Optimal Scalar Quantization for Matrix Multiplication: Closed-Form Density and Phase Transition
📰 ArXiv cs.AI
Optimal scalar quantization for matrix multiplication is achieved through closed-form density and phase transition analysis
Action Steps
- Determine the optimal number of quantization levels for each matrix entry
- Derive the closed-form density for the quantized matrix product
- Analyze the phase transition to minimize the matrix multiplication mean-squared error
- Apply the optimal scalar quantization to matrix multiplication in machine learning models
Who Needs to Know This
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
Key Insight
💡 Closed-form density and phase transition analysis can be used to optimize scalar quantization for matrix multiplication
Share This
💡 Optimal scalar quantization for matrix multiplication reduces MSE!
Key Takeaways
Optimal scalar quantization for matrix multiplication is achieved through closed-form density and phase transition analysis
Full Article
Title: Optimal Scalar Quantization for Matrix Multiplication: Closed-Form Density and Phase Transition
Abstract:
arXiv:2603.19559v1 Announce Type: cross Abstract: We study entrywise scalar quantization of two matrices prior to multiplication. Given $A\in R^{m\times k}$ and $B\in R^{k\times n}$, we quantize entries of $A$ and $B$ independently using scalar quantizers with $K_X$ and $K_Y$ levels per entry, and form $\widehat C=\widehat A\,\widehat B$. The objective is to minimize the matrix multiplication mean-squared error (MSE) $E[\|{AB-\widehat A\widehat B}\|_F^2]$ under a pair-i.i.d.\ inner-product model
Abstract:
arXiv:2603.19559v1 Announce Type: cross Abstract: We study entrywise scalar quantization of two matrices prior to multiplication. Given $A\in R^{m\times k}$ and $B\in R^{k\times n}$, we quantize entries of $A$ and $B$ independently using scalar quantizers with $K_X$ and $K_Y$ levels per entry, and form $\widehat C=\widehat A\,\widehat B$. The objective is to minimize the matrix multiplication mean-squared error (MSE) $E[\|{AB-\widehat A\widehat B}\|_F^2]$ under a pair-i.i.d.\ inner-product model
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