Training Quantized Neural Networks to Global Optimality via Semidefinite Programming

TL;DR

This paper introduces a convex optimization approach using semidefinite programming to train quantized neural networks to global optimality, overcoming the non-convexity challenge in quantized NN training.

Contribution

It presents a novel polynomial-time semidefinite relaxation method for training quantized neural networks to global optimality, leveraging recent convexity results.

Findings

Certain quantized NN problems can be solved to global optimality in polynomial time.

Numerical examples demonstrate the effectiveness of the proposed method.

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.