Smooth interpretation

We present smooth interpretation, a method to systematically approximate numerical imperative programs by smooth mathematical functions. This approximation facilitates the use of numerical search techniques like gradient descent for program analysis and synthesis. The method extends to programs the notion of Gaussian smoothing, a popular signal-processing technique that filters out noise and discontinuities from a signal by taking its convolution with a Gaussian function. In our setting, Gaussian smoothing executes a program according to a probabilistic semantics; the execution of program P on an input x after Gaussian smoothing can be summarized as follows: (1) Apply a Gaussian perturbation to x—the perturbed input is a random variable following a normal distribution with mean x. (2) Compute and return the expected output of P on this perturbed input. Computing the expectation explicitly would require the execution of P on all possible inputs, but smooth interpretation bypasses th...

• Type: Conference
• Year: 2010
• Where: PLDI
• Authors: Swarat Chaudhuri, Armando Solar-Lezama
• Keywords: Gaussian Smoothing, Numerical, PLDI 2010, Smooth Interpretation