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Researcher profile

Jan Schuchardt

Jan Schuchardt contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningCryptography and Security

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Published work

4 published item(s)

preprint2026arXiv

Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise

We establish the first population risk bounds for Kolmogorov-Arnold Networks (KANs) trained by mini-batch SGD with gradient clipping, covering non-private SGD as well as differentially private SGD (DP-SGD) with Gaussian perturbations that interpolate between independent and temporally correlated noise. This setting is substantially closer to practice than prior KAN theory along two axes: training is by mini-batch SGD, the standard recipe for modern networks, rather than full-batch gradient descent (GD); and correlated-noise mechanisms have empirically shown a more favorable privacy-utility tradeoff than independent-noise mechanisms. Our results cover the corresponding full-batch GD and independent-noise DP-GD results for KANs by Wang et al. (2026), while yielding sharper fixed-second-layer specializations. The technical core is a new analysis route for correlated-noise DP training in the non-convex regime. Temporal dependence breaks the conditional-centering structure underlying standard one-step SGD arguments, and the projection step obstructs the exact cancellation structure of correlated perturbations. We address these difficulties through an auxiliary unprojected dynamics, a shifted iterate that absorbs the current noise perturbation, and a high-probability bootstrap certifying projection inactivity. Combining this optimization analysis with a stability-based generalization argument yields the stated population risk bounds. To the best of our knowledge, this is the first optimization and population risk analysis of a correlated-noise mechanism for DP training beyond convex learning, in particular for neural networks.

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preprint2023arXiv

Invariance-Aware Randomized Smoothing Certificates

Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction, medical imaging, protein folding or LiDAR classification. For the first time, we study how the invariances of a model can be leveraged to provably guarantee the robustness of its predictions. We propose a gray-box approach, enhancing the powerful black-box randomized smoothing technique with white-box knowledge about invariances. First, we develop gray-box certificates based on group orbits, which can be applied to arbitrary models with invariance under permutation and Euclidean isometries. Then, we derive provably tight gray-box certificates. We experimentally demonstrate that the provably tight certificates can offer much stronger guarantees, but that in practical scenarios the orbit-based method is a good approximation.

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preprint2023arXiv

Training Differentially Private Graph Neural Networks with Random Walk Sampling

Deep learning models are known to put the privacy of their training data at risk, which poses challenges for their safe and ethical release to the public. Differentially private stochastic gradient descent is the de facto standard for training neural networks without leaking sensitive information about the training data. However, applying it to models for graph-structured data poses a novel challenge: unlike with i.i.d. data, sensitive information about a node in a graph cannot only leak through its gradients, but also through the gradients of all nodes within a larger neighborhood. In practice, this limits privacy-preserving deep learning on graphs to very shallow graph neural networks. We propose to solve this issue by training graph neural networks on disjoint subgraphs of a given training graph. We develop three random-walk-based methods for generating such disjoint subgraphs and perform a careful analysis of the data-generating distributions to provide strong privacy guarantees. Through extensive experiments, we show that our method greatly outperforms the state-of-the-art baseline on three large graphs, and matches or outperforms it on four smaller ones.

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preprint2022arXiv

Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness

End-to-end (geometric) deep learning has seen first successes in approximating the solution of combinatorial optimization problems. However, generating data in the realm of NP-hard/-complete tasks brings practical and theoretical challenges, resulting in evaluation protocols that are too optimistic. Specifically, most datasets only capture a simpler subproblem and likely suffer from spurious features. We investigate these effects by studying adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. For this purpose, we derive perturbation models for SAT and TSP. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound, allowing us to determine the true label of perturbed samples without a solver. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning. Although such robust solvers exist, we show empirically that the assessed neural solvers do not generalize well w.r.t. small perturbations of the problem instance.

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