Yi Lu

Chenghao Li, Chaoning Zhang, Yi Lu et al.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Chenghao Li, Chaoning Zhang, Boheng Zeng et al.

Attention mechanisms have significantly advanced visual models by capturing global context effectively. However, their reliance on large-scale datasets and substantial computational resources poses challenges in data-scarce and resource-constrained scenarios. Moreover, traditional self-attention mechanisms lack inherent spatial inductive biases, making them suboptimal for modeling local features critical to tasks involving smaller datasets. In this work, we introduce Large Kernel Convolutional Attention (LKCA), a novel formulation that reinterprets attention operations as a single large-kernel convolution. This design unifies the strengths of convolutional architectures locality and translation invariance with the global context modeling capabilities of self-attention. By embedding these properties into a computationally efficient framework, LKCA addresses key limitations of traditional attention mechanisms. The proposed LKCA achieves competitive performance across various visual tasks, particularly in data-constrained settings. Experimental results on CIFAR-10, CIFAR-100, SVHN, and Tiny-ImageNet demonstrate its ability to excel in image classification, outperforming conventional attention mechanisms and vision transformers in compact model settings. These findings highlight the effectiveness of LKCA in bridging local and global feature modeling, offering a practical and robust solution for real-world applications with limited data and resources.

Yi Lu, Aifan Ling, Chaoqun Wang et al.

In recent years, China's bond market has seen a surge in defaults amid regulatory reforms and macroeconomic volatility. Traditional machine learning models struggle to capture financial data's irregularity and temporal dependencies, while most deep learning models lack interpretability-critical for financial decision-making. To tackle these issues, we propose EMDLOT (Explainable Multimodal Deep Learning for Time-series), a novel framework for multi-class bond default prediction. EMDLOT integrates numerical time-series (financial/macroeconomic indicators) and unstructured textual data (bond prospectuses), uses Time-Aware LSTM to handle irregular sequences, and adopts soft clustering and multi-level attention to boost interpretability. Experiments on 1994 Chinese firms (2015-2024) show EMDLOT outperforms traditional (e.g., XGBoost) and deep learning (e.g., LSTM) benchmarks in recall, F1-score, and mAP, especially in identifying default/extended firms. Ablation studies validate each component's value, and attention analyses reveal economically intuitive default drivers. This work provides a practical tool and a trustworthy framework for transparent financial risk modeling.