# More Than Memory Savings: Zeroth-Order Optimization Mitigates Forgetting in Continual Learning

arXiv: https://arxiv.org/abs/2510.21019 · HTML: https://mlsanity.com/paper/2510.21019/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 56 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 30 of 42)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Revisiting Class-Incremental Learning with Pre-Trained Models: Generalizability and Adaptivity are All You Need](https://mlsanity.com/paper/2303.07338/) (2023)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [A Unified Continual Learning Framework with General Parameter-Efficient Tuning](https://mlsanity.com/paper/2303.10070/) (2023)
- [Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima](https://mlsanity.com/paper/2111.01549/) (2021)
- [Expandable Subspace Ensemble for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2403.12030/) (2024)
- [Don't forget, there is more than forgetting: new metrics for Continual Learning](https://mlsanity.com/paper/1810.13166/) (2018)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)

## Built on by (most cited first, 1 of 1)

- [Why Zeroth-Order Adaptation May Forget Less: A Randomized Shaping Theory](https://mlsanity.com/paper/2605.10658/) (2026)

## Abstract (arXiv)

Zeroth-order (ZO) optimization has gained attention as a memory-efficient alternative to first-order (FO) methods, particularly in settings where gradient computation is expensive or even impractical. Beyond its memory efficiency, in this work, we investigate ZO optimization for continual learning (CL) as a novel approach to address the plasticity-stability-efficiency trilemma. Through theoretical analysis and empirical evidence, we show that ZO optimization naturally leads to flatter loss landscapes, which in turn reduce forgetting in CL. However, this stability comes at a cost of plasticity: due to its imprecise gradient estimates and slower convergence, ZO optimization tends to be less effective than FO in acquiring new task-specific knowledge, particularly under constrained training budgets. To better understand this trade-off, we conduct a holistic evaluation of ZO optimization applied to various existing CL methods. Our findings reveal that ZO optimization enhances stability but often undermines plasticity, particularly when used with learnable classifiers. Motivated by this insight, we propose ZO-FC, a simple but effective approach that applies ZO optimization to a single adapter-based PEFT module with FO optimized classifier. This design leverages the stability benefits of ZO while preserving the adaptability of FO updates with negligible memory overhead. Experiments demonstrate that ZO-FC achieves an effective balance between stability and plasticity, offering a practical and memory-efficient solution for on-device CL.