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ParetoGS: High-Quality Continuous-Budget 3D Gaussian Splatting with Sparse Adapted Anchors

Xiaobin Deng, Changyu Diao, Min Li, Duanqing Xu

arXiv:2610.34235v1cs.CV

TL;DR

Scalable 3D Gaussian Splatting serves multiple Gaussian-count budgets, but its quality-budget curve can lag behind models optimized separately for each count. ParetoGS builds a small set of adapted nested anchors and decodes intermediate budgets from them. Across 13 scenes, it outperforms compared prefix methods at 10% retention while using fewer Gaussians, and compresses the adapted state.

  • Problem

    Scalable 3DGS can serve multiple Gaussian-count budgets, but its quality-budget curve may lag behind separately optimized models, while per-budget pruning and retraining requires repeated training and multiple assets.

    Source: §1 · p. 1

  • Method

    ParetoGS alternates pruning and fixed-member adaptation to build nested anchors, then uses persistent identities, a compact residual atlas, and interpolation with opacity gating to decode intermediate budgets.

    Source: §1 · p. 2

  • Results

    Across 13 scenes, ParetoGS outperforms CLOD-3DGS and MGS at 10% of each method’s own full model while using fewer Gaussians.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Organizing budget-specific states into one asset provides higher-quality multi-budget decoding from a single scene representation.

    Source: §5 · p. 10

Abstract

from arXiv · show

Scalable 3D Gaussian Splatting allows one scene representation to serve different Gaussian-count budgets, yet its quality-budget curve may lag behind models optimized separately for each budget. Reducing the number of Gaussians changes both the selected members and the reconstruction tasks carried by the survivors; parameters inherited from a high-budget model may fit a low-budget representation poorly. We propose ParetoGS, which describes member changes and parameter evolution with a small set of adapted budget anchors and decodes intermediate budgets without separate optimization at every requested count. ParetoGS alternates pruning and fixed-member adaptation to build nested anchors with persistent identities, and encodes their parameter changes relative to the full model in a compact residual atlas. At decoding, it interpolates the states of shared members and gradually introduces the rendering contributions of new members, connecting sparse anchors into a continuous-budget representation. Across 13 scenes, ParetoGS attains better average PSNR, SSIM, and LPIPS with fewer Gaussians than the compared prefix methods at 10% of each method's own full model. From a shared full model, it also outperforms FlexGS-imp at its trained 1%, 5%, and 10% budgets and NanoGS-imp at the 1% and 0.1% budgets. On Garden, its non-anchor quality approaches an empirical reference from independently optimized GNS models at higher retention ratios and exceeds it at some lower-budget points. Across 13 scenes, encoding reduces mean additional state from 390.0 to 85.7 MB with an average PSNR change of 0.01 dB. Project page: https://xiaobin2001.github.io/ParetoGS-Web/

1 INTRODUCTION

ParetoGS targets the gap between scalable Gaussian-count representations and models optimized separately for each budget. It uses sparsely adapted nested anchors to represent both member changes and parameter evolution, then decodes intermediate counts; across 13 scenes, it improves on compared prefix methods at 10% retention while using fewer Gaussians.

1 INTRODUCTION

  • Reducing Gaussian count changes both membership and survivors’ reconstruction tasks, so parameters inherited from the full model may fit a smaller representation poorly.Adapted states also provide a new starting point for subsequent pruning decisions.Source: §1 · p. 1
  • ParetoGS alternates pruning and fixed-member adaptation to build nested anchors, preserving identities and encoding parameter changes relative to the full model in a compact residual atlas.It interpolates shared-member states and gradually activates entering members to decode intermediate budgets without separate optimization at each requested count.Source: §1 · p. 2, Figure 1 · p. 2
  • Across 13 scenes, ParetoGS outperforms CLOD-3DGS and MGS at 10% of each method’s own full model while using fewer Gaussians.From a shared full model, it also improves mean quality over FlexGS-imp at its trained 1%, 5%, and 10% budgets and over NanoGS-imp at 1% and 0.1%.Source: §1 · p. 2
  • The paper frames continuous-budget 3DGS as a joint trajectory of nested membership and budget-specific parameter states organized by progressively adapted anchors.Persistent identities and aligned residual encoding connect those states for intermediate-count decoding.Source: §1 · pp. 1–2
  • The evaluation includes 13-scene multi-budget comparisons, non-anchor evaluation, and ablations of adapted states and interval decoding, alongside compact storage of the anchor family.The reported mean additional state falls from 390.0 to 85.7 MB across 13 scenes.Source: §1 · p. 2

2 RELATED WORK

Related work addresses compact storage, pruning, multilevel organization, and arbitrary-budget decoding through varied representations and training strategies. ParetoGS focuses on explicitly adapted nested anchors whose aligned parameter states can be decoded at arbitrary Gaussian budgets.

2 RELATED WORK

  • Other 3DGS work extends primitives and dynamic scenes, surface reconstruction, visibility, rendering efficiency, initialization, and real-capture appearance or blur; ParetoGS organizes an already trained scene for arbitrary Gaussian budgets.Source: §2 · p. 3
  • Compact representations encode attributes, pruning methods select members, and multilevel approaches organize models by resolution or capacity; ParetoGS uses GNS to build budget anchors and connects aligned parameter states.The cited approaches include context coding, grids, vector quantization, sensitivity-based pruning, sampling, and spatial or scale hierarchies.Source: §2 · p. 3
  • Arbitrary-budget methods include prefix training, count-truncatable orderings, incremental reordering, layer interpolation, feature refinement, merging, and budget-conditioned selection or geometry transformation.ParetoGS instead stores explicitly optimized nested anchors, continues pruning from adapted states, and connects corresponding members’ geometry, opacity, and appearance.Source: §2 · p. 3

3 METHOD

ParetoGS represents budget evolution through nested membership and budget-specific parameter states, organized by progressively adapted anchors. Persistent identities align members, while a residual atlas stores anchor changes relative to the full model.

3.1 BUDGET-CONDITIONED SCENE REPRESENTATION

  • The budget-conditioned model selects exactly K persistent-identity Gaussians, with nested active sets and parameters that may change as the budget grows.Source: §3.1 · p. 4

3.2 SPARSE ADAPTED ANCHORS AND MEMBER CORRESPONDENCE

  • Eleven approximately doubling anchors span 0.1% of Full to the full count; each contraction adapts survivors at fixed membership before the next stage.The adapted state serves as both a decoding endpoint and the next contraction’s starting point.Source: §3.2 · p. 4

3.3 PIECEWISE BUDGET DECODING

  • Between anchors, ParetoGS interpolates aligned states of shared members and admits upper-anchor members with a progress-controlled opacity gate.The interpolation exponent controls how quickly shared-member parameters approach the upper-anchor state.Source: §3.3 · p. 4

3.4 LAYERED RESIDUAL ATLAS

  • The residual atlas stores anchor-to-Full changes by member layer and parameter field; higher-order SH channels are factorized, and decoding restores only neighboring endpoints.The final asset combines the ordered full model, residual atlas, interval exponents, and member-order metadata.Source: §3.4 · p. 5

4 EXPERIMENTS

The experiments compare ParetoGS with prefix methods across 13 scenes and evaluate budget-specific states, continuous decoding, decoder components, and storage. They report stronger low-budget quality in the tested comparisons and a compact residual atlas with little average PSNR change.

4.1 EXPERIMENTAL SETUP

  • Experiments use 13 scenes, common test views and image sizes, and equally weighted scene means; comparisons use either each method’s own full model or a shared full model.The shared-model protocol evaluates FlexGS-imp at sampled 1%, 5%, and 10% budgets and also queries 0.1% and 30%.Source: §4.1 · p. 6

4.2 RECONSTRUCTION QUALITY AND OFFLINE COST

  • At 10% retention, ParetoGS reaches 27.17 dB with about 162K Gaussians, versus 25.59 dB with 303K for CLOD-3DGS and 25.74 dB with 492K for MGS.Across 10%, 5%, 1%, and 0.1%, ParetoGS gains about 3.50 dB in PSNR over MGS on average; at Full and 30%, MGS has slightly better mean LPIPS.Source: Table 1 · p. 6, §4.2 · p. 6
  • At 5% of a shared full model, ParetoGS records 26.48 dB PSNR, 0.791 SSIM, and 0.315 LPIPS, versus FlexGS-imp’s 24.03 dB, 0.712, and 0.386.At 1%, ParetoGS reaches 24.40 dB PSNR versus NanoGS-imp’s 18.84 dB; at 0.1%, it improves PSNR from 16.37 to 21.15 dB, SSIM from 0.470 to 0.580, and LPIPS from 0.637 to 0.539.Source: §4.2 · pp. 6–7, Table 2 · p. 7

4.3 BUDGET-SPECIFIC STATES AND CONTINUOUS DECODING

  • With the same 24K Garden members, changing only their parameters lets them progress from covering a small part of the full-state view to reconstructing the whole view at 0.8%.From 1% to 50% retention on Garden, decoded SSIM and LPIPS closely track independently optimized GNS points; below about 1%, ParetoGS is favored, with a similar budget-dependent pattern reported for the other 12 scenes.Source: §4.3 · pp. 8–9

4.4 DECODER COMPONENTS AND ANCHOR ABLATIONS

  • At interval midpoints, fixing shared members at the lower-anchor state reduces mean PSNR by 0.13 dB and SSIM by 0.0018, and increases LPIPS by 0.0019; using Full-model parameters for the same IDs lowers PSNR from 25.47 to 17.07 dB.Decoded quality curves remain smooth when anchor spacing doubles or quadruples, with mean SSIM changing from 0.6569 to 0.6467 and 0.6180; intermediate anchors raise the connecting curve’s average quality.Source: Table 3 · p. 9, §4.4 · pp. 9–10, Figure 5 · p. 9

4.5 STATE ENCODING AND STORAGE

  • Across 13 scenes, atlas encoding reduces mean additional state from 390.0 MB to 85.7 MB, with a 0.01 dB PSNR drop, 0.0005 SSIM drop, and 0.0005 LPIPS increase.FP16 residuals use 195.0 MB with the same quality at shown precision.Source: Table 4 · p. 9, §4.5 · p. 10

5 CONCLUSION

ParetoGS connects nested Gaussian memberships and budget-specific parameter states through sparse adapted anchors, enabling decoding at requested counts from one representation. Across 13 scenes, it improves mean quality over the compared prefix methods at 10% retention while using fewer Gaussians, and compresses the additional state with little average quality change.

5 CONCLUSION

  • ParetoGS represents budget evolution through nested membership and budget-specific parameter states organized by progressively adapted anchors.Persistent identities and shared-state interpolation connect the anchors into models decodable at requested counts, while a residual atlas compresses the additional adapted states.Source: §5 · p. 10
  • Across 13 scenes, ParetoGS achieves better mean quality than the compared prefix methods with fewer Gaussians at 10% retention.From a shared full model, it also improves over FlexGS-imp at its sampled 1%, 5%, and 10% budgets and over NanoGS-imp at 1% and 0.1%.Source: §5 · p. 10

A STATE ENCODING, CALIBRATION, AND BUDGET DECODING

  • Given nested adapted anchors and the full model, the runtime procedure returns parameters for exactly K Gaussians at any valid integer budget.Exact anchor requests restore that anchor, and K equal to the full count uses Full.Source: A STATE ENCODING, CALIBRATION, AND… · p. 15

A.1 MEMBER ORDERING AND RESIDUAL ATLAS

  • The nested ordering is built by reversing anchor deletion traces, concatenating member-entry sequences, and aligning anchor states by persistent ID.Residuals are computed against Full in raw coordinates for six parameter fields, totaling 59 scalar components per Gaussian at SH degree three.Source: §A.1 · p. 15
  • Non-full anchor residuals are compressed through FP16 conversion, state-axis decomposition, and symmetric INT8 quantization, with no further image optimization after compression.The 45 higher-order SH channels use a rank-36 channel subspace while decoding still outputs all 45; quantization scales and several atlas components use FP16.Source: §A.1 · p. 15

A.2 INTERVAL CALIBRATION AND BUDGET DECODING

For each neighboring anchor interval, calibration selects interpolation and entering-member gate exponents using a small set of training views. At runtime, the decoder restores endpoints and produces standard parameters for the requested Gaussian count.

A.2 INTERVAL CALIBRATION AND BUDGET DECODING

  • Calibration compares 72 shared-state and entering-member gate exponent pairs at rounded budgets corresponding to normalized progress values 0.25, 0.5, and 0.75.It uses FP16 anchor states, up to ten training views, and no test views or Gaussian-parameter updates.Source: §A.2 · p. 15
  • The interval objective combines image loss with penalties based on activation and interpolation variation across selected views.Image loss is 0.8L1 + 0.2(1 − SSIM), and each interval stores the minimizing p and q, with ties favoring larger p and then larger q.Source: §A.2 · p. 15
  • At non-anchor counts, shared members follow the interpolation rule while entering members use their upper-anchor state with opacity activated by t^q and clipped before conversion back to a logit.The decoder outputs standard K-Gaussian parameters; the deployed asset includes reordered Full, the compressed atlas, interval exponents, and member-order metadata.Source: §A.2 · p. 16

B PER-SCENE EXPERIMENTAL RESULTS

The per-scene appendix tables expand the paper’s aggregate comparisons by reporting quality, Gaussian counts, and construction or conversion times across scenes.

B PER-SCENE EXPERIMENTAL RESULTS

  • Tables 5–7 report per-scene PSNR, SSIM, and LPIPS at retention ratios measured from each method’s own Full.Source: Table 5 · p. 16, Table 6 · p. 17, Table 7 · p. 18
  • Tables 8–10 report per-scene PSNR, SSIM, and LPIPS at requested ratios from the shared Full.Source: Table 8 · p. 18, Table 9 · p. 19, Table 10 · p. 20
  • Tables 11–12 give per-scene actual Gaussian counts for own-Full retention ratios and for requested and FlexGS-imp outputs from the shared Full.Source: Table 11 · p. 21, Table 12 · p. 22
  • Tables 13–14 report per-scene NanoGS-imp conversion times and offline times for method training and ParetoGS postprocessing stages.Table 14 gives CLOD, MGS, FlexGS, ParetoGS training, and total in minutes, while encoding, calibration, and packaging are in seconds.Source: Table 14 · p. 23, Table 13 · p. 23

B.1 PER-SCENE DECODER COMPONENTS

Table 15 expands the Table 3 per-scene results and specifies how its interval-midpoint and Full-parameter entries are formed.

B.1 PER-SCENE DECODER COMPONENTS

  • Table 15 expands Table 3 over all 13 scenes.Source: §B.1 · p. 23
  • Each scene averages ten interval midpoints in Table 15.Source: Table 15 · p. 24
  • The Full-parameter row uses the same member IDs in the per-scene comparison.Source: Table 15 · p. 24

B.2 PER-SCENE STATE ENCODING

Table 16 expands Table 4 with per-scene quality and additional-state storage results.

B.2 PER-SCENE STATE ENCODING

  • Table 16 reports per-scene quality and additional state storage, expanding Table 4.Its quality values average ten interval midpoints per scene, and storage is measured in MB.Source: §B.2 · p. 25, Table 16 · p. 25
  • Quality is averaged over ten interval midpoints for each scene.Source: Table 16 · p. 25
  • Additional state storage is reported in MB.Source: Table 16 · p. 25

C BUDGET-SWITCH PARAMETER CONSTRUCTION TIME

The section measures budget-switch parameter construction time with endpoints resident, then presents cross-budget visual comparisons across additional scenes.

C BUDGET-SWITCH PARAMETER CONSTRUCTION TIME

  • The timing evaluation pools 1,404 switches per method across 13 scenes, after three repetitions of 108 switches per scene.Methods start with their respective parameters and selection data resident on the GPU; ParetoGS has all anchor fields predecoded and resident.Source: Table 17 · p. 26, C BUDGET-SWITCH PARAMETER CONSTRUCTION… · p. 26
  • ParetoGS budget switches take a median 0.27 ms, P95 2.77 ms, and maximum 5.65 ms across the reported timing evaluation.One-time anchor predecoding averages 0.39 s, and decoded endpoints average 390.0 MB of GPU storage; the switch timings assume endpoints are already resident.Source: C BUDGET-SWITCH PARAMETER CONSTRUCTION… · p. 26, Table 17 · p. 26

D CROSS-BUDGET VISUAL COMPARISONS ON OTHER SCENES

E CONTINUOUS-BUDGET QUALITY CURVES ON OTHER SCENES

Figures 12–14 present continuous-budget quality curves for the 12 scenes beyond Garden.

E CONTINUOUS-BUDGET QUALITY CURVES ON OTHER SCENES

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