arXiv subjects

Merkouris Papamichail

Publications and source records attributed to Merkouris Papamichail.

4 recordsLinked to original sources

arXiv2026

Are Safety Guarantees in Neural Networks Safe? How to Compute Trustworthy Robustness Certifications

A primary challenge in AI safety is the existence of adversarial examples -- slightly distorted inputs that cause a neural network (NN) to misclassify. To mitigate this problem, recent research focuses on the computation of robustness certifications, which, for a given input, determine the largest distortion the input may receive without breaking the network's prediction. Robustness certifications can be interpreted as an axis-aligned hyper-rectangle (multi-dimensional intervals). Most existing approaches focus on maximizing the certification's volume, but recent intractability results prohibit the computation of volume-optimal certifications in reasonable time. We introduce the apothem measure and show how to compute apothem-optimal certifications in a linear number of calls to a NN verifier (oracle) w.r.t. the input domain's diameter. Moreover, we prove that we cannot have a volume-optimal, oracle-based algorithm, even if we discard the oracle costs. Also, we introduce dual certifications -- an interval including all instances of a class -- thus providing apothem-minimum upper bounds to a robustness certification. Further, we present the ParallelepipedoNN system, which we evaluate on the standard MNIST and Fashion MNIST benchmarks. A preliminary comparison with existing work on the same datasets reveals at least two-fold improvement w.r.t. the minimum edge length.

cs.LG↗

arXiv2026

The Cost of Relaxation: Evaluating the Error in Convex Neural Network Verification

Many neural network (NN) verification systems represent the network's input-output relation as a constraint program. Sound and complete, representations involve integer constraints, for simulating the activations. Recent works convexly relax the integer constraints, improving performance, at the cost of soundness. Convex relaxations consider outputs that are unreachable by the original network. We study the worst case divergence between the original network and its convex relaxations; both qualitatively and quantitatively. The relaxations' space forms a lattice, where the top element corresponds to a full relaxation, with every neuron linearized. The bottom element corresponds to the original network. We provide analytical upper and lower bounds for the $\ell_\infty$-distance between the fully relaxed and original outputs. This distance grows exponentially, w.r.t. the network's depth, and linearly w.r.t. the input's radius. The misclassification probability exhibits a step-like behavior, w.r.t. input radius. Our results are supported by experiments on MNIST, Fashion MNIST and random networks.

cs.LG↗

arXiv2026

Interval Certifications for Multilayered Perceptrons via Lattice Traversal

In this work we present a rigorous theoretical framework to a foundational problem of AI safety, namely adversarial robustness. In particular, we show that the adversarial robustness problem can be reduced to a lattice traversal problem. Each element of this lattice corresponds to an interval, i.e., an axis-aligned hyper-rectangle, containing an input point $\mathbf{x}$. Consider a multilayered perceptron classifier (MLP). An interval $I$ constitutes a sound certification if $\mathbf{x} \in I$ and $\mathbf{x}$ can be freely perturbed in $I$ without changing the MLP's prediction. Complementarily, an interval $I$ constitutes a complete certification if $\mathbf{x} \in I$ and when $\mathbf{x}$ moves outside of $I$ the MLP's prediction is guaranteed to change. While the sound certification problem corresponds to the well-studied adversarial robustness, complete certifications have not been examined in the literature. We develop lattice traversal operators, which we apply in a refine & verify iterative scheme. Using formal MLP verifiers, sound maximality and complete minimality are guaranteed. Moreover, we examine objective optimization problems. There we discover some interesting asymmetries. For complete certifications, the minimum solution is obtained in polynomial oracle calls. This does not hold for sound certifications, where we prove strong intractability results. Additionally, we examine optimization problems in symmetric intervals (i.e., $\ell_\infty$-spheres), where we provide logarithmic algorithms. Finally, we present an empirical evaluation, using the novel ParallelepipedoNN system.

cs.AI↗

arXiv2024

Adaptation Procedure in Misinformation Games

We study interactions between agents in multi-agent systems, in which the agents are misinformed with regards to the game that they play, essentially having a subjective and incorrect understanding of the setting, without being aware of it. For that, we introduce a new game-theoretic concept, called misinformation games, that provides the necessary toolkit to study this situation. Subsequently, we enhance this framework by developing a time-discrete procedure (called the Adaptation Procedure) that captures iterative interactions in the above context. During the Adaptation Procedure, the agents update their information and reassess their behaviour in each step. We demonstrate our ideas through an implementation, which is used to study the efficiency and characteristics of the Adaptation Procedure.

cs.GT↗