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Shuo Shang

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Data Structures and Algorithms Computation and Language Databases

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preprint2026arXiv

Hint Tuning: Less Data Makes Better Reasoners

Large reasoning models achieve high accuracy through extended chain-of-thought but generate 5--8 more tokens than necessary, applying verbose reasoning uniformly regardless of problem difficulty. We propose Hint Tuning, a data-efficient approach that teaches models to calibrate reasoning depth. Our key insight: the corresponding instruct model serves as an ideal difficulty probe. By testing what the instruct model can solve with varying guidance, we automatically construct training data across three states: No-Hint (direct answer), Sparse-Hint (minimal prefix), and Full-Hint (complete reasoning). This converts the abstract challenge of difficulty labeling into a measurable consistency check between the instruct and reasoning models. With only 1K self-annotated samples, Hint Tuning achieves 24--66% token reduction (31.5% average) across mainstream reasoning models (Qwen3-Thinking, DeepSeek-R1-Distill) at multiple scales (4B--32B) while maintaining competitive accuracy on five benchmarks. Unlike methods requiring massive distillation datasets or expensive RL, we achieve superior efficiency through simple alignment with the instruct model's capabilities.

preprint2016arXiv

A Novel Framework for Online Amnesic Trajectory Compression in Resource-constrained Environments

State-of-the-art trajectory compression methods usually involve high space-time complexity or yield unsatisfactory compression rates, leading to rapid exhaustion of memory, computation, storage and energy resources. Their ability is commonly limited when operating in a resource-constrained environment especially when the data volume (even when compressed) far exceeds the storage limit. Hence we propose a novel online framework for error-bounded trajectory compression and ageing called the Amnesic Bounded Quadrant System (ABQS), whose core is the Bounded Quadrant System (BQS) algorithm family that includes a normal version (BQS), Fast version (FBQS), and a Progressive version (PBQS). ABQS intelligently manages a given storage and compresses the trajectories with different error tolerances subject to their ages. In the experiments, we conduct comprehensive evaluations for the BQS algorithm family and the ABQS framework. Using empirical GPS traces from flying foxes and cars, and synthetic data from simulation, we demonstrate the effectiveness of the standalone BQS algorithms in significantly reducing the time and space complexity of trajectory compression, while greatly improving the compression rates of the state-of-the-art algorithms (up to 45%). We also show that the operational time of the target resource-constrained hardware platform can be prolonged by up to 41%. We then verify that with ABQS, given data volumes that are far greater than storage space, ABQS is able to achieve 15 to 400 times smaller errors than the baselines. We also show that the algorithm is robust to extreme trajectory shapes.

preprint2014arXiv

Bounded Quadrant System: Error-bounded Trajectory Compression on the Go

Long-term location tracking, where trajectory compression is commonly used, has gained high interest for many applications in transport, ecology, and wearable computing. However, state-of-the-art compression methods involve high space-time complexity or achieve unsatisfactory compression rate, leading to rapid exhaustion of memory, computation, storage and energy resources. We propose a novel online algorithm for error-bounded trajectory compression called the Bounded Quadrant System (BQS), which compresses trajectories with extremely small costs in space and time using convex-hulls. In this algorithm, we build a virtual coordinate system centered at a start point, and establish a rectangular bounding box as well as two bounding lines in each of its quadrants. In each quadrant, the points to be assessed are bounded by the convex-hull formed by the box and lines. Various compression error-bounds are therefore derived to quickly draw compression decisions without expensive error computations. In addition, we also propose a light version of the BQS version that achieves $\mathcal{O}(1)$ complexity in both time and space for processing each point to suit the most constrained computation environments. Furthermore, we briefly demonstrate how this algorithm can be naturally extended to the 3-D case. Using empirical GPS traces from flying foxes, cars and simulation, we demonstrate the effectiveness of our algorithm in significantly reducing the time and space complexity of trajectory compression, while greatly improving the compression rates of the state-of-the-art algorithms (up to 47%). We then show that with this algorithm, the operational time of the target resource-constrained hardware platform can be prolonged by up to 41%.