$\text{Log}_\text{b}$Quant: Quantizing Language Models in Logarithmic Space

Quantization has become an invaluable tool to reduce memory requirements and inference speed of modern language models, in particular to make them available for consumer setups and edge devices. While previous work has primarily focused on uniform quantization codebooks, such approaches are prone to suboptimal representations due to low-frequency high-magnitude weights. We introduce Log$_\text{b}$Quant, a novel logarithmic quantization approach with adjustable bases, to adapt to common parameter distributions. We show that our method exhibits superior performance at 4-bit precision on several