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Majid Darehmiraki

Publications and source records attributed to Majid Darehmiraki.

4 recordsLinked to original sources
arXiv2025

Port--Hamiltonian Diffusion Models: A Control-Theoretic Perspective on Generative Modeling

Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a control-theoretic foundation for diffusion models by embedding them within the port--Hamiltonian (PH) systems framework. We show that the score function can be interpreted as the gradient of a learnable Hamiltonian energy, allowing both the forward and reverse diffusion processes to be formulated as structured PH dynamics. The reverse-time generative process is further interpreted as a feedback-controlled PH system, where dissipation plays a fundamental role in stabilizing sampling dynamics. This formulation yields intrinsic stability guarantees that are independent of score estimation accuracy. A simple analytical example illustrates the proposed framework.

math-ph↗
arXiv2025

A parametric activation function based on Wendland RBF

This paper introduces a novel parametric activation function based on Wendland radial basis functions (RBFs) for deep neural networks. Wendland RBFs, known for their compact support, smoothness, and positive definiteness in approximation theory, are adapted to address limitations of traditional activation functions like ReLU, sigmoid, and tanh. The proposed enhanced Wendland activation combines a standard Wendland component with linear and exponential terms, offering tunable locality, improved gradient propagation, and enhanced stability during training. Theoretical analysis highlights its mathematical properties, including smoothness and adaptability, while empirical experiments on synthetic tasks (e.g., sine wave approximation) and benchmark datasets (MNIST, Fashion-MNIST) demonstrate competitive performance. Results show that the Wendland-based activation achieves superior accuracy in certain scenarios, particularly in regression tasks, while maintaining computational efficiency. The study bridges classical RBF theory with modern deep learning, suggesting that Wendland activations can mitigate overfitting and improve generalization through localized, smooth transformations. Future directions include hybrid architectures and domain-specific adaptations.

cs.LG↗