Open-vocabulary 3D occupancy prediction represents scene geometry and semantics in a unified voxel grid, enabling recognition beyond predefined categories. One approach reconstructs scenes with 3D Gaussians and converts them into voxel occupancy. However, Gaussian scale inflation and excessive overlap can distort voxel occupancy predictions, while semantic mixing can arise within Gaussians spanning multiple categories and during 3D--2D semantic feature alignment. We propose GCSR-OCC, which combines geometry calibration and multi-mode query-conditioned semantic routing for indoor occupancy prediction from a single RGB image. The Evidence-Conserving Gaussian-to-Occupancy operator (EC-G2O) uses kernel mass normalization, $p$-norm aggregation, and a learnable gain to suppress scale inflation and excessive local evidence accumulation while calibrating occupancy responses. Multi-mode Query-First Gaussian Semantic Routing (MM-QGSR) matches multiple semantic modes per Gaussian to text queries and aggregates query-specific evidence into voxels through a learnable text-conditioned router. Fine-grained subclass queries and smoothed semantic aggregation further refine voxel-level predictions. Without 3D semantic annotations, GCSR-OCC achieves state-of-the-art performance in open-vocabulary occupancy prediction on Occ-ScanNet, with 63.31% geometric IoU and 27.44% semantic mIoU. It also reduces geometric aggregation latency from 19.76 ms to 12.88 ms. Our code will be made publicly available.
The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.