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The many-body correlation function is a fundamental computation kernel in modern physics computing applications, e.g., Hadron Contractions in Lattice quantum chromodynamics (QCD). This kernel is both computation and memory intensive, involving a series of tensor contractions, and thus usually runs on accelerators like GPUs. Existing optimizations on many-body correlation mainly focus on individual tensor contractions (e.g., cuBLAS libraries and others). In contrast, this work discovers a new optimization dimension for many-body correlation by exploring the optimization opportunities among tensor contractions. More specifically, it targets general GPU architectures (both NVIDIA and AMD) and optimizes many-body correlation’s memory management by exploiting a set of memory allocation and communication redundancy elimination opportunities: first, GPU memory allocation redundancy : the intermediate output frequently occurs as input in the subsequent calculations; second, CPU-GPU communication redundancy : although all tensors are allocated on both CPU and GPU, many of them are used (and reused) on the GPU side only, and thus, many CPU/GPU communications (like that in existing Unified Memory designs) are unnecessary; third, GPU oversubscription: limited GPU memory size causes oversubscription issues, and existing memory management usually results in near-reuse data eviction, thus incurring extra CPU/GPU memory communications. Targeting these memory optimization opportunities, this article proposes MemHC, an optimized systematic GPU memory management framework that aims to accelerate the calculation of many-body correlation functions utilizing a series of new memory reduction designs. These designs involve optimizations for GPU memory allocation, CPU/GPU memory movement, and GPU memory oversubscription, respectively. More specifically, first, MemHC employs duplication-aware management and lazy release of GPU memories to corresponding host managing for better data reusability. Second, it implements data reorganization and on-demand synchronization to eliminate redundant (or unnecessary) data transfer. Third, MemHC exploits an optimized Least Recently Used (LRU) eviction policy called Pre-Protected LRU to reduce evictions and leverage memory hits. Additionally, MemHC is portable for various platforms including NVIDIA GPUs and AMD GPUs. The evaluation demonstrates that MemHC outperforms unified memory management by \( 2.18\times \) to \( 10.73\times \) . The proposed Pre-Protected LRU policy outperforms the original LRU policy by up to \( 1.36\times \) improvement. 1 

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions. 

Alternating Least Square (ALS) is a classic algorithm to solve matrix factorization widely used in recommendation systems. Existing efforts focus on parallelizing ALS on multi-/many-core platforms to handle large datasets. Recently, an optimized ALS variant called eALS was proposed, and it yields significantly lower time complexity and higher recommending accuracy than ALS. However, it is challenging to parallelize eALS on modern parallel architectures (e.g., CPUs and GPUs) because: 1) eALS’ data dependence prevents it from fine-grained parallel execution, thus eALS cannot fully utilize GPU's massive parallelism, 2) the sparsity of input data causes poor data locality and unbalanced workload, and 3) its large memory usage cannot fit into GPU's limited on-device memory, particularly for real-world large datasets. This paper proposes an efficient CPU/GPU heterogeneous recommendation system based on fast eALS for the first time (called HEALS) that consists of a set of system optimizations. HEALS employs newly designed architecture-adaptive data formats to achieve load balance and good data locality on CPU and GPU. HEALS also presents a CPU/GPU collaboration model that can explore both task parallelism and data parallelism. HEALS also optimizes this collaboration model with data communication overlapping and dynamic workload partition between CPU and GPU. Moreover, HEALS is further enhanced by various parallel techniques (e.g., loop unrolling, vectorization, and GPU parallel reduction). Evaluation results show that HEALS outperforms other state-of-the-art baselines in both performance and recommendation quality. Particularly, HEALS achieves up to 5.75 x better performance than a state-of-the-art ALS GPU library. This work also demonstrates the possibility of conducting fast recommendations on large datasets with constrained (or relaxed) hardware resources, e.g, a single CPU/GPU node.