mlsanityData to 7 Oct 2026

Towards the Limit of Network Quantization

arXiv 1612.01543 ↗First posted 5 Dec 2016cs.CV cs.LG cs.NEcited by 49

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Abstract (arXiv)

Network quantization is one of network compression techniques to reduce the redundancy of deep neural networks. It reduces the number of distinct network parameter values by quantization in order to save the storage for them. In this paper, we design network quantization schemes that minimize the performance loss due to quantization given a compression ratio constraint. We analyze the quantitative relation of quantization errors to the neural network loss function and identify that the Hessian-weighted distortion measure is locally the right objective function for the optimization of network quantization. As a result, Hessian-weighted k-means clustering is proposed for clustering network parameters to quantize. When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression, we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative solution similar to Lloyd's algorithm. Finally, using the simple uniform quantization followed by Huffman coding, we show from our experiments that the compression ratios of 51.25, 22.17 and 40.65 are achievable for LeNet, 32-layer ResNet and AlexNet, respectively.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Dec 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 16; 2022: 10; 2023: 6; 2024: 5; 2025: 10; 2026: 2.

49 papers.

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  1. 2021A Survey of Quantization Methods for Efficient Neural Network Inferencecited by 798
  2. 2023SqueezeLLM: Dense-and-Sparse Quantizationcited by 285
  3. 2021Pruning and Quantization for Deep Neural Network Acceleration: A Surveycited by 259
  4. 2022The case for 4-bit precision: k-bit Inference Scaling Lawscited by 247
  5. 2022Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communicationscited by 166
  6. 2022LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Modelscited by 98
  7. 2021Trustworthy AI: A Computational Perspectivecited by 93
  8. 2022PAC-Bayes Compression Bounds So Tight That They Can Explain Generalizationcited by 75
  9. 2021A Survey on Green Deep Learningcited by 52
  10. 2021DKM: Differentiable K-Means Clustering Layer for Neural Network Compressioncited by 31
  11. 2025GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidancecited by 28
  12. 2022It's All In the Teacher: Zero-Shot Quantization Brought Closer to the Teachercited by 20
37 more
  1. 2025The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithmcited by 18
  2. 2021Stealthy Backdoors as Compression Artifactscited by 17
  3. 2021Qu-ANTI-zation: Exploiting Quantization Artifacts for Achieving Adversarial Outcomescited by 16
  4. 2021ECQx: Explainability-Driven Quantization for Low-Bit and Sparse DNNscited by 15
  5. 2022HFedMS: Heterogeneous Federated Learning with Memorable Data Semantics in Industrial Metaversecited by 14
  6. 2022FIT: A Metric for Model Sensitivitycited by 10
  7. 2021Fixed-point Quantization of Convolutional Neural Networks for Quantized Inference on Embedded Platformscited by 7
  8. 2022Mixed-Precision Neural Networks: A Surveycited by 7
  9. 2023On the Opportunities of Green Computing: A Surveycited by 7
  10. 2021Compacting Deep Neural Networks for Internet of Things: Methods and Applicationscited by 6
  11. 2021Training Deep Neural Networks with Joint Quantization and Pruning of Weights and Activationscited by 6
  12. 2021Low-rank Tensor Decomposition for Compression of Convolutional Neural Networks Using Funnel Regularizationcited by 6
  13. 2024Content-Aware Radiance Fields: Aligning Model Complexity with Scene Intricacy Through Learned Bitwidth Quantizationcited by 6
  14. 2023Lossy and Lossless (L2) Post-training Model Size Compressioncited by 4
  15. 2021Model compression as constrained optimization, with application to neural nets. Part V: combining compressionscited by 3
  16. 2024Effect of Weight Quantization on Learning Models by Typical Case Analysiscited by 3
  17. 2025ViM-VQ: Efficient Post-Training Vector Quantization for Visual Mambacited by 3
  18. 2025Binarized Neural Networks Converge Toward Algorithmic Simplicity: Empirical Support for the Learning-as-Compression Hypothesiscited by 3
  19. 2021Universal Approximation Theorems of Fully Connected Binarized Neural Networkscited by 2
  20. 2023Inshrinkerator: Compressing Deep Learning Training Checkpoints via Dynamic Quantizationcited by 2
  21. 2024One-Step Forward and Backtrack: Overcoming Zig-Zagging in Loss-Aware Quantization Trainingcited by 2
  22. 2025MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Networkcited by 2
  23. 2021Multi-Glimpse Network: A Robust and Efficient Classification Architecture based on Recurrent Downsampled Attentioncited by 1
  24. 2023Object Motion Sensitivity: A Bio-inspired Solution to the Ego-motion Problem for Event-based Camerascited by 1
  25. 2023YFlows: Systematic Dataflow Exploration and Code Generation for Efficient Neural Network Inference using SIMD Architectures on CPUscited by 1
  26. 2024Advanced Knowledge Transfer: Refined Feature Distillation for Zero-Shot Quantization in Edge Computingcited by 1
  27. 2025BackSlash: Rate Constrained Optimized Training of Large Language Modelscited by 1
  28. 2025Optimal Formats for Weight Quantisationcited by 1
  29. 2025Deep Learning-Driven Peptide Classification in Biological Nanoporescited by 1
  30. 2021Q-Rater: Non-Convex Optimization for Post-Training Uniform Quantizationcited by 0
  31. 2022A Closer Look at Hardware-Friendly Weight Quantizationcited by 0
  32. 2022Zero-Shot Learning of a Conditional Generative Adversarial Network for Data-Free Network Quantizationcited by 0
  33. 2024TinySeg: Model Optimizing Framework for Image Segmentation on Tiny Embedded Systemscited by 0
  34. 2025A Novel Structure-Agnostic Multi-Objective Approach for Weight-Sharing Compression in Deep Neural Networkscited by 0
  35. 2025AdaVid: Adaptive Video-Language Pretrainingcited by 0
  36. 2026SemKV: Semantic Mixed-Precision KV Cache Quantization Guided by the Quality Cliff for Long-Context LLM Inferencecited by 0
  37. 2026Only What Was Seen: Observation-Gram Compaction of View-Dependent Appearance in 3D Gaussian Splattingcited by 0