SMN: Subtractive Modulative Network with Learnable Periodic Activations

Official PyTorch implementation of Subtractive Modulative Network (SMN), accepted at IEEE ICASSP 2026.

Paper | Project Page | Supplementary Material

SMN is a signal-processing-inspired implicit neural representation (INR) architecture. Instead of treating a coordinate MLP as a monolithic black box, SMN decomposes representation learning into a structured pipeline:

• Oscillator: a learnable periodic activation layer that generates a multi-frequency basis
• Filter: modulative mask modules that sculpt the spectrum and generate higher-order harmonics
• Amplifier: a lightweight self-mask stage that increases non-linearity without adding parameters

The same idea is used in this repository for:

• 2D image representation on Kodak and DIV2K
• 3D novel view synthesis in a NeRF pipeline

Highlights

• Structured INR design inspired by subtractive synthesis rather than additive feature superposition
• Strong 2D reconstruction quality with 41.40 dB on Kodak and 42.53 dB on DIV2K
• Strong 3D generalization with 32.98 dB average PSNR on the 8-scene synthetic NeRF benchmark
• Parameter-efficient model design with only 264,216 parameters for the 2D SMN setting reported in the paper

Results

The following numbers are reported in the paper.

2D Image Representation

Method	Kodak PSNR	DIV2K PSNR	Parameters
MLP	28.63	30.21	272,415
Gauss	37.90	38.34	272,703
SIREN	33.65	33.73	272,703
WIRE	40.24	38.90	265,523
RINR	32.96	34.03	289,716
SMN (Ours)	41.40	42.53	264,216

3D NeRF Novel View Synthesis

Average PSNR on the 8 synthetic NeRF scenes at 400x400 resolution:

Method	Avg. PSNR	Parameters
PE + Gauss	32.00	287,749
PE + SIREN	29.06	287,749
PE + WIRE	25.14	283,479
PE + RINR	26.84	314,703
PE + MLP	26.66	290,370
PE + SMN (Ours)	32.98	287,749

Method Overview

SMN is designed around three ideas drawn from the paper:

1. Learnable Oscillator The first stage uses a learnable combination of sinusoidal bases instead of relying only on fixed positional encodings. This gives the network a more adaptive frequency basis for representing detailed signals.

2. Modulative Filtering The core filtering stages use multiplicative modulation, which the paper shows is more effective than simple additive combinations for harmonic generation and spectral sculpting.

3. Self-Mask Amplifier A final self-mask operation increases non-linearity and helps generate higher-order harmonics without increasing parameter count.

Repository Structure

SMN/
|-- docs/
|   `-- SMN_2601.pdf
|-- inr_base/
|   |-- app/           # 2D training scripts and utilities
|   |-- dataio/        # image and NeRF-style data loaders
|   |-- lib/           # INR / SMN model definitions
|   |-- codak/         # bundled Kodak images
|   `-- div2k/         # bundled DIV2K images
|-- nerf/
|   |-- configs/       # scene configs for NeRF experiments
|   |-- lib/           # auxiliary model variants and layers
|   |-- run_nerf.py    # main NeRF training / rendering entry point
|   `-- modelinr.py    # SMN-style backbone used in the NeRF pipeline
`-- README.md

Installation

This repository contains research code for two related pipelines, so there is no single fully-pinned environment file for everything. A practical setup is:

pip install -r nerf/requirements.txt
pip install pandas scikit-image Pillow trimesh openpyxl

Notes:

• nerf/requirements.txt pins torch==1.11.0; if you install PyTorch separately for your CUDA version, adjust accordingly.
• The 2D pipeline exports PSNR values to Excel, so openpyxl is helpful.
• The 2D and 3D entry scripts rely on relative imports and paths. Run them from their respective subdirectories.

Quick Start

2D Image Representation

Run the 2D pipeline from inr_base/:

cd inr_base
python app/train.py --data_dir div2k --output_dir outputs/div2k

Useful arguments:

• --data_dir: image directory, for example div2k or codak
• --output_dir: directory for reconstructed images
• --image_size: resized training resolution, default 768 512
• --n_adaptation: number of images to process
• --hidden_features: hidden width of the INR backbone
• --n_hidden_layers: model depth
• --inr_type: INR type, default siren

Outputs:

• reconstructed images are written to output_dir
• PSNR values are saved to psnrvaluesMLP.xlsx

3D NeRF Synthesis

Run the NeRF pipeline from nerf/:

cd nerf
python run_nerf.py --config configs/lego.txt

Render from a trained checkpoint:

cd nerf
python run_nerf.py --config configs/lego.txt --render_only

Notes:

• scene configs live in nerf/configs/*.txt
• example synthetic data is expected under nerf/data/nerf_synthetic/<scene_name>
• outputs are written to nerf/logs/<expname>/

Main Entry Points

If you want to understand or modify the core code, start here:

• inr_base/app/train.py: 2D training entry point
• inr_base/lib/modelinr.py: 2D SMN and INR backbone definitions
• nerf/run_nerf.py: 3D NeRF training and rendering entry point
• nerf/modelinr.py: SMN backbone used by the NeRF pipeline

Acknowledgements

The NeRF pipeline builds on the excellent nerf-pytorch implementation. Please also see nerf/README.md for the upstream workflow background.

Citation

If you find this project useful, please cite the paper:

@misc{wang2026smn,
  title={Subtractive Modulative Network with Learnable Periodic Activations},
  author={Tiou Wang and Zhuoqian Yang and Markus Flierl and Mathieu Salzmann and Sabine Susstrunk},
  year={2026},
  note={IEEE ICASSP 2026}
}