A central problem in quantum mechanics involves solving the Electronic Schrödinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and then optimizes this approximated objective over a chosen parameterized family of wavefunctions, known as the ansatz. Recently neural networks have been used as the ansatz, with accompanying success. However, sampling from such wavefunctions has required the use of a Markov Chain Monte Carlo approach, which is inherently inefficient. In this work, we propose a solution to this problem via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties. We prove that a normalizing flow using the following two essential ingredients satisfies our requirements: (a) a base distribution which is constructed from Determinantal Point Processes; (b) flow layers which are equivariant to a particular subgroup of the permutation group. We then show how to construct both continuous and discrete normalizing flows which satisfy the requisite equivariance. We further demonstrate the manner in which the non-smooth nature (``cusps'') of the wavefunction may be captured, and how the framework may be generalized to provide induction across multiple molecules. The resulting theoretical framework entails an efficient approach to solving the Electronic Schrödinger Equation.

We argue for a richer view of the space of lightweight compression schemes for columnar DBMSes: We demonstrate how even simple simple schemes used in DBMSes decompose into constituent schemes through a columnar perspective on their decompression. With our concrete examples, we touch briefly on what follows from these and other decompositions: Composition of alternative compression schemes as well as other practical and analytical implications.

This short paper present a collection of GPU lightweight decompression algorithms implementations within a FOSS library, Giddy - the first to be published to offer such functionality. As the use of compression is important in ameliorating PCIe data transfer bottlenecks, we believe this library and its constituent implementations can serve as useful building blocks in GPU-accelerated DBMSes --- as well as other data-intensive systems.