arXiv:2606.10913v1 Announce Type: new Abstract: We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss function is analytic and non-polynomial, we prove that data symmetries generically do not induce any additional integrals of motion. For mean squared error (MSE) loss, on the other hand, there are situations in which data augmentation yields extra conserved quantities. We build a framework, utilizing \emph{tensorizable networks} to describe this phenomenon. Tensorizable netw
This research is emerging as the field of AI grapples with the fundamental properties and explainability of neural networks, coinciding with advancements in understanding their training dynamics.
For a strategic reader, this research provides deeper theoretical insights into the learning processes of neural networks, potentially informing future architectural designs and training methodologies to achieve more robust and predictable AI systems.
The understanding of how data symmetries influence conserved quantities during neural network training is refined, offering new avenues for optimizing AI performance and predictability, especially with specific loss functions like MSE.
- · AI researchers
- · Machine learning framework developers
- · Data scientists
- · AI development relying solely on heuristic methods
Improved theoretical understanding of neural network training dynamics.
Development of new AI models and training techniques that leverage or mitigate these conservation laws.
More robust, efficient, and explainable AI systems across various applications, potentially reducing compute overhead for certain tasks.
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