lpNTK: Better Generalisation with Less Data via Sample Interaction During Learning
This work addresses generalization issues in neural networks for researchers and practitioners by providing a novel theoretical tool, though it is incremental as it builds on existing NTK frameworks.
The paper tackled the problem of improving neural network generalization by analyzing sample interactions during training, proposing a labeled pseudo Neural Tangent Kernel (lpNTK) that incorporates label information to measure these interactions, and demonstrated its utility in understanding learning phenomena and mitigating poisoning attacks without harming performance.
Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.