# DOME: Improving Signal-to-Noise in Stochastic Gradient Descent via Sharp-Direction Subspace Filtering

arXiv: https://arxiv.org/abs/2507.03545 · HTML: https://mlsanity.com/paper/2507.03545/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 30 of 35)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability](https://mlsanity.com/paper/2209.15594/) (2022)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [A Bayesian Perspective on Generalization and Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06451/) (2017)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [One-for-All: Generalized LoRA for Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2306.07967/) (2023)
- [AutoMix: Unveiling the Power of Mixup for Stronger Classifiers](https://mlsanity.com/paper/2103.13027/) (2021)
- [Measurements of Three-Level Hierarchical Structure in the Outliers in the Spectrum of Deepnet Hessians](https://mlsanity.com/paper/1901.08244/) (2019)
- [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022)

## Built on by (most cited first, 2 of 2)

- [First-Order Predictable but Pairwise Fragile: Local Task Adaptation in Trained Transformers](https://mlsanity.com/paper/2607.16821/) (2026)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)

## Abstract (arXiv)

Stochastic gradients for deep neural networks exhibit strong correlations along the optimization trajectory, and are often aligned with a small set of Hessian eigenvectors associated with outlier eigenvalues. Recent work shows that projecting gradients away from this Hessian outlier subspace has little impact on optimization, despite capturing a large fraction of gradient variability. Since computing the Hessian is intractable in practice, we introduce a principled first-order characterization of the nuisance subspace based on the covariance of stochastic gradients, and propose an efficient method to estimate it online. We show that removing this subspace also has little impact on optimization, and yields practical benefits for applications sensitive to gradient signal-to-noise ratio such as gradient compression.