Softmax is the most commonly used output function for multiclass problems and is widely used in areas such as vision, natural language processing, and recommendation. A softmax model has linear costs in the number of classes which makes it too expensive for many real-world problems. A common approach to speed up training involves sampling only some of the classes at each training step. It is known that this method is biased and that the bias increases the more the sampling distribution deviates from the output distribution. Nevertheless, almost any recent work uses simple sampling distributions that require a large sample size to mitigate the bias. In this work, we propose a new class of kernel based sampling methods and develop an efficient sampling algorithm. Kernel based sampling adapts to the model as it is trained, thus resulting in low bias. Kernel based sampling can be easily applied to many models because it relies only on the model's last hidden layer. We empirically study the trade-off of bias, sampling distribution and sample size and show that kernel based sampling results in low bias with few samples.

本文提出了基于核函数的采样方法并发展了高效的采样算法以减少对于大量样本情况下传统采样方法的偏倚问题。实验结果表明此方法相较于传统采样方法偏差较小并且需要的样本数更少。

基于核采样的自适应采样Softmax