Towards Lossless Implicit Neural Representation via Bit Plane Decomposition

TL;DR

This work addresses the challenge that the implicit neural representation (INR) size grows exponentially with required bit-precision. It introduces bit-plane decomposition to reduce the effective bit-depth, enabling lossless representations by learning bit-planes via an added bit index coordinate; the authors quantify the upper bound $U_d(n)=C(2^{n+1}-2)^{2d}$ and show that approaching this bound accelerates lossless convergence. They demonstrate lossless fitting for 16-bit and 8-bit images and high-bit-depth audio, reveal bit bias where MSBs converge faster than LSBs, and extend the method to bit-depth expansion, lossless compression, and ternary INRs, with code available. The results offer a practical route to exact, bit-for-bit INR representations, with implications for compression, quantization-aware modeling, and low-precision networks.

Abstract

We quantify the upper bound on the size of the implicit neural representation (INR) model from a digital perspective. The upper bound of the model size increases exponentially as the required bit-precision increases. To this end, we present a bit-plane decomposition method that makes INR predict bit-planes, producing the same effect as reducing the upper bound of the model size. We validate our hypothesis that reducing the upper bound leads to faster convergence with constant model size. Our method achieves lossless representation in 2D image and audio fitting, even for high bit-depth signals, such as 16-bit, which was previously unachievable. We pioneered the presence of bit bias, which INR prioritizes as the most significant bit (MSB). We expand the application of the INR task to bit depth expansion, lossless image compression, and extreme network quantization. Our source code is available at https://github.com/WooKyoungHan/LosslessINR

Figures (19)

• Figure 1: Overview of the proposed method and error maps at 1,500 iterations. The upper bound on the number of parameters ($\mathcal{P}(f_\theta)\propto 2^n$) of INR ($f_\theta$) grow proportionally to a bit-precision ($n$). We propose a bit-plane decomposition method, reducing the upper bound, enabling faster convergence, and ultimately achieving a lossless representation. The closer $\mathcal{P}(f_\theta)$ is to the upper bound, the faster it converges, enabling lossless representation
• Figure 1: Schematic diagram of the parallel model used for the validation in the experiment section. $f_{\theta,n=k}$ indicates INRs that require $k$-bit precision with a given parameter $\theta$.
• Figure 2: Visual Demonstration of representing 2D Image (PSNR(dB) $\uparrow$/ Bit-Error-Rate (BER) $\downarrow$ at top of images). ReLU with position encoding (P.E) mildenhall2020nerf, WIRE wirewavelet2023, gaussian activation activationinr_gauss_etc, SIREN sitzmann2019siren, FINERliu2023finer and ours. We highlight the occurrence of significant errors with red dots.
• Figure 2: Quantized representations depending on $k$-bit precision.
• Figure 3: Training curve on a single image of DIV2KDIV2kdataset dataset. Bit-Error-Rate(BER) (left) and PSNR (right). Vertical lines indicate the iteration when the model achieves lossless representation.

Theorems & Definitions (9)

• Theorem
• Proposition 1
• Definition 1
• Definition 2
• Proposition 2
• Proposition 3
• Lemma 1
• Proposition 4
• Proposition 5