The reparameterization trick enables the optimization of large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack continuous reparameterizations due to the discontinuous nature of discrete states. In this work we introduce concrete random variables -- continuous relaxations of discrete random variables. The concrete distribution is a new family of distributions with closed form densities and a simple reparameterization. Whenever a discrete stochastic node of a computation graph can be refactored into a one-hot bit representation that is treated continuously, concrete stochastic nodes can be used with automatic differentiation to produce low-variance biased gradients of objectives (including objectives that depend on the log-likelihood of latent stochastic nodes) on the corresponding discrete graph. We demonstrate their effectiveness on density estimation and structured prediction tasks using neural networks.

该论文提供了一种通过引入Concrete随机变量的连续放松方法解决离散状态下无法使用重参数化技巧的问题，使得在离散计算图上也能有效地使用自动微分来产生低方差偏向梯度和低方差无偏梯度以优化损失函数。

具体分布：离散随机变量的连续松弛