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arXiv:2502.03402 (cs)
[Submitted on 5 Feb 2025 (v1), last revised 7 Feb 2025 (this version,
v2)]

Title:Tensor Evolution: A Framework for Fast Evaluation of Tensor
Computations using Recurrences

Authors:Javed Absar, Samarth Narang, Muthu Baskaran
View a PDF of the paper titled Tensor Evolution: A Framework for Fast
Evaluation of Tensor Computations using Recurrences, by Javed Absar
and Samarth Narang and Muthu Baskaran
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    Abstract:This paper introduces a new mathematical framework for
    analysis and optimization of tensor expressions within an
    enclosing loop. Tensors are multi-dimensional arrays of values.
    They are common in high performance computing (HPC) and machine
    learning domains. Our framework extends Scalar Evolution - an
    important optimization pass implemented in both LLVM and GCC - to
    tensors. Scalar Evolution (SCEV) relies on the theory of `Chain
    of Recurrences' for its mathematical underpinnings. We use the
    same theory for Tensor Evolution (TeV). While some concepts from
    SCEV map easily to TeV -- e.g. element-wise operations; tensors
    introduce new operations such as concatenation, slicing,
    broadcast, reduction, and reshape which have no equivalent in
    scalars and SCEV. Not all computations are amenable to TeV
    analysis but it can play a part in the optimization and analysis
    parts of ML and HPC compilers. Also, for many mathematical/
    compiler ideas, applications may go beyond what was initially
    envisioned, once others build on it and take it further. We hope
    for a similar trajectory for the tensor-evolution concept.

Subjects: Programming Languages (cs.PL); Mathematical Software
          (cs.MS)
Cite as:  arXiv:2502.03402 [cs.PL]
          (or arXiv:2502.03402v2 [cs.PL] for this version)
          https://doi.org/10.48550/arXiv.2502.03402
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Javed Absar [view email]
[v1] Wed, 5 Feb 2025 17:43:17 UTC (108 KB)
[v2] Fri, 7 Feb 2025 16:07:14 UTC (108 KB)
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