Probabilistic programming languages (PPLs) are a popular tool for high-level modelling across many fields. They provide a range of algorithms for probabilistic inference, which analyse models by learning their parameters from a dataset or estimating their posterior distributions. However, probabilistic inference is known to be very costly. One of the bottlenecks of probabilistic inference stems from the iteration over entries of a large dataset or a long series of random samples. Vectorisation can mitigate this cost, but manual vectorisation is error-prone, and existing automatic techniques are often ad-hoc and limited, unable to handle general repetition structures, such as nested loops and loops with data-dependent control flow, without significant user intervention. To address this bottleneck, we propose a sound and effective method for automatically vectorising loops in probabilistic programs. Our method achieves high throughput using speculative parallel execution of loop iterations, while preserving the semantics of the original loop through a fixed-point check. We formalise our method as a translation from an imperative PPL into a lower-level target language with primitives geared towards vectorisation. We implemented our method for the Pyro PPL and evaluated it on a range of probabilistic models. Our experiments show significant performance gains against an existing vectorisation baseline, achieving 1.1–6× speedups and reducing GPU memory usage in many cases. Unlike the baseline, which is limited to a subset of models, our method effectively handled all the tested models.

SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik's cube show the substantial improvement of SymSATNet over the baseline SATNet.