# ElasticZO: A Memory-Efficient On-Device Learning with Combined Zeroth- and First-Order Optimization

arXiv: https://arxiv.org/abs/2501.04287 · HTML: https://mlsanity.com/paper/2501.04287/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 51 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 30 of 35)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1603.06160/) (2016)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [Efficient Domain Generalization via Common-Specific Low-Rank Decomposition](https://mlsanity.com/paper/2003.12815/) (2020)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [Federated Full-Parameter Tuning of Billion-Sized Language Models with Communication Cost under 18 Kilobytes](https://mlsanity.com/paper/2312.06353/) (2023)
- [Sparse MeZO: Less Parameters for Better Performance in Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2402.15751/) (2024)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [Improved Zeroth-Order Variance Reduced Algorithms and Analysis for Nonconvex Optimization](https://mlsanity.com/paper/1910.12166/) (2019)
- [A Comprehensive Linear Speedup Analysis for Asynchronous Stochastic Parallel Optimization from Zeroth-Order to First-Order](https://mlsanity.com/paper/1606.00498/) (2016)
- [Private Fine-tuning of Large Language Models with Zeroth-order Optimization](https://mlsanity.com/paper/2401.04343/) (2024)
- [Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimization](https://mlsanity.com/paper/2008.08170/) (2020)
- [How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspective](https://mlsanity.com/paper/2203.14195/) (2022)
- [Zeroth-Order Optimization Meets Human Feedback: Provable Learning via Ranking Oracles](https://mlsanity.com/paper/2303.03751/) (2023)
- [Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsity](https://mlsanity.com/paper/2406.02913/) (2024)
- [ZO-AdaMU Optimizer: Adapting Perturbation by the Momentum and Uncertainty in Zeroth-order Optimization](https://mlsanity.com/paper/2312.15184/) (2023)
- [AdaZeta: Adaptive Zeroth-Order Tensor-Train Adaption for Memory-Efficient Large Language Models Fine-Tuning](https://mlsanity.com/paper/2406.18060/) (2024)
- [Zeroth-Order Online Alternating Direction Method of Multipliers: Convergence Analysis and Applications](https://mlsanity.com/paper/1710.07804/) (2017)
- [NITI: Training Integer Neural Networks Using Integer-only Arithmetic](https://mlsanity.com/paper/2009.13108/) (2020)
- [On the Convergence of Zeroth-Order Federated Tuning for Large Language Models](https://mlsanity.com/paper/2402.05926/) (2024)

## Built on by (most cited first, 5 of 5)

- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.12384/) (2025)
- [On the Optimal Construction of Unbiased Gradient Estimators for Zeroth-Order Optimization](https://mlsanity.com/paper/2510.19953/) (2025)
- [Why Zeroth-Order Adaptation May Forget Less: A Randomized Shaping Theory](https://mlsanity.com/paper/2605.10658/) (2026)
- [Event-triggered Implicit Perturbation for Zeroth-Order Fine-Tuning of Spiking Transformers](https://mlsanity.com/paper/2608.21223/) (2026)

## Abstract (arXiv)

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 inference, making it well-suited for edge devices with limited computing and memory resources. In this paper, we propose ZO-based on-device learning (ODL) methods for full-precision and 8-bit quantized deep neural networks (DNNs), namely ElasticZO and ElasticZO-INT8. ElasticZO lies in the middle between pure ZO- and pure BP-based approaches, and is based on the idea to employ BP for the last few layers and ZO for the remaining layers. ElasticZO-INT8 achieves integer arithmetic-only ZO-based training for the first time, by incorporating a novel method for computing quantized ZO gradients from integer cross-entropy loss values. Experimental results on the classification datasets show that ElasticZO effectively addresses the slow convergence of vanilla ZO and shrinks the accuracy gap to BP-based training. Compared to vanilla ZO, ElasticZO achieves 5.2-9.5% higher accuracy with only 0.072-1.7% memory overhead, and can handle fine-tuning tasks as well as full training. ElasticZO-INT8 further reduces the memory usage and training time by 1.46-1.60x and 1.38-1.42x without compromising the accuracy. These results demonstrate a better tradeoff between accuracy and training cost compared to pure ZO- and BP-based approaches, and also highlight the potential of ZO optimization in on-device learning.