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Learning Optimal Lattice Vector Quantizers for End-to-end Neural Image Compression
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Learns rate-distortion optimal lattice vector quantizer bases (with orthogonality constraints and Babai rounding) end-to-end for neural image compression, improving BD-rate over scalar quantization across three codecs and four context models.
Problem
Uniform scalar quantization in end-to-end neural image compression cannot exploit inter-feature dependencies, while fixed lattice vector quantizers are designed for uniform source distributions and are suboptimal for real latent distributions.
Approach
Instead of fixing lattice geometry to be near-spherical, learn the basis matrix of the lattice from latent sample statistics end-to-end, with an orthogonality regularizer so Babai rounding approximates the true closest lattice point, and a factorized per-dimension entropy model.
Key results
- Optimized lattice VQ gives BD-rate savings of -22.60% (Bmshj2018, factorized) vs. scalar quantization, shrinking to -0.95% for LIC-TCM with spatial autoregressive context.
- Optimized 24-dimensional lattice reaches -20.49% vs. -12.82% for the Leech lattice on Bmshj2018 with factorized context.
- Removing the orthogonality constraint drops Bmshj2018 factorized savings from -22.60% to -18.2%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace scalar quantization with OLVQ | Bmshj2018, SwinT-ChARM, and LIC-TCM · All tested context models | BD-rate savings over scalar quantizer: -22.60% to -0.95% | Helped |
| Use OLVQ with Factorized rather than Spatial-wise Autoregressive context | Bmshj2018 · Bmshj2018 context models | BD-rate savings over scalar quantizer: -22.60% vs -8.31% | Mixed |
| Increase quantizer dimension from 8 to 24 | Optimized LVQ and GVQ · Bmshj2018 and SwinT-ChARM, Factorized and Checkerboard | BD-rate savings over scalar quantizer: -10.92% to -20.49%; -12.10% to -22.74% | Helped |
| Replace optimized LVQ with optimized GVQ | Bmshj2018 and SwinT-ChARM · 8-, 16-, and 24-dimension; Factorized and Checkerboard | BD-rate savings over scalar quantizer: -10.92% vs -12.10%; -15.73% vs -17.59%; -20.49% vs -22.74% | Helped |
| Add the orthogonal constraint (ablation) | OLVQ · Bmshj2018 and SwinT-ChARM, all four context models | BD-rate savings over scalar quantizer: -18.2% -> -22.60%; -7.94% -> -11.94%; -6.34% -> -10.61%; -4.20% -> -8.31%; -8.09% -> -12.44%; -2.25% -> -6.37%; -1.22% - | Helped |
| Set lambda_2 excessively large or excessively small (ablation) | OLVQ training objective · Image compression | Performance | Hurt |
| Use SSIM rather than MSE as the loss term L (ablation) | OLVQ training objective · Image compression | Performance trends | No clear effect |
Surprising findings
- Gains shrink as context model complexity grows; on SwinT-ChARM with spatial autoregressive context the orthogonal-constraint-free variant gives +2.08% (a loss).
- Learned lattice VQ nearly matches general (free-form) VQ at a fraction of the inference cost (about 40ms vs 454ms at dimension 32).
Limitations
- Gains are modest for heavy models with complex autoencoders and sophisticated context models.
- Orthogonality constraint is needed for BRT consistency, and its weight lambda_2 must be tuned; too large or too small hurts performance.
- Inference time is several times that of scalar quantization.
Experimental setup
Datasets: ImageNet (filtered high-resolution subset)
Benchmarks: Kodak CLIC validation
Metrics: BD-rate MSE SSIM inference time
Baselines: Uniform scalar quantization E8 Gosset lattice A16 Barnes-Wall lattice A24 Leech lattice General vector quantizer SHVQ McQUIC
Builds on: Ballé et al. end-to-end image compression Babai rounding CompressAI Kudo et al. QMC mixture entropy model
Closest papers by meaning
- Multirate Neural Image Compression with Adaptive Lattice Vector Quantization (CVPR 2025 · similarity 0.94)
- Approaching Rate-Distortion Limits in Neural Compression with Lattice Transform Coding (ICLR 2025 · similarity 0.91)
- Learning Grouped Lattice Vector Quantizers for Low-Bit LLM Compression (NeurIPS 2025 · similarity 0.87)
- Robustly overfitting latents for flexible neural image compression (NeurIPS 2024 · similarity 0.86)
- HyperVQ: Enabling Hyperprior Entropy Modeling for VQ-Based Generative Image Compression (NeurIPS 2026 · similarity 0.86)
- On Quantizing Neural Representation for Variable-Rate Video Coding (ICLR 2025 · similarity 0.86)
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