# HELENE: Hessian Layer-wise Clipping and Gradient Annealing for Accelerating Fine-tuning LLM with Zeroth-order Optimization

arXiv: https://arxiv.org/abs/2411.10696 · HTML: https://mlsanity.com/paper/2411.10696/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 59 references that are in the map.
- First posted on arXiv 16 Nov 2024.

## Builds on (most cited first, 19 of 19)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [Second-Order Fine-Tuning without Pain for LLMs:A Hessian Informed Zeroth-Order Optimizer](https://mlsanity.com/paper/2402.15173/) (2024)
- [Scalable Second Order Optimization for Deep Learning](https://mlsanity.com/paper/2002.09018/) (2020)
- [Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information](https://mlsanity.com/paper/2109.05198/) (2021)
- [Hessian-Aware Zeroth-Order Optimization for Black-Box Adversarial Attack](https://mlsanity.com/paper/1812.11377/) (2018)

## Built on by (most cited first, 9 of 9)

- [FZOO: Fast Zeroth-Order Optimizer for Fine-Tuning Large Language Models towards Adam-Scale Speed](https://mlsanity.com/paper/2506.09034/) (2025)
- [SharpZO: Hybrid Sharpness-Aware Vision Language Model Prompt Tuning via Forward-Only Passes](https://mlsanity.com/paper/2506.20990/) (2025)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [Fact or Guesswork? Evaluating Large Language Models' Medical Knowledge with Structured One-Hop Judgments](https://mlsanity.com/paper/2502.14275/) (2025)
- [Subspace-based Approximate Hessian Method for Zeroth-Order Optimization](https://mlsanity.com/paper/2507.06125/) (2025)
- [TransMem: Transforming Hidden States into Memory for Large Language Models](https://mlsanity.com/paper/2607.29032/) (2026)
- [AGGC: Adaptive Group Gradient Clipping for Stabilizing Large Language Model Training](https://mlsanity.com/paper/2601.11864/) (2026)
- [One Algorithm, Two Goals: Dual Scoring for Parameter and Data Selection in LLM Fine-Tuning](https://mlsanity.com/paper/2605.06166/) (2026)
- [StructZO: Structured Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2610.16451/) (2026)

## Abstract (arXiv)

Fine-tuning large language models (LLMs) poses significant memory challenges, as the back-propagation process demands extensive resources, especially with growing model sizes. Recent work, MeZO, addresses this issue using a zeroth-order (ZO) optimization method, which reduces memory consumption by matching the usage to the inference phase. However, MeZO experiences slow convergence due to varying curvatures across model parameters. To overcome this limitation, we introduce HELENE, a novel scalable and memory-efficient optimizer that integrates annealed A-GNB gradients with a diagonal Hessian estimation and layer-wise clipping, serving as a second-order pre-conditioner. This combination allows for faster and more stable convergence. Our theoretical analysis demonstrates that HELENE improves convergence rates, particularly for models with heterogeneous layer dimensions, by reducing the dependency on the total parameter space dimension. Instead, the method scales with the largest layer dimension, making it highly suitable for modern LLM architectures. Experimental results on RoBERTa-large and OPT-1.3B across multiple tasks show that HELENE achieves up to a 20x speedup compared to MeZO, with average accuracy improvements of 1.5%. Furthermore, HELENE remains compatible with both full parameter tuning and parameter-efficient fine-tuning (PEFT), outperforming several state-of-the-art optimizers. The codes will be released after reviewing.