arXiv:2606.02993v1 Announce Type: new Abstract: Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict $g_1 \star g_2$ for elements of a finite group $G$. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this fl
This research provides a foundational understanding of neural network learning dynamics, published as AI capabilities continue to rapidly advance, demanding deeper theoretical grounding.
Understanding how neural networks internally represent and process structured data is critical for developing more robust, transparent, and efficient AI systems, impacting future model design.
The theoretical proof demonstrates how neural networks learn spectral representations for group composition, offering a mathematical framework to interpret and potentially improve deep learning architectures.
- · AI researchers
- · Deep learning practitioners
- · Academic institutions
Increased theoretical understanding of neural network learning mechanisms, particularly for structured data.
Development of new neural network architectures or training methodologies inspired by these theoretical insights.
Enhanced AI systems capable of more efficiently processing symbolic reasoning and complex relational data across various applications.
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