# AdaFisher: Adaptive Second Order Optimization via Fisher Information

arXiv: https://arxiv.org/abs/2405.16397 · HTML: https://mlsanity.com/paper/2405.16397/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 91 references that are in the map.
- First posted on arXiv 26 May 2024.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [ResNet strikes back: An improved training procedure in timm](https://mlsanity.com/paper/2110.00476/) (2021)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)

## Built on by (most cited first, 14 of 14)

- [Fishers for Free? Approximating the Fisher Information Matrix by Recycling the Squared Gradient Accumulator](https://mlsanity.com/paper/2507.18807/) (2025)
- [SPICE: Submodular Penalized Information-Conflict Selection for Efficient Large Language Model Training](https://mlsanity.com/paper/2601.23155/) (2026)
- [SASSHA: Sharpness-aware Adaptive Second-order Optimization with Stable Hessian Approximation](https://mlsanity.com/paper/2502.18153/) (2025)
- [Stochastic Approximation with Block Coordinate Optimal Stepsizes](https://mlsanity.com/paper/2507.08963/) (2025)
- [KOALA++: Efficient Kalman-Based Optimization with Gradient-Covariance Products](https://mlsanity.com/paper/2506.04432/) (2025)
- [A Mechanistic Study of Transformers Training Dynamics](https://mlsanity.com/paper/2410.24050/) (2024)
- [Dynamic Momentum Recalibration in Online Gradient Learning](https://mlsanity.com/paper/2603.06120/) (2026)
- [Layerwise LQR for Geometry-Aware Optimization of Deep Networks](https://mlsanity.com/paper/2605.04230/) (2026)
- [Information-Geometric Forward Policy Training in GFlowNets](https://mlsanity.com/paper/2608.03967/) (2026)
- [Frankenstein Optimizer: Harnessing the Potential by Revisiting Optimization Tricks](https://mlsanity.com/paper/2503.02147/) (2025)
- [Motivation is Something You Need](https://mlsanity.com/paper/2602.21064/) (2026)
- [Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit](https://mlsanity.com/paper/2605.08352/) (2026)
- [Fisher-Guided Progressive Parameter Selection for Adaptive Fine-Tuning](https://mlsanity.com/paper/2606.10196/) (2026)
- [On the second-order optimization for spiking neural networks](https://mlsanity.com/paper/2609.29379/) (2026)

## Abstract (arXiv)

First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their widespread, second-order optimization algorithms exhibit superior convergence properties compared to their first-order counterparts e.g. Adam and SGD. However, their practicality in training DNNs is still limited due to increased per-iteration computations compared to the first-order methods. We present AdaFisher--an adaptive second-order optimizer that leverages a diagonal block-Kronecker approximation of the Fisher information matrix for adaptive gradient preconditioning. AdaFisher aims to bridge the gap between enhanced convergence/generalization capabilities and computational efficiency in second-order optimization framework for training DNNs. Despite the slow pace of second-order optimizers, we showcase that AdaFisher can be reliably adopted for image classification, language modeling and stands out for its stability and robustness in hyper-parameter tuning. We demonstrate that AdaFisher outperforms the SOTA optimizers in terms of both accuracy and convergence speed. Code is available from https://github.com/AtlasAnalyticsLab/AdaFisher.