# DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training

arXiv: https://arxiv.org/abs/2310.02025 · HTML: https://mlsanity.com/paper/2310.02025/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 109 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 30 of 70)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [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)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Prior Convictions: Black-Box Adversarial Attacks with Bandits and Priors](https://mlsanity.com/paper/1807.07978/) (2018)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)

## Built on by (most cited first, 30 of 76)

- [To Generate or Not? Safety-Driven Unlearned Diffusion Models Are Still Easy To Generate Unsafe Images ... For Now](https://mlsanity.com/paper/2310.11868/) (2023)
- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [ZeroG: Investigating Cross-dataset Zero-shot Transferability in Graphs](https://mlsanity.com/paper/2402.11235/) (2024)
- [Sparse MeZO: Less Parameters for Better Performance in Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2402.15751/) (2024)
- [Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures](https://mlsanity.com/paper/2410.07698/) (2024)
- [Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsity](https://mlsanity.com/paper/2406.02913/) (2024)
- [DPZero: Private Fine-Tuning of Language Models without Backpropagation](https://mlsanity.com/paper/2310.09639/) (2023)
- [DiffZOO: A Purely Query-Based Black-Box Attack for Red-teaming Text-to-Image Generative Model via Zeroth Order Optimization](https://mlsanity.com/paper/2408.11071/) (2024)
- [Harmony in Divergence: Towards Fast, Accurate, and Memory-efficient Zeroth-order LLM Fine-tuning](https://mlsanity.com/paper/2502.03304/) (2025)
- [Differentially Private Zeroth-Order Methods for Scalable Large Language Model Finetuning](https://mlsanity.com/paper/2402.07818/) (2024)
- [Achieving Dimension-Free Communication in Federated Learning via Zeroth-Order Optimization](https://mlsanity.com/paper/2405.15861/) (2024)
- [Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization](https://mlsanity.com/paper/2602.17155/) (2026)
- [Test-Time Model Adaptation for Quantized Neural Networks](https://mlsanity.com/paper/2508.02180/) (2025)
- [ZeroFlow: Overcoming Catastrophic Forgetting is Easier than You Think](https://mlsanity.com/paper/2501.01045/) (2025)
- [TeleSparse: Practical Privacy-Preserving Verification of Deep Neural Networks](https://mlsanity.com/paper/2504.19274/) (2025)
- [PLA: Prompt Learning Attack against Text-to-Image Generative Models](https://mlsanity.com/paper/2508.03696/) (2025)
- [COAP: Memory-Efficient Training with Correlation-Aware Gradient Projection](https://mlsanity.com/paper/2412.00071/) (2024)
- [ZO2: Scalable Zeroth-Order Fine-Tuning for Extremely Large Language Models with Limited GPU Memory](https://mlsanity.com/paper/2503.12668/) (2025)
- [Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approach](https://mlsanity.com/paper/2411.05873/) (2024)
- [ElasticZO: A Memory-Efficient On-Device Learning with Combined Zeroth- and First-Order Optimization](https://mlsanity.com/paper/2501.04287/) (2025)
- [Half-order Fine-Tuning for Diffusion Model: A Recursive Likelihood Ratio Optimizer](https://mlsanity.com/paper/2502.00639/) (2025)
- [LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM](https://mlsanity.com/paper/2502.19571/) (2025)
- [KerZOO: Kernel Function Informed Zeroth-Order Optimization for Accurate and Accelerated LLM Fine-Tuning](https://mlsanity.com/paper/2505.18886/) (2025)
- [Improving the Straight-Through Estimator with Zeroth-Order Information](https://mlsanity.com/paper/2510.23926/) (2025)
- [Towards training digitally-tied analog blocks via hybrid gradient computation](https://mlsanity.com/paper/2409.03306/) (2024)
- [FLOPS: Forward Learning with OPtimal Sampling](https://mlsanity.com/paper/2410.05966/) (2024)
- [Stepping Forward on the Last Mile](https://mlsanity.com/paper/2411.04036/) (2024)
- [ZOQO: Zero-Order Quantized Optimization](https://mlsanity.com/paper/2501.06736/) (2025)
- [MaZO: Masked Zeroth-Order Optimization for Multi-Task Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2502.11513/) (2025)

## Abstract (arXiv)

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.