# Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise

arXiv: https://arxiv.org/abs/2508.15523 · HTML: https://mlsanity.com/paper/2508.15523/

## 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 21 Aug 2025.

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

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Large Language Models Can Be Strong Differentially Private Learners](https://mlsanity.com/paper/2110.05679/) (2021)
- [Bypassing the Ambient Dimension: Private SGD with Gradient Subspace Identification](https://mlsanity.com/paper/2007.03813/) (2020)
- [Differentially Private Optimization on Large Model at Small Cost](https://mlsanity.com/paper/2210.00038/) (2022)
- [Exploring the Limits of Differentially Private Deep Learning with Group-wise Clipping](https://mlsanity.com/paper/2212.01539/) (2022)
- [Private Fine-tuning of Large Language Models with Zeroth-order Optimization](https://mlsanity.com/paper/2401.04343/) (2024)
- [Dynamic Differential-Privacy Preserving SGD](https://mlsanity.com/paper/2111.00173/) (2021)
- [Fast and Memory Efficient Differentially Private-SGD via JL Projections](https://mlsanity.com/paper/2102.03013/) (2021)
- [One Parameter Defense -- Defending against Data Inference Attacks via Differential Privacy](https://mlsanity.com/paper/2203.06580/) (2022)
- [Differentially Private and Fair Classification via Calibrated Functional Mechanism](https://mlsanity.com/paper/2001.04958/) (2020)
- [Gradients Look Alike: Sensitivity is Often Overestimated in DP-SGD](https://mlsanity.com/paper/2307.00310/) (2023)
- [Making the Most of Parallel Composition in Differential Privacy](https://mlsanity.com/paper/2109.09078/) (2021)
- [Dimension Independent Generalization of DP-SGD for Overparameterized Smooth Convex Optimization](https://mlsanity.com/paper/2206.01836/) (2022)
- [Zero redundancy distributed learning with differential privacy](https://mlsanity.com/paper/2311.11822/) (2023)
- [Task-aware Distributed Source Coding under Dynamic Bandwidth](https://mlsanity.com/paper/2305.15523/) (2023)
- [Active Learning for WBAN-based Health Monitoring](https://mlsanity.com/paper/2408.02849/) (2024)

## Abstract (arXiv)

We propose SPOF (Stabilization of Perturbed Loss Function), a differentially private training mechanism intended for multi-user local differential privacy (LDP). SPOF perturbs a stabilized Taylor expanded polynomial approximation of a model's training loss function, where each user's data is privatized by calibrated noise added to the coefficients of the polynomial. Unlike gradient-based mechanisms such as differentially private stochastic gradient descent (DP-SGD), SPOF does not require injecting noise into the gradients of the loss function, which improves both computational efficiency and stability. This formulation naturally supports simultaneous privacy guarantees across all users. Moreover, SPOF exhibits robustness to environmental noise during training, maintaining stable performance even when user inputs are corrupted. We compare SPOF with a multi-user extension of DP-SGD, evaluating both methods in a wireless body area network (WBAN) scenario involving heterogeneous user data and stochastic channel noise from body sensors. Our results show that SPOF achieves, on average, up to 3.5% higher reconstruction accuracy and reduces mean training time by up to 57.2% compared to DP-SGD, demonstrating superior privacy-utility trade-offs in multi-user environments.