A Unified Kernel for Neural Network Learning
This provides a theoretical unification for researchers studying neural network dynamics, though it appears incremental as it builds directly on existing NNGP and NTK frameworks.
The paper tackles the theoretical disconnect between neural network learning and kernel methods by proposing the Unified Neural Kernel (UNK), which bridges the Neural Network Gaussian Process (NNGP) and Neural Tangent Kernel (NTK) approaches, showing it converges to NNGP with infinite learning steps and behaves like NTK with finite steps.
Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian processes. Two predominant approaches have emerged: the Neural Network Gaussian Process (NNGP) and the Neural Tangent Kernel (NTK). The former, rooted in Bayesian inference, represents a zero-order kernel, while the latter, grounded in the tangent space of gradient descents, is a first-order kernel. In this paper, we present the Unified Neural Kernel (UNK), which {is induced by the inner product of produced variables and characterizes the learning dynamics of neural networks with gradient descents and parameter initialization.} The proposed UNK kernel maintains the limiting properties of both NNGP and NTK, exhibiting behaviors akin to NTK with a finite learning step and converging to NNGP as the learning step approaches infinity. Besides, we also theoretically characterize the uniform tightness and learning convergence of the UNK kernel, providing comprehensive insights into this unified kernel. Experimental results underscore the effectiveness of our proposed method.