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In Search of a Data Transformation That Accelerates Neural Field Training
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Shows that randomly permuting pixel locations of an image speeds up SGD-based neural field training (about 1.08-1.50x over the original image), and analyzes why via PSNR curves, loss landscapes, and error patterns.
Problem
Neural field training is slow because overfitting a network to a signal requires many SGD steps to reach high fidelity; the paper asks whether data transformations can reduce this encoding cost.
Approach
Instead of fighting SGD's spectral bias with architectural priors, transform the data before fitting: random pixel permutation removes easy-to-fit smooth patterns, which slows early training but accelerates reaching high PSNR, counterintuitively speeding overall convergence.
Key results
- Random pixel permutation accelerates SIREN training by 1.08x-1.30x and Instant-NGP by 1.32x-1.50x on average across Kodak, DIV2K, and CLIC.
- Original images need about 30% more SGD steps than RPP images to reach similar fidelity, per the paper's summary.
- Loss barrier on the late-phase linear path is 15.3dB for original images versus 28.3dB for RPP (averaged over Kodak).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Randomly permute pixel locations | SIREN · Kodak, DIV2K, and CLIC | acceleration factor: 1.26×, 1.30×, 1.08× | Helped |
| Randomly permute pixel locations | Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: 1.50×, 1.32×, 1.35× | Helped |
| Use zigzag pixel permutation instead of the original image | SIREN · Kodak, DIV2K, and CLIC | acceleration factor: 17.90×, 21.74×, 17.07× | Helped |
| Use zigzag pixel permutation instead of the original image | Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: 0.86×, 0.80×, 0.78× | Mixed |
| Invert pixel intensities | SIREN and Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: SIREN: 0.72×, 0.70×, 0.68×; Instant-NGP: 0.21×, 0.20×, 0.07× | Hurt |
| Standardize pixel intensities | SIREN and Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: SIREN: 2.20×, 2.36×, 2.18×; Instant-NGP: 0.45×, 0.61×, 0.53× | Hurt |
| Scale pixel intensities by t = 0.5 | SIREN and Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: SIREN: 0.79×, 0.82×, 0.76×; Instant-NGP: 1.15×, 1.12×, 1.03× | Mixed |
| Apply gamma correction | SIREN and Instant-NGP · Kodak, DIV2K, and CLIC | acceleration factor: γ = 0.5: SIREN 0.36×, 0.30×, 0.24×; Instant-NGP 0.29×, 0.14×, 0.12× | Hurt |
| Randomly permute pixel locations | SIREN · Kodak, PSNR 30dB | steps: 105.8 -> 851.8 | Hurt |
| Randomly permute pixel locations | SIREN · Kodak, PSNR 50dB | steps: 1371.4 -> 1100.5 | Helped |
| Randomly permute pixel locations | SIREN · Kodak, PSNR 20, 30, 40, and 50 | pixel loss variance: 10.51e-04 -> 5.68e-04; 23.68e-06 -> 5.89e-06; 19.46e-08 -> 7.59e-08; 5.90e-10 -> 5.81e-10 | Helped |
Surprising findings
- Random pixel permutation, which increases high-frequency content, speeds up training despite spectral bias predicting slower fitting.
- Zigzag permutation speeds up SIREN by over 17x but slows down Instant-NGP.
Limitations
- Applicability is limited for tasks like classification and regression where regularization and generalization matter.
- Random pixel permutation does not preserve interpolatability, so it is unsuitable for applications needing generalization or interpolation.
- Theoretical understanding of why RPP helps remains incomplete; the study is limited to 2D image regression.
Experimental setup
Datasets: Kodak DIV2K CLIC
Benchmarks: Kodak DIV2K CLIC
Metrics: acceleration factor (ratio of SGD steps to reach 50dB PSNR) PSNR loss variance over pixels
Baselines: SIREN Instant-NGP
Builds on: SIREN Instant-NGP BACON
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