  InfoNCE loss is a widely used loss function for contrastive model training.
It aims to estimate the mutual information between a pair of variables by
discriminating between each positive pair and its associated $K$ negative
pairs. It is proved that when the sample labels are clean, the lower bound of
mutual information estimation is tighter when more negative samples are
incorporated, which usually yields better model performance. However, in many
real-world tasks the labels often contain noise, and incorporating too many
noisy negative samples for model training may be suboptimal. In this paper, we
study how many negative samples are optimal for InfoNCE in different scenarios
via a semi-quantitative theoretical framework. More specifically, we first
propose a probabilistic model to analyze the influence of the negative sampling
ratio $K$ on training sample informativeness. Then, we design a training
effectiveness function to measure the overall influence of training samples on
model learning based on their informativeness. We estimate the optimal negative
sampling ratio using the $K$ value that maximizes the training effectiveness
function. Based on our framework, we further propose an adaptive negative
sampling method that can dynamically adjust the negative sampling ratio to
improve InfoNCE based model training. Extensive experiments on different
real-world datasets show our framework can accurately predict the optimal
negative sampling ratio in different tasks, and our proposed adaptive negative
sampling method can achieve better performance than the commonly used fixed
negative sampling ratio strategy.
