TL;DR
ViscoReg introduces a viscosity-based regularizer for neural signed distance functions, improving stability and accuracy in 3D reconstruction tasks, backed by theoretical guarantees and superior empirical performance.
Contribution
The paper proposes ViscoReg, a new viscosity solution-based regularizer that stabilizes neural SDF training and enhances 3D reconstruction accuracy.
Findings
Outperforms SIREN, DiGS, and StEik on multiple datasets.
Provides theoretical generalization error bounds for neural SDFs.
Demonstrates improved stability and accuracy in 3D scene reconstruction.
Abstract
Implicit Neural Representations (INRs) that learn Signed Distance Functions (SDFs) from point cloud data represent the state-of-the-art for geometrically accurate 3D scene reconstruction. However, training these Neural SDFs often requires enforcing the Eikonal equation, an ill-posed equation that also leads to unstable gradient flows. Numerical Eikonal solvers have relied on viscosity approaches for regularization and stability. Motivated by this well-established theory, we introduce ViscoReg, a novel regularizer that provably stabilizes Neural SDF training. Empirically, ViscoReg outperforms state-of-the-art approaches such as SIREN, DiGS, and StEik on ShapeNet, the Surface Reconstruction Benchmark, and 3D scene reconstruction datasets. Additionally, we establish novel generalization error estimates for Neural SDFs in terms of the training error, using the theory of viscosity solutions.
Peer Reviews
Decision·Submitted to ICLR 2026
1. This paper provides a generalization error bound for Neural SDFs, guaranteeing in the $L^{\infty}$ sense that the error between the learned function and the true SDF is controlled by the training loss. This addresses the theoretical challenge posed by the ill-posedness of the Eikonal equation. 2. On multiple public benchmarks, ViscoReg significantly outperforms SOTA methods. For instance, on ShapeNet, the mean squared Chamfer distance is reduced by approximately 35%, demonstrating its effecti
**Dependence on the decay strategy of the viscosity coefficient ($\epsilon$)**: The paper notes that the decay strategy of $\epsilon$ affects performance, and certain shapes (e.g., anchor and gargoyle) require adjustments to the decay rate. Although a baseline decay schedule is provided, its complex, piecewise-linear design means that applying the method to new datasets or novel shapes may require additional hyperparameter tuning, increasing the overall usage complexity. **Experimentally**: 1.
Originality: The method introduces a viscosity-based regularizer for neural SDFs, connecting numerical PDE theory and neural implicit representations. This is a novel way to stabilize training using a mathematically grounded approach instead of ad hoc methods. Quality: The paper includes both theoretical and empirical contributions. The generalization bound links training errors to the viscosity solution, and the gradient flow analysis clearly explains how the viscosity term improves stability.
My main concern is that the paper treats Sitzman et al from 2020 as its baseline. This is an old old paper - especially in today's world where things move so rapidly. Could the authors please comment on this Also most of the analysis is done on scenes/objects without significant noise.The theoretical analysis depends on strong assumptions, such as bounded gradients and smoothness, which may not hold in practice. It is unclear how these assumptions relate to realistic neural SDF training dynamics
*Exposition:* The proposed method is clearly explained, such that I am confident I could implement the method after reading the paper. Furthermore, the experiments are described in sufficient detail, such that I could also reproduce them. *Performance:* The method shows slightly improved performance on two benchmarks. Furthermore, Figure 1 demonstrate that it is even suitable to handle complicated examples with high-frequency details.
*Novelty:* I am mostly concerned about the novelty of the method. The cited paper ViscoGrids follows essentially the same idea, by using the regularized Eikonal equation instead of the usual one. The main differences are that ViscoGrids uses, well, grids and does not modify the viscosity coefficient. (This is also discussed in l.120) For me, these two changes to not justify a new publication at ICLR. There would be the contribution of generalization estimate, but this brings me to my second poin
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