The Center for AI Research (CAIR) at VinUniversity is proud to highlight a major achievement by Bùi Khánh Vĩnh, whose paper, “Conservation Laws for Modern Neural Architectures”, has been accepted to ICML 2026 in Seoul, South Korea. This work explores the hidden mathematical structures within neural network parameter spaces, offering fresh insights into how modern deep learning models learn, adapt, and preserve knowledge during training.
Vĩnh’s research focuses on moving beyond the conventional black-box view of neural networks. Instead of treating these systems as opaque, his work uncovers latent geometric and dynamical structures that govern their behavior. The ICML 2026 paper introduces the concept of conservation laws in neural networks – quantities that remain invariant during gradient-based optimization and analyzes how these invariants shape the learning process. By examining architectures such as attention mechanisms, positional encodings, and Mixture-of-Experts models, the study reveals that even highly complex networks exhibit stable, predictable patterns in their parameter spaces.
The journey to this discovery was far from straightforward. Formulating the problem rigorously required integrating ideas from optimization, differential equations, symmetry, and geometry with the practical realities of modern neural architectures. The project demanded rapid exploration of multiple proof strategies, careful testing of special cases, and continual refinement of formulations to ensure accuracy. Collaboration and mentorship at CAIR were essential in navigating these challenges, providing guidance that helped clarify theoretical concepts and improve the presentation of results.
This paper not only contributes to the theoretical understanding of deep learning but also provides tools for analyzing training dynamics and functional equivalence in neural networks. By identifying invariant structures, Vĩnh’s work opens the door to designing more interpretable, robust, and adaptive AI systems, a crucial step as neural architectures continue to grow in complexity and scale.
Being accepted to ICML 2026 gives Vĩnh the opportunity to share his findings with an international community of AI researchers, receive feedback from leading experts, and engage in discussions that may shape future directions in machine learning research. The platform also highlights the increasing presence of VinUniversity researchers on the global stage, demonstrating how rigorous training and innovative thinking at CAIR can produce work recognized at the highest academic levels.
Beyond this publication, Vĩnh continues to explore the mathematical foundations of deep learning, with a particular focus on symmetry, geometry, and dynamics in neural networks. “Studying the hidden structures in neural networks has strengthened my understanding of the interplay between theory and practice in AI,” he said.
“This project has shown that careful mathematical analysis can reveal patterns that are otherwise invisible, guiding research and practical applications alike.”
Vĩnh’s achievement illustrates the value of early research exposure, mentorship, and collaborative inquiry. From developing a deep interest in the underlying mathematics of neural networks to producing work recognized at ICML, his journey reflects the potential of CAIR researchers to contribute meaningfully to global AI research. Through perseverance, collaboration, and rigorous inquiry, this work sets a standard for aspiring researchers and highlights the innovative spirit that drives CAIR’s mission in advancing artificial intelligence.
