Xi Luo

Dingzirui Wang, Xuanliang Zhang, Rongyu Cao et al.

Generating and voting multiple answers is an effective method to mitigate reasoning inconsistencies of large language models (LLMs). Prior works have shown that multiple reasoning formats outperform a single format when generating multiple answers. However, previous works using multiple formats rely on formats labeled by humans, which could be unsuitable for all tasks and have high labeling costs. To address this issue, we adapt suitable formats to the given tasks by generating and selecting formats. We first propose how to measure the reasoning error when generating multiple answers. Then, we introduce Format-Adapter, which utilizes LLMs to generate and select suitable reasoning formats by minimizing the error measurement we present. We conduct experiments on math and commonsense reasoning tasks, where Format-Adapter achieves a 4.3% performance improvement on average over previous works, demonstrating the effectiveness.

Weidong Liu, Xi Luo

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.