Polyhedral techniques have been widely used for automatic code optimization in low-level compilers and higher-level processes. Loop optimization is central to this technique, and several polyhedral schedulers like Feautrier, Pluto, isl and Tensor Scheduler have been proposed, each of them targeting a different architecture, parallelism model, or application scenario. The need for scenario-specific optimization is growing due to the heterogeneity of architectures. One of the most critical cases is represented by NPUs (Neural Processing Units) used for AI, which may require loop optimization with different objectives. Another factor to be considered is the framework or compiler in which polyhedral optimization takes place. Different scenarios, depending on the target architecture, compilation environment, and application domain, may require different kinds of optimization to best exploit the architecture feature set. We introduce a new configurable polyhedral scheduler, PolyTOPS, that can be adjusted to various scenarios with straightforward, high-level configurations. This scheduler allows the creation of diverse scheduling strategies that can be both scenario-specific (like state-of-the-art schedulers) and kernel-specific, breaking the concept of a one-size-fits-all scheduler approach. PolyTOPS has been used with isl and CLooG as code generators and has been integrated in MindSpore AKG deep learning compiler. Experimental results in different scenarios show good performance: a geomean speedup of 7.66x on MindSpore (for the NPU Ascend architecture) hybrid custom operators over isl scheduling, a geomean speedup up to 1.80× on PolyBench on different multicore architectures over Pluto scheduling. Finally, some comparisons with different state-of-the-art tools are presented in the PolyMage scenario.

Automatic parallel code generation from high-level abstractions such as those manipulated by artificial intelligence and deep learning (AI/DL) frameworks heavily rely on compiler techniques for automatic parallelization and optimization. Many recent advances rely on the polyhedral framework for this task because of its ability to model and to apply a wide range of loop transformations. However, modeling the complexity of the target architecture and of efficient cost models to decide about the best transformation is in general out of reach for a framework based on linear/affine constraints. In this work, we propose to decouple the polyhedral framework into linear and non-linear components. We introduce the constraint tree abstraction which may be generated by a non-linear optimizer and injected to the polyhedral optimization process to build better solutions. We present how to benefit from such a mechanism to generate efficient codes for GPU in the context of AI/DL operators. Our constraint injection allows to drive the polyhedral scheduler towards efficient solutions for load/store vectorization relying both on memory coalescing and vector types. We implemented our scheduler supporting constraint injection and our constraint construction system within a production AI/DL framework. Experiments on well known neural networks show the efficiency of this approach with respect to state-of-the-art polyhedral scheduling for GPU.

Many modern application domains crucially rely on tensor operations. The optimization of programs that operate on tensors poses difficulties that are not adequately addressed by existing languages and tools. Frameworks such as TensorFlow offer good abstractions for tensor operations, but target a specific domain, i.e. machine learning, and their optimization strategies cannot easily be adjusted to other domains. General-purpose optimization tools such as Pluto and existing meta-languages offer more flexibility in applying optimizations but lack abstractions for tensors. This work closes the gap between domain-specific tensor languages and general-purpose optimization tools by proposing the Tensor optimizations Meta-Language (TeML). TeML offers high-level abstractions for both tensor operations and loop transformations, and enables flexible composition of transformations into effective optimization paths. This compositionality is built into TeML's design, as our formal language specification will reveal. We also show that TeML can express tensor computations as comfortably as TensorFlow and that it can reproduce Pluto's optimization paths. Thus, optimized programs generated by TeML execute at least as fast as the corresponding Pluto programs. In addition, TeML enables optimization paths that often allow outperforming Pluto.

Many numerical algorithms are naturally expressed as operations on tensors (i.e. multi-dimensional arrays). Hence, tensor expressions occur in a wide range of application domains, e.g. quantum chemistry and physics; big data analysis and machine learning; and computational fluid dynamics. Each domain, typically, has developed its own strategies for efficiently generating optimized code, supported by tools such as domain-specific languages, compilers, and libraries. However, strategies and tools are rarely portable between domains, and generic solutions typically act as ''black boxes'' that offer little control over code generation and optimization. As a consequence, there are application domains without adequate support for easily generating optimized code, e.g. computational fluid dynamics. In this paper we propose a generic and easily extensible intermediate language for expressing tensor computations and code transformations in a modular and generative fashion. Beyond being an intermediate language, our solution also offers meta-programming capabilities for experts in code optimization. While applications from the domain of computational fluid dynamics serve to illustrate our proposed solution, we believe that our general approach can help unify research in tensor optimizations and make solutions more portable between domains.