Equivariant neural networks (ENNs) are a powerful framework for modeling 3D geometric data in physical and biological systems. The Clebsch–Gordan tensor product (CGTP)—a core operation for preserving equivariance—remains the primary computational bottleneck in ENNs. Although Clebsch–Gordan (CG) coefficients exhibit pronounced structural sparsity, prior work has neither fully leveraged this property nor adopted hardware-friendly quantization, leading to limited efficiency. We present Equicore, a software–hardware co-design framework to accelerate CGTP in ENNs. Equicore introduces three key innovations: (1) a sparse-bypass strategy that exploits the CG structural sparsity together with a novel CG data format to pack the overlapping non-zeros, bypassing redundant data accesses and computations comparing to previous sparse solutions; (2) a merged-shift quantization strategy that enables full Int8 representation of irreps, weights, and CG coefficients using shift-only operations; and (3) a cascaded processing unit that tightly couples the FPGA hardware resources to achieve high operating frequency while supporting efficient sparse and quantized computation. Deployed on a AMD Virtex VCU128 platform, Equicore delivers up to 10.5× speedup and 17.4× energy-efficiency improvement over state-of-the-art GPU libraries and FPGA designs across diverse CGTP types in a benchmark of eleven ENN models.
Tang, S, Zhang, C, Chen, R, Lv, Y, da Silva, B & Ling, M 2026, Equicore: Accelerating Clebsch-Gordan Tensor Product of Equivariant Neural Networks on FPGA. in 2026 Design, Automation & Test in Europe Conference (DATE). IEEExplore, pp. 1-7, 2026 Design, Automation & Test in Europe Conference (DATE), Verona, Italy, 20/04/26. https://doi.org/10.23919/DATE69613.2026.11539429
Tang, S., Zhang, C., Chen, R., Lv, Y., da Silva, B., & Ling, M. (2026). Equicore: Accelerating Clebsch-Gordan Tensor Product of Equivariant Neural Networks on FPGA. In 2026 Design, Automation & Test in Europe Conference (DATE) (pp. 1-7). IEEExplore. https://doi.org/10.23919/DATE69613.2026.11539429
@inproceedings{40c4cb342c654748a9ab6fd477a5decc,
title = "Equicore: Accelerating Clebsch-Gordan Tensor Product of Equivariant Neural Networks on FPGA",
abstract = "Equivariant neural networks (ENNs) are a powerful framework for modeling 3D geometric data in physical and biological systems. The Clebsch–Gordan tensor product (CGTP)—a core operation for preserving equivariance—remains the primary computational bottleneck in ENNs. Although Clebsch–Gordan (CG) coefficients exhibit pronounced structural sparsity, prior work has neither fully leveraged this property nor adopted hardware-friendly quantization, leading to limited efficiency. We present Equicore, a software–hardware co-design framework to accelerate CGTP in ENNs. Equicore introduces three key innovations: (1) a sparse-bypass strategy that exploits the CG structural sparsity together with a novel CG data format to pack the overlapping non-zeros, bypassing redundant data accesses and computations comparing to previous sparse solutions; (2) a merged-shift quantization strategy that enables full Int8 representation of irreps, weights, and CG coefficients using shift-only operations; and (3) a cascaded processing unit that tightly couples the FPGA hardware resources to achieve high operating frequency while supporting efficient sparse and quantized computation. Deployed on a AMD Virtex VCU128 platform, Equicore delivers up to 10.5× speedup and 17.4× energy-efficiency improvement over state-of-the-art GPU libraries and FPGA designs across diverse CGTP types in a benchmark of eleven ENN models. ",
author = "Shidi Tang and Chuanzhao Zhang and Ruiqi Chen and Yuxuan Lv and \{da Silva\}, Bruno and Ming Ling",
year = "2026",
month = jun,
day = "4",
doi = "10.23919/DATE69613.2026.11539429",
language = "English",
isbn = "979-8-3315-4565-9",
pages = "1--7",
booktitle = "2026 Design, Automation \& Test in Europe Conference (DATE)",
publisher = "IEEExplore",
note = " 2026 Design, Automation \& Test in Europe Conference (DATE), DATE ; Conference date: 20-04-2026 Through 22-04-2026",
url = "https://ieeexplore.ieee.org/xpl/conhome/11539023/proceeding",
}