Chenghao Li

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.

Seth Farrell, Chenghao Li, Hongzhan Yu et al.

The integration of autonomous mobile robots (AMRs) in industrial environments, particularly warehouses, has revolutionized logistics and operational efficiency. However, ensuring the safety of human workers in dynamic, shared spaces remains a critical challenge. This work proposes a novel methodology that leverages control barrier functions (CBFs) to enhance safety in warehouse navigation. By integrating learning-based CBFs with the Open Robotics Middleware Framework (OpenRMF), the system achieves adaptive and safety-enhanced controls in multi-robot, multi-agent scenarios. Experiments conducted using various robot platforms demonstrate the efficacy of the proposed approach in avoiding static and dynamic obstacles, including human pedestrians. Our experiments evaluate different scenarios in which the number of robots, robot platforms, speed, and number of obstacles are varied, from which we achieve promising performance.

Chenghao Li, Chaoning Zhang, Joseph Cho et al.

Generative AI has made significant progress in recent years, with text-guided content generation being the most practical as it facilitates interaction between human instructions and AI-generated content (AIGC). Thanks to advancements in text-to-image and 3D modeling technologies, like neural radiance field (NeRF), text-to-3D has emerged as a nascent yet highly active research field. Our work conducts a comprehensive survey on this topic and follows up on subsequent research progress in the overall field, aiming to help readers interested in this direction quickly catch up with its rapid development. First, we introduce 3D data representations, including both Structured and non-Structured data. Building on this pre-requisite, we introduce various core technologies to achieve satisfactory text-to-3D results. Additionally, we present mainstream baselines and research directions in recent text-to-3D technology, including fidelity, efficiency, consistency, controllability, diversity, and applicability. Furthermore, we summarize the usage of text-to-3D technology in various applications, including avatar generation, texture generation, scene generation and 3D editing. Finally, we discuss the agenda for the future development of text-to-3D.