5 accepted papers
Existing works on the expressive power of neural networks typically assume real-valued parameters and exact mathematical operations during the evaluation of networks. However, neural networks run on actual computers can take parameters only from a small subset of the reals and perform inexact mathem…
Forward- or reverse-mode automatic differentiation (AD) is a popular algorithm for computing the derivative of a function expressed by a program. AD always outputs the correct derivative if a program does not use any non-differentiable functions and control flows; however, it may return an arbitrary…
Recent work has shown that forward- and reverse- mode automatic differentiation (AD) over the reals is almost always correct in a mathematically precise sense. However, actual programs work with machine-representable numbers (e.g., floating-point numbers), not reals. In this paper, we study the corr…
Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable functions, but in practice, they are commonly applied to fun…
We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by g…