Spectral clustering methods have gained widespread recognition for their
effectiveness in clustering high-dimensional data. Among these techniques,
constrained spectral clustering has emerged as a prominent approach,
demonstrating enhanced performance by integrating pairwise constraints.
However, the application of such constraints to semidefinite spectral
clustering, a variant that leverages semidefinite programming to optimize
clustering objectives, remains largely unexplored. In this paper, we introduce
a novel framework for seamlessly integrating pairwise constraints into
semidefinite spectral clustering. Our methodology systematically extends the
capabilities of semidefinite spectral clustering to capture complex data
structures, thereby addressing real-world clustering challenges more
effectively. Additionally, we extend this framework to encompass both active
and self-taught learning scenarios, further enhancing its versatility and
applicability. Empirical studies conducted on well-known datasets demonstrate
the superiority of our proposed framework over existing spectral clustering
methods, showcasing its robustness and scalability across diverse datasets and
learning settings. By bridging the gap between constrained learning and
semidefinite spectral clustering, our work contributes to the advancement of
spectral clustering techniques, offering researchers and practitioners a
versatile tool for addressing complex clustering challenges in various
real-world applications. Access to the data, code, and experimental results is
provided for further exploration (this https URL).

我们引入了一种能够很好地将约束引入到半定谱聚类的新框架，通过扩展半定谱聚类的能力来捕捉复杂的数据结构，以更有效地解决现实世界中的聚类挑战。此框架在各种真实数据集和学习场景中展示了超越现有光谱聚类方法的优越性，为处理复杂聚类问题提供了一种多功能工具。

凸约束下的谱聚类

Spectral Clustering in Convex and Constrained Settings

Large language models (LLMs) have made significant progress in code
generation tasks, but their performance in tackling programming problems with
complex data structures and algorithms remains suboptimal. To address this
issue, we propose an in-context learning approach that guides LLMs to debug by
using a "print debugging" method, which involves inserting print statements to
trace and analysing logs for fixing the bug. We collect a Leetcode problem
dataset and evaluate our method using the Leetcode online judging system.
Experiments with GPT-4 demonstrate the effectiveness of our approach,
outperforming rubber duck debugging in easy and medium-level Leetcode problems
by 1.5% and 17.9%.

通过在上下文中学习的方法，引导大型语言模型使用 “print debugging” 方法进行调试，其中包括插入打印语句以跟踪和分析日志，以解决编程问题中复杂的数据结构和算法的性能问题。在 Leetcode 问题数据集上的实验表明，我们的方法在易和中等难度的 Leetcode 问题中比橡皮鸭调试提高了 1.5% 和 17.9%。

利用打印调试提升大型语言模型代码生成

Leveraging Print Debugging to Improve Code Generation in Large Language  Models

In recent years, several models have improved the capacity to generate
synthetic tabular datasets. However, such models focus on synthesizing simple
columnar tables and are not useable on real-life data with complex structures.
This paper puts forward a generic framework to synthesize more complex data
structures with composite and nested types. It then proposes one practical
implementation, built with causal transformers, for struct (mappings of types)
and lists (repeated instances of a type). The results on standard benchmark
datasets show that such implementation consistently outperforms current
state-of-the-art models both in terms of machine learning utility and
statistical similarity. Moreover, it shows very strong results on two complex
hierarchical datasets with multiple nesting and sparse data, that were
previously out of reach.

这篇论文提出了一种通用框架来合成更复杂的数据结构，其中包括复合和嵌套类型，并通过因果变换器构建了一种实际的解决方案，用于结构（类型映射）和列表（类型的重复实例），在标准基准数据集上的结果表明，这种方式的实现在机器学习实用性和统计相似性方面均明显优于当前最先进的模型，并且对于以前无法解决的具有多重嵌套和稀疏数据的两个复杂层次数据集表现出非常强的结果。