ALT lord yupa from nausicaa of the valley of the wind wearing his signature wide-brim hat

ALT QTed paper screenshot: In this paper, we describe an auto-diff framework that takes a computation specified in relational algebra (RA) as input and automatically produces a second RA computation that evaluates the gradient of input computation, taken with respect to one or more database tables.

ALT The gradient operation V is a function-to-function transformation: it takes as input a function F, and returns a new function V F that returns the direction of the fastest increase in F from location x. Classically, RA is defined operationally (each RA operation takes one or more relations as input and returns a relation). As such, we define a functional version of the RA, as well as gradients of RA functions.

ALT Constant relations vs. queries. Rx is an example of a relation or a simple function; given any value in the key set, a corresponding real number (or a multi-dimensional tensor in the general case) is produced. However, to build queries, we also need some notion of a higher-order function over relations: a function from one or more input relations to a output relation. It is over such higher-order functions that the gradient operation will itself operate.

ALT However, there were some clear advantages of the auto-diffed RA solution. As the auto-diffed RA is running on what is essentially a high-performance database system, it avoided all out-of-memory errors. RA-GCN was able to scale to the largest data set (friendster), even for full graph training-thus avoiding the potential pitfalls of cutting important edges during training. In fact, the RA-based solution was the only solution able to scale to full-graph training. Further, RA-GCN was able to do this on only one machine- automatically adapting to the limited memory as required (a hallmark of scalable database engines). The other solutions failed even to perform mini-batch training on fewer than eight machines for this data set.

ALT a screenshot of jack's talk recording, where the slides show a screenshot of tylr

ALT a screenshot of my TyDe talk recording, where the slides show a high-level schematic of the concepts of tile-based editing