# Jacobian-Guided Anisotropic Noise Reshaping for Enhancing Representation Utility under Local Differential Privacy

arXiv: https://arxiv.org/abs/2605.16812 · HTML: https://mlsanity.com/paper/2605.16812/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 16 May 2026.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Toward Training at ImageNet Scale with Differential Privacy](https://mlsanity.com/paper/2201.12328/) (2022)
- [Locally Private Graph Neural Networks](https://mlsanity.com/paper/2006.05535/) (2020)
- [Discrete Distribution Estimation under Local Privacy](https://mlsanity.com/paper/1602.07387/) (2016)
- [Collecting and Analyzing Multidimensional Data with Local Differential Privacy](https://mlsanity.com/paper/1907.00782/) (2019)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Optimal Algorithms for Mean Estimation under Local Differential Privacy](https://mlsanity.com/paper/2205.02466/) (2022)
- [Adaptive Laplace Mechanism: Differential Privacy Preservation in Deep Learning](https://mlsanity.com/paper/1709.05750/) (2017)
- [Heterogeneous Differential Privacy](https://mlsanity.com/paper/1504.06998/) (2015)
- [Stronger Privacy Amplification by Shuffling for R'enyi and Approximate Differential Privacy](https://mlsanity.com/paper/2208.04591/) (2022)
- [PrE-Text: Training Language Models on Private Federated Data in the Age of LLMs](https://mlsanity.com/paper/2406.02958/) (2024)
- [Privacy amplification by random allocation](https://mlsanity.com/paper/2502.08202/) (2025)
- [Answering Range Queries Under Local Differential Privacy](https://mlsanity.com/paper/1812.10942/) (2018)
- [Locally Differentially Private Frequency Estimation with Consistency](https://mlsanity.com/paper/1905.08320/) (2019)
- [PLAN: Variance-Aware Private Mean Estimation](https://mlsanity.com/paper/2306.08745/) (2023)
- [Dimension-free Private Mean Estimation for Anisotropic Distributions](https://mlsanity.com/paper/2411.00775/) (2024)
- [Task-aware Privacy Preservation for Multi-dimensional Data](https://mlsanity.com/paper/2110.02329/) (2021)
- [Calibrate: Frequency Estimation and Heavy Hitter Identification with Local Differential Privacy via Incorporating Prior Knowledge](https://mlsanity.com/paper/1812.02055/) (2018)
- [Utility Analysis and Enhancement of LDP Mechanisms in High-Dimensional Space](https://mlsanity.com/paper/2201.07469/) (2022)
- [Differential Privacy with Higher Utility by Exploiting Coordinate-wise Disparity: Laplace Mechanism Can Beat Gaussian in High Dimensions](https://mlsanity.com/paper/2302.03511/) (2023)

## Abstract (arXiv)

While Local Differential Privacy (LDP) serves as a foundational primitive for distributed data collection, its stringent randomization requirements often lead to severe degradation in data representation utility. This degradation stems from the task-agnostic nature of conventional LDP mechanisms, which perturb all dimensions without accounting for their relative importance to the downstream objective. To address this issue, we propose a novel approach that mitigates noise in task-relevant subspaces of the data representation. Our method identifies task-critical subspaces via the Jacobian of a public downstream model, selectively attenuates noise along these directions, and reshapes the isotropic noise of standard LDP mechanisms into an anisotropic distribution. The resulting mechanism preserves the privacy guarantee of the underlying LDP randomizer while heterogeneously modulating the impact of noise across task directions, thereby substantially enhancing data utility. The approach is applicable to both linear and nonlinear models and can be seamlessly integrated with existing LDP mechanisms. Extensive experiments on CIFAR-10-C under brightness corruption at the highest severity level demonstrate that integrating our approach improves classification accuracy by approximately 8 percentage points for Laplace and 20 percentage points for PrivUnit variants at ε=7.5. The source code is available at https://github.com/ymha/jacobian-anr-ldp.