In a technical analysis published on her personal blog, AI expert Lilian Weng delves deep into the mathematical theoretical foundation of the Neural Tangent Kernel (NTK)—a key concept introduced by Jacot et al. in 2018. This analysis focuses on explaining how artificial neural networks with an extremely large number of parameters behave and consistently converge during training using the gradient descent algorithm.
Background
Modern neural networks are often over-parameterized, meaning the number of parameters is far larger than the actual number of training data points. Even though these parameters are initially randomized, the optimization process still consistently leads to good results with training errors near zero. According to Lilian Weng's analysis, the NTK tool emerges to describe the dynamics of these neural networks throughout the optimization process. As the network width approaches infinity, the NTK becomes a constant value, allowing the convergence process to be analyzed as a simpler linear system.
Why It Matters
For the AI research community in Vietnam, understanding the mathematical nature of NTK helps shed light on the inner workings of today's large deep learning models. Research indicates that sufficiently wide neural networks can always converge to a global minimum when trained to minimize empirical loss. This provides a solid theoretical foundation rather than relying solely on trial-and-error empirical experiments. Understanding how NTK works helps engineers optimize network architectures and better predict model performance without consuming excessive computational resources for continuous trial and error.