Large language models often encounter challenges with static knowledge and hallucinations, which undermine their reliability. Retrieval-augmented generation (RAG) mitigates these issues by incorporating external information. However, user queries frequently contain noise and intent deviations, necessitating query rewriting to improve the relevance of retrieved documents. In this paper, we introduce DMQR-RAG, a Diverse Multi-Query Rewriting framework designed to improve the performance of both document retrieval and final responses in RAG. Specifically, we investigate how queries with varying information quantities can retrieve a diverse array of documents, presenting four rewriting strategies that operate at different levels of information to enhance the performance of baseline approaches. Additionally, we propose an adaptive strategy selection method that minimizes the number of rewrites while optimizing overall performance. Our methods have been rigorously validated through extensive experiments conducted in both academic and industry settings.

Transformers have been the cornerstone of current Large Language Models (LLMs); however, its linear growth in overhead during inference with respect to sequence length poses challenges for modeling long sequences. In this context, Mamba has gradually attracted attention due to its constant-level size during inference and existing empirical results have shown that it can perform comparably to Transformers in sequence modeling while offering significant savings. However, one may ask that, can Mamba always enjoy the "free lunch"? In this paper, we focus on analyzing the expressive ability of Mamba from a theoretical standpoint. First, inspired by the connection between Mamba and linear attention, we investigate potential shortcomings of the Mamba when performing the COPY operation. Our results indicate that Mamba with constant size may encounter bottlenecks when handling COPY, while it can achieve perfect performance when the size scales linearly with sequence length. Based on this observation, we analyze Mamba's ability to tackle DP problems when equipped with Chain of Thought (CoT). Our findings suggest that to solve arbitrary DP problems, the total cost of Mamba is comparable to standard and efficient Transformers. However, similar to efficient Transformers, when facing DP problems with favorable properties such as locality, Mamba can provide savings in overhead. Our results contribute to a deeper understanding of Mamba. Reccently, Transformer-based large language models (LLMs) have become the mainstream of modern neural network architectures due to their outstanding performance across a wide range of tasks (V aswani et al., 2017; Kenton & Toutanova, 2019; Brown et al., 2020; Dosovitskiy et al., 2020; Min et al., 2022). However, the core component of Transformers--the attention layer--while providing excellent performance, also leads to emerging drawbacks: during training, the computational cost scales quadratically with sequence length, and during inference, the cost scales linearly with sequence length. This limitation becomes increasingly unacceptable when dealing with long sequence tasks. To address this issue, many works have attempted to improve the attention mechanism to reduce its time and storage costs (Tay et al., 2023; Choromanski et al., 2020; Katharopoulos et al., 2020; Beltagy et al., 2020; Child et al., 2019). However, these improved structures often achieve efficiency in the attention layer at the expense of some performance.

It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the concerned fairness definition and solve a constrained optimization problem. However, it is intriguing in previous work that such fairness surrogate functions may yield unfair results and high instability. In this work, in order to deeply understand them, taking a widely used fairness definition--demographic parity as an example, we show that there is a surrogate-fairness gap between the fairness definition and the fairness surrogate function. Also, the theoretical analysis and experimental results about the "gap" motivate us that the fairness and stability will be affected by the points far from the decision boundary, which is the large margin points issue investigated in this paper. To address it, we propose the general sigmoid surrogate to simultaneously reduce both the surrogate-fairness gap and the variance, and offer a rigorous fairness and stability upper bound. Interestingly, the theory also provides insights into two important issues that deal with the large margin points as well as obtaining a more balanced dataset are beneficial to fairness and stability. Furthermore, we elaborate a novel and general algorithm called Balanced Surrogate, which iteratively reduces the "gap" to mitigate unfairness. Finally, we provide empirical evidence showing that our methods consistently improve fairness and stability while maintaining accuracy comparable to the baselines in three real-world datasets.