Marvel: A Data-Centric Approach for Mapping Deep Learning Operators on Spatial Accelerators

A spatial accelerator’s efficiency depends heavily on both its mapper and cost models to generate optimized mappings for various operators of DNN models. However, existing cost models lack a formal boundary over their input programs (operators) for accurate and tractable cost analysis of the mappings, and this results in adaptability challenges to the cost models for new operators. We consider the recently introduced Maestro Data-Centric (MDC) notation and its analytical cost model to address this challenge because any mapping expressed in the notation is precisely analyzable using the MDC’s cost model. In this article, we characterize the set of input operators and their mappings expressed in the MDC notation by introducing a set of conformability rules . The outcome of these rules is that any loop nest that is perfectly nested with affine tensor subscripts and without conditionals is conformable to the MDC notation. A majority of the primitive operators in deep learning are such loop nests. In addition, our rules enable us to automatically translate a mapping expressed in the loop nest form to MDC notation and use the MDC’s cost model to guide upstream mappers. Our conformability rules over the input operators result in a structured mapping space of the operators, which enables us to introduce a mapper based on our decoupled off-chip/on-chip approach to accelerate mapping space exploration. Our mapper decomposes the original higher-dimensional mapping space of operators into two lower-dimensional off-chip and on-chip subspaces and then optimizes the off-chip subspace followed by the on-chip subspace. We implemented our overall approach in a tool called Marvel , and a benefit of our approach is that it applies to any operator conformable with the MDC notation. We evaluated Marvel over major DNN operators and compared it with past optimizers.

Space-Time Loop Tiling for Dynamic Programming Codes

We present a new space-time loop tiling approach and demonstrate its application for the generation of parallel tiled code of enhanced locality for three dynamic programming algorithms. The technique envisages that, for each loop nest statement, sub-spaces are first generated so that the intersection of them results in space tiles. Space tiles can be enumerated in lexicographical order or in parallel by using the wave-front technique. Then, within each space tile, time slices are formed, which are enumerated in lexicographical order. Target tiles are represented with multiple time slices within each space tile. We explain the basic idea of space-time loop tiling and then illustrate it by means of an example. Then, we present a formal algorithm and prove its correctness. The algorithm is implemented in the publicly available TRACO compiler. Experimental results demonstrate that parallel codes generated by means of the presented approach outperform closely related manually generated ones or those generated by using affine transformations. The main advantage of code generated by means of the presented approach is its enhanced locality due to splitting each larger space tile into multiple smaller tiles represented with time slices.

Tiling arbitrarily nested loops by means of the transitive

A novel approach to generation of tiled code for arbitrarily nested loops is presented. It is derived via a combination of the polyhedral and iteration space slicing frameworks. Instead of program transformations represented by a set of affine functions, one for each statement, it uses the transitive closure of a loop nest dependence graph to carry out corrections of original rectangular tiles so that all dependences of the original loop nest are preserved under the lexicographic order of target tiles. Parallel tiled code can be generated on the basis of valid serial tiled code by means of applying affine transformations or transitive closure using on input an inter-tile dependence graph whose vertices are represented by target tiles while edges connect dependent target tiles. We demonstrate how a relation describing such a graph can be formed. The main merit of the presented approach in comparison with the well-known ones is that it does not require full permutability of loops to generate both serial and parallel tiled codes; this increases the scope of loop nests to be tiled.