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Towards Lossless Implicit Neural Representation via Bit Plane Decomposition
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Proposes bit-plane decomposition for implicit neural representations (INRs) that predicts bit-planes with a bit coordinate, achieving lossless 8/16-bit image and audio fitting and enabling bit-depth expansion, lossless compression, and ternary INRs.
Problem
INRs fail to represent digital signals losslessly at high bit precision (e.g., 16-bit images), since the theoretical parameter upper bound grows exponentially with bit depth and convergence to exact quantized values is slow.
Approach
Quantifies an INR size upper bound as a function of bit precision and decomposes n-bit signals into bit-planes predicted by one INR with an extra bit coordinate i, reducing the effective precision to 1-bit and thus the upper bound; also identifies a "bit bias" where MSBs are learned before LSBs.
Key results
- Achieves lossless (BER 0, PSNR infinite) 16-bit and 8-bit image fitting in 778 iterations on Kodak 8-bit, versus 1,000+ for baselines such as FINER at 2,000 iterations on TESTIMAGES.
- Ternary-weight INR achieves lossless image representation with model size 656.18KB versus 1.27MB for FP32 SIREN.
- Bit-depth expansion from 8-bit to 16-bit on TESTIMAGES reaches 59.39 dB PSNR, beating BitNet (53.60 dB) and rule-based baselines; lossless compression on MNIST gives 2.58 bpp vs PNG 3.52 bpp.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use bit-plane decomposition instead of a conventional INR | INR image fitting · TESTIMAGES 16-bit | BER: 0.1498 -> 0.0000 | Helped |
| Use bit-plane decomposition instead of a conventional INR | INR image fitting · MIT-5k 16-bit | BER: 0.1138 -> 0.0000 | Helped |
| Use bit-plane decomposition instead of a conventional INR | INR image fitting · DIV2K 8-bit | BER: 0.0528 -> 0.0000 | Helped |
| Use bit-plane decomposition instead of a conventional INR | INR image fitting · Kodak 8-bit | BER: 0.0447 -> 0.0000 | Helped |
| Add a color coordinate to the bit-plane input (ablation) | Proposed method on Kodak · Kodak | iterations: 790 -> 1438 | Hurt |
| Use BCE loss instead of MSE or MAE (ablation) | Proposed method · TESTIMAGE | convergence speed | Helped |
| Use MSE loss instead of BCE (ablation) | Proposed method · TESTIMAGE | convergence speed | Hurt |
| Use MAE loss instead of BCE (ablation) | Proposed method · TESTIMAGE | convergence speed | Hurt |
| Quantize network weights to ternary values (ablation) | Proposed method · Image fitting | lossless representation | No clear effect |
Surprising findings
- Bit bias: INRs learn MSBs faster than LSBs regardless of activation function, analogous to spectral bias.
- Plain INR baselines like Gauss or SIREN can fail to converge to lossless even with many more iterations, while adding bit-plane decomposition converges quickly.
Limitations
- Upper bound grows extremely with input dimension d (e.g., for d=5 radiance fields), making high-dimensional data hard.
- Ternary INR requires GELU activation and periodic activations break under weight quantization.
- Salt-and-pepper impulse noise artifacts appear during training.
Experimental setup
Datasets: MIT-Adobe FiveK TESTIMAGES DIV2K Kodak MNIST Fashion MNIST Librispeech MIT-5k
Benchmarks: TESTIMAGES MIT-5k DIV2K Kodak MNIST Fashion MNIST Librispeech
Metrics: PSNR SSIM RMSE BER iterations to lossless bpp model size BitOps
Baselines: ReLU+P.E WIRE Gauss SIREN FINER Instant-NGP DINER BitNet BECNN BR PNG JPEG2000
Builds on: SIREN Jentzen et al. explicit parameter bounds Han et al. dequantization with bit-planes (ABCD) RECOMBINER BitNet
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