Differentially Private Non-convex Learning for Multi-layer Neural Networks Article Swipe
Hanpu Shen
,
Chenglong Wang
,
Zihang Xiang
,
Yiming Ying
,
Di Wang
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.08425
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.08425
This paper focuses on the problem of Differentially Private Stochastic Optimization for (multi-layer) fully connected neural networks with a single output node. In the first part, we examine cases with no hidden nodes, specifically focusing on Generalized Linear Models (GLMs). We investigate the well-specific model where the random noise possesses a zero mean, and the link function is both bounded and Lipschitz continuous. We propose several algorithms and our analysis demonstrates the feasibility of achieving an excess population risk that remains invariant to the data dimension. We also delve into the scenario involving the ReLU link function, and our findings mirror those of the bounded link function. We conclude this section by contrasting well-specified and misspecified models, using ReLU regression as a representative example. In the second part of the paper, we extend our ideas to two-layer neural networks with sigmoid or ReLU activation functions in the well-specified model. In the third part, we study the theoretical guarantees of DP-SGD in Abadi et al. (2016) for fully connected multi-layer neural networks. By utilizing recent advances in Neural Tangent Kernel theory, we provide the first excess population risk when both the sample size and the width of the network are sufficiently large. Additionally, we discuss the role of some parameters in DP-SGD regarding their utility, both theoretically and empirically.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2310.08425
- https://arxiv.org/pdf/2310.08425
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4387635780
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- OpenAlex ID
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https://openalex.org/W4387635780Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2310.08425Digital Object Identifier
- Title
-
Differentially Private Non-convex Learning for Multi-layer Neural NetworksWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-10-12Full publication date if available
- Authors
-
Hanpu Shen, Chenglong Wang, Zihang Xiang, Yiming Ying, Di WangList of authors in order
- Landing page
-
https://arxiv.org/abs/2310.08425Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2310.08425Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2310.08425Direct OA link when available
- Concepts
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Sigmoid function, Bounded function, Activation function, Artificial neural network, Lipschitz continuity, Computer science, Population, Dimension (graph theory), Mathematical optimization, Mathematics, Artificial intelligence, Pure mathematics, Demography, Mathematical analysis, SociologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.connected | 14, 167 |
| abstract_inverted_index.function, | 96 |
| abstract_inverted_index.function. | 106 |
| abstract_inverted_index.functions | 144 |
| abstract_inverted_index.invariant | 81 |
| abstract_inverted_index.involving | 92 |
| abstract_inverted_index.networks. | 170 |
| abstract_inverted_index.possesses | 49 |
| abstract_inverted_index.regarding | 211 |
| abstract_inverted_index.two-layer | 136 |
| abstract_inverted_index.utilizing | 172 |
| abstract_inverted_index.Stochastic | 9 |
| abstract_inverted_index.activation | 143 |
| abstract_inverted_index.algorithms | 66 |
| abstract_inverted_index.dimension. | 85 |
| abstract_inverted_index.guarantees | 157 |
| abstract_inverted_index.parameters | 208 |
| abstract_inverted_index.population | 77, 185 |
| abstract_inverted_index.regression | 119 |
| abstract_inverted_index.Generalized | 36 |
| abstract_inverted_index.continuous. | 62 |
| abstract_inverted_index.contrasting | 112 |
| abstract_inverted_index.feasibility | 72 |
| abstract_inverted_index.investigate | 41 |
| abstract_inverted_index.multi-layer | 168 |
| abstract_inverted_index.theoretical | 156 |
| abstract_inverted_index.Optimization | 10 |
| abstract_inverted_index.demonstrates | 70 |
| abstract_inverted_index.empirically. | 217 |
| abstract_inverted_index.misspecified | 115 |
| abstract_inverted_index.specifically | 33 |
| abstract_inverted_index.sufficiently | 199 |
| abstract_inverted_index.(multi-layer) | 12 |
| abstract_inverted_index.Additionally, | 201 |
| abstract_inverted_index.theoretically | 215 |
| abstract_inverted_index.well-specific | 43 |
| abstract_inverted_index.Differentially | 7 |
| abstract_inverted_index.representative | 122 |
| abstract_inverted_index.well-specified | 113, 147 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/17 |
| sustainable_development_goals[0].score | 0.46000000834465027 |
| sustainable_development_goals[0].display_name | Partnerships for the goals |
| citation_normalized_percentile |