A Mean Field Theory of Quantized Deep Networks: The Quantization-Depth Trade-Off

2019/06/03 by Yaniv Blumenfeld, Dar Gilboa, Blumenfeld, Yaniv +3 · 3 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1906.00771

NIPS 2019

openalex publication_date 2019/06/03 · openalex created_date 2019/06/07 · arxiv created 2019/10/31 · arxiv updated 2019/11/01 · openalex updated_date 2026/07/28

Abstract

Reducing the precision of weights and activation functions in neural network training, with minimal impact on performance, is essential for the deployment of these models in resource-constrained environments. We apply mean-field techniques to networks with quantized activations in order to evaluate the degree to which quantization degrades signal propagation at initialization. We derive initialization schemes which maximize signal propagation in such networks and suggest why this is helpful for generalization. Building on these results, we obtain a closed form implicit equation for L_max, the maximal trainable depth (and hence model capacity), given N, the number of quantization levels in the activation function. Solving this equation numerically, we obtain asymptotically: L_max∝ N^1.82.

Citations

• Binarized Neural Networks
• Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations
• MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications
• The High-Dimensional Geometry of Binary Neural Networks
• Training Quantized Nets: A Deeper Understanding
• Deep Neural Networks as Gaussian Processes
• Mixed Precision Training of Convolutional Neural Networks using Integer Operations
• Training Deep Neural Networks with 8-bit Floating Point Numbers
• Understanding deep learning requires rethinking generalization
• Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks

Cited by

• Finite Versus Infinite Neural Networks: an Empirical Study
• Using a thousand optimization tasks to learn hyperparameter search strategies
• Towards NNGP-guided Neural Architecture Search

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