Shiheng Nie | Searcharxiv

arXiv2026

Online Change-Point Detection with Persistent Laplacian Features

Online change-point detection in high-dimensional nonlinear time series faces two challenges. The underlying distributions are difficult to model, and state changes are difficult to characterize. We propose persistent Laplacian cumulative sum (PL-CUSUM) to address these challenges. PL-CUSUM maps delay-embedded sliding windows to point clouds. It extracts persistent Betti vectors and the positive spectra of persistent Laplacians from the same Vietoris-Rips filtration. A ridge-whitened projection converts these features into a scalar score. Page's CUSUM recursion then accumulates this score over time. The positive spectra capture within-scale connectivity and geometric information that persistent Betti vectors do not record. Under a finite-support local model, we prove that the oracle upper bound on detection delay and a local minimax lower bound have the same order. This common order is the logarithm of the average run length constraint divided by the squared ridge-whitened separation. We also establish finite-horizon false-alarm and expected-delay bounds for plug-in whitened scores under weak dependence within each state. The method has two phases. Phase I estimates the projection parameters, selects the feature configuration, and calibrates the control limit. Phase II updates the resulting CUSUM statistic online. Experiments on simulated and real monitoring data show stable false-alarm control and competitive detection performance.

stat.ME↗

arXiv2026

Physical Knot Classification Beyond Accuracy: A Benchmark and Diagnostic Study

Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather than genuine topological understanding. In this work, we introduce dataset (1,440 images, 10 classes), which trains models on loosely tied knots and evaluates them on tightly dressed configurations to probe whether structure-guided training yields topology-specific gains. We demonstrate that topological distance successfully predicts residual inter-class confusion across multiple backbone architectures, validating the utility of our topology-aware evaluation framework. Furthermore, we propose topology-aware centroid alignment (TACA) and an auxiliary crossing-number prediction objective as two complementary forms of structural supervision. Notably, Swin-T with TACA achieves a consistent positive specificity gain (Delta_spec = +1.18 pp) across all random seeds under the canonical protocol, and auxiliary crossing-number prediction exhibits robust performance across data regimes without the real-versus-random reversal observed for centroid alignment. Causal probes reveal that background changes alone flip 17-32% of predictions and phone-photo accuracy drops by 58-69 percentage points, underscoring that appearance bias remains the principal obstacle to deployment. These results collectively demonstrate that our diagnostic workflow provides a principled and practical tool for evaluating whether a hand-crafted structural prior delivers genuine task-relevant benefit beyond generic regularization.

cs.CV↗