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ARXIV:2601.16294 · MATRIX MULTIPLICATION OPTIMIZATION · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2601.16294MATRIX MULTIPLICATION OPTIMIZATIONSUBMITTED 02 APR · 02:30 UTCFRESHNESS STALEarXiv
Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms.
Opportunity summary
Pain Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms.
Evidence 0 refs | 0 sources | 17% coverage
Blocker Evidence unverified
Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes implementing optimal matrix multiplication challenging.
General Matrix Multiplication (GEMM) is the cornerstone of Deep Learning and HPC workloads; accordingly, academia and industry have heavily optimized this kernel. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which…
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The integration of CA-algorithms is seamless and yields compact code (~30 LOC), yet it achieves state-of-the-art results on multiple CPU platforms, outperforming vendor libraries…
Matrix Multiplication Optimization moved forward this cycle; last verified April 2026. Public score 2.0/10.
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Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms.
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10.48550/arXiv.2601.16294Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms.
Abstract
General Matrix Multiplication (GEMM) is the cornerstone of Deep Learning and HPC workloads; accordingly, academia and industry have heavily optimized this kernel. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes implementing optimal matrix multiplication challenging. On modern CPU platforms with matrix engines, state-of-the-art vendor libraries tune input tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory hierarchy and maximize throughput. However, the best settings for these parameters depend strongly on the target platform (number of cores, memory hierarchy, cache sizes) and on the shapes of the matrices, making exhaustive tuning infeasible; in practice this leads to performance "glass jaws". In this work we revisit space filling curves (SFC) to alleviate the problem of this cumbersome tuning. SFC convert multi-dimensional coordinates (e.g. 2D) into a single dimension (1D), keeping nearby points in the high-dimensional space close in the 1D order. We partition the Matrix Multiplication computation space using recent advancements in generalized SFC (Generalized Hilbert Curves), and we obtain platform-oblivious and shape-oblivious matrix-multiplication schemes that exhibit inherently high degree of data locality. Furthermore, we extend the SFC-based work partitioning to implement Communication-Avoiding (CA) algorithms that replicate the input tensors and provably minimize communication/data-movement on the critical path. The integration of CA-algorithms is seamless and yields compact code (~30 LOC), yet it achieves state-of-the-art results on multiple CPU platforms, outperforming vendor libraries by up to 2x(geometric-mean speedup) for a range of GEMM shapes.
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PROBLEM
Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes implementing optimal matrix multiplication...
METHOD
General Matrix Multiplication (GEMM) is the cornerstone of Deep Learning and HPC workloads; accordingly, academia and industry have heavily optimized this kernel. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes impleme...
RESULT
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The integration of CA-algorithms is seamless and yields compact code (~30 LOC), yet it achieves state-of-the-art results on multiple CPU platforms, outperforming vendor libraries by up to 2x(geometric-mea...
WHY NOW
Matrix Multiplication Optimization moved forward this cycle; last verified April 2026. Public score 2.0/10.
Abstract-backed public claims while anchored extraction refreshes.
Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes implementing optimal matrix multiplication challenging.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
General Matrix Multiplication (GEMM) is the cornerstone of Deep Learning and HPC workloads; accordingly, academia and industry have heavily optimized this kernel. Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance, which makes implementing optimal matrix multiplication challenging.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The integration of CA-algorithms is seamless and yields compact code (~30 LOC), yet it achieves state-of-the-art results on multiple CPU platforms, outperforming vendor libraries by up to 2x(geometric-mean speedup) for a range of GEMM shapes.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Matrix Multiplication Optimization moved forward this cycle; last verified April 2026. Public score 2.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Develop a space-filling-curve-based matrix multiplication method to optimize computational efficiency on diverse CPU platforms.
Segment
Matrix Multiplication Optimization
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Commercial read
2.0/10 public viability
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reason
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proof status
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passport absent
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Artifact maturity
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Technical feasibility
partial
Current read
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Evidence
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Integration burden
missing
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No public implementation surface observed.
Evidence
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Write integration checklist from prototype path and target workflow.
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ARTIFACTS
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DEFENSIBILITY
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