← 研踪 PaperTrailarXiv:2611.05729 · v2
FRESHPart: Feedback-Reshaped Spectral Embedding for Hypergraph Partitioning
首次提交 2026-11-04 07:00
版本更新 2026-11-05 10:27
雷达观测 2026-11-06 11:06
摘要
With scalable Laplacian solvers now available, the next frontier is to exploit them more effectively for high-quality hypergraph partitioning. In this work, we revisit spectral hypergraph partitioning from the perspective of spectral embedding geometry. Through a systematic analysis of circuit hypergraphs and controlled synthetic (hyper)graphs, we identify a ray-like embedding structure that helps explain the effectiveness of projection-based partitioning. We further show that the geometry of spectral embeddings can be systematically influenced through Laplacian design and hyperedge reweighting. Guided by these insights, we propose FRESHPart, a feedback-reshaped spectral partitioning framework that refines the spectral embedding through Geometry Feedback and Search Feedback, producing embeddings that are better aligned with projection-based partitioning. On the Titan23 benchmark, FRESHPart achieves average cut reductions over hMETIS of 13.09% at $ε=2\%$ and 25.21% at $ε=20\%$, surpassing the strongest previously reported results (12.16% and 22.53%, respectively), while completing every benchmark in under 120 s on a single GPU.
作者备注：Accepted to ASP-DAC 2027
观测到的版本
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v2 · 2026-11-05 10:27 · 最新观测版本
FRESHPart: Feedback-Reshaped Spectral Embedding for Hypergraph Partitioning
With scalable Laplacian solvers now available, the next frontier is to exploit them more effectively for high-quality hypergraph partitioning. In this work, we revisit spectral hypergraph partitioning from the perspective of spectral embedding geometry. Through a systematic analysis of circuit hypergraphs and controlled synthetic (hyper)graphs, we identify a ray-like embedding structure that helps explain the effectiveness of projection-based partitioning. We further show that the geometry of spectral embeddings can be systematically influenced through Laplacian design and hyperedge reweighting. Guided by these insights, we propose FRESHPart, a feedback-reshaped spectral partitioning framework that refines the spectral embedding through Geometry Feedback and Search Feedback, producing embeddings that are better aligned with projection-based partitioning. On the Titan23 benchmark, FRESHPart achieves average cut reductions over hMETIS of 13.09% at $ε=2\%$ and 25.21% at $ε=20\%$, surpassing the strongest previously reported results (12.16% and 22.53%, respectively), while completing every benchmark in under 120 s on a single GPU.
查看此版本解读 →查看此版本原文 ↗v1 · 2026-11-04 07:00
RESHPart: Feedback-Reshaped Spectral Embedding for Hypergraph Partitioning
With scalable Laplacian solvers now available, the next frontier is to exploit them more effectively for high-quality hypergraph partitioning. In this work, we revisit spectral hypergraph partitioning from the perspective of spectral embedding geometry. Through a systematic analysis of circuit hypergraphs and controlled synthetic (hyper)graphs, we identify a ray-like embedding structure that helps explain the effectiveness of projection-based partitioning. We further show that the geometry of spectral embeddings can be systematically influenced through Laplacian design and hyperedge reweighting. Guided by these insights, we propose FRESHPart, a feedback-reshaped spectral partitioning framework that refines the spectral embedding through Geometry Feedback and Search Feedback, producing embeddings that are better aligned with projection-based partitioning. On the Titan23 benchmark, FRESHPart achieves average cut reductions over hMETIS of 13.09% at $ε=2\%$ and 25.21% at $ε=20\%$, surpassing the strongest previously reported results (12.16% and 22.53%, respectively), while completing every benchmark in under 120 s on a single GPU.
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