Packet-Loss Robust 3D Gaussian Compression via Atomic Packaging and GNN-based Error Concealment

3D Gaussian Splatting (3DGS) and recent compression schemes such as HAC++ enable high-fidelity real-time neural rendering, but their bitstreams are fragile under packet loss during network streaming. Existing compression methods often separate correlated anchor attributes into independent streams, so losing one packet can create attribute-inconsistent broken anchors and severe rendering artifacts. We propose a packet-loss robust 3DGS transmission and error concealment framework. On the encoder side, anchor-level atomic packaging jointly encapsulates all attributes of each anchor, converting corrupted-attribute failures into clean missing-anchor erasures. Stratified random grouping further disperses packet losses across the spatial domain to avoid large contiguous voids. On the decoder side, we formulate recovery as prior-aware attribute inpainting. A Context-Aware Residual Interpolation (CARI) branch uses hash-grid prior predictions and neighboring residuals to build a robust baseline, while a lightweight two-layer graph neural network with cross-attention over hash-grid priors refines high-frequency attribute residuals. Attribute-wise confidence control falls back to interpolation when learned predictions are unreliable. Experiments under 20 percent random packet loss on BungeeNeRF, Mip-NeRF 360, and Tanks and Temples show that the proposed method substantially improves over no-concealment transmission and limits average PSNR degradation to about 3 dB relative to the lossless HAC++ reference.

Differentially Private Model-X Knockoffs via Johnson-Lindenstrauss Transform

We introduce a novel privatization framework for high-dimensional controlled variable selection. Our framework enables rigorous False Discovery Rate (FDR) control under differential privacy constraints. While the Model-X knockoff procedure provides FDR guarantees by constructing provably exchangeable ``negative control" features, existing privacy mechanisms like Laplace or Gaussian noise injection disrupt its core exchangeability conditions. Our key innovation lies in privatizing the data knockoff matrix through the Gaussian Johnson-Lindenstrauss Transformation (JLT), a dimension reduction technique that simultaneously preserves covariate relationships through approximate isometry for $(\epsilon,\delta)$-differential privacy. We theoretically characterize both FDR and the power of the proposed private variable selection procedure, in an asymptotic regime. Our theoretical analysis characterizes the role of different factors, such as the JLT's dimension reduction ratio, signal-to-noise ratio, differential privacy parameters, sample size and feature dimension, in shaping the privacy-power trade-off. Our analysis is based on a novel `debiasing technique' for high-dimensional private knockoff procedure. We further establish sufficient conditions under which the power of the proposed procedure converges to one. This work bridges two critical paradigms -- knockoff-based FDR control and private data release -- enabling reliable variable selection in sensitive domains. Our analysis demonstrates that structural privacy preservation through random projections outperforms the classical noise addition mechanism, maintaining statistical power even under strict privacy budgets.