Quantize What Counts: More for Keys, Less for Values
This addresses the inference-time memory efficiency problem for LLM users, offering a significant improvement over heuristic approaches.
The paper tackles the memory bottleneck in Large Language Models caused by the attention Key-Value cache by proposing a theoretically grounded method for mixed-precision quantization, showing that prioritizing bits for keys over values retains up to 98.3% accuracy while conserving memory.
Large Language Models (LLMs) suffer inference-time memory bottlenecks dominated by the attention Key-Value (KV) cache, which scales with model size and context length. While KV-cache quantization alleviates this cost, bit allocation between keys and values is often tuned heuristically, lacking theoretical grounding and generalizability. This paper proposes two theorems that anchor mixed-precision KV quantization in the intrinsic geometry of Transformer models. First, key projections systematically have larger spectral and Frobenius norms than value matrices, implying higher information density along the key path. Second, for any given memory budget, prioritizing precision for keys over values strictly reduces quantization error and better preserves accuracy. Empirical evaluations across various prominent LLMs and benchmarks show that key-favored allocations (e.g., 4-bit keys, 2-bit values) retain up to 98.3\% accuracy compared to uniform allocations (e.g., 4-bit for both), while conserving memory. These results transform bit allocation from ad hoc tuning into a theoretically grounded, geometry-driven design principle for efficient LLM inference. Source code is available at https://github.com/mohsenhariri/spectral-kv.