Neural Networks with Few Multiplications
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Abstract (arXiv)
For most deep learning algorithms training is notoriously time consuming. Since most of the computation in training neural networks is typically spent on floating point multiplications, we investigate an approach to training that eliminates the need for most of these. Our method consists of two parts: First we stochastically binarize weights to convert multiplications involved in computing hidden states to sign changes. Second, while back-propagating error derivatives, in addition to binarizing the weights, we quantize the representations at each layer to convert the remaining multiplications into binary shifts. Experimental results across 3 popular datasets (MNIST, CIFAR10, SVHN) show that this approach not only does not hurt classification performance but can result in even better performance than standard stochastic gradient descent training, paving the way to fast, hardware-friendly training of neural networks.
Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Oct 2015.
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Citing papers per year: 2021: 13; 2022: 16; 2023: 7; 2024: 5; 2025: 5.
46 papers.
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- 2021A Survey of Quantization Methods for Efficient Neural Network Inferencecited by 798
- 2021Pruning and Quantization for Deep Neural Network Acceleration: A Surveycited by 259
- 2021Distributed Learning in Wireless Networks: Recent Progress and Future Challengescited by 125
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- 2022DQ-BART: Efficient Sequence-to-Sequence Model via Joint Distillation and Quantizationcited by 23
- 2021Distance-aware Quantizationcited by 19
- 2022On-device Training: A First Overview on Existing Systemscited by 18
34 more
- 2024EasyQuant: An Efficient Data-free Quantization Algorithm for LLMscited by 17
- 2024PYRA: Parallel Yielding Re-Activation for Training-Inference Efficient Task Adaptationcited by 17
- 2021Binary Complex Neural Network Acceleration on FPGAcited by 14
- 2022SPIQ: Data-Free Per-Channel Static Input Quantizationcited by 12
- 2022Adaptive Low-Precision Training for Embeddings in Click-Through Rate Predictioncited by 11
- 2022MKQ-BERT: Quantized BERT with 4-bits Weights and Activationscited by 10
- 2021S3: Sign-Sparse-Shift Reparametrization for Effective Training of Low-bit Shift Networkscited by 7
- 2021Random matrices in service of ML footprint: ternary random features with no performance losscited by 7
- 2022Mixed-Precision Neural Networks: A Surveycited by 7
- 2025Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applicationscited by 6
- 2021Boosting Binary Masks for Multi-Domain Learning through Affine Transformationscited by 5
- 2021XnODR and XnIDR: Two Accurate and Fast Fully Connected Layers For Convolutional Neural Networkscited by 5
- 2023Distributed Machine Learning for UAV Swarms: Computing, Sensing, and Semanticscited by 5
- 2023Number Systems for Deep Neural Network Architectures: A Surveycited by 4
- 2022MinUn: Accurate ML Inference on Microcontrollerscited by 3
- 2023ATHEENA: A Toolflow for Hardware Early-Exit Network Automationcited by 3
- 2022The Ecological Footprint of Neural Machine Translation Systemscited by 2
- 2022PalQuant: Accelerating High-precision Networks on Low-precision Acceleratorscited by 2
- 2023Ternary Quantization: A Surveycited by 2
- 2023Inshrinkerator: Compressing Deep Learning Training Checkpoints via Dynamic Quantizationcited by 2
- 2024The Impact of Quantization on the Robustness of Transformer-based Text Classifierscited by 2
- 2025Neutralizing Token Aggregation via Information Augmentation for Efficient Test-Time Adaptationcited by 2
- 2021CBP: Backpropagation with constraint on weight precision using a pseudo-Lagrange multiplier methodcited by 1
- 2024Gradient-Free Training of Quantized Neural Networkscited by 1
- 2025BiVM: Accurate Binarized Neural Network for Efficient Video Mattingcited by 1
- 2021Learning Gradual Argumentation Frameworks using Genetic Algorithmscited by 0
- 2022Energy awareness in low precision neural networkscited by 0
- 2022Combinatorial optimization for low bit-width neural networkscited by 0
- 2022Compilation and Optimizations for Efficient Machine Learning on Embedded Systemscited by 0
- 2022Asymptotic Soft Cluster Pruning for Deep Neural Networkscited by 0
- 2023AutoQNN: An End-to-End Framework for Automatically Quantizing Neural Networkscited by 0
- 2023Guaranteed Quantization Error Computation for Neural Network Model Compressioncited by 0
- 2024Evolving Efficient Genetic Encoding for Deep Spiking Neural Networkscited by 0
- 2025HadamRNN: Binary and Sparse Ternary Orthogonal RNNscited by 0
- 2025Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications20 Aug 2025
- 2025Neutralizing Token Aggregation via Information Augmentation for Efficient Test-Time Adaptation5 Aug 2025
- 2025BiVM: Accurate Binarized Neural Network for Efficient Video Matting6 Jul 2025
- 2025HadamRNN: Binary and Sparse Ternary Orthogonal RNNs28 Jan 2025
- 2025Quantization Meets Reasoning: Exploring LLM Low-Bit Quantization Degradation for Mathematical Reasoning6 Jan 2025
- 2024Evolving Efficient Genetic Encoding for Deep Spiking Neural Networks11 Nov 2024
- 2024Gradient-Free Training of Quantized Neural Networks13 Oct 2024
- 2024PYRA: Parallel Yielding Re-Activation for Training-Inference Efficient Task Adaptation14 Mar 2024
- 2024The Impact of Quantization on the Robustness of Transformer-based Text Classifiers8 Mar 2024
- 2024EasyQuant: An Efficient Data-free Quantization Algorithm for LLMs5 Mar 2024
- 2023Number Systems for Deep Neural Network Architectures: A Survey11 Jul 2023
- 2023Inshrinkerator: Compressing Deep Learning Training Checkpoints via Dynamic Quantization20 Jun 2023
34 more
- 2023Guaranteed Quantization Error Computation for Neural Network Model Compression26 Apr 2023
- 2023ATHEENA: A Toolflow for Hardware Early-Exit Network Automation17 Apr 2023
- 2023AutoQNN: An End-to-End Framework for Automatically Quantizing Neural Networks7 Apr 2023
- 2023Ternary Quantization: A Survey2 Mar 2023
- 2023Distributed Machine Learning for UAV Swarms: Computing, Sensing, and Semantics3 Jan 2023
- 2022Adaptive Low-Precision Training for Embeddings in Click-Through Rate Prediction12 Dec 2022
- 2022On-device Training: A First Overview on Existing Systems1 Dec 2022
- 2022MinUn: Accurate ML Inference on Microcontrollers29 Oct 2022
- 2022Mixed-Precision Neural Networks: A Survey11 Aug 2022
- 2022PalQuant: Accelerating High-precision Networks on Low-precision Accelerators3 Aug 2022
- 2022Asymptotic Soft Cluster Pruning for Deep Neural Networks16 Jun 2022
- 2022Compilation and Optimizations for Efficient Machine Learning on Embedded Systems6 Jun 2022
- 2022Combinatorial optimization for low bit-width neural networks4 Jun 2022
- 2022A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classification14 May 2022
- 2022Enable Deep Learning on Mobile Devices: Methods, Systems, and Applications25 Apr 2022
- 2022SPIQ: Data-Free Per-Channel Static Input Quantization28 Mar 2022
- 2022MKQ-BERT: Quantized BERT with 4-bits Weights and Activations25 Mar 2022
- 2022DQ-BART: Efficient Sequence-to-Sequence Model via Joint Distillation and Quantization21 Mar 2022
- 2022Hardware Approximate Techniques for Deep Neural Network Accelerators: A Survey16 Mar 2022
- 2022Energy awareness in low precision neural networks6 Feb 2022
- 2022The Ecological Footprint of Neural Machine Translation Systems4 Feb 2022
- 2021XnODR and XnIDR: Two Accurate and Fast Fully Connected Layers For Convolutional Neural Networks21 Nov 2021
- 2021Edge-Cloud Polarization and Collaboration: A Comprehensive Survey for AI11 Nov 2021
- 2021Applications and Techniques for Fast Machine Learning in Science25 Oct 2021
- 2021CBP: Backpropagation with constraint on weight precision using a pseudo-Lagrange multiplier method6 Oct 2021
- 2021Random matrices in service of ML footprint: ternary random features with no performance loss5 Oct 2021
- 2021Distance-aware Quantization16 Aug 2021
- 2021Binary Complex Neural Network Acceleration on FPGA10 Aug 2021
- 2021S3: Sign-Sparse-Shift Reparametrization for Effective Training of Low-bit Shift Networks7 Jul 2021
- 2021Learning Gradual Argumentation Frameworks using Genetic Algorithms25 Jun 2021
- 2021Distributed Learning in Wireless Networks: Recent Progress and Future Challenges5 Apr 2021
- 2021Boosting Binary Masks for Multi-Domain Learning through Affine Transformations25 Mar 2021
- 2021A Survey of Quantization Methods for Efficient Neural Network Inference25 Mar 2021
- 2021Pruning and Quantization for Deep Neural Network Acceleration: A Survey24 Jan 2021
- 2021A Survey of Quantization Methods for Efficient Neural Network Inferencecited by 798
- 2021Pruning and Quantization for Deep Neural Network Acceleration: A Surveycited by 259
- 2021Distributed Learning in Wireless Networks: Recent Progress and Future Challengescited by 125
- 2022A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classificationcited by 64
- 2022Hardware Approximate Techniques for Deep Neural Network Accelerators: A Surveycited by 39
- 2021Edge-Cloud Polarization and Collaboration: A Comprehensive Survey for AIcited by 38
- 2021Applications and Techniques for Fast Machine Learning in Sciencecited by 32
- 2022Enable Deep Learning on Mobile Devices: Methods, Systems, and Applicationscited by 32
- 2022DQ-BART: Efficient Sequence-to-Sequence Model via Joint Distillation and Quantizationcited by 23
- 2021Distance-aware Quantizationcited by 19
- 2022On-device Training: A First Overview on Existing Systemscited by 18
- 2024EasyQuant: An Efficient Data-free Quantization Algorithm for LLMscited by 17
12 most cited of 45 All 45 (JSON)
- 2025Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications20 Aug 2025
- 2025Neutralizing Token Aggregation via Information Augmentation for Efficient Test-Time Adaptation5 Aug 2025
- 2025BiVM: Accurate Binarized Neural Network for Efficient Video Matting6 Jul 2025
- 2025HadamRNN: Binary and Sparse Ternary Orthogonal RNNs28 Jan 2025
- 2024Evolving Efficient Genetic Encoding for Deep Spiking Neural Networks11 Nov 2024
- 2024Gradient-Free Training of Quantized Neural Networks13 Oct 2024
- 2024PYRA: Parallel Yielding Re-Activation for Training-Inference Efficient Task Adaptation14 Mar 2024
- 2024The Impact of Quantization on the Robustness of Transformer-based Text Classifiers8 Mar 2024
- 2024EasyQuant: An Efficient Data-free Quantization Algorithm for LLMs5 Mar 2024
- 2023Number Systems for Deep Neural Network Architectures: A Survey11 Jul 2023
- 2023Inshrinkerator: Compressing Deep Learning Training Checkpoints via Dynamic Quantization20 Jun 2023
- 2023Guaranteed Quantization Error Computation for Neural Network Model Compression26 Apr 2023
12 newest of 45 All 45 (JSON)