31.07.2025

 

From Vulnerable to Verified: Exact Certificates Shield Models From Label‑Flipping

MCML Research Insight - With Lukas Gosch, Stephan Günnemann and Debarghya Ghoshdastidar

How the certification works

©Gosch et al.

Figure 1: Illustration of the label-flipping certificate

• Neural‑tangent view. In the wide‑network limit, training behaves like a support‑vector machine using the network’s neural tangent kernel (NTK).
• Single‑level reformulation. Substituting this NTK model allows to convert the attacker‑versus‑learner game for certification into one optimization problem.
• Mixed‑integer linear program. That problem is expressed as a mixed‑integer linear program whose solution yields (i) sample‑wise certificates for individual test nodes and (ii) collective certificates for the entire test set.

What experiments show

©Gosch et al.

Figure 2: Certified ratios (the share of test‑set predictions that the certificate proves cannot be overturned even if an attacker flips up to a fraction of the training labels) of selected architectures as calculated with the sample-wise and collective certificate on the Cora-MLb dataset.

• No universal best architecture. The most robust GNN depends on the data set.
• Design choices matter. Linear activations improve robustness, while deeper architectures often weaken it.
• A robustness plateau. Collective certificates reveal a flattening of vulnerability at medium attack budgets - an effect not noted before (see Figure 2).

Practical Implications

Because the approach relies only on the NTK, it extends to standard (non‑graph) wide neural networks, giving practitioners the first provable defence against label poisoning in deep learning.

Key takeaway

Exact certification shifts robustness from a best‑effort practice to a provable property. For anyone concerned about poisoned training data, this work provides a clear path toward verifiably trustworthy machine‑learning models.

Interested in Exploring Further?

Published as a spotlight presentation at at the A* conference ICLR 2025, you can explore the full paper—including proofs, algorithmic details, and additional experiments—and find the open-source code on GitHub.

M. Sabanayagam, L. Gosch, S. Günnemann and D. Ghoshdastidar.
Exact Certification of (Graph) Neural Networks Against Label Poisoning.
ICLR 2025 - 13th International Conference on Learning Representations. Singapore, Apr 24-28, 2025. Spotlight Presentation. URL GitHub

Abstract

Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test predictions remain unaffected and to understand worst-case robustness behavior. However, for Graph Neural Networks (GNNs), the problem of certifying label flipping has so far been unsolved. We change this by introducing an exact certification method, deriving both sample-wise and collective certificates. Our method leverages the Neural Tangent Kernel (NTK) to capture the training dynamics of wide networks enabling us to reformulate the bilevel optimization problem representing label flipping into a Mixed-Integer Linear Program (MILP). We apply our method to certify a broad range of GNN architectures in node classification tasks. Thereby, concerning the worst-case robustness to label flipping: (i) we establish hierarchies of GNNs on different benchmark graphs; (ii) quantify the effect of architectural choices such as activations, depth and skip-connections; and surprisingly, (iii) uncover a novel phenomenon of the robustness plateauing for intermediate perturbation budgets across all investigated datasets and architectures. While we focus on GNNs, our certificates are applicable to sufficiently wide NNs in general through their NTK. Thus, our work presents the first exact certificate to a poisoning attack ever derived for neural networks, which could be of independent interest.

MCML Authors

Lukas Gosch

→ Group Stephan Günnemann
 Data Analytics & Machine Learning

Stephan Günnemann

Prof. Dr.

Principal Investigator

Data Analytics & Machine Learning

Debarghya Ghoshdastidar

Prof. Dr.

Principal Investigator

Theoretical Foundations of Artificial Intelligence