SALD: Sign Agnostic Learning with Derivatives

💡 Research Summary

This paper introduces SALD (Sign‑Agnostic Learning with Derivatives), a method for learning implicit neural representations of 3‑D shapes directly from raw, unoriented data such as point clouds, triangle soups, or non‑manifold meshes. The approach builds on the earlier Sign‑Agnostic Learning (SAL) framework, which regresses an unsigned distance function h(x)=min_{y∈X}‖x−y‖ to a neural network f(x;θ) using a loss that is invariant to the sign of the output. SAL can recover a signed distance field, but it relies only on function values, which may require many samples to uniquely determine the network.

SALD extends this idea by also incorporating gradient information of the unsigned distance field. The authors define an unsigned similarity measure τ that, for scalars, is τ(a,b)=|| |a|−b || and for vectors τ(a,b)=min{‖a−b‖,‖a+b‖}. The full SALD loss is:
loss(θ)=E_{x∼D}