Speaker: Navid Azizan (MIT)

Title: Hard-Constrained Neural Networks

Abstract: Incorporating prior knowledge and domain-specific input-output requirements, such as safety or stability, as hard constraints into neural networks is a key enabler for their deployment in highstakes applications. However, existing methods often rely on soft penalties, which are insufficient, especially on out-ofdistribution samples. In this talk, I will introduce hardconstrained neural networks (HardNet), a general framework for enforcing hard, input-dependent constraints by appending a differentiable enforcement layer to any neural network. This approach enables end-to-end training and, crucially, is proven to preserve the network’s universal approximation capabilities, ensuring model expressivity is not sacrificed. We demonstrate the versatility and effectiveness of HardNet across various applications: learning with piecewise constraints, learning optimization solvers with guaranteed feasibility, and optimizing control policies in safety-critical systems. This framework can be used even for problems where the constraints themselves are not fully known and must be learned from data in a parametric form, for which I will present two key applications: data-driven control with inherent Lyapunov stability and learning chaotic dynamical systems with guaranteed boundedness. Together, these results demonstrate a unified methodology for embedding formal constraints into deep learning, paving the way for more reliable AI.

Biography:  Navid Azizan is the Alfred H. (1929) and Jean M. Hayes Assistant Professor at MIT, where he holds dual appointments in Mechanical Engineering (Control, Instrumentation & Robotics) and IDSS and is a Principal Investigator in LIDS. His research interests broadly lie in machine learning, systems and control, mathematical optimization, and network science. His research lab focuses on various aspects of reliable intelligent systems, with an emphasis on principled learning and optimization algorithms with applications to autonomy and sociotechnical systems. His work has been recognized by several awards, including Research Awards from Google, Amazon, MathWorks, and IBM, and Best Paper awards and nominations at conferences including ACM Greenmetrics and the Learning for Dynamics & Control (L4DC). He was named in the list of Outstanding Academic Leaders in Data by CDO Magazine for two consecutive years in 2024 and 2023, received the 2020 Information Theory and Applications (ITA) “Sun” (Gold) Graduation Award, and was named an Amazon Fellow in AI in 2017 and a PIMCO Fellow in Data Science in 2018.