…

Machine Learning · Computer Science 2025-10-22 Zhendong Mi , Qitao Tan , Grace Li Zhang , Zhaozhuo Xu , Geng Yuan , Shaoyi Huang

Zeroth-order (ZO) optimization is being recognized as a simple yet powerful alternative to standard backpropagation (BP)-based training. Notably, ZO optimization allows for training with only forward passes and (almost) the same memory as…

Machine Learning · Computer Science 2025-01-09 Keisuke Sugiura , Hiroki Matsutani

Zeroth-order optimization (ZO) has been a powerful framework for solving black-box problems, which estimates gradients using zeroth-order data to update variables iteratively. The practical applicability of ZO critically depends on the…

Optimization and Control · Mathematics 2026-03-03 Ruiyang Jin , Yuke Zhou , Yujie Tang , Jie Song , Siyang Gao

Fine-tuning language models (LMs) with the Adam optimizer often demands excessive memory, limiting accessibility. The "in-place" version of Stochastic Gradient Descent (IP-SGD) and Memory-Efficient Zeroth-order Optimizer (MeZO) have been…

Machine Learning · Computer Science 2024-10-10 Zeman Li , Xinwei Zhang , Peilin Zhong , Yuan Deng , Meisam Razaviyayn , Vahab Mirrokni

Zeroth-order (ZO) optimization, learning from finite differences of function evaluations without backpropagation, has recently regained attention in deep learning due to its memory efficiency and applicability to gray- or black-box…

Modern language models have historically relied on two dominant design choices: subword tokenization and autoregressive (AR) ordering. These design decisions bake in priors that dictate a model's learning. Recently, two alternative…

Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In…

Machine Learning · Computer Science 2020-11-25 Gauthier Guinet , Valerio Perrone , Cédric Archambeau

Molecule optimization is an important problem in chemical discovery and has been approached using many techniques, including generative modeling, reinforcement learning, genetic algorithms, and much more. Recent work has also applied…

Biomolecules · Quantitative Biology 2022-10-31 Elvin Lo , Pin-Yu Chen