arXiv Machine Learning
Scalable Incremental Robustness Analysis of Neural Network Feedback Systems
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L-Lipschitz Gershgorin ResNet Network
The paper introduces a method for constructing L-Lipschitz deep residual networks (ResNets) using a Linear Matrix Inequality (LMI) framework. By reformulating the ResNet architecture as a pseudo-tridiagonal LMI and applying the Gershgorin circle theorem, the authors derive closed‑form constraints on network parameters that guarantee Lipschitz continuity. The work also presents a compositional framework for handling recursive systems in hierarchical architectures, while noting that the Gershgorin-based approximations can over‑constrain the system, reducing expressive capacity.
arXiv Machine Learning
Jun 4
Certified Neural Approximations of Nonlinear Dynamics
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
arXiv AI
Jun 3
Neural Network Verification using Partial Multi-Neuron Relaxation
arXiv:2605. 30155v3 Announce Type: replace-cross Abstract: The increasing integration of deep neural networks in critical systems has spawned a theoretical and practical interest in formally guaranteeing safety properties about their behavior.
arXiv Machine Learning
Aug 26
$(\text{DNN})^2$: Doubly Non-Negative Relaxations for Deep Neural Networks
arXiv:2608.24743v1 Announce Type: new Abstract: Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-...
arXiv AI
Sep 16
Closing the Loop: Branch-and-Bound for Scalable Verification of Nonlinear Neural Feedback Systems
arXiv:2609. 16298v1 Announce Type: new Abstract: Despite recent advances in the verification of nonlinear neural feedback systems, scalability remains the central obstacle, as state-of-the-art solvers do not yet handle the network sizes and nonlinear dynamics of autonomy applications.
arXiv Machine Learning
Sep 10
Stability and Generalization of Straight-Through Estimators for Training Two-Layer Quantized Neural Networks
arXiv:2609.06430v1 Announce Type: new Abstract: We study the identity straight-through estimator (STE) for training a two-layer binary-activation network with hinge loss from the perspective of Stati...