Subtractive Modulative Network with Learnable Periodic Activations

Tiou Wang^*, Zhuoqian Yang^†, Markus Flierl^*, Mathieu Salzmann^†, Sabine Süsstrunk^†

^*School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Sweden
^†School of Computer and Communication Sciences, EPFL, Switzerland

📄 Paper (arXiv) 📄 Supplementary 💾 Code

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.

Highlights

                    41.40 / 42.53 dB
                    PSNR on Kodak / DIV2K — state-of-the-art 2D image representation
                

                    264K params
                    Most compact model among top performers; 4× fewer FLOPs than WIRE
                

                    +0.98 dB
                    Margin over next-best on 3D NeRF novel view synthesis (avg. 8 scenes)
                

Method

SMN is inspired by classical subtractive synthesis from audio signal processing: a spectrally rich signal is generated first, then progressively shaped. Given a coordinate input, the network processes it through three interpretable stages:

Oscillator Learnable periodic activation layer. Generates a multi-frequency basis by adaptively weighting sinusoidal components across multiple learned frequencies.

→

Filter (×2) Modulative mask modules with dual pathways: additive modulation combines features, while multiplicative masking sculpts the spectrum and generates high-order harmonics.

→

Amplifier Self-mask stage using a squaring operation for non-linear amplification, enabling fine detail recovery without additional parameters.

End-to-end architecture of the Subtractive Modulative Network, illustrating the Oscillator, multi-stage Filter (main and masking pathways), and the Amplifier (Self-Mask) stage.

Results

2D Image Representation

Method	Kodak PSNR	DIV2K PSNR	Parameters	GFLOPs
MLP	28.63 dB	30.21 dB	272,415	—
RINR	32.96 dB	34.03 dB	289,716	—
SIREN	33.65 dB	33.73 dB	272,703	214
Gauss	37.90 dB	38.34 dB	272,703	—
WIRE	40.24 dB	38.90 dB	265,523	835
SMN (Ours)	41.40 dB	42.53 dB	264,216	208

SMN achieves the highest PSNR on both datasets with fewer parameters than all baselines and 4× lower GFLOPs than WIRE.

3D NeRF Novel View Synthesis (avg. over 8 scenes, 400×400)

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

PE = Positional Encoding. SMN outperforms the next-best method (PE + Gauss) by +0.98 dB on average across all 8 NeRF scenes.

Visual Comparison — 2D Image Reconstruction

SIREN

RINR

Gauss

WIRE

SMN (Ours)

Magnified crops from Kodak. SMN preserves fine textures and edge details most faithfully among all methods.

Ablation Study

Modulation Mechanism (Kodak)

SMN-Add (element-wise addition) 40.25 dB

SMN (multiplicative masking) 41.40 dB

Multiplicative masking yields a +1.15 dB gain — confirming the importance of spectral sculpting over simple addition.

Learnable Sine Layer Variants (Kodak)

Variant 1 — fixed amplitudes 35.08 dB

Variant 2 — K=1 learnable basis 42.87 dB

Variant 3 — K=2 learnable bases 43.09 dB

Final — K=3 learnable bases 43.68 dB

Each additional learnable basis consistently improves performance; K=3 is selected as the final design.

Citation

@inproceedings{wang2026smn,
  title     = {Subtractive Modulative Network with Learnable Periodic Activations},
  author    = {Wang, Tiou and Yang, Zhuoqian and Flierl, Markus and
               Salzmann, Mathieu and S{\"u}sstrunk, Sabine},
  booktitle = {Proceedings of ICASSP},
  year      = {2026}
}