Training Quantized Neural Networks to Global Optimality via Semidefinite Programming

2021/05/04 by Burak Bartan, Bartan, Burak, Mert Pilancı +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2105.01420

openalex publication_date 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Neural networks (NNs) have been extremely successful across many tasks in machine learning. Quantization of NN weights has become an important topic due to its impact on their energy efficiency, inference time and deployment on hardware. Although post-training quantization is well-studied, training optimal quantized NNs involves combinatorial non-convex optimization problems which appear intractable. In this work, we introduce a convex optimization strategy to train quantized NNs with polynomial activations. Our method leverages hidden convexity in two-layer neural networks from the recent literature, semidefinite lifting, and Grothendieck's identity. Surprisingly, we show that certain quantized NN problems can be solved to global optimality in polynomial-time in all relevant parameters via semidefinite relaxations. We present numerical examples to illustrate the effectiveness of our method.

Cited by

• The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program

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