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Hardware-friendly compression and hardware acceleration for transformer: A survey


  • Received: 18 June 2022 Accepted: 27 July 2022 Published: 16 August 2022
  • The transformer model has recently been a milestone in artificial intelligence. The algorithm has enhanced the performance of tasks such as Machine Translation and Computer Vision to a level previously unattainable. However, the transformer model has a strong performance but also requires a high amount of memory overhead and enormous computing power. This significantly hinders the deployment of an energy-efficient transformer system. Due to the high parallelism, low latency, and low power consumption of field-programmable gate arrays (FPGAs) and application specific integrated circuits (ASICs), they demonstrate higher energy efficiency than Graphics Processing Units (GPUs) and Central Processing Units (CPUs). Therefore, FPGA and ASIC are widely used to accelerate deep learning algorithms. Several papers have addressed the issue of deploying the Transformer on dedicated hardware for acceleration, but there is a lack of comprehensive studies in this area. Therefore, we summarize the transformer model compression algorithm based on the hardware accelerator and its implementation to provide a comprehensive overview of this research domain. This paper first introduces the transformer model framework and computation process. Secondly, a discussion of hardware-friendly compression algorithms based on self-attention and Transformer is provided, along with a review of a state-of-the-art hardware accelerator framework. Finally, we considered some promising topics in transformer hardware acceleration, such as a high-level design framework and selecting the optimum device using reinforcement learning.

    Citation: Shizhen Huang, Enhao Tang, Shun Li, Xiangzhan Ping, Ruiqi Chen. Hardware-friendly compression and hardware acceleration for transformer: A survey[J]. Electronic Research Archive, 2022, 30(10): 3755-3785. doi: 10.3934/era.2022192

    Related Papers:

  • The transformer model has recently been a milestone in artificial intelligence. The algorithm has enhanced the performance of tasks such as Machine Translation and Computer Vision to a level previously unattainable. However, the transformer model has a strong performance but also requires a high amount of memory overhead and enormous computing power. This significantly hinders the deployment of an energy-efficient transformer system. Due to the high parallelism, low latency, and low power consumption of field-programmable gate arrays (FPGAs) and application specific integrated circuits (ASICs), they demonstrate higher energy efficiency than Graphics Processing Units (GPUs) and Central Processing Units (CPUs). Therefore, FPGA and ASIC are widely used to accelerate deep learning algorithms. Several papers have addressed the issue of deploying the Transformer on dedicated hardware for acceleration, but there is a lack of comprehensive studies in this area. Therefore, we summarize the transformer model compression algorithm based on the hardware accelerator and its implementation to provide a comprehensive overview of this research domain. This paper first introduces the transformer model framework and computation process. Secondly, a discussion of hardware-friendly compression algorithms based on self-attention and Transformer is provided, along with a review of a state-of-the-art hardware accelerator framework. Finally, we considered some promising topics in transformer hardware acceleration, such as a high-level design framework and selecting the optimum device using reinforcement learning.



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    [1] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, et al., Attention is All you Need, in Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017. https://doi.org/10.48550/arXiv.2206.09457
    [2] Q. Wang, B. Li, T. Xiao, J. Zhu, C. Li, D. F. Wong, et al., Learning deep transformer models for machine translation, preprint, arXiv: 1906.01787.
    [3] S. A. Chowdhury, A. Abdelali, K. Darwish, J. Soon-Gyo, J. Salminen, B. J. Jansen, Improving arabic text categorization using transformer training diversification, in Proceedings of the Fifth Arabic Natural Language Processing Workshop (COLING-WANLP), (2020), 226–236. https://aclanthology.org/2020.wanlp-1.21
    [4] X. Ma, P. Zhang, S. Zhang, N. Duan, Y. Hou, M. Zhou, et al., A tensorized transformer for language modeling, preprint, arXiv: 1906.09777.
    [5] J. Devlin, M. W. Chang, K. Lee, K. Toutanova, BERT: Pre-training of deep bidirectional transformers for language understanding, preprint, arXiv: 1810.04805.
    [6] Y. Liu, M. Ott, N. Goyal, J. Du, M. Joshi, D. Chen, et al., RoBERTa: A robustly optimized BERT pretraining approach, preprint, arXiv: 1907.11692.
    [7] H. Xu, B. Liu, L. Shu, P. S. Yu, BERT post-training for review reading comprehension and aspect-based sentiment analysis, preprint, arXiv: 1904.02232.
    [8] P. Shi, J. Lin, Simple BERT models for relation extraction and semantic role labeling, preprint, arXiv: 1904.05255.
    [9] V. Sanh, L. Debut, J. Chaumond, T. Wolf, DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter, preprint, arXiv: 1910.01108.
    [10] Y. Cheng, D. Wang, P. Zhou, T. Zhang, Model compression and acceleration for deep neural networks: The principles, progress, and challenges, IEEE Signal Process. Mag., 35 (2018), 126–136. https://doi.org/10.1109/MSP.2017.2765695 doi: 10.1109/MSP.2017.2765695
    [11] S. Cheng, D. Lucor, J. P. Argaud, Observation data compression for variational assimilation of dynamical systems, J. Comput. Sci., 53 (2021), 101405. https://doi.org/10.1016/j.jocs.2021.101405 doi: 10.1016/j.jocs.2021.101405
    [12] S. Liu, Y. Lin, Z. Zhou, K. Nan, H. Liu, J. Du, On-demand deep model compression for mobile devices: A usage-driven model selection framework, in Proceedings of the 16th Annual International Conference on Mobile Systems, Applications, and Services, (2018), 389–400. https://doi.org/10.1145/3210240.3210337
    [13] S. Liu, J. Du, K. Nan, Z. Zhou, H. Liu, Z. Wang, et al., AdaDeep: A usage-driven, automated deep model compression framework for enabling ubiquitous intelligent mobiles, IEEE Trans. Mob. Comput., 20 (2021), 3282–3297. https://doi.org/10.1109/TMC.2020.2999956 doi: 10.1109/TMC.2020.2999956
    [14] V. L. Tran, S. E. Kim, Efficiency of three advanced data-driven models for predicting axial compression capacity of CFDST columns, Thin-Walled Struct., 152 (2020), 106744. https://doi.org/10.1016/j.tws.2020.106744 doi: 10.1016/j.tws.2020.106744
    [15] Z. X. Hu, Y. Wang, M. F. Ge, J. Liu, Data-driven fault diagnosis method based on compressed sensing and improved multiscale network, IEEE Trans. Ind. Electron., 67 (2020), 3216–3225. https://doi.org/10.1109/TIE.2019.2912763 doi: 10.1109/TIE.2019.2912763
    [16] S. Cheng, I. C. Prentice, Y. Huang, Y. Jin, Y. K. Guo, R. Arcucci, Data-driven surrogate model with latent data assimilation: Application to wildfire forecasting, J. Comput. Phys., 464 (2022). https://doi.org/10.1016/j.jcp.2022.111302
    [17] S. Yang, Z. Zhang, C. Zhao, X. Song, S. Guo, H. Li, CNNPC: End-edge-cloud collaborative CNN inference with joint model partition and compression, IEEE Trans. Parallel Distrib. Syst., (2022), 1–1. https://doi.org/10.1109/TPDS.2022.3177782 doi: 10.1109/TPDS.2022.3177782
    [18] H. He, S. Jin, C. K. Wen, F. Gao, G. Y. Li, Z. Xu, Model-driven deep learning for physical layer communications, IEEE Wireless Commun., 26 (2019), 77–83. https://doi.org/10.1109/MWC.2019.1800447 doi: 10.1109/MWC.2019.1800447
    [19] Z. Liu, M. del Rosario, Z. Ding, A markovian model-driven deep learning framework for massive MIMO CSI feedback, IEEE Trans. Wireless Commun., 21 (2022), 1214–1228. https://doi.org/10.1109/TWC.2021.3103120 doi: 10.1109/TWC.2021.3103120
    [20] W. Wang, F. Wei, L. Dong, H. Bao, N. Yang, M. Zhou, MiniLM: Deep self-attention distillation for task-agnostic compression of pre-trained transformers, preprint, arXiv: 2002.10957.
    [21] X. Jiao, Y. Yin, L. Shang, X. Jiang, X. Chen, L. Li, et al., TinyBERT: Distilling BERT for natural language understanding, preprint, arXiv: 1909.10351.
    [22] S. Sun, Y. Cheng, Z. Gan, J. Liu, Patient knowledge distillation for BERT model compression, preprint, arXiv: 1908.09355.
    [23] H. Touvron, M. Cord, M. Douze, F. Massa, A. Sablayrolles, H. Jegou, Training data-efficient image transformers & distillation through attention, in Proceedings of the 38th International Conference on Machine Learning (ICML), (2021), 10347–10357. https://doi.org/10.48550/arXiv.2012.12877
    [24] P. Michel, O. Levy, G. Neubig, Are sixteen heads really better than one?, Adv. Neural Inf. Process. Syst., preprint, arXiv: 1905.10650.
    [25] M. A. Gordon, K. Duh, N. Andrews, Compressing BERT: Studying the effects of weight pruning on transfer learning, preprint, arXiv: 2002.08307.
    [26] T. Chen, Y. Cheng, Z. Gan, L. Yuan, L. Zhang, Z. Wang, Chasing sparsity in vision transformers: An end-to-end exploration, Adv. Neural Inf. Process. Syst., (2021), 19974–19988. https://doi.org/10.48550/arXiv.2106.04533 doi: 10.48550/arXiv.2106.04533
    [27] T. Chen, J. Frankle, S. Chang, S. Liu, Y. Zhang, Z. Wang, et al., The lottery ticket hypothesis for pre-trained BERT networks, Adv. Neural Inf. Process. Syst., (2020), 15834–15846. https://doi.org/10.48550/arXiv.2007.12223 doi: 10.48550/arXiv.2007.12223
    [28] S. Shen, Z. Dong, J. Ye, L. Ma, Z. Yao, A. Gholami, et al., Q-BERT: Hessian based ultra low precision quantization of BERT, preprint, arXiv: 1909.05840.
    [29] Z. Liu, Y. Wang, K. Han, S. Ma, W. Gao, Post-training quantization for vision transformer, preprint, arXiv: 2106.14156.
    [30] H. Bai, W. Zhang, L. Hou, L. Shang, J. Jin, X. Jiang, et al., BinaryBERT: Pushing the limit of BERT quantization, preprint, arXiv: 2012.15701.
    [31] O. Zafrir, G. Boudoukh, P. Izsak, M. Wasserblat, Q8BERT: Quantized 8Bit BERT, in the 5th Workshop on Energy Efficient Machine Learning and Cognitive Computing-NeurIPS 2019, (2019), 36–39. https://doi.org/10.1109/EMC2-NIPS53020.2019.00016
    [32] Z. Wu, Z. Liu, J. Lin, Y. Lin, S. Han, Lite transformer with long-short range attention, preprint, arXiv: 2004.11886.
    [33] L. Hou, Z. Huang, L. Shang, X. Jiang, X. Chen, Q. Liu, DynaBERT: Dynamic BERT with adaptive width and depth, preprint, arXiv: 2004.04037.
    [34] M. Chen, H. Peng, J. Fu, H. Ling, AutoFormer: Searching transformers for visual recognition, in 2021 IEEE/CVF International Conference on Computer Vision (ICCV), (2021), 12250–12260. https://doi.org/10.1109/ICCV48922.2021.01205
    [35] P. Ganesh, Y. Chen, X. Lou, M. A. Khan, Y. Yang, H. Sajjad, et al., Compressing large-scale transformer-based models: A case study on BERT, Trans. Assoc. Comput. Linguist., 9 (2021), 1061–1080. https://doi.org/10.1162/tacl_a_00413 doi: 10.1162/tacl_a_00413
    [36] S. Hochreiter, J. Schmidhuber, Long short-term memory, Neural Comput., 9 (1997), 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735 doi: 10.1162/neco.1997.9.8.1735
    [37] J. Chung, C. Gulcehre, K. Cho, Y. Bengio, Empirical evaluation of gated recurrent neural networks on sequence modeling, preprint, arXiv: 1412.3555.
    [38] D. Bahdanau, K. Cho, Y. Bengio, Neural machine translation by jointly learning to align and translate, preprint, arXiv: 1409.0473.
    [39] B. Li, S. Pandey, H. Fang, Y. Lyv, J. Li, J. Chen, et al., FTRANS: energy-efficient acceleration of transformers using FPGA, in Proceedings of the ACM/IEEE International Symposium on Low Power Electronics and Design (ISLPED), (2020), 175–180. https://doi.org/10.1145/3370748.3406567
    [40] T. J. Ham, S. J. Jung, S. Kim, Y. H. Oh, Y. Park, Y. Song, et al., A.3: Accelerating attention mechanisms in neural networks with approximation, in 2020 IEEE International Symposium on High Performance Computer Architecture (HPCA), (2020), 328–341. https://doi.org/10.1109/HPCA47549.2020.00035
    [41] T. J. Ham, Y. Lee, S. H. Seo, S. Kim, H. Choi, S. J. Jung, et al., ELSA: Hardware-software co-design for efficient, lightweight self-attention mechanism in neural networks, in 2021 ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA), (2021), 692–705. https://doi.org/10.1109/ISCA52012.2021.00060
    [42] X. Zhang, Y. Wu, P. Zhou, X. Tang, J. Hu, Algorithm-hardware co-design of attention mechanism on FPGA devices, ACM Trans. Embed. Comput. Syst., 20 (2021), 1–24. https://doi.org/10.1145/3477002 doi: 10.1145/3477002
    [43] S. Lu, M. Wang, S. Liang, J. Lin, Z. Wang, Hardware accelerator for multi-head attention and position-wise feed-forward in the transformer, in IEEE International SOC Conference, (2020), 84–89. https://doi.org/10.1109/ISCA52012.2021.00060
    [44] A. Parikh, O. Tä ckströ m, D. Das, J. Uszkoreit, A decomposable attention model for natural language inference, in Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, (2016), 2249–2255. https://doi.org/10.48550/arXiv.1606.01933
    [45] Z. Lin, M. Feng, C. N. dos Santos, M. Yu, B. Xiang, B. Zhou, et al., A structured self-attentive sentence embedding, preprint, arXiv: 1703.03130
    [46] M. S. Charikar, Similarity estimation techniques from rounding algorithms, in Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing, (2002), 380–388. https://doi.org/10.1145/509907.509965
    [47] X. Zhang, F. X. Yu, R. Guo, S. Kumar, S. Wang, S. F. Chang, Fast orthogonal projection based on kronecker product, in 2015 IEEE International Conference on Computer Vision (ICCV), (2015), 2929–2937. https://doi.org/10.1109/ICCV.2015.335
    [48] Y. Gong, S. Kumar, H. A. Rowley, S. Lazebnik, Learning binary codes for high-dimensional data using bilinear projections, in 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2013), 484–491. https://doi.org/10.1109/CVPR.2013.69
    [49] M. Wang, S. Lu, D. Zhu, J. Lin, Z. Wang, A high-speed and low-complexity architecture for softmax function in deep learning, in 2018 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS), (2018), 223–226. https://doi.org/10.1109/APCCAS.2018.8605654
    [50] R. Hu, B. Tian, S. Yin, S. Wei, Efficient hardware architecture of softmax layer in deep neural network, in 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), (2018), 1–5. https://doi.org/10.1109/ICDSP.2018.8631588
    [51] L. Deng, G. Li, S. Han, L. Shi, Y. Xie, Model compression and hardware acceleration for neural networks: A comprehensive survey, Proc. IEEE, 108 (2020), 485–532. https://doi.org/10.1109/JPROC.2020.2976475 doi: 10.1109/JPROC.2020.2976475
    [52] C. Ding, S. Liao, Y. Wang, Z. Li, N. Liu, Y. Zhuo, et al., C ir CNN: Accelerating and compressing deep neural networks using block-circulant weight matrices, in Proceedings of the 50th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO), (2017), 395–408. https://doi.org/10.1145/3123939.3124552
    [53] S. Wang, Z. Li, C. Ding, B. Yuan, Q. Qiu, Y. Wang, et al., C-LSTM: Enabling efficient LSTM using structured compression techniques on FPGAs, in Proceedings of the 2018 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA), (2018), 11–20. https://doi.org/10.1145/3174243.3174253
    [54] L. Zhao, S. Liao, Y. Wang, Z. Li, J. Tang, B. Yuan, Theoretical properties for neural networks with weight matrices of low displacement rank, in Proceedings of the 34th International Conference on Machine Learning (ICML), (2017), 4082–4090. https://doi.org/10.48550/arXiv.1703.00144
    [55] V. Y. Pan, Structured matrices and displacement operators, in Structured Matrices and Polynomials: Unified Superfast Algorithms, Springer Science & Business Media, (2001), 117–153. https://doi.org/10.1007/978-1-4612-0129-8
    [56] J. O. Smith, Mathematics of the discrete fourier transform (DFT): with audio applications, in Mathematics of the Discrete Fourier Transform (DFT): With Audio Applications, Julius Smith, (2007), 115–164. https://ccrma.stanford.edu/~jos/st/
    [57] Z. Liu, G. Li, J. Cheng, Hardware acceleration of fully quantized BERT for efficient natural language processing, in 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE), (2021), 513–516. https://doi.org/10.23919/DATE51398.2021.9474043
    [58] M. Sun, H. Ma, G. Kang, Y. Jiang, T. Chen, X. Ma, et al., VAQF: Fully automatic software-hardware co-design framework for low-bit vision transformer, preprint, arXiv: 2201.06618.
    [59] Z. Liu, Z. Shen, M. Savvides, K. T. Cheng, ReActNet: Towards precise binary neural network with generalized activation functions, in Computer Vision–ECCV 2020 (ECCV), (eds. Vedaldi. A., Bischof. H., Brox. T., Frahm. J.-M.), Cham, Springer International Publishing, (2020), 143–159. https://doi.org/10.1007/978-3-030-58568-6_9
    [60] M. Rastegari, V. Ordonez, J. Redmon, A. Farhadi, XNOR-Net: ImageNet classification using binary convolutional neural networks, in Computer Vision–ECCV 2016 (ECCV), (eds. Leibe. B., Matas. J., Sebe. N., Welling. M.), Cham, Springer International Publishing, (2016), 525–542. https://doi.org/10.1007/978-3-319-46493-0_32
    [61] S. Han, H. Mao, W. J. Dally, Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding, preprint, arXiv: 1510.00149.
    [62] W. Wen, C. Wu, Y. Wang, Y. Chen, H. Li, Learning structured sparsity in deep neural networks, in Advances in Neural Information Processing Systems (NeurIPS), Curran Associates, (2016). https://doi.org/10.48550/arXiv.1608.03665
    [63] X. Ma, F. M. Guo, W. Niu, X. Lin, J. Tang, K. Ma, et al., PCONV: The missing but desirable sparsity in DNN weight pruning for real-time execution on mobile devices, in Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), (2020), 5117–5124. https://doi.org/10.1609/aaai.v34i04.5954
    [64] B. Li, Z. Kong, T. Zhang, J. Li, Z. Li, H. Liu, et al., Efficient transformer-based large scale language representations using hardware-friendly block structured pruning, preprint, arXiv: 2009.08065.
    [65] S. Cao, C. Zhang, Z. Yao, W. Xiao, L. Nie, D. Zhan, et al., Efficient and effective sparse LSTM on FPGA with bank-balanced sparsity, in Proceedings of the 2019 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA), (2019), 63–72. https://doi.org/10.1145/3289602.3293898
    [66] H. Peng, S. Huang, T. Geng, A. Li, W. Jiang, H. Liu, et al., Accelerating transformer-based deep learning models on FPGAs using column balanced block pruning, in 2021 22nd International Symposium on Quality Electronic Design (ISQED), (2021), 142–148. https://doi.org/10.1109/ISQED51717.2021.9424344
    [67] C. Ding, A. Ren, G. Yuan, X. Ma, J. Li, N. Liu, et al., Structured weight matrices-based hardware accelerators in deep neural networks: FPGAs and ASICs, in Proceedings of the 2018 on Great Lakes Symposium on VLSI (GLSVLSI), Chicago, IL, USA, Association for Computing Machinery, (2018), 353–358. https://doi.org/10.1145/3194554.3194625
    [68] S. Narang, E. Undersander, G. Diamos, Block-sparse recurrent neural networks, preprint, arXiv: 1711.02782.
    [69] P. Qi, E. H. M. Sha, Q. Zhuge, H. Peng, S. Huang, Z. Kong, et al., Accelerating framework of transformer by hardware design and model compression co-optimization, in 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD), (2021), 1–9. https://doi.org/10.1109/ICCAD51958.2021.9643586
    [70] P. Qi, Y. Song, H. Peng, S. Huang, Q. Zhuge, E. H. M. Sha, Accommodating transformer onto FPGA: Coupling the balanced model compression and FPGA-implementation optimization, in Proceedings of the 2021 on Great Lakes Symposium on VLSI (GLSVLSI), Virtual Event, USA, Association for Computing Machinery, (2021), 163–168. https://doi.org/10.1145/3453688.3461739
    [71] D. So, Q. Le, C. Liang, The evolved transformer, in Proceedings of the 36th International Conference on Machine Learning (ICML), PMLR, (2019), 5877–5886. https://doi.org/10.48550/arXiv.1901.11117
    [72] H. Wang, Efficient algorithms and hardware for natural language processing, Graduate Theses, Retrieved from the Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/127440.
    [73] H. Sharma, J. Park, N. Suda, L. Lai, B. Chau, V. Chandra, et al., Bit fusion: Bit-Level dynamically composable architecture for accelerating deep neural network, in 2018 ACM/IEEE 45th Annual International Symposium on Computer Architecture (ISCA), (2018), 764–775. https://doi.org/10.1109/ISCA.2018.00069
    [74] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, et al., Templates for the solution of linear systems: Building blocks for iterative methods, in Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Society for Industrial and Applied Mathematics, (1994), 39–55. https://doi.org/10.1137/1.9781611971538
    [75] W. Liu, B. Vinter, CSR5: An efficient storage format for cross-platform sparse matrix-vector multiplication, in Proceedings of the 29th ACM on International Conference on Supercomputing (ICS), Newport Beach, California, USA, Association for Computing Machinery, (2015), 339–350. https://doi.org/10.1145/2751205.2751209
    [76] R. Kannan, Efficient sparse matrix multiple-vector multiplication using a bitmapped format, in 20th Annual International Conference on High Performance Computing (HiPC), (2013), 286–294. https://doi.org/10.1109/HiPC.2013.6799135
    [77] W. Jiang, X. Zhang, E. H. M. Sha, L. Yang, Q. Zhuge, Y. Shi, et al., Accuracy vs. efficiency: achieving both through FPGA-implementation aware neural architecture search, in Proceedings of the 56th Annual Design Automation Conference 2019 (DAC), Las Vegas NV USA, ACM, (2019), 1–6. https://doi.org/10.1145/3316781.3317757
    [78] W. Jiang, E. H. M. Sha, X. Zhang, L. Yang, Q. Zhuge, Y. Shi, et al., Achieving super-linear speedup across multi-FPGA for real-time DNN inference, preprint, arXiv: 1907.08985.
    [79] W. Jiang, X. Zhang, E. H. M. Sha, Q. Zhuge, L. Yang, Y. Shi, et al., XFER: A novel design to achieve super-linear performance on multiple FPGAs for real-time AI, in Proceedings of the 2019 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA), Seaside, CA, USA, Association for Computing Machinery, (2019), 305. https://doi.org/10.1145/3289602.3293988
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