Polyhedral Complex Derivation from Piecewise Trilinear Networks

arXiv:2402.10403v1 Announce Type: new
Abstract: Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Focusing on trilinear interpolating methods as positional encoding, we present theoretical insights and an analytical mesh extraction, showing the transformation of hypersurfaces to flat planes …

abstract arxiv bias challenges continuous cs.ai cs.cv cs.gr cs.lg derivation encoding extraction functions insights linear mesh networks neural networks non-linear positional encoding representation representation learning surface type