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Machine learning has emerged as a cornerstone of innovation in this digital world, driving advancements across various fields, from autonomous vehicles to personalised medicine. However, despite its capabilities, traditional machine-learning approaches often need to be revised when confronted with vast datasets or complex patterns. Tahmasebi, an MIT PhD student, has gained new insight inspired by Weyl’s law and promises to overcome these barriers by offering a novel framework for scalable and efficient data processing.
Tahmasebi has made a breakthrough that could reshape the machine-learning landscape. As a PhD in Department of Electrical Engineering and Computer Science (EECS) member and an affiliate of the Computer Science and Artificial Intelligence Laboratory (CSAIL), he found himself at the intersection of mathematics and technology during a differential equations course in late 2021. Here, Tahmasebi encountered Weyl’s law, a mathematical principle formulated over a century ago by the German mathematician Hermann Weyl.
Weyl’s law, originally devised to measure the complexity of spectral information within physical phenomena like the vibrations of strings or electromagnetic radiation, seemed worlds apart from the contemporary challenges of machine learning. However, Tahmasebi’s keen insight led him to explore the potential application of Weyl’s law in artificial intelligence, particularly in understanding the complexity of data input to neural networks.
Driven by the idea of reducing data complexity to enhance machine learning processes, Tahmasebi embarked on a collaborative journey with his advisor, Stefanie Jegelka, an associate professor in EECS and an affiliate of CSAIL and the MIT Institute for Data, Systems, and Society. Together, they sought to bridge the gap between mathematical theory and practical application in machine learning.
Their efforts gave the result when they modified Weyl’s law to incorporate symmetry into the assessment of dataset complexity. This advancement marked the first time Weyl’s law had been applied to enhance machine learning through symmetry. As a testament to its initiative’s potential impact on machine learning, their paper has received a designation as a “Spotlight” at the Machine Learning Conference last December 2023.
Soledad Villar, an applied mathematician at Johns Hopkins University, praised the research for its implications in scientific domains with limited training data. By leveraging dataset symmetries, models can produce predictions with smaller errors, using fewer training points—a crucial advantage in fields like computational chemistry and beyond.
In their paper, Tahmasebi and Jegelka delved into the practical benefits of incorporating symmetries, or “invariances,” into machine learning tasks. They illustrated how algorithms that recognise and exploit symmetries can significantly streamline complex tasks, such as identifying specific objects in images.
One of the key findings of their research is the potential for exponential gains from symmetries operating across multiple dimensions. By harnessing multidimensional symmetries, machine learning algorithms can achieve disproportionately large returns, offering unprecedented efficiency and accuracy in data analysis and prediction.
Their work introduced mathematical theorems and formulas predicting gains from symmetries in various applications, providing a theoretical basis for guiding further developments in “Geometric Deep Learning.” Rooted in differential geometry, this framework lays the groundwork for advancements in graph learning, 3D data analysis, and beyond.
Haggai Maron, a computer scientist, commended their approach for its theoretical contributions, highlighting its potential to shape the future of machine learning. By bridging the gap between mathematical theory and practical application, Tahmasebi and Jegelka’s research offers new insights with far-reaching implications for technology and science.
MIT’s Tahmasebi and Jegelka have opened new frontiers in machine learning, where age-old mathematical principles intersect with cutting-edge technology. As the field continues to evolve, their work promises to pave the way for advancements in artificial intelligence, unlocking new possibilities for data analysis, prediction, and beyond.
