Related papers: Robust Machine Learning Modeling for Predictive Co…

Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…

The rapid growth of resource-constrained mobile platforms, including mobile robots, wearable systems, and Internet-of-Things devices, has increased the demand for computationally efficient neural network controllers (NNCs) that can operate…

Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these…

We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems.…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the…

Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it…

This paper aims to discuss and analyze the potentialities of Recurrent Neural Networks (RNN) in control design applications. The main families of RNN are considered, namely Neural Nonlinear AutoRegressive eXogenous, (NNARX), Echo State…

This paper studies the approximation capabilities of neural networks that combine layer normalization (LN) with linear layers. We prove that networks consisting of two linear layers with parallel layer normalizations (PLNs) inserted between…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against…

Despite recent success, state-of-the-art learning-based models remain highly vulnerable to input changes such as adversarial examples. In order to obtain certifiable robustness against such perturbations, recent work considers…

Improving the efficiency of current neural networks and modeling them in biological neural systems have become popular research directions in recent years. Pulse-coupled neural network (PCNN) is a well applicated model for imitating the…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

Normalization layers are critical components of modern AI systems, such as ChatGPT, Gemini, DeepSeek, etc. Empirically, they are known to stabilize training dynamics and improve generalization ability. However, the underlying theoretical…

Model predictive control (MPC) provides a useful means for controlling systems with constraints, but suffers from the computational burden of repeatedly solving an optimization problem in real time. Offline (explicit) solutions for MPC…

Lipschitz-based certification offers efficient, deterministic robustness guarantees but has struggled to scale in model size, training efficiency, and ImageNet performance. We introduce \emph{LipNeXt}, the first \emph{constraint-free} and…

The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks…

Machine-learning architectures, such as Convolutional Neural Networks (CNNs) are vulnerable to adversarial attacks: inputs crafted carefully to force the system output to a wrong label. Since machine-learning is being deployed in…

Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks. A key challenge, supported both theoretically and empirically, is that robustness demands…