mlsanityData to 14 Oct 2026

Multiplying Matrices Without Multiplying

arXiv 2106.10860 ↗First posted 21 Jun 2021cs.LG cs.AR cs.PFcited by 30

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Abstract (arXiv)

Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm for this task that greatly outperforms existing methods. Experiments using hundreds of matrices from diverse domains show that it often runs 100× faster than exact matrix products and 10× faster than current approximate methods. In the common case that one matrix is known ahead of time, our method also has the interesting property that it requires zero multiply-adds. These results suggest that a mixture of hashing, averaging, and byte shuffling-the core operations of our method-could be a more promising building block for machine learning than the sparsified, factorized, and/or scalar quantized matrix products that have recently been the focus of substantial research and hardware investment.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). Builds on 26 of its 78 references that are in the map. First posted on arXiv 21 Jun 2021.

Builds on

26 of 78 references.

References · 26

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2016Densely Connected Convolutional Networkscited by 6,720
  3. 2016Identity Mappings in Deep Residual Networkscited by 1,965
  4. 2017In-Datacenter Performance Analysis of a Tensor Processing Unitcited by 618
  5. 2020What is the State of Neural Network Pruning?cited by 583
  6. 2016EIE: Efficient Inference Engine on Compressed Deep Neural Networkcited by 295
  7. 2015Compressing Neural Networks with the Hashing Trickcited by 150
  8. 2017SCNN: An Accelerator for Compressed-sparse Convolutional Neural Networkscited by 135
  9. 2019SLIDE : In Defense of Smart Algorithms over Hardware Acceleration for Large-Scale Deep Learning Systemscited by 46
  10. 2015Frequent Directions : Simple and Deterministic Matrix Sketchingcited by 39
  11. 2015Learning to Hash for Indexing Big Data - A Surveycited by 39
  12. 2014Hashing for Similarity Search: A Surveycited by 34
14 more
  1. 2017Polynomial Codes: an Optimal Design for High-Dimensional Coded Matrix Multiplicationcited by 32
  2. 2014Stacked Quantizers for Compositional Vector Compressioncited by 30
  3. 2016Scalable and Sustainable Deep Learning via Randomized Hashingcited by 17
  4. 2018Quicker ADC : Unlocking the hidden potential of Product Quantization with SIMDcited by 14
  5. 2017Accelerated Nearest Neighbor Search with Quick ADCcited by 9
  6. 2017Bolt: Accelerated Data Mining with Fast Vector Compressioncited by 7
  7. 2014Approximate Matrix Multiplication with Application to Linear Embeddingscited by 3
  8. 2016Generalized residual vector quantization for large scale datacited by 2
  9. 2019All Sparse PCA Models Are Wrong, But Some Are Useful. Part I: Computation of Scores, Residuals and Explained Variancecited by 2
  10. 2014Fast Approximate Matrix Multiplication by Solving Linear Systemscited by 1
  11. 2015Improved Practical Matrix Sketching with Guaranteescited by 1
  12. 2015Speeding Up Neural Networks for Large Scale Classification using WTA Hashingcited by 1
  13. 2016Pairwise Quantizationcited by 1
  14. 2016Co-Occuring Directions Sketching for Approximate Matrix Multiplycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 6; 2024: 8; 2025: 5; 2026: 5.

30 papers.

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  1. 2024Extreme Compression of Large Language Models via Additive Quantizationcited by 232
  2. 2021Linear algebra with transformerscited by 63
  3. 2024T-MAC: CPU Renaissance via Table Lookup for Low-Bit LLM Deployment on Edgecited by 55
  4. 2022Compute-Efficient Deep Learning: Algorithmic Trends and Opportunitiescited by 38
  5. 2025Bitnet.cpp: Efficient Edge Inference for Ternary LLMscited by 22
  6. 2023LUT-NN: Empower Efficient Neural Network Inference with Centroid Learning and Table Lookupcited by 20
  7. 2023Channelformer: Attention based Neural Solution for Wireless Channel Estimation and Effective Online Trainingcited by 14
  8. 2024Optimal Quantization for Matrix Multiplicationcited by 14
  9. 2024NoMAD-Attention: Efficient LLM Inference on CPUs Through Multiply-add-free Attentioncited by 12
  10. 2025LUT-DLA: Lookup Table as Efficient Extreme Low-Bit Deep Learning Acceleratorcited by 9
  11. 2022PECAN: A Product-Quantized Content Addressable Memory Networkcited by 6
  12. 2023PQA: Exploring the Potential of Product Quantization in DNN Hardware Accelerationcited by 6
18 more
  1. 2022Memory-Efficient Backpropagation through Large Linear Layerscited by 4
  2. 2022Look-ups are not (yet) all you need for deep learning inferencecited by 4
  3. 2024Accurate Compression of Text-to-Image Diffusion Models via Vector Quantizationcited by 3
  4. 2023A Unified View of Long-Sequence Models towards Modeling Million-Scale Dependenciescited by 2
  5. 2025Pegasus: A Universal Framework for Scalable Deep Learning Inference on the Dataplanecited by 2
  6. 2026EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecturecited by 2
  7. 2022ARM 4-BIT PQ: SIMD-based Acceleration for Approximate Nearest Neighbor Search on ARMcited by 1
  8. 2023Stella Nera: A Differentiable Maddness-Based Hardware Accelerator for Efficient Approximate Matrix Multiplicationcited by 1
  9. 2023Attention, Distillation, and Tabularization: Towards Practical Neural Network-Based Prefetchingcited by 1
  10. 2024TabConv: Low-Computation CNN Inference via Table Lookupscited by 1
  11. 2025Pushing the Envelope of LLM Inference with Ultra-Low-Bit Quantized Modelscited by 1
  12. 2026AXELRAM: Quantize Once, Never Dequantizecited by 1
  13. 2026FASQ: Flexible Accelerated Subspace Quantization for Calibration-Free LLM Compressioncited by 1
  14. 2026Breaking the 1.58-bit Barrier for Ternary LLMscited by 1
  15. 2024Mitigating scalability challenges in LUT-based neural networks via pruning optimisationscited by 0
  16. 2024QoS-Nets: Adaptive Approximate Neural Network Inferencecited by 0
  17. 2025Optimal Approximate Matrix Multiplication over Sliding Windowscited by 0
  18. 2026LeanStream: A Speculate-and-Refine Streaming Framework for Efficient on-Device LLM Inferencecited by 0

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