Title: Neural Tangent Kernel Perspective on Parameter-Space Symmetries
Primary area: learning theory
Keywords: Symmetries, Parater Space Symmetries, Parater-Space Symmetries, Neural Teleporation, Neural Tangent Kernel, Wide Neural Networks, Linearization, NTK

Abstract: Parameter-space symmetries are transformations that modify model parameters without altering the outputs. These transformations can be leveraged to accelerate optimization and enhance generalization. Remarkably, applying a single transformation either before or during training often suffices to realize these benefits. While the effectiveness of this approach is very promising, its underlying mechanisms remain poorly understood. In this paper, we offer an explanation within the Neural Tangent Kernel (NTK) framework, by analyzing how such transformations affect the kernel's properties. In particular, we show that maximizing the alignment between the loss gradient and the data kernel is equivalent to maximizing the alignment between the NTK and the data. Since kernel alignment is known to correlate with optimization rate in the NTK limit, this insight elucidates how loss gradient optimization facilitates faster training. To establish the validity of this approach, we prove that parameter-space symmetries preserve the NTK limit.