Multiplicative Fourier Level of Detail
We develop a simple yet surprisingly effective implicit representing scheme called Multiplicative Fourier Level of Detail (MFLOD) motivated by the recent success of multiplicative filter network. Built on multi-resolution feature grid/volume (e.g., the sparse voxel octree), each level's feature is first modulated by a sinusoidal function and then element-wisely multiplied by a linear transformation of previous layer's representation in a layer-to-layer recursive manner, yielding the scale-aggregated encodings for a subsequent simple linear forward to get final output. In contrast to previous hybrid representations relying on interleaved multilevel fusion and nonlinear activation-based decoding, MFLOD could be elegantly characterized as a linear combination of sine basis functions with varying amplitude, frequency, and phase upon the learned multilevel features, thus offering great feasibility in Fourier analysis. Comprehensive experimental results on implicit neural representation learning tasks including image fitting, 3D shape representation, and neural radiance fields well demonstrate the superior quality and generalizability achieved by the proposed MFLOD scheme.
Code (0)
등록된 구현이 없습니다.
Tasks
3D Shape RepresentationRepresentation LearningSimilar Papers 제목 키워드 기반
Quaternionic Fourier-Mellin Transform
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invarian…
Image ReconstructionA Novel Hierarchical Light Field Coding Scheme Based on Hybrid Stacked Multiplicative Layers and Fourier Disparity Layers for Glasses-Free 3D Displays
This paper presents a novel hierarchical coding scheme for light fields based on transmittance patterns of low-rank multiplicative layers and Fourier disparity layers. The proposed scheme identifies multiplicative layers…
DecoderMultiplicative Filter Networks
Although deep networks are typically used to approximate functions over high dimensional inputs, recent work has increased interest in neural networks as function approximators for low-dimensional-but-complex functions, …
Fast Discrete Fourier Transform algorithms requiring less than 0(NlogN) multiplications
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting …
The Discrete-Log Clock: How a Transformer Learns Modular Multiplication
When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set o…