Research Tools & Code·arXiv cs.CL·2d ago

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

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

LogbQuant introduces a logarithmic quantization method that adapts to real weight distributions in language models, addressing a core inefficiency in current 4-bit compression schemes. Unlike uniform quantization approaches that struggle with sparse high-magnitude outliers, this technique uses adjustable bases to match parameter geometry more precisely. The result: competitive or superior accuracy versus asymmetric linear methods at 4-bit precision, with meaningful speedup and memory gains suitable for consumer and edge deployment. This matters because quantization remains the primary lever for making frontier models accessible outside data centers, and distribution-aware compression directly impacts the feasibility of on-device inference.

Modelwire context

Explainer

LogbQuant's key insight is that weight distributions in language models aren't just sparse with outliers, they're geometrically skewed in ways that logarithmic scaling captures better than linear bucketing. The method adapts the quantization base per layer rather than applying a fixed scheme globally, which is a departure from both uniform and asymmetric linear approaches.

This connects directly to the alignment-diversity tradeoff work from early July, which exposed how current layer-importance metrics miss what actually matters during compression. Where that paper argued practitioners need richer sensitivity frameworks, LogbQuant offers a concrete alternative: instead of ranking which layers to compress harder, adapt the compression method itself to each layer's actual parameter geometry. The GSRQ work on KV cache quantization from the same period tackled a related problem (centroid shrinkage in high dimensions), but LogbQuant targets weight quantization rather than activation caching. Together, these suggest the field is moving from one-size-fits-all quantization toward distribution-aware adaptation as the baseline expectation.

If LogbQuant achieves the claimed speedups on consumer hardware (Raspberry Pi, mobile chips) within the next two quarters while maintaining the accuracy margins shown on standard benchmarks like MMLU and GSM8K, the approach has real deployment legs. If the gains narrow or vanish on newer 3-bit schemes, it signals logarithmic scaling is primarily a 4-bit phenomenon.

Coverage we drew on

Beyond Activation Alignment:The Alignment-Diversity Tradeoff in Task-Aware LLM Quantization · arXiv cs.LG

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