Using second-order depth responses to decide where to split 3D Gaussians cut Gaussian count and storage by nearly 60 percent during training instead of compressing afterwards
AspireAI community · arXiv
3D Gaussian Splatting densifies Gaussians using first-order screen-space gradients, which cannot tell a true geometric discontinuity from a high-frequency texture or a noisy residual, and the usual result is redundant Gaussian proliferation. ACD-GS instead uses second-order depth responses as the structural prior and regulates cloning and splitting asymmetrically, adds a multi-view photometric consistency constraint so single-view errors do not trigger densification, and balances densification against pruning with a capacity-aware strategy. Because it prevents redundant Gaussians from being created in the first place rather than compressing them afterwards, the authors report nearly 60 percent reductions in Gaussian count and storage while maintaining competitive rendering fidelity and consistently outperforming existing methods across multiple datasets. The savings are relative to the baselines the paper compares against, and the approach adds training-time cost rather than reducing it.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.