3D Gaussian Splatting (3DGS) has emerged as a powerful paradigm for real-time photorealistic novel view synthesis. However, its training-time densification remains largely heuristic, often resulting in redundant Gaussian proliferation and inaccurate geometric reconstruction. Existing methods predominantly rely on first-order screen-space gradients to trigger cloning and splitting, which fail to distinguish true geometric discontinuities from high-frequency textures or noisy residuals. To address this limitation, we propose ACD-GS, an Asymmetric Curvature-aware Densification framework for compact and geometry-aware 3D Gaussian optimization. Our key insight is that second-order depth responses provide a more reliable structural prior for density control, enabling asymmetric regulation of cloning and splitting to better capture geometric discontinuities. Building on this, we introduce a multi-view photometric consistency constraint to suppress transient single-view errors, together with a capacity-aware adaptive regulation strategy that balances densification and pruning during training. Unlike post-hoc compression or quantization-based approaches, ACD-GS directly prevents redundant Gaussian generation during training, yielding inherently compact representations. Extensive experiments demonstrate that our method reduces nearly 60% of Gaussian count and storage while maintaining competitive rendering fidelity, consistently outperforming existing methods across multiple datasets. Our code is available in https://waveviewer.github.io/ACD-GS/.
Generative communication uses transmitted information to control stochastic generation at the receiver. A fundamental question is how much source-specific information must be communicated so that outputs generated at the receiver satisfy prescribed fidelity and reliability requirements while preserving the conditional source distribution. We address this question for sources on compact Riemannian manifolds by developing a generative rate-distortion-perception (GRDP) framework without common randomness. We formulate an asymptotic operational GRDP function under a geodesic distortion radius and a failure-probability constraint, and establish its single-letter characterization through an equivalent informational formulation. Furthermore, for the informational formulation with the high-reliability limit, we derive a geometric lower bound determined by the largest source probability mass of a region with bounded geodesic diameter, together with an upper bound based on probabilistic coverings of the source manifold. Small-radius analysis of the lower bound reveals the roles of intrinsic dimension and scalar curvature in the required communication rate. For uniformly distributed sources on compact homogeneous Riemannian manifolds, we prove that the bounds coincide, yielding an exact characterization of the limiting GRDP function. We further specialize this result to unit spheres, obtaining an explicit expression that relates the minimum communication rate to the geodesic distortion radius and intrinsic dimension, revealing that for the $d$-dimensional unit sphere with $d\ge2$, increasing the communication rate by $d$ bits per source symbol can reduce the distortion radius by more than half.
Benchmark researchers and developers of large language models (LLMs) and other AI systems need to find relevant evaluations, locate their benchmark datasets and code, and understand the settings behind reported scores. We present Benchmark Radar, a living database and search engine for retrieval and discovery of AI benchmarks, covering LLM evaluation, agentic and tool-use benchmarks, coding, reasoning, safety, and domain-specific evaluations. The system combines daily discovery of benchmark papers, repositories, datasets, and releases with a searchable benchmark catalog, mentions in model cards and technical reports, and score histories. It retains source identities and citations so readers can inspect candidate benchmarks and their evaluation evidence. Daily discovery draws on 37 sources: 13 direct connectors and 24 first-party research and engineering feeds. The catalog contains 1,283 source records drawn from 4 benchmark catalogs and 12,916 numeric observations on 790 records. We describe collection and retrieval, audit the full catalog, and examine benchmark saturation, adoption trends, and the limits of score comparisons. A worked example walks through a complete prior-art search, showing how to query the catalog and inspect benchmark evidence when designing a new evaluation. We release the web dashboard with a benchmark leaderboard, a Pareto frontier view of score against measured use, saturation and trend views, daily feeds, downloadable evidence, a command-line interface (CLI) for offline queries, and reproducible analysis.