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We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

Databases · Computer Science 2021-08-10 Binhang Yuan , Dimitrije Jankov , Jia Zou , Yuxin Tang , Daniel Bourgeois , Chris Jermaine

We introduce Mirage, the first multi-level superoptimizer for tensor programs. A key idea in Mirage is $\mu$Graphs, a uniform representation of tensor programs at the kernel, thread block, and thread levels of the GPU compute hierarchy.…

Machine Learning · Computer Science 2025-06-09 Mengdi Wu , Xinhao Cheng , Shengyu Liu , Chunan Shi , Jianan Ji , Kit Ao , Praveen Velliengiri , Xupeng Miao , Oded Padon , Zhihao Jia

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

The shift to data-intensive processing from the cloud to the edge has introduced new challenges and expectations for the next generation of intelligent computing systems. As the memory wall continues to grow, modern systems can only meet…

Hardware Architecture · Computer Science 2026-04-16 Denis Hoornaert , Cole Strickler , Manos Athanassoulis , Marco Caccamo , Heechul Yun , Renato Mancuso

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

Numerical Analysis · Mathematics 2020-01-03 Misha Kilmer , Lior Horesh , Haim Avron , Elizabeth Newman

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Machine Learning · Computer Science 2023-10-31 Guillem Simeon , Gianni de Fabritiis

The last few years have seen gigantic leaps in algorithms and systems to support efficient deep learning inference. Pruning and quantization algorithms can now consistently compress neural networks by an order of magnitude. For a compressed…

Machine Learning · Computer Science 2021-07-22 Ziheng Wang

This paper shows how to optimize sparse tensor algebraic expressions by introducing temporary tensors, called workspaces, into the resulting loop nests. We develop a new intermediate language for tensor operations called concrete index…

Mathematical Software · Computer Science 2023-10-18 Fredrik Kjolstad , Willow Ahrens , Shoaib Kamil , Saman Amarasinghe

Personalized recommendations are one of the most widely deployed machine learning (ML) workload serviced from cloud datacenters. As such, architectural solutions for high-performance recommendation inference have recently been the target of…

Hardware Architecture · Computer Science 2020-10-27 Youngeun Kwon , Yunjae Lee , Minsoo Rhu

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Machine Learning · Computer Science 2025-03-18 Maolin Wang , Yu Pan , Zenglin Xu , Guangxi Li , Xiangli Yang , Danilo Mandic , Andrzej Cichocki

Evolutionary multiobjective optimization has witnessed remarkable progress during the past decades. However, existing algorithms often encounter computational challenges in large-scale scenarios, primarily attributed to the absence of…

Neural and Evolutionary Computing · Computer Science 2024-07-23 Zhenyu Liang , Tao Jiang , Kebin Sun , Ran Cheng

This paper introduces the continuous tensor abstraction, allowing indices to take real-number values (for example, A[3.14]). It also presents continuous tensor algebra expressions, such as C(x,y) = A(x,y) * B(x,y), where indices are defined…

Programming Languages · Computer Science 2025-10-23 Jaeyeon Won , Willow Ahrens , Teodoro Fields Collin , Joel S. Emer , Saman Amarasinghe

This paper presents a meta-compilation framework, the MCompiler. The main idea is that different segments of a program can be compiled with different compilers/optimizers and combined into a single executable. The MCompiler can be used in a…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-05-31 Aniket Shivam , Alexandru Nicolau , Alexander V. Veidenbaum

Many artificial intelligence models process input data of different lengths and resolutions, making the shape of the tensors dynamic. The performance of these models depends on the shape of the tensors, which makes it difficult to optimize…

Machine Learning · Computer Science 2024-08-01 Pengyu Mu , Linquan Wei , Yi Liu , Rui Wang

Heterogeneous deep learning systems (DLS) such as GPUs and ASICs have been widely deployed in industrial data centers, which requires to develop multiple low-level tensor programs for different platforms. An attractive solution to relieve…

Computation and Language · Computer Science 2025-05-06 Shouyang Dong , Yuanbo Wen , Jun Bi , Di Huang , Jiaming Guo , Jianxing Xu , Ruibai Xu , Xinkai Song , Yifan Hao , Xuehai Zhou , Tianshi Chen , Qi Guo , Yunji Chen

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

Machine Learning · Computer Science 2023-09-21 Taehyung Kwon , Jihoon Ko , Jinhong Jung , Kijung Shin

Advanced compiler technology is crucial for enabling machine learning applications to run on novel hardware, but traditional compilers fail to deliver performance, popular auto-tuners have long search times and expert-optimized libraries…

Machine Learning · Computer Science 2023-11-09 Dejan Grubisic , Bram Wasti , Chris Cummins , John Mellor-Crummey , Aleksandar Zlateski

Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…

Programming Languages · Computer Science 2024-01-11 Saurabh Raje , Yufan Xu , Atanas Rountev , Edward F. Valeev , Saday Sadayappan

We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…

Strongly Correlated Electrons · Physics 2026-03-09 Xing-Yu Zhang , Qi Yang , Philippe Corboz , Jutho Haegeman , Wei Tang

It has been demonstrated that specialised architectures, such as FPGAs and AMD's AI Engines (AIEs), have the potential to deliver energy and performance advantages for scientific computing. Given the integration of AIEs into AMD's CPUs,…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-06 Nick Brown , Gabriel Rodriguez-Canal