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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 trave","title":"Interval Certifications for Multilayered Perceptrons via Lattice Traversal","url":"https://arxiv.org/abs/2607.08773","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.08773v1 Announce Type: new \nAbstract: 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. 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