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Approaching Rate-Distortion Limits in Neural Compression with Lattice Transform Coding
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Proposes Lattice Transform Coding (LTC), which replaces scalar rounding in neural transform coding with lattice quantization, approaching optimal vector quantization and R(D) on synthetic and real sources.
Problem
Neural transform coding (NTC) uses scalar quantization (integer rounding) in the latent space, which is suboptimal for sources whose latent dimensionality exceeds one; it is unknown whether NTC can reach optimal vector quantization (VQ) performance at low complexity.
Approach
Replace the latent integer rounding of NTC with general lattice quantization (best-known lattices A2, D4*, E8, Leech with efficient CVP decoders), training with STE or dithered noise, estimating the lattice PMF by Monte-Carlo integration over Voronoi regions, and extending to nested-lattice fixed-rate coding and block coding.
Key results
- On Kodak, Cheng2020-LTC-Λ24 achieves -16.708% BD-rate versus Cheng2020-NTC (NTC anchor), while Cheng2020-LTC-E8 achieves -5.274%.
- On 2-D Gaussians, LTC with the hexagonal A2 lattice produces quantization regions and rate-distortion performance closely matching optimal ECVQ, whereas NTC merely matches ECSQ.
- For Sawbridge, block-LTC bridges the gap between the one-shot bound H(D) and R(D), enabled by coding across i.i.d. samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace scalar quantization with lattice quantization in Cheng2020 | Cheng2020 NTC · Kodak | BD-rate (NTC anchor): -2.337; -5.274; -16.708 | Helped |
| Use Λ24 instead of E8 lattice quantization (ablation) | Cheng2020 LTC · Kodak | BD-rate (NTC anchor): -5.274 -> -16.708 | Helped |
| Use Λ24 instead of E8 lattice quantization (ablation) | Cheng2020 LTC · Kodak | runtime (sec.): 4.002 -> 8.634 | Hurt |
| Use sub-optimal A_n or D_n* lattices instead of the best-known lattice for the dimension (ablation) | LTC · i.i.d. Gaussian sequences | rate-distortion performance | Hurt |
| Use dithering instead of STE for the rate term (ablation) | LTC · Synthetic sources | cross-entropy | Mixed |
| Use a normalizing-flow density model instead of a factorized density model (ablation) | LTC · i.i.d. Gaussian | cross-entropy gap to H(y-hat) | Helped |
| Remove the analysis and synthesis transforms, using ECLQ directly on the source (ablation) | LTC · Gaussian and Banana | rate-distortion performance | Hurt |
| Increase Monte Carlo integration samples from 1024 to 4096 (ablation) | LTC · i.i.d. Gaussian, n=8 | rate-distortion performance: 1024 -> 4096 | Helped |
| Replace scalar quantization with a Leech lattice at inference using pretrained NTC weights (ablation) | Cheng2020 NTC · Kodak | BD-rate (NTC anchor): -12.984% | Helped |
Surprising findings
- NTC with a trained scalar quantizer replaced by Leech lattice quantization at inference (no retraining) already gives -12.984% BD-rate on Kodak, close to training from scratch.
- Increasing the latent dimension or changing depth/width/nonlinearities of NTC did not get NTC beyond ECSQ performance on 2-D i.i.d. Gaussians.
Limitations
- Uses best known lattices only up to dimension 24; larger dimensions would improve performance but need efficient CVP solvers.
- Monte-Carlo PMF estimation with 4096 samples is costly; Leech lattice needs more samples and GPU memory, and LTC training is roughly 2x NTC for low-dimensional sources.
- Dithered rate estimates are over-smoothed and sub-optimal at low rates, while STE training is less stable.
Experimental setup
Datasets: Vimeo-90k Physics Speech Kodak Banana (TensorFlow Compression) Sawbridge (synthetic process) i.i.d. Gaussian i.i.d. Laplacian
Benchmarks: Kodak Physics Speech i.i.d. Gaussian i.i.d. Laplacian Banana Sawbridge
Metrics: rate-distortion BD-rate runtime (sec per image) rate-redundancy
Baselines: NTC (scalar quantization) ECVQ ECLQ LVQAC NVTC ELIC VTM Cheng2020-NTC
Builds on: nonlinear transform coding entropy-constrained vector quantization RealNVP Cheng2020
Closest papers by meaning
- Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff (NeurIPS 2025 · similarity 0.92)
- Learning Optimal Lattice Vector Quantizers for End-to-end Neural Image Compression (NeurIPS 2024 · similarity 0.91)
- Multirate Neural Image Compression with Adaptive Lattice Vector Quantization (CVPR 2025 · similarity 0.91)
- On Quantizing Neural Representation for Variable-Rate Video Coding (ICLR 2025 · similarity 0.87)
- Robustly overfitting latents for flexible neural image compression (NeurIPS 2024 · similarity 0.87)
- Learning Grouped Lattice Vector Quantizers for Low-Bit LLM Compression (NeurIPS 2025 · similarity 0.86)
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