Optimal Scalar Quantization for Matrix Multiplication: Closed-Form Density and Phase Transition

1. 1Determine the optimal number of quantization levels for each matrix entry
2. 2Derive the closed-form density for the quantized matrix product
3. 3Analyze the phase transition to minimize the matrix multiplication mean-squared error
4. 4Apply the optimal scalar quantization to matrix multiplication in machine learning models

This research benefits machine learning engineers and researchers working on efficient matrix multiplication algorithms, as it provides a framework for minimizing mean-squared error in quantized matrix multiplication

💡 Closed-form density and phase transition analysis can be used to optimize scalar quantization for matrix multiplication

💡 Optimal scalar quantization for matrix multiplication reduces MSE!