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Subtractive Modulative Network with Learnable Periodic Activations

Tiou Wang, Zhuoqian Yang, Markus Flierl, Mathieu Salzmann, Sabine Süsstrunk

TL;DR

The paper tackles spectral bias in implicit neural representations by proposing the Subtractive Modulative Network (SMN), a structured INR that aligns with subtractive synthesis. It introduces a Learnable Sine Layer oscillator to create a flexible multi-frequency basis and a multi-stage Modulative Mask filter that uses multiplicative interactions to sculpt spectra and generate higher harmonics. Empirical results show SMN achieves PSNRs exceeding 40 dB on 2D image datasets and around 33 dB on 3D NeRF tasks, with superior parameter efficiency and competitive FLOPs compared to state-of-the-art baselines. The work demonstrates that spectral-aware, interpretable architectural design can outperform monolithic additive INRs in both image reconstruction and novel-view synthesis, offering practical benefits for high-fidelity representations.

Abstract

We propose the Subtractive Modulative Network (SMN), a novel, parameter-efficient Implicit Neural Representation (INR) architecture inspired by classical subtractive synthesis. The SMN is designed as a principled signal processing pipeline, featuring a learnable periodic activation layer (Oscillator) that generates a multi-frequency basis, and a series of modulative mask modules (Filters) that actively generate high-order harmonics. We provide both theoretical analysis and empirical validation for our design. Our SMN achieves a PSNR of $40+$ dB on two image datasets, comparing favorably against state-of-the-art methods in terms of both reconstruction accuracy and parameter efficiency. Furthermore, consistent advantage is observed on the challenging 3D NeRF novel view synthesis task. Supplementary materials are available at https://inrainbws.github.io/smn/.

Subtractive Modulative Network with Learnable Periodic Activations

TL;DR

The paper tackles spectral bias in implicit neural representations by proposing the Subtractive Modulative Network (SMN), a structured INR that aligns with subtractive synthesis. It introduces a Learnable Sine Layer oscillator to create a flexible multi-frequency basis and a multi-stage Modulative Mask filter that uses multiplicative interactions to sculpt spectra and generate higher harmonics. Empirical results show SMN achieves PSNRs exceeding 40 dB on 2D image datasets and around 33 dB on 3D NeRF tasks, with superior parameter efficiency and competitive FLOPs compared to state-of-the-art baselines. The work demonstrates that spectral-aware, interpretable architectural design can outperform monolithic additive INRs in both image reconstruction and novel-view synthesis, offering practical benefits for high-fidelity representations.

Abstract

We propose the Subtractive Modulative Network (SMN), a novel, parameter-efficient Implicit Neural Representation (INR) architecture inspired by classical subtractive synthesis. The SMN is designed as a principled signal processing pipeline, featuring a learnable periodic activation layer (Oscillator) that generates a multi-frequency basis, and a series of modulative mask modules (Filters) that actively generate high-order harmonics. We provide both theoretical analysis and empirical validation for our design. Our SMN achieves a PSNR of dB on two image datasets, comparing favorably against state-of-the-art methods in terms of both reconstruction accuracy and parameter efficiency. Furthermore, consistent advantage is observed on the challenging 3D NeRF novel view synthesis task. Supplementary materials are available at https://inrainbws.github.io/smn/.
Paper Structure (13 sections, 2 equations, 3 figures, 3 tables)

This paper contains 13 sections, 2 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. RELATED WORK
  3. Subtractive Synthesis and Modulation
  4. Method
  5. The Oscillator: A Learnable Sine Layer
  6. The Filter: A Multi-Stage Modulative Mask
  7. Overall Architecture and Training
  8. EXPERIMENTS
  9. Experimental Setup
  10. Main Results on 2D Image Representation
  11. Generalization to 3D Scene Representation
  12. Ablation Studies and Analysis
  13. CONCLUSION

Figures (3)

  • Figure 1: The end-to-end architecture of our SMN, illustrating the Oscillator, the multi-stage Filter with its main and masking pathways, and the final Amplifier (Self-Mask) stage.
  • Figure 2: Visual comparison of reconstruction quality for different INR methods on a Kodak image. Our method preserves fine textures and edges most faithfully. Best viewed on screen when zooming in.
  • Figure 3: Qualitative comparison of view synthesis on the Lego NeRF dataset. Our method reconstructs fine geometric details more faithfully and reduces common artifacts such as floater noise and blurriness. Best viewed on screen when zooming in.