Puyuan Zhang | Searcharxiv

arXiv2026

G$^2$ARD-GS: Geometry-Guided Anchor-Regularized Gaussian Splatting Distillation

Dense colored LiDAR maps provide accurate city-scale geometry, but lifting them into 3D Gaussian Splatting (3DGS) retains millions of primitives, making the resulting models costly to store, transmit, render, and adapt. Aggressive primitive reduction alleviates this burden, but can remove the local surface support needed for stable novel-view synthesis and downstream geometric use. We introduce G$^2$ARD-GS, a geometry-guided distillation method that converts a dense Gaussian prior instantiated either as a training-free point-cloud lift or a trained GS model into a compact, reusable representation. G$^2$ARD-GS progressively consolidates the prior into surface-aware representatives, then recovers appearance on the resulting fixed topology under construction-time anchor constraints, with no primitives added or removed during recovery. Under limited supervision, geometry-aware view selection allocates the available view budget. On MatrixCity, G$^2$ARD-GS achieves the best PSNR, SSIM, and LPIPS across matched $5\times$--$30\times$ compression budgets, outperforming PUP by $3.2$--$6.8$,dB in PSNR. When reused as frozen geometry, the compact model improves off-trajectory appearance adaptation by $3.7$--$4.9$,dB over PUP 3D-GS and preserves image-to-model registration accuracy on Cambridge KingsCollege at $30\times$ compression. Project page: https://patrick1159.github.io/gardGS-page/.

cs.CV↗

arXiv2026

StanBKT: Rethinking Parameter Estimation in Bayesian Knowledge Tracing

Bayesian Knowledge Tracing (BKT) is a widely used and interpretable student modeling approach in intelligent tutoring systems and educational data mining. However, most implementations rely on expectation-maximization or related optimization methods that yield only point estimates, limiting uncertainty quantification and principled comparisons across learners and conditions. We introduce StanBKT, an open-source Python package for estimating BKT models using Bayesian inference in Stan. StanBKT provides a unified framework supporting Hamiltonian Monte Carlo, variational inference, Pathfinder, and optimization-based estimation while preserving the hidden Markov structure and interpretability of classical BKT. It supports standard, grouped, and hierarchical BKT models, flexible prior specification, posterior predictive inference, and utilities for visualization and diagnostics. We evaluate StanBKT on large-scale observational and controlled educational datasets. On the ASSISTments 2020 dataset, we show that supported inference methods achieve comparable predictive performance while differing in computational efficiency and posterior fidelity. We further demonstrate how posterior inference enables principled comparison of condition-specific parameters in an educational intervention involving perceptual cue manipulations. Results illustrate how uncertainty quantification facilitates more reliable interpretation of differences in learning, forgetting, guessing, and slipping parameters across experimental conditions. Overall, StanBKT extends BKT beyond point estimation by providing a flexible framework for probabilistic student modeling, uncertainty quantification, and hierarchical inference in educational data mining.

cs.HC↗