Paul Liu

Paul Liu, Jui-Hsien Wang

Trajectory estimation is a fundamental component of racket sport analytics, as the trajectory contains information not only about the winning and losing of each point, but also how it was won or lost. In sports such as badminton, players benefit from knowing the full 3D trajectory, as the height of shuttlecock or ball provides valuable tactical information. Unfortunately, 3D reconstruction is a notoriously hard problem, and standard trajectory estimators can only track 2D pixel coordinates. In this work, we present the first complete end-to-end system for the extraction and segmentation of 3D shuttle trajectories from monocular badminton videos. Our system integrates badminton domain knowledge such as court dimension, shot placement, physical laws of motion, along with vision-based features such as player poses and shuttle tracking. We find that significant engineering efforts and model improvements are needed to make the overall system robust, and as a by-product of our work, improve state-of-the-art results on court recognition, 2D trajectory estimation, and hit recognition.

Travis Thompson, Seung-Hwan Lim, Paul Liu et al.

Large Language Models (LLMs) have achieved impressive capabilities in language understanding and generation, yet they continue to underperform on knowledge-intensive reasoning tasks due to limited access to structured context and multi-hop information. Retrieval-Augmented Generation (RAG) partially mitigates this by grounding generation in retrieved context, but conventional RAG and GraphRAG methods often fail to capture relational structure across nodes in knowledge graphs. We introduce Inference-Scaled GraphRAG, a novel framework that enhances LLM-based graph reasoning by applying inference-time compute scaling. Our method combines sequential scaling with deep chain-of-thought graph traversal, and parallel scaling with majority voting over sampled trajectories within an interleaved reasoning-execution loop. Experiments on the GRBench benchmark demonstrate that our approach significantly improves multi-hop question answering performance, achieving substantial gains over both traditional GraphRAG and prior graph traversal baselines. These findings suggest that inference-time scaling is a practical and architecture-agnostic solution for structured knowledge reasoning with LLMs

Paul Liu, Jack Spalding-Jamieson, Brandon Zhang et al.

This paper examines the approach taken by team gitastrophe in the CG:SHOP 2021 challenge. The challenge was to find a sequence of simultaneous moves of square robots between two given configurations that minimized either total distance travelled or makespan (total time). Our winning approach has two main components: an initialization phase that finds a good initial solution, and a $k$-opt local search phase which optimizes this solution. This led to a first place finish in the distance category and a third place finish in the makespan category.