Training Quantized Neural Networks to Global Optimality via Semidefinite Programming
This provides a method for training optimal quantized neural networks, which is important for energy efficiency and hardware deployment, though it appears incremental as it builds on existing convexity results.
The paper tackles the combinatorial non-convex optimization problem of training quantized neural networks by introducing a convex optimization strategy using semidefinite programming, showing that certain quantized NN problems can be solved to global optimality in polynomial time.
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.