Look-up Tables

Last Updated 24 June, 2026

by David Spuler, Ph.D.

Look-up tables (LUTs) are a well-known simple data structure for optimizing code. They have been used to optimize neural networks in various ways. Some examples include:

Zero-multiplier networks: Look-up tables have been used instead of multiplication to create Zero-Multiplication Models.
Approximation algorithms. The use of approximations using table lookups also speeds up various non-linear operations; see Approximation Optimizations

Some of the more advanced data structures that extend look-up tables include:

Table Lookup: Book Excerpts and Blog Articles

Free online book excerpts with full text chapters online and free PDF downloads, and the Aussie AI blog, including related articles:

David Spuler, March 2024, Lookup Table Precomputation, in Generative AI in C++, https://www.aussieai.com/book/ch13-lookup-table-precomputation
David Spuler, March 2024, Chapter 13. Algorithm Speedups, in book "Generative AI in C++", https://www.aussieai.com/book/ch13-algorithms
David Spuler, March 2024, Chapter 21. Activation Functions, in book "Generative AI in C++", https://www.aussieai.com/book/ch21-activation-functions
David Spuler, March 2024, Chapter 30. Vectorization, in book "Generative AI in C++", https://www.aussieai.com/book/ch30-vectorization
David Spuler, March 2024, Chapter 35. Lookup Tables & Precomputation, in book "Generative AI in C++", https://www.aussieai.com/book/ch35-lut-precomputation
David Spuler, March 2024, Chapter 51. Zero-Multiplication Models, in book "Generative AI in C++", https://www.aussieai.com/book/ch51-zero-multiplication
David Spuler, March 2024, Generative AI in C++: Coding Transformers and LLMs, https://www.aussieai.com/book/toc PDF: https://www.aussieai.com/pdf/BOOK-Generative-AI-CPP-Spuler-2024.pdf

Research Papers on Lookup Tables (LUTs)

Research papers include:

Zhou, A.; Yao, A.; Guo, Y.; Xu, L.; and Chen, Y., 2017, Incremental network quantization: Towards lossless CNNs with low-precision weight, arXiv preprint arXiv:1702.03044, https://arxiv.org/abs/1702.03044 (bitshifting)
S Fanning, Fixed Point Multiplication-Free Implementation of Deep Neural Networks for Embedded Systems, Masters Thesis, School of Electrical and Electronic Engineering, University College Dublin 2018, https://seanfanning.eu/posts/projects/low-bitwidth-neural-networks/Thesis_SeanFanning_13360951.pdf
Mohammad Samragh Razlighi; Mohsen Imani; Farinaz Koushanfar; Tajana Rosing LookNN: Neural network with no multiplication, Design, Automation & Test in Europe Conference & Exhibition (DATE), 27-31 March 2017, https://ieeexplore.ieee.org/document/7927280 (Lookup-table based multiplication.)
Covell M, Marwood D, Baluja S, Johnston N., Table-based neural units: Fully quantizing networks for multiply-free inference, 2019, arXiv preprint arXiv:1906.04798, http://arxiv.org/abs/1906.04798
E Yvinec, A Dapogny, K Bailly, Sep 2023, Network Memory Footprint Compression Through Jointly Learnable Codebooks and Mappings, arXiv preprint arXiv:2309.17361, https://arxiv.org/abs/2309.17361 (Uses "codebooks", i.e. look-up tables, to reduce memory usage.)
Song Han, Jeff Pool, John Tran, and William Dally, 2015, Learning both weights and connections for efficient neural network, Advances in neural information processing systems, 28, 2015, https://arxiv.org/abs/1506.02626
Gunho Park, Baeseong Park, Minsub Kim, Sungjae Lee, Jeonghoon Kim, Beomseok Kwon, Se Jung Kwon, Byeongwook Kim, Youngjoo Lee, Dongsoo Lee, Apr 2023, LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models https://arxiv.org/abs/2206.09557
Joonsang Yu, Junki Park, Seongmin Park, Minsoo Kim, Sihwa Lee, Dong Hyun Lee, Jungwook Choi, Dec 2021, NN-LUT: Neural Approximation of Non-Linear Operations for Efficient Transformer Inference, https://arxiv.org/pdf/2112.02191
Tae Jun Ham, Sung Jun Jung, Seonghak Kim, Young H Oh, Yeonhong Park, Yoonho Song, Jung-Hun Park, Sanghee Lee, Kyoung Park, Jae W Lee, et al. A^3: Accelerating attention mechanisms in neural networks with approximation. In 2020 IEEE International Symposium on High Performance Computer Architecture (HPCA), pages 328–341. IEEE, 2020. https://arxiv.org/abs/2002.10941
Neelesh Gupta, Narayanan Kannan, Pengmiao Zhang, Viktor Prasanna, 8 Apr 2024, TabConv: Low-Computation CNN Inference via Table Lookups, https://arxiv.org/abs/2404.05872
Darshan C. Ganji, Saad Ashfaq, Ehsan Saboori, Sudhakar Sah, Saptarshi Mitra, MohammadHossein AskariHemmat, Alexander Hoffman, Ahmed Hassanien, Mathieu Léonardon, 18 Apr 2023, DeepGEMM: Accelerated Ultra Low-Precision Inference on CPU Architectures using Lookup Tables, https://arxiv.org/abs/2304.09049
Xiaohu Tang, Yang Wang, Ting Cao, Li Lyna Zhang, Qi Chen, Deng Cai, Yunxin Liu, Mao Yang, 6 Sep 2023 (v2), LUT-NN: Empower Efficient Neural Network Inference with Centroid Learning and Table Lookup, https://arxiv.org/abs/2302.03213
Grigor Gatchev, Valentin Mollov, 4 Apr 2021, Faster Convolution Inference Through Using Pre-Calculated Lookup Tables, https://arxiv.org/abs/2104.01681
NM Ho, DT Nguyen, JL Gustafson, WF Wong, 2023, Bedot: Bit Efficient Dot Product for Deep Generative Models, CoNGA 2023: Next Generation Arithmetic, pp. 19–37, https://link.springer.com/chapter/10.1007/978-3-031-32180-1_2 https://www.comp.nus.edu.sg/~wongwf/papers/CONGA23-Bedot.pdf
David Spuler, March 2024, Chapter 35. Lookup Tables & Precomputation, Generative AI in C++: Coding Transformers and LLMs, https://www.amazon.com/dp/B0CXJKCWX9
H. Bagherinezhad, M. Rastegari, and A. Farhadi. Lcnn: Lookup-based convolutional neural network. arXiv preprint arXiv:1611.06473, 2016, https://arxiv.org/abs/1611.06473
Tianyi Zhang, Jonah Wonkyu Yi, Bowen Yao, Zhaozhuo Xu, Anshumali Shrivastava, 2 Mar 2024, NoMAD-Attention: Efficient LLM Inference on CPUs Through Multiply-add-free Attention, https://arxiv.org/abs/2403.01273 Code: https://github.com/tonyzhang617/nomad-dist (Converts 4-bit vector dot products to using SIMD registers as lookup tables on CPUs.)
Wang, J., Chen, K., Chen, G., Shou, L., McAuley, J.: Skipbert: Efficient inference with shallow layer skipping. In: Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 7287–7301 (2022) https://aclanthology.org/2022.acl-long.503/ (Skips early layers of a model via precomputed lookup tables based on detecting known token n-grams in the prompt.)
Jianyu Wei, Shijie Cao, Ting Cao, Lingxiao Ma, Lei Wang, Yanyong Zhang, Mao Yang, 25 Jun 2024, T-MAC: CPU Renaissance via Table Lookup for Low-Bit LLM Deployment on Edge, https://arxiv.org/abs/2407.00088 Code: https://github.com/microsoft/T-MAC (Table lookup for low-bit quantization on CPUs.)
Han Guo, William Brandon, Radostin Cholakov, Jonathan Ragan-Kelley, Eric P. Xing, Yoon Kim, 15 Jul 2024, Fast Matrix Multiplications for Lookup Table-Quantized LLMs, https://arxiv.org/abs/2407.10960
Beom Jin Kang, Hae In Lee, Seok Kyu Yoon, Young Chan Kim, Sang Beom Jeong, Seong Jun O, Hyun Kim, October 2024, A survey of FPGA and ASIC designs for transformer inference acceleration and optimization, Journal of Systems Architecture, Volume 155, 103247, https://www.sciencedirect.com/science/article/abs/pii/S138376212400184X
Zhiwen Mo, Lei Wang, Jianyu Wei, Zhichen Zeng, Shijie Cao, Lingxiao Ma, Naifeng Jing, Ting Cao, Jilong Xue, Fan Yang, Mao Yang, 12 Aug 2024, LUT Tensor Core: Lookup Table Enables Efficient Low-Bit LLM Inference Acceleration, https://arxiv.org/abs/2408.06003 (Lookup tables for mixed-precision MatMul/GEMM kernels using low-bit quantization mixed with full precision.)
Fangzhou He, Ke Ding, DingjiangYan, Jie Li, Jiajun Wang, Mingzhe Chen, A Novel Quantization and Model Compression Approach for Hardware Accelerators in Edge Computing, https://cdn.techscience.cn/files/cmc/2024/TSP_CMC-80-2/TSP_CMC_53632/TSP_CMC_53632.pdf (Power-of-two quantization with bitshifting further accelerated with LUTs.)
Zachary Susskind 2024, Weightless Neural Networks for Fast, Low-Energy Inference, Ph.D. Dissertation, The University of Texas at Austin, https://zsknd.com/dissertation_final.pdf
J. Li, C. Chen, Z. Cheng and Z. Xiong, 2024, Toward DNN of LUTs: Learning Efficient Image Restoration with Multiple Look-Up Tables, IEEE Transactions on Pattern Analysis and Machine Intelligence, doi: 10.1109/TPAMI.2024.3401048, https://ieeexplore.ieee.org/abstract/document/10530442 Code: https://github.com/ddlee-cn/MuLUT
David Spuler, March 2024, Lookup Table Precomputation, in Generative AI in C++, https://www.aussieai.com/book/ch13-lookup-table-precomputation
SZ Lin, YC Chen, YH Chang, TW Kuo, HP Li, 2024, LUTIN: Efficient Neural Network Inference with Table Lookup, ISLPED ’24, August 5-7, 2024, Newport Beach, CA, USA, https://dl.acm.org/doi/pdf/10.1145/3665314.3670804
Davis Blalock, John Guttag, 21 Jun 2021, Multiplying Matrices Without Multiplying, https://arxiv.org/abs/2106.10860
Q. Deng, Y. Zhang, M. Zhang and J. Yang, "LAcc: Exploiting Lookup Table-based Fast and Accurate Vector Multiplication in DRAM-based CNN Accelerator," 2019 56th ACM/IEEE Design Automation Conference (DAC), Las Vegas, NV, USA, 2019, pp. 1-6. https://ieeexplore.ieee.org/document/8806810 PDF: https://dl.acm.org/doi/pdf/10.1145/3316781.3317845
Yongkweon Jeon, Baeseong Park, Se Jung Kwon, Byeongwook Kim, Jeongin Yun, Dongsoo Lee, 31 Aug 2020 (v2), BiQGEMM: Matrix Multiplication with Lookup Table For Binary-Coding-based Quantized DNNs, https://arxiv.org/abs/2005.09904
Duy-Thanh Nguyen, Abhiroop Bhattacharjee, Abhishek Moitra, Priyadarshini Panda, 9 Feb 2023, DeepCAM: A Fully CAM-based Inference Accelerator with Variable Hash Lengths for Energy-efficient Deep Neural Networks, https://arxiv.org/abs/2302.04712
Jie Ran, Rui Lin, Jason Chun Lok Li, Jiajun Zhou, Ngai Wong, 13 Aug 2022, PECAN: A Product-Quantized Content Addressable Memory Network, https://arxiv.org/abs/2208.13571
S. Nag et al., "LogicNets vs. ULEEN : Comparing two novel high throughput edge ML inference techniques on FPGA," 2024 IEEE 67th International Midwest Symposium on Circuits and Systems (MWSCAS), Springfield, MA, USA, 2024, pp. 1206-1211, doi: 10.1109/MWSCAS60917.2024.10658913. https://ieeexplore.ieee.org/abstract/document/10658913/ (Analyzing two lookup-table methods.)
18 Jan 2025, LUT-DLA: Lookup Table as Efficient Extreme Low-Bit Deep Learning Accelerator, Guoyu Li, Shengyu Ye, Chunyun Chen, Yang Wang, Fan Yang, Ting Cao, Cheng Liu, Mohamed M. Sabry, Mao Yang, https://arxiv.org/abs/2501.10658 (Extremely low-bit quantization below 1-bit (!) with vector quantization to table lookup.)
Hui Wang, Yuan Cheng, Xiaomeng Han, Zhengpeng Zhao, Dawei Yang, Zhe Jiang, 21 Jan 2025, Pushing the Limits of BFP on Narrow Precision LLM Inference, https://arxiv.org/abs/2502.00026
Songhao Wu, Ang Lv, Xiao Feng, Yufei Zhang, Xun Zhang, Guojun Yin, Wei Lin, Rui Yan, 1 Feb 2025, PolarQuant: Leveraging Polar Transformation for Efficient Key Cache Quantization and Decoding Acceleration, https://arxiv.org/abs/2502.00527
Jinheng Wang, Hansong Zhou, Ting Song, Shijie Cao, Yan Xia, Ting Cao, Jianyu Wei, Shuming Ma, Hongyu Wang, Furu Wei, 17 Feb 2025, Bitnet.cpp: Efficient Edge Inference for Ternary LLMs, https://arxiv.org/abs/2502.11880
Gunho Park, Hyeokjun Kwon, Jiwoo Kim, Jeongin Bae, Baeseong Park, Dongsoo Lee, Youngjoo Lee, 10 Mar 2025, FIGLUT: An Energy-Efficient Accelerator Design for FP-INT GEMM Using Look-Up Tables, https://arxiv.org/abs/2503.06862
Zhou, J., Song, K., Lei, B. (2025). Fast Encrypted Image Classification Based on Approximate Matrix Multiplication Without Multiplying. In: Wang, G., Yan, Z., Li, KC., Wu, Y. (eds) Ubiquitous Security. UbiSec 2024. Communications in Computer and Information Science, vol 2469. Springer, Singapore. https://doi.org/10.1007/978-981-96-4836-8_16 https://link.springer.com/chapter/10.1007/978-981-96-4836-8_16
X. Geng, S. Liu, H. Wang, J. Han and H. Jiang, "Lookup Table Refactoring: Towards Efficient Logarithmic Number System Addition for Large Language Models," 2025 Design, Automation & Test in Europe Conference (DATE), Lyon, France, 2025, pp. 1-7, doi: 10.23919/DATE64628.2025.10993215. https://ieeexplore.ieee.org/document/10993215
Zhang, J., Wang, Z., Ma, C. et al. Learning Extensible Series-Parallel Lookup Tables for Efficient Image Super-Resolution. Int J Comput Vis (2025). https://doi.org/10.1007/s11263-025-02516-1 https://link.springer.com/article/10.1007/s11263-025-02516-1
Ye Qiao, Zhiheng Chen, Yifan Zhang, Yian Wang, Sitao Huang, 3 Oct 2025, TeLLMe v2: An Efficient End-to-End Ternary LLM Prefill and Decode Accelerator with Table-Lookup Matmul on Edge FPGAs, https://arxiv.org/abs/2510.15926
Lino Gerlach, Liv V{\aa}ge, Thore Gerlach, Elliott Kauffman, 17 Oct 2025, WARP-LUTs - Walsh-Assisted Relaxation for Probabilistic Look Up Tables, https://arxiv.org/abs/2510.15655
Xin Nie, Liang Dong, HaiCheng Zhang, JiaWang Xiao, G. Sun, 22 Oct 2025, ELUTQ: Efficient LUT-Aware Quantization for Deploying Large Language Models on Edge Devices, https://arxiv.org/abs/2510.19482
Mandar Karhade, MD. PhD. March 2026, DeepSeek’s Engram: The Lookup Table That Eats Transformer Layers: Why a glorified N-gram hash might be the most important architectural idea since Mixture-of-Experts, https://generativeai.pub/deepseeks-engram-the-lookup-table-that-eats-transformer-layers-90b5f6a99a90
Raaida Noor Mahbub 0009-0005-8343-7340, Hani Saleh, and Ghada Alsuhli, Hardware Accelerators for Softmax in Large Language Models: A Survey, 26 February 2026, https://doi.org/10.36227/techrxiv.177208047.71459791/v1 https://www.techrxiv.org/doi/full/10.36227/techrxiv.177208047.71459791/v1 https://www.techrxiv.org/doi/pdf/10.36227/techrxiv.177208047.71459791/v1?onload=true (Survey of Softmax optimization through hardware, approximations, LUTs, numeric representations, Flash Attention, and more.)
Ian W. Kennedy, Nafise Sadat Moosavi, 9 Apr 2026, Initialisation Determines the Basin: Efficient Codebook Optimisation for Extreme LLM Quantization, https://arxiv.org/abs/2604.08118
David Spuler, March 2024, Chapter 13. Algorithm Speedups, in book "Generative AI in C++", https://www.aussieai.com/book/ch13-algorithms
David Spuler, March 2024, Chapter 21. Activation Functions, in book "Generative AI in C++", https://www.aussieai.com/book/ch21-activation-functions
David Spuler, March 2024, Chapter 30. Vectorization, in book "Generative AI in C++", https://www.aussieai.com/book/ch30-vectorization
David Spuler, March 2024, Chapter 35. Lookup Tables & Precomputation, in book "Generative AI in C++", https://www.aussieai.com/book/ch35-lut-precomputation
David Spuler, March 2024, Chapter 51. Zero-Multiplication Models, in book "Generative AI in C++", https://www.aussieai.com/book/ch51-zero-multiplication
David Spuler, March 2024, Generative AI in C++: Coding Transformers and LLMs, https://www.aussieai.com/book/toc PDF: https://www.aussieai.com/pdf/BOOK-Generative-AI-CPP-Spuler-2024.pdf
Weibang Dai, Xiaogang Chen, Houpeng Chen, Sannian Song, Shunfen Li, Tao Hong, and Zhitang Song. 2026. Lookup Table-based Computing: A Survey from Software Implementations to Hardware Architectures. ACM Comput. Surv. 58, 7, Article 184 (May 2026), 34 pages. https://doi.org/10.1145/3779417 https://dl.acm.org/doi/abs/10.1145/3779417 https://dl.acm.org/doi/pdf/10.1145/3779417
F. Merchant, N. Choudhary, S. K. Nandy and R. Narayan, "Efficient Realization of Table Look-Up Based Double Precision Floating Point Arithmetic," 2016 29th International Conference on VLSI Design and 2016 15th International Conference on Embedded Systems (VLSID), Kolkata, India, 2016, pp. 415-420, doi: 10.1109/VLSID.2016.113, https://ieeexplore.ieee.org/abstract/document/7434989