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However, existing tensor compilers struggle to fuse complex reduction computations involving loop-carried dependencies, such as attention mechanisms.<\/jats:p>\n                  <jats:p>This paper introduces Neptune, a tensor compiler for advanced operator fusion for sequences of reduction operators. Neptune presents a new approach for advanced operator fusion, which intentionally breaks some existing dependencies and compensates by constructing algebraic correction expressions that allow the kernel to produce the correct result. Applying Neptune\u2019s advanced operator fusion to a plain attention operator generates operators equivalent to FlashAttention and FlashDecoding.<\/jats:p>\n                  <jats:p>On ten attention-based benchmarks, Neptune, starting from a plain attention code and a high\u2013level scheduling template, outperforms existing compilers like Triton, TVM, and Flex Attention, including Triton\u2013based implementations of FlashAttention. Across four different GPU architectures from NVIDIA and AMD, Neptune\u2013generated kernels have an average speedup of 1.35\u00d7 over the next best alternative, with up to 2.65 \u00d7 speedup on Nvidia GPUs and up to 3.32 \u00d7 on AMD GPUs, demonstrating its effectiveness for deep learning workloads.<\/jats:p>","DOI":"10.1145\/3808298","type":"journal-article","created":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T18:04:09Z","timestamp":1780941849000},"page":"1278-1302","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Neptune: Advanced ML Operator Fusion for Locality and Parallelism on GPUs"],"prefix":"10.1145","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7080-891X","authenticated-orcid":false,"given":"Yifan","family":"Zhao","sequence":"first","affiliation":[{"name":"University of Illinois Urbana-Champaign, Urbana, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2989-2212","authenticated-orcid":false,"given":"Egan","family":"Johnson","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Urbana, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0974-4001","authenticated-orcid":false,"given":"Prasanth","family":"Chatarasi","sequence":"additional","affiliation":[{"name":"IBM Research, Yorktown Heights, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0760-9690","authenticated-orcid":false,"given":"Vikram","family":"Adve","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Urbana, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7319-8845","authenticated-orcid":false,"given":"Sasa","family":"Misailovic","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Urbana, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"Mart\u00edn Abadi Paul Barham Jianmin Chen Zhifeng Chen Andy Davis Jeffrey Dean Matthieu Devin Sanjay GhemawatGeoffrey Irving and Michael Isard et al. 2026. 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