Training and Inference with Integers in Deep Neural Networks
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Abstract (arXiv)
Researches on deep neural networks with discrete parameters and their deployment in embedded systems have been active and promising topics. Although previous works have successfully reduced precision in inference, transferring both training and inference processes to low-bitwidth integers has not been demonstrated simultaneously. In this work, we develop a new method termed as "WAGE" to discretize both training and inference, where weights (W), activations (A), gradients (G) and errors (E) among layers are shifted and linearly constrained to low-bitwidth integers. To perform pure discrete dataflow for fixed-point devices, we further replace batch normalization by a constant scaling layer and simplify other components that are arduous for integer implementation. Improved accuracies can be obtained on multiple datasets, which indicates that WAGE somehow acts as a type of regularization. Empirically, we demonstrate the potential to deploy training in hardware systems such as integer-based deep learning accelerators and neuromorphic chips with comparable accuracy and higher energy efficiency, which is crucial to future AI applications in variable scenarios with transfer and continual learning demands.
Key facts. Cited by 84 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Feb 2018.
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Citing papers per year: 2021: 21; 2022: 15; 2023: 14; 2024: 13; 2025: 12; 2026: 9.
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- 2021Pruning and Quantization for Deep Neural Network Acceleration: A Surveycited by 259
- 2021Understanding and Overcoming the Challenges of Efficient Transformer Quantizationcited by 139
- 2022LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Modelscited by 98
- 2023Training Transformers with 4-bit Integerscited by 58
- 2021A Survey on Green Deep Learningcited by 52
- 2021Differentiable Model Compression via Pseudo Quantization Noisecited by 44
- 2022GACT: Activation Compressed Training for Generic Network Architecturescited by 31
- 2021Distribution Adaptive INT8 Quantization for Training CNNscited by 27
- 2025GSQ-Tuning: Group-Shared Exponents Integer in Fully Quantized Training for LLMs On-Device Fine-tuningcited by 21
- 2022POLICE: Provably Optimal Linear Constraint Enforcement for Deep Neural Networkscited by 19
- 2023Data Quality-aware Mixed-precision Quantization via Hybrid Reinforcement Learningcited by 17
- 2022Low-Precision Stochastic Gradient Langevin Dynamicscited by 12
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- 2026A Target-Centric Survey of Quantization-Aware Training30 Aug 2026
- 2026Latency-Constrained DNN Architecture Learning for Edge Systems using Zerorized Batch Normalization8 Jul 2026
- 2026Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention5 Jul 2026
- 2026Deep Learning Approaches for 3D Medical Scene Completion: From Geometric Modeling to Generative Paradigms23 Jun 2026
- 2026True 4-Bit Quantized Convolutional Neural Network Training on CPU: Achieving Full-Precision Parity14 Mar 2026
- 2026Large-Margin Hyperdimensional Computing: A Learning-Theoretical Perspective4 Mar 2026
- 2026XBTorch: A Unified Framework for Modeling and Co-Design of Crossbar-Based Deep Learning Accelerators11 Jan 2026
- 2025Batch Normalization-Free Fully Integer Quantized Neural Networks via Progressive Tandem Learning18 Dec 2025
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