HSE Researchers Introduce Novel Symmetry-Aware Neural Network Architecture
Researchers at the HSE Laboratory for Geometric Algebra and Applications have developed a new neural network architecture that can accelerate and streamline data analysis in physics, biology, and engineering. The scientists presented their solution on July 16 in Vancouver at ICML 2025, one of the world's leading conferences on machine learning. Both the paper and the source code are publicly available.
Many physical systems—from robots to molecules to charged particles—exhibit the same behaviour when rotated or mirrored. Modern equivariant neural networks are specifically designed to recognise and preserve such symmetries in data, making them especially valuable for scientific and technological applications ranging from modelling chemical compounds and analysing physical processes to image recognition.
However, these models have a drawback: their high accuracy comes at the cost of increased complexity. They often require a large number of trainable parameters, making them resource-intensive and prone to overfitting—especially when training data is limited.
Ekaterina Filimoshina and Dmitry Shirokov, researchers at the Department of Mathematics and the Laboratory for Geometric Algebra and Applications of the HSE Faculty of Economic Sciences, have developed GLGENN (Generalized Lipschitz Group Equivalent Neural Networks), a neural network architecture designed to overcome these limitations. It enables models to preserve data symmetries using significantly fewer parameters. The authors based their design on the well-established mathematical framework of Clifford (geometric) algebras and introduced a novel weight-sharing technique that respects the underlying algebraic structures.
'We set out to design a model that is both intelligent and lightweight,' says Ekaterina Filimoshina, Research Assistant at the HSE FES Laboratory for Geometric Algebra and Applications. 'GLGENN demonstrates that equivariant neural networks don’t need to be large and complex—they can learn effectively, even from limited data, without compromising quality.'
The model has been tested on a variety of tasks, ranging from simulating physical processes to handling geometric data, and has demonstrated results comparable to or better than existing methods. Additionally, GLGENN operates faster and more efficiently due to its reduced number of trainable parameters, making it more accessible for practical applications.
Dmitry Shirokov
'These results could mark a significant step toward the development of new neural-network tools for science and technology' adds Dmitry Shirokov, Head of the HSE FES Laboratory for Geometric Algebra and Applications. 'We are confident that the geometric-algebra approach will find applications across a wide range of fields, including bioinformatics, robotics, and geoinformatics.'
Participation in ICML served as recognition of the high level of machine learning research conducted at HSE University. The scientists plan to further develop the GLGENN architecture by expanding its capabilities to handle new types of data and exploring its potential applications in physics, robotics, and computer vision.
The study was supported by the HSE Mirror Laboratories project titled 'Quaternions, geometric algebras, and applications.'
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