Wei Liu

Dingyu Yao, Chenxu Yang, Zhengyang Tong et al.

The Key-Value (KV) cache introduces substantial memory overhead during large language model (LLM) inference. Although existing vector quantization (VQ) methods reduce KV cache usage and provide flexible representational capacity across bit-widths, they suffer severe performance degradation at ultra-low bit-widths due to key cache outliers that hinder effective codebook utilization. To address this challenge, we propose VecInfer, a novel VQ method for aggressive KV cache compression while enabling efficient inference. By applying smooth and Hadamard transformations, VecInfer suppresses outliers in the key cache, enabling the codebook to comprehensively cover the original data distribution and thereby reducing quantization difficulty. To facilitate efficient deployment, we design an optimized CUDA kernel that fuses computation with dequantization to minimize memory access overhead. Extensive evaluations demonstrate that VecInfer consistently outperforms existing quantization baselines across both long-context understanding and mathematical reasoning tasks. With only 2-bit quantization, VecInfer achieves performance comparable to full precision, while delivering up to $\mathbf{2.7\times}$ speedup in large-batch self-attention computation and $\mathbf{8.3\times}$ reduction in single-batch end-to-end latency on Llama-3.1-8B with a 196k sequence length.

Qi Wu, Shumin Ma, Cheuk Hang Leung et al.

This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size of the ambiguity set, which is often lack of business meaning, through the chance parameters constraining the objective function. We first show that, for general $φ$-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problems. These mean-deviation problems are not subject to uncertain distributions, and the ambiguity radius in the original DRO problem now plays the role of controlling the risk preference of the decision-maker. We then demonstrate that a DRO problem can be cast as a chance-constrained optimization (CCO) problem when a boundedness constraint is added to the decision variables. Without the boundedness constraint, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Thanks to our high-order expansion result, a notable feature of our analysis is that it applies to divergence measures that accommodate well heavy tail distributions such as the student $t$-distribution and the lognormal distribution, besides the widely-used Kullback-Leibler (KL) divergence, which requires the distribution of the objective function to be exponentially bounded. Using the portfolio selection problem as an example, our comprehensive testings on multivariate heavy-tail datasets, both synthetic and real-world, shows that this business-interpretation approach is indeed useful and insightful.