# A Hessian-informed hyperparameter optimization for differential learning rate

arXiv: https://arxiv.org/abs/2501.06954 · HTML: https://mlsanity.com/paper/2501.06954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 55 references that are in the map.
- First posted on arXiv 12 Jan 2025.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [How to Fine-Tune BERT for Text Classification?](https://mlsanity.com/paper/1905.05583/) (2019)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning](https://mlsanity.com/paper/2308.03303/) (2023)
- [Prodigy: An Expeditiously Adaptive Parameter-Free Learner](https://mlsanity.com/paper/2306.06101/) (2023)
- [Why Transformers Need Adam: A Hessian Perspective](https://mlsanity.com/paper/2402.16788/) (2024)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)
- [DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedule](https://mlsanity.com/paper/2302.12022/) (2023)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [Tuning LayerNorm in Attention: Towards Efficient Multi-Modal LLM Finetuning](https://mlsanity.com/paper/2312.11420/) (2023)
- [A Deeper Look at the Hessian Eigenspectrum of Deep Neural Networks and its Applications to Regularization](https://mlsanity.com/paper/2012.03801/) (2020)

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

- [Continuous Visual Autoregressive Generation via Score Maximization](https://mlsanity.com/paper/2505.07812/) (2025)

## Abstract (arXiv)

Differential learning rate (DLR), a technique that applies different learning rates to different model parameters, has been widely used in deep learning and achieved empirical success via its various forms. For example, parameter-efficient fine-tuning (PEFT) applies zero learning rates to most parameters so as to significantly save the computational cost. At the core, DLR leverages the observation that different parameters can have different loss curvature, which is hard to characterize in general. We propose the Hessian-informed differential learning rate (Hi-DLR), an efficient approach that solves the hyperparameter optimization (HPO) of learning rates and captures the loss curvature for any model and optimizer adaptively. Given a proper grouping of parameters, we empirically demonstrate that Hi-DLR can improve the convergence by dynamically determining the learning rates during the training.