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Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff
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Proposes low-complexity lattice transform coding variants (shared-dither SD-LTC, private-dither PD-LTC, and nested-lattice quantized shared-dither QSD-LTC) for the rate-distortion-perception tradeoff, proves optimality on Gaussian sources, and validates on synthetic and real data.
Problem
Neural compressors for the rate-distortion-perception (RDP) tradeoff lack constructive, low-complexity schemes that achieve RDP-optimal performance, and it is unclear how shared randomness and quantization should be combined for RDP.
Approach
Combine lattice quantization in the latent space with dithering: shared uniform lattice-cell dither (SD-LTC) for infinite shared randomness, private decoder-only dither (PD-LTC) for no shared randomness, and a nested-lattice discrete shared dither (QSD-LTC) that interpolates with finite shared randomness rate R_c = log Γ.
Key results
- On the Gaussian source (n=8, P=0), SD-LTC with E8 and QSD-LTC with nesting ratio 3 (R_c = log 3) nearly match SD-LTC performance, and both outperform PD-LTC and deterministic NTC at moderate-to-high rates.
- SD-LTC is proven to achieve the RDP function R(D,P) for Gaussian sources with squared 2-Wasserstein perception under infinite shared randomness, and PD-LTC achieves R(D/2, ∞) at P→0 with no shared randomness.
- Across MNIST, Physics and Speech, performance improves with better lattice packing and more shared randomness; QSD-LTC with R_c=log 3 nearly matches SD-LTC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase shared randomness | LTC · i.i.d. Gaussian, P=0 | R-D tradeoff | Helped |
| use a more efficient lattice | LTC · i.i.d. Gaussian, P=0 | R-D tradeoff | Helped |
| increase shared randomness | LTC · MNIST, Physics, and Speech | RDP tradeoff | Helped |
| increase the QSD-LTC nesting ratio from 2 to 3 | QSD-LTC · MNIST, Physics, and Speech | RDP tradeoff: R_c = \log 2 = 1; R_c = \log 3 \approx 1.58 | Helped |
| use QSD-LTC with finite shared randomness instead of SD-LTC | LTC · i.i.d. Gaussian, P=0 | RDP tradeoff: R_c = \log 3 | Hurt |
| use QSD-LTC with R_c=\log 3 instead of SD-LTC | LTC · MNIST, Physics, and Speech | RDP tradeoff: R_c=\log 3 | Hurt |
| use deterministic NTC or LTC instead of a randomized compressor | Neural transform coding · MNIST, Physics, and Speech | perception constraint | Hurt |
| increase RCC block dimension from 1 to 8 | RCC · i.i.d. Gaussian | RDP tradeoff: n=1; n=8 | Helped |
| replace SD-LTC with 8-dimensional RCC | RDP compressor · i.i.d. Gaussian | RDP tradeoff: n=8 | Hurt |
| use the D_n^* lattice instead of the integer or Barnes-Wall lattice (ablation) | SD-LTC · Speech | RDP tradeoff | Mixed |
| train PD-LTC with the noisy proxy instead of STE with hard quantization (ablation) | PD-LTC · Speech | RDP tradeoff | No clear effect |
Surprising findings
- Deterministic NTC/LTC cannot enforce the perception constraint at low rates regardless of the perception weight lambda_2.
- Sending a pseudorandom seed of k bits does not simulate infinite shared randomness; it provides only 2^k possible dithers.
Limitations
- QSD-LTC rates are restricted to log of integer nesting ratios; intermediate R_c values in (0,1) are left to future work.
- Theory covers only i.i.d. Gaussian sources with linear transforms and asymptotic blocklength; extension to state-of-the-art image compression architectures is not addressed.
- Monte-Carlo estimation of latent likelihoods for non-integer lattices causes suboptimality at low rates.
Experimental setup
Datasets: MNIST Physics Speech i.i.d. Gaussian source (synthetic)
Benchmarks: MNIST Physics Speech i.i.d. Gaussian source
Metrics: rate MSE distortion squared sliced Wasserstein perception RDP tradeoff curves
Baselines: NTC (deterministic integer-lattice transform coding) LTC with E8 lattice reverse channel coding (RCC) PD-LTC SD-LTC
Builds on: nonlinear transform coding lattice transform coding reverse channel coding dithered quantization lattice Gaussian coding
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