Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2508.03730

PILOT-C: Physics-Informed Low-Distortion Optimal Trajectory Compression

Kefei Wu·Baihua Zheng·Weiwei Sun
View original source ↗Read source document ↗Export metadata ↓

Abstract

Location-aware devices continuously generate massive volumes of trajectory data, creating demand for efficient compression. Line simplification is a common solution but typically assumes 2D trajectories and ignores time synchronization and motion continuity. We propose PILOT-C, a novel trajectory compression framework that integrates frequency-domain physics modeling with error-bounded optimization. Unlike existing line simplification methods, PILOT-C supports trajectories in arbitrary dimensions, including 3D, by compressing each spatial axis independently. Evaluated on four real-world datasets, PILOT-C achieves superior performance across multiple dimensions. In terms of compression ratio, PILOT-C outperforms CISED-W, the current state-of-the-art SED-based line simplification algorithm, by an average of 19.2%. For trajectory fidelity, PILOT-C achieves an average of 32.6% reduction in error compared to CISED-W. Additionally, PILOT-C seamlessly extends to three-dimensional trajectories while maintaining the same computational complexity, achieving a 49% improvement in compression ratios over SQUISH-E, the most efficient line simplification algorithm on 3D datasets.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kefei Wu, Baihua Zheng, Weiwei Sun. 2025-07-30. PILOT-C: Physics-Informed Low-Distortion Optimal Trajectory Compression. https://arxiv.org/abs/2508.03730

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Efficient Constrained Graph Search for Post-hoc Error Correction in Binary Classifiers

We introduce a model-agnostic framework for constrained post-hoc error correction in binary classifiers. Given a frozen base classifier, the method searches for an interpretable conjunction of feature--threshold rules that corrects residual false-positive or false-negative errors while explicitly constraining newly introduced errors. The approach combines graph-based search over candidate rule paths, depth-dependent dynamic constraints, and a reduced-histogram procedure for efficient threshold evaluation. Unlike retraining or modifying the base classifier, the learned correction path operates on its predictions and can therefore be applied to arbitrary binary classifiers with suitable input features. Experiments on a large binary-classification problem demonstrate that the method can identify compact correction rules efficiently; for example, one configuration removes 90\% of false positives while sacrificing 5\% of true positives.

cs.LG↗
arXiv2026

Stochastic Bilevel Optimization with Heavy-Tailed Noise

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased stochastic gradient evaluation with heavy-tailed noise, which is prevalent in many machine learning applications, such as training large language models and reinforcement learning. We propose a nested-loop normalized stochastic bilevel approximation (N$^2$SBA) for finding an $ε$-stationary point with the stochastic first-order oracle (SFO) complexity of $\tilde{\mathcal{O}}\big(κ^{\frac{7p-3}{p-1}} σ^{\frac{p}{p-1}} ε^{-\frac{4 p - 2}{p-1}}\big)$, where $κ$ is the condition number, $p\in(1,2]$ is the order of central moment for the noise, and $σ$ is the noise level. Furthermore, we specialize our idea to solve the nonconvex-strongly-concave minimax optimization problem, achieving an $ε$-stationary point with the SFO complexity of~$\tilde{\mathcal O}\big(κ^{\frac{2p-1}{p-1}} σ^{\frac{p}{p-1}} ε^{-\frac{3p-2}{p-1}}\big)$. All the above upper bounds match the best-known results under the special case of the bounded variance setting, i.e., $p=2$. We also conduct the numerical experiments to show the empirical superiority of the proposed methods.

cs.LG↗
arXiv2026

FLAME: Flow Enhanced Legendre Memory Models for General Time Series Forecasting

In this work, we introduce FLAME, a family of extremely lightweight and capable Time Series Foundation Models, which support versatile forecasting tasks via generative probabilistic modeling, while ensuring both efficiency and robustness. FLAME utilizes the Legendre Memory for strong generalization capabilities. By adapting variants of Legendre Memory, i.e., translated Legendre (LegT) and scaled Legendre (LegS), in the Encoding and Decoding phases, FLAME can effectively capture the inherent inductive bias within data and make efficient long-range inferences. To enhance the accuracy of probabilistic forecasting while remaining efficient, FLAME adopts a normalizing-flow-based forecasting head, which can model complex distributions over the forecasting horizon in a generative manner. Comprehensive experiments on three well-recognized benchmarks, including TSFM-Bench, ProbTS, and TFB, demonstrate that FLAME is a strong out-of-the-box tool for decision intelligence.

cs.LG↗