LocusGS: Spatially Grounded Tokens for Feed-Forward 3D Gaussian Splatting

Abstract: Recent query-based feed-forward 3DGS methods represent a scene using learnable queries, each aggregating multi-view evidence and decoding a group of Gaussians. Ideally, different queries should specialize in coherent local regions of the scene. However, we observe that Gaussians decoded from the same query often scatter across distant scene regions, resulting in weak query-level spatial coherence and poor alignment with the scene structure. We attribute this behavior to the purely latent representation of existing Gaussian queries. To address this limitation, we introduce LocusGS, which augments each Gaussian query with a 3D anchor state consisting of a center and a support radius. The anchor state is progressively refined across decoder layers and is used throughout query interaction, multi-view feature aggregation, and Gaussian generation. Specifically, an anchor-to-ray geometric bias guides each query toward spatially relevant image observations, while anchor-centered decoding organizes its Gaussians within a local region. Experiments on novel view synthesis benchmarks show that LocusGS improves rendering quality over query-based Gaussian token baselines under the same Gaussian budget. Further analysis shows that the learned anchors form coherent spatial layouts and lead to more structured Gaussian distributions, demonstrating that explicit anchor states improve the spatial organization. Our project page: https://leo-frank.github.io/LocusGS_viewer.

• The paper introduces explicit 3D anchor centers and adaptive support radii that guide self-attention, ray-based cross-attention, and Gaussian decoding for spatially coherent reconstruction.
• LocusGS improves TokenGS at matched budgets, reaching 28.89 PSNR and 0.916 SSIM on RealEstate10K with 262K Gaussians, while achieving 25.78 PSNR on six-view DL3DV.
• The method reduces token-level Gaussian dispersion from 5.12 to 0.20 on RealEstate10K and demonstrates that anchor-centered decoding and geometric attention are the most important components in ablation studies.

LocusGS addresses a structural weakness in query-based feed-forward 3D Gaussian Splatting (3DGS): the Gaussian tokens used by methods such as TokenGS are purely latent embeddings with no explicit notion of where they operate in 3D space. The authors observe that Gaussians decoded from a single token frequently scatter across distant scene regions, producing weak query-level spatial coherence and poor alignment with scene geometry. Their diagnosis is that a latent query specifies neither its 3D location nor the extent of its spatial responsibility, so neither the multi-view evidence it aggregates nor the Gaussians it decodes is constrained to a coherent local region (2608.12825).

Explicit anchor states

The proposed remedy is to augment each of the $N$ learnable Gaussian queries with an explicit 3D anchor state $\mathbf{a}_i^l = (\boldsymbol{\mu}_i^l, r_i^l)$, consisting of a center and a scalar support radius. The radius is parameterized through softplus over an unconstrained variable to guarantee positivity, and both components are initialized as learnable parameters shared across scenes. The anchor state is progressively refined layer by layer: after each decoder block, lightweight heads predict residual updates to the center and radius from the updated token feature.

The anchors influence three stages of decoding:

• Anchor-aware self-attention: an MLP-encoded positional embedding derived from the current anchor center is added to each token feature before self-attention, so token-to-token interactions depend on 3D location rather than content alone.
• Anchor-to-ray geometric bias in cross-attention: for each image token with Plücker ray $\boldsymbol{\ell}_j$, a bias $$b_{ij}^l = -\tfrac{1}{2}\left(D(\boldsymbol{\mu}_i^l, \boldsymbol{\ell}_j)/(\sigma_0 r_i^l)\right)^2$$ is added to the content-based attention logits, scaled by a learnable non-negative factor $\gamma$. The point-to-ray distance is computed exactly from normalized Plücker coordinates, and the bias is clamped to $[-20, 0]$ for stability. The support radius modulates the bandwidth: larger radii yield smoother, less selective geometric priors.
• Anchor-centered Gaussian decoding: each token decodes $K = 64$ local offsets, and Gaussian centers are formed as $$\boldsymbol{\mu}_{i,k}^{G} = \boldsymbol{\mu}_i^{L} + r_i^{L}\boldsymbol{\delta}_{i,k}$$, tying every primitive to its token's final anchor position and support scale.

Training follows TokenGS's rendering objective (MSE plus SSIM loss with visibility regularization), extended to supervise intermediate decoder layers and applied to both decoded Gaussian centers and anchor centers. Supervising layers {6, 12} outperforms final-layer-only supervision (24.28 vs. 23.55 PSNR on DL3DV) and slightly beats a denser four-layer schedule, indicating that middle-layer supervision suffices.

Quantitative results

On RealEstate10K two-view reconstruction at $256\times256$, LocusGS improves over TokenGS at matched budgets. The 1024-token variant reaches 28.50 PSNR / 0.909 SSIM / 0.135 LPIPS versus TokenGS's 28.02 / 0.896 / 0.147 — notably surpassing GS-LRM in PSNR and SSIM while using only half the Gaussians (66K vs. 131K). The 4096-token variant achieves the best PSNR (28.89) and SSIM (0.916) among all compared methods at 262K Gaussians.

On DL3DV, trained with four views and evaluated at 2/4/6 views at $448\times256$, LocusGS consistently outperforms TokenGS under identical Gaussian counts and generalizes to unseen context lengths. At six input views it attains 25.78 PSNR / 0.836 SSIM, exceeding DepthSplat's PSNR while maintaining a fixed view-count-independent budget of 262K Gaussians, whereas pixel-aligned baselines scale their budgets with view count (688K at six views). This confirms that the fixed-budget property of query-based prediction is preserved without sacrificing reconstruction quality.

Setting	Method	PSNR	SSIM	LPIPS	#GS
RE10K, 2 views	TokenGS (4096 tok)	28.41	0.903	0.135	262K
	LocusGS (4096 tok)	28.89	0.916	0.124	262K
DL3DV, 4 views	TokenGS (4096 tok)	23.44	0.757	0.312	262K
	LocusGS (4096 tok)	24.80	0.812	0.248	262K
DL3DV, 6 views	TokenGS (4096 tok)	24.16	0.770	0.296	262K
	LocusGS (4096 tok)	25.78	0.836	0.225	262K

The cost of these gains is modest but nonzero: parameter count grows from 222.0M to 241.5M and pure forward latency on an A100 increases from 341 ms to 407 ms per sample relative to TokenGS.

Spatial organization and interpretability

Beyond rendering metrics, the paper quantifies token-level Gaussian dispersion via the mean distance of each token's decoded centers from their centroid. On RE10K, LocusGS reduces mean dispersion from 5.12 to 0.20; on DL3DV, from 0.59 to 0.04. This order-of-magnitude reduction indicates that explicit anchoring successfully converts diffuse token-associated Gaussian clouds into compact local groups — the central claim of the paper, supported directly by measurement rather than only by visualization.

Qualitative analyses reinforce this picture. Projected anchors form a coarse spatial scaffold covering main scene structures, with adaptive placement concentrated around informative regions; learned radii are larger in sparse or weakly constrained areas and smaller around detailed structures. Cross-attention maps become localized and view-consistent around projected anchor positions, and decomposing attention into content and geometry terms shows that the geometry branch supplies a localized prior that disambiguates appearance-driven responses. Self-attention visualizations reveal sparse information-exchange neighborhoods among anchors rather than uniform interaction. Training curves additionally show faster convergence and higher train/validation PSNR than TokenGS, suggesting the anchor-guided formulation also provides a better-conditioned optimization path.

Ablations

Component ablations on DL3DV (4 views, base model) identify which parts of the design matter most. Removing the radius state costs 0.64 PSNR; keeping it static costs 0.31. Replacing anchor-aware self-attention with content-only self-attention costs 0.11. Removing the cross-attention geometric bias entirely is more damaging (−1.53 PSNR), and the radius-adaptive bias outperforms a center-only variant by 0.51 PSNR. The largest drop comes from predicting Gaussian centers freely instead of as radius-scaled offsets around the anchor: −2.21 PSNR and a large LPIPS degradation (0.397 vs. 0.271). Anchor-centered decoding is therefore the single most important component, followed by the geometric attention bias — consistent with the paper's thesis that grounding must extend through to Gaussian generation, not merely feature aggregation.

Limitations and open questions

The paper concedes two constraints. First, LocusGS assumes calibrated input views, since anchor-aware aggregation depends on camera rays derived from known poses; extending to pose-free inputs or jointly modeling pose uncertainty remains open. Second, the center-plus-scalar-radius anchor is isotropic, which cannot represent elongated structures or direction-dependent support; whether anisotropic or visibility-aware uncertainty states would improve reconstruction in geometrically complex regions is left untested. Additionally, the evaluation isolates spatial grounding against TokenGS specifically because other concurrent query-based systems (e.g., C3G, GlobalSplat) confound the comparison with pretrained backbones and differing architectures, so the reported gains should be read as attributable to grounding within one controlled instantiation rather than as superiority over all query-based variants.

Conclusion

LocusGS demonstrates that replacing latent-only Gaussian queries with explicitly anchored, progressively refined 3D states yields better novel view synthesis at equal token and Gaussian budgets, substantially more compact token-level Gaussian groups, and interpretable anchor layouts that act as a spatial scaffold for reconstruction. The evidence supports the paper's central claim that explicit spatial grounding — particularly anchor-centered Gaussian decoding and radius-adaptive geometric attention — is an effective prior for feed-forward query-based 3DGS, while leaving pose-free operation and richer anchor geometries as unresolved questions.