While large language models (LLMs) have achieved remarkable success in various natural language processing tasks, their strengths have yet to be fully demonstrated in grammatical error correction (GEC). This is partly due to the misalignment between their pre-training objectives and the GEC principle of making minimal edits. In this work, we aim to bridge this gap by introducing a novel method called Edit-wise Preference Optimization (EPO). By distinguishing the importance of different tokens and assigning higher reward weights to edit tokens during preference optimization, our method captures fine-grained distinctions in GEC that traditional preference learning often overlooks. Extensive experiments on both English and Chinese datasets show that our framework consistently outperforms strong baselines, achieving state-of-the-art performance and demonstrating the advantages of LLMs in GEC.

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we would like to compute $\frac{1}{n}\sum_{i=1}^{n} f(x_i,y)$ for any query point $y \in \mathbb{R}^d$. Recently, there has been a growing trend of using data structures for efficient KDE. However, the proposed KDE data structures focus on static settings. The robustness of KDE data structures over dynamic changing data distributions is not addressed. In this work, we focus on the dynamic maintenance of KDE data structures with robustness to adversarial queries. Especially, we provide a theoretical framework of KDE data structures. In our framework, the KDE data structures only require subquadratic spaces. Moreover, our data structure supports the dynamic update of the dataset in sublinear time. Furthermore, we can perform adaptive queries with the potential adversary in sublinear time.

Over the last decade, deep neural networks have transformed our society, and they are already widely applied in various machine learning applications. State-of-the-art deep neural networks are becoming larger in size every year to deliver increasing model accuracy, and as a result, model training consumes substantial computing resources and will only consume more in the future. Using current training methods, in each iteration, to process a data point $x \in \mathbb{R}^d$ in a layer, we need to spend $\Theta(md)$ time to evaluate all the $m$ neurons in the layer. This means processing the entire layer takes $\Theta(nmd)$ time for $n$ data points. Recent work [Song, Yang and Zhang, NeurIPS 2021] reduces this time per iteration to $o(nmd)$, but requires exponential time to preprocess either the data or the neural network weights, making it unlikely to have practical usage. In this work, we present a new preprocessing method that simply stores the weight-data correlation in a tree data structure in order to quickly and dynamically detect which neurons fire at each iteration. Our method requires only $O(nmd)$ time in preprocessing and still achieves $o(nmd)$ time per iteration. We complement our new algorithm with a lower bound, proving that assuming a popular conjecture from complexity theory, one could not substantially speed up our algorithm for dynamic detection of firing neurons.