# SMA-DP: Spectral Memory-Aware Differential Privacy for Deep Learning

arXiv: https://arxiv.org/abs/2605.20450 · HTML: https://mlsanity.com/paper/2605.20450/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (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)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Scalable Private Learning with PATE](https://mlsanity.com/paper/1802.08908/) (2018)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)
- [Statistical Roughness-Informed Machine Unlearning](https://mlsanity.com/paper/2602.09304/) (2026)
- [When Gradient Clipping Becomes a Control Mechanism for Differential Privacy in Deep Learning](https://mlsanity.com/paper/2602.10584/) (2026)

## Abstract (arXiv)

Differentially private stochastic gradient descent (DP-SGD) enables private deep learning through per-example clipping and calibrated Gaussian noise, but its high-variance updates can reduce utility on challenging datasets. We propose SMA-DP-SGD, a Spectral Memory-Aware Differentially Private Stochastic Gradient Descent method that augments DP-SGD with a fractional memory branch built only from previously privatized noisy releases. WeightWatcher-inspired power-law spectral exponents provide group-wise reliability signals, instantiated layer-wise in our experiments, to adapt the decay and effective memory depth. Private-history alignment, norm matching, and warm-up activation stabilize the memory contribution. Privacy remains transparent: conditioned on the private release history, the memory branch is fixed, and the only newly data-dependent term is the current clipped sum scaled by a fixed coefficient (β). Hence, SMA-DP-SGD preserves a clean conditional sensitivity structure and exactly recovers group-wise DP-SGD when (β=1). Experiments on CIFAR-100, CIFAR-10, and MNIST show competitive or superior accuracy over several DP optimization baselines, with the largest gains on CIFAR-100 and CIFAR-10. CIFAR-10 ablations show that (β) controls the privacy--utility trajectory, while spectral and memory diagnostics confirm a controlled short-to-moderate effective memory depth and a small memory-branch ratio. Runtime analysis shows that the mechanism incurs additional overhead, about (2.94×) DP-SGD in our CIFAR-10 implementation, revealing a practical trade-off between adaptive private memory and computational cost.