Beyond Lipschitz: Data-Driven Robustness via Discrete Modulus of Continuity
Jürgen Dölz, Michael Multerer, Michele Palma
Read on arXiv →Key claim
DMOC provides a finer measure of neural network robustness.
This paper presents a new framework called the discrete modulus of continuity (DMOC) for assessing the robustness of neural networks. DMOC offers a more nuanced measure of robustness compared to traditional Lipschitz constants and is applicable to large datasets. A key result is that DMOC can effectively distinguish between trained and untrained networks, revealing underfitting and overfitting regimes.
In plain English
This paper presents a new framework called the discrete modulus of continuity (DMOC) for assessing the robustness of neural networks. DMOC offers a more nuanced measure of robustness compared to traditional Lipschitz constants and is applicable to large datasets. A key result is that DMOC can effectively distinguish between trained and untrained networks, revealing underfitting and overfitting regimes.
The introduction of DMOC as a data-driven robustness measure significantly extends the understanding of neural network robustness.
The paper provides empirical results and establishes convergence for DMOC, supporting its claims with a scalable algorithm.
Deep reliability assessment
The methodology supports DMOC as a black-box, data-dependent diagnostic for comparing model regularity across scales, with theoretical convergence claims for the estimator and a minibatch approximation for scalability. The robustness framing may be overclaimed if read as adversarial certification: the provided text supports diagnostic comparison and Lipschitz-estimation recovery, but not necessarily guarantees against worst-case perturbations off the sampled data distribution.
Reproducibility
No open-source code or repository is mentioned in the provided abstract, introduction, conclusion, or footnote text. Datasets are only partially specified: ImageNet is mentioned as a large-scale application, but the provided text does not include full experimental settings, model lists, hyperparameters, or numeric result tables.
Discussion questions
- 1.Does measuring regularity relative to the observed data distribution miss precisely the rare or off-manifold perturbations that make robustness hard in deployed systems?
- 2.For builders, is DMOC more useful as a training-time model selection/debugging signal, a post-hoc safety diagnostic, or a replacement for Lipschitz-style robustness estimates?
- 3.What empirical result would falsify the paper's central claim: for example, if DMOC fails to distinguish trained from untrained networks, underfitting from overfitting, or correlates poorly with adversarial robustness across architectures?
Key figure
No Figure 1 or key architectural diagram is available in the provided text; the central concept appears to be a data-driven computation of pairwise input-output changes across distance scales to form a discrete modulus of continuity curve.